WATER IN BIOLOGICAL SYSTEMS

STRUKTURA I ROL' VODY V ZHIVOM ORGANIZME

CTPYKTYPA VI POJlb BOllbI B )f{VlBOM OprAHVl3ME

WATER IN BIOLOGICAL SYSTEMS

Volume 2

Edited by M. F. Vuks and A. I. Sidorova

Trans lated from Russian

® SPRINGER SCIENCE+BUSINESS MEDIA, LLC 1971

The present volume comprises the translation of selected papers from Volumes 1 and 2 of Struktura i Rol' Vody v Zhivom Organizme, the original Russian editions of which were published in 1966 and 1968 by Leningrad University Press, The English translation is published under an agreement with Mezhdunarodnaya Kniga, the

Soviet book export agency.

CTPYKTYPA VI POJlb BOD.bl B )f{VlBOM OprAHVl3ME

M. CP. BYKC, A. H. CUaOpoBa

Library of Congress Catalog Card Number 69-12513 ISBN 978-1-4757-6957-9 ISBN 978-1-4757-6955-5 (eBook)DOI 10.1007/978-1-4757-6955-5

© 1971 Springer Science+Business Media New York Originally published by Plenum Publishing Corporation, New York in 1971

All rights reserved

No pat of this publication may be reproduced in any form without written permission from the publisher

CONTENTS

Concentration Fluctuations and Their Influence on Sound Absorption V. P. Romanov and V. A. Solov' ev. . . . . . . . . . . . ...

Spectrum of Aqueous Urea Solutions in the Near-Infrared Region I. N. Kochnev, L. V. Moiseeva, and A. I. Sidorova ....

Influence of the Effective (Local) Light-Wave Field on the Infrared Absorption Spectrum of Liquid Water in Vicinity of the Valence-Vibration Band

V. M. Zolotarev and N. G. Bakhshi ev. . . . . . . . . . . . . .

Raman Spectra of Water, Saturated Aqueous Electrolyte Solutions, and Ice Crystals

Z. A. Gabrichidze ......................... .

The Germanium- Water Interface V. M. Zolotarev ..... .

State of Water in Certain Perchlorate Crystal Hydrates Formed by Elements of Periodic Group II

T. G. Balicheva and T. I. Grishaeva . . . . . . . . . . . . . .

Investigation of Aqueous Nonelectrolyte Solutions by the Spin Echo Method Yu. I. Neronov and G. M. Drabkin .................... .

Temperature-Related Changes in the Infrared Absorption Spectrum of Water in the Cerebral and Muscle Tissues of the Frog

A. I. Sidorova and A. I. Khaloimov .................. .

A Mass-Spectrometric Study of Disturbances of Water Exchange through the Pulmonary Barrier in Animals

L. A. Kachur and A. N. Shutko . . . . . . . . . . . . . . . . . . . . . . .

Possible Role of Water in Neuromuscular Excitation Yu. V. Dubikaitis and V. V. Dubikaitis .....

Two-Structure Model and the Heat Capacity of Water Yu. P. Syrnikov ...... , ............. .

Study of the Structural Characteristics of Water from the Infrared Absorption Spectra of Aqueous Acetonitrile Solutions

B. N. Narziev and A. I. Sidorova ................ .

Concentration-Related Changes in the Spectra Characteristics of the Libration Band of Liquid Water in Acetonitrile and Acetone Solutions

A. I. Sidorova and L. V. Moiseeva. . ........... .

v

1

12

15

19

26

30

39

43

47

51

56

60

68

vi CONTENTS

Investigation of Aqueous Electrolyte Solutions by the Deflected Total Internal Reflection (DTIR) Method

L. V. Ivanova and V. M. Zolotarev ................ .

Concentration Fluctuations and Light Scattering in Aqueous Solutions of Propyl Alcohols

M. F. Vuks, L. 1. Li snyanskii, and L. V. Shurupova . . . . .

Interpretation of the Spectrum of Ice and Water in the Valence- and Deformation-Vibration Regions

B. A. Mikhailov and V. M. Zolotarev. . . . . . . . ...... .

Chemical Proton Shifts in H20 - D20 Solutions V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin

Self-Diffusion in Aqueous Solutions of Amino Acids, Peptides, and Proteins L. K. Altunina, 0. F. Bezrukov, N. A. Smirnova, I. A. Moskvicheva, and V. p. Fokanov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Use of Infrared Absorption Spectroscopy to Investigate the Influence on Water Structure of a Number of Compounds with a Protective Action during Freezing of Human Erythrocytes

A. 1. Sidorova and A. I. Khaloimov ....... : .......... .

Accessibility of Water in Muscle Fibers to Molecules of Different Sizes N. N. Nikol'skii .......................... .

Calculation of Binary Distribution Functions and Thermodynamic Characteristics of Aqueous Solutions of Strong Electrolytes by the Monte Carlo Method

P. N. Vorontsov-Vel'yaminov and A. M. EI'yashevich.

72

79

83

89

94

104

106

111

CONCENTRATION FLUCTUATIONS AND THEIR INFLUENCE ON SOUND ABSORPTION·

v. P. Romanov and V. A. Solov'ev

Maxima are usually observed in the curves representing ultrasound absorption as a func­tion of concentration for mixtures of associated liquids, particularly aqueous solutions of sub­stances with polar molecules [1]. They are due to relaxation processes caused by molecular association. A qualitative interpretation of this type was proposed by Bazhulin and Merson (2] in 1938. Attempts at a quantitative calculation of the additional absorption caused by associ­ation have been made on the basis of the quasi-chemical model, treating the associates as mole­cules of strictly defined stoichiometric composition [2-5]. This theory is a good approximation if saturated bonds are formed between the molecules. It can be used only for very rough esti­mates if the composition of the associate has not been unambiguously determined, and detailed conclusions drawn from it are totally invalid.

Another possible approach to description of association processes lies in representing the associates as regions of altered concentration, or concentration fluctuations. This model is better justified when saturated bonds are absent, since it deals with associates of any composi­tion. The fact that it cannot be used for a detailed description of the short-range ordering must be regarded as a drawback. Conversely, the quasi-chemical model only permits consideration of the short-range ordering and then on the basis of very arbitrary assumptions regarding its character. The actual pattern should lie between these two models.

This paper is an attempt to calculate sound absorption in mixtures on the basis of the theory of associates as concentration fluctuations. Vuks and Lisnyanskii [6,7] hypothesized that there is a relationship between anomalous absorption and concentration fluctuations and called attention to the correlation between sound absorption and light scattering in solutions.

In articles devoted to sound absorption in the critical region, Fixman [8,9] considered absorption in fluctuations with the aid of a strict method of correlative distribution functions. He took into account two energy-dissipation mechanisms: 1) by thermal conduction between regions with different densities or concentrations (similar to the Ziner-Isakovich mechanism); 2) by diffusive concentration redistribution under the influence of the change in temperature in the sound wave. It can be demonstrated that the contribution made to absorption by the first effect is small, at least in regions not overly close to the critical region [10 J. In dealing with the second effect, Fixman investigated only the influence of temperature on fluctuations and did not give consideration to the influence of pressure. Moreover, Fixman's calculations cannot

* Translated from Struktura i Rol' Vody v Zhivom Organizme, 1:36-48 (1966).

1

2 V.P. ROMANOV AND V.A. SOLOV'EV

withstand direct comparison with experimental data. It should be noted that the problem of the applicability of Fixman's theory outside the critical region requires special investigation.

The process of sound absorption in a solution can be represented in the following manner. During passage of a sound wave, the density p and temperature T in each element of the solution volume undergo periodic changes. Since the average magnitude of the concentration fluctuations depends on p and T, it should also vary, in turn causing fluctuations in the excess energy E and pressure p. However, the change in fluctuation magnitude is not instantaneous, being governed by the diffusion rate. There is therefore a phase shift between the change in p and p, which should lead to sound absorption.

In order to take into account the influence of fluctuations on sound propagation, the fol­lowing additional relationships must be introduced into the system of acoustic equations: 1) expressions for the thermodynamic functions representing the influence of the inhomogeneous concentration distribution; 2) equations describing the change in the average fluctuation with time.

The influence of fluctuations has often been considered in connection with the theories of light scattering and critical opalescence [8,11,12,13,23], proceeding from hypotheses regard­ing thermodynamic functions "at a point." This is not wholly consistent and, in addition, the coefficients of the gradient terms (see below) are usually introduced formally, which hinders discussion and evaluation. Debye [131 considered the gradient terms on the basis of a molecu­lar model, but he made certain limiting assumptions. We will use the most general method of correlative distribution functions, neglecting only the molecular orientation.

I

A liquid with an inhomogenous concentration distribution is in a nonequilibrium state. According to the general rule of the thermodynamics of irreversible processes [14], the thermo­dynamic functions for this state are identical to those for the analogous state brought to equi­librium by an appropriate potential. Since the instantaneous concentration-distribution pat-tern can always be expanded into a Fourier series, it is sensible to take the sine potential

uA=Asin/x, uB=-Bsln/x, (1)

where uA and uB are the potential energies of molecules of types A and B respectively and / is the wave number. We will assume cyclic boundary conditions.

The concentration fluctuations are isobaric, since pressure inhomogeneities are usually dissipated very rapidly (at the speed of sound). We must therefore impose on the potential in Eq. (1) the condition that the total force acting on an element of the solution volume equals zero:

ANA BNB -v-=-V-,

where NA and NB are the numbers of particles of types A and B in a macroscopic volume V.

The configuration integral for a solution in field (1) is

(2)

Expanding Eq. (2) into a series for powers NkT and B/kT and limiting ourselves to the quadra­tic terms, we obtain

CONCENTRATION FLUCTUATIONS AND THEIR INFLUENCE ON SOUND ABSORPTION 3

Z* =Zo {I - ~A kAJ S [Ff (r)-Ff (r)] slnj xdr + ~~ (:r r S [Ff (r) + Ff (r)] sln2 j xdr+

(3)

Here Zo is the configuration integral of the unperturbed medium,* while Ft. Ft F~~ F{~ and F{-B are the first- and second-order correlative functions in the unperturbed medium [15,16], which are defined by equations of the type

(4)

The linear term in Eq. (3) disappears, since F1 is readily calculated. The variables

F~ == 1. The integral containing sin2jx

must be substituted into the latter term. Introducing the function

we obtain

{ N~ A2 [V V S ]} Z* = Zo 1 + 4V(kTP NA + NB + ['1AA (r)+~BB(r)-2vAB(r)] cos! x dr . (5)

In view of the fact that the correlation functions vAA' v BB ' and vAB disappear at large r, we expand cosjx into a series and limit ourselves to the quadratic term. Then

(6)

Here

12 = ---,,-----::f_"_r;-;2 _dr_-;-;-_

S V V '1dr+ NA + N8

(7)

The function v in Eq. (7) reverts to zero if the correlation between the positions of the heterogeneous molecules is the same as the average correlation in the pure components. It can therefore be termed the true correlation function of the solution. The value of 1 reflects the ordering distance, although it cannot, strictly speaking, be called the correlation radius [8].

*Here Zo is the integral over all states of the system, i.e., it actually takes into account all possible fluctuations. Strictly speaking. we are oalculating not the contribution made to Zo by the fluctuations but the influence of an addit ional imposed inhomogeneity. Since the fluctu­ations are small, however, we can identify Zo with the configuration integral for the system without fluctuations.

4 V.P. ROMANOV AND V.A. SOLOV'EV

The free energy of the solution in the field is

N~A2l V V 5 ]( /2/2) F* = FO- 4VkT NA + NB + ~(r)dr 1 --6- , (8)

where Fo is the free energy of the homogeneous solution. The value of F'* includes the poten­tial energy of the molecules in the hypothetical field represented by Eq. (1). The free energy of the inhomogeneous solution without the field differs from F* by the magnitude of this potential energy: F = F* - U*. In order to calculate U'*, it is necessary to find the spatial distribution of the molecules of each solution component. For example, the unary distribution function for component A in the field is

(9)

As in calculating Z'*, we obtain

(10)

The corresponding expression for F * is found in the same manner. Calculating the potential Bl

energy

and subtracting it from F'*, we find the free energy of the nonequilibrium solution:

(11)

We must now exclude from Eq. (11) the amplitude of the applied potential A. In order to do so, we find the concentration distribution from Eq. (10) and the analogous formula for FBr:

(12)

Expressing A in terms of Cf and substituting this into Eq. (11), we finally obtain

VkTNfc} (13)

The expression in the denominator can be represented in terms of thermodynamic func -tions. According to the literature [16, 18], the average fluctuations in the number of particles in solution are defined by the equations

S t:.N2 V V BB dr = V -? - N .

NB B

CONCENTRATION FLUCTUATIONS AND THEIR INFLUENCE ON SOUND ABSORPTION 5

On the other hand, it follows from the thermodynamic theory of fluctuations that

t:.N2 = kT iJ2F A 2A iJN~ ,

where

Hence,

where

a- -(a2F) - aC2 T, V,p

The latter equality can be checked by direct calculation.

Substituting the value of 5 v dV into Eq. (13) and assuming l2 to be small, we obtain

F=Fo++ a(l + f~12 )c;= Fo ++(a+bp)cj.

Equation (14) is also valid near the critical mixing point, where there is a long-range correlation. In this case, it should be derivable from the Ornstein -Cernick equation (the method used by Vuks and Lisnyanskii [17]). ,

With an arbitrary concentration distribution c - c = ~ c,el(/, rl we obtain I

F=Fo++ ~(a+bJ2)cJ. , This yields an expression for the average fluctuation amplitude (see [12]):

(14)

(15)

(16)

Equation (15) formally agrees with the relationship obtained by Andon and Cox [12] from expan­sionof F "at a point" for the powers c -c and V'c. If we differentiate Eq. (15) over the volume V, we obtain an equation of state relating the average pressure in the system to the average concentr:ation -distribution inhomogeneity:

_ (aF) I ~ (iJa + ab fa) 2 P-- av T =PO-T ~ av dV cf , , (17)

where Po is the pressure in the absence of fluctuations.

6 V.P. ROMANOV AND V.A. SOLOV'EV

II

The kinetics of concentration redistribution can be represented in the following manner. The existing fluctuations are dissipated by diffusion. On the other hand, there is a continuous accumulation of fluctuations as a result of thermal movement. On the average, the two proces­ses are equilibrated, so that the average fluctuation distribution represented by Eq. (16) is estab­lished. In describing these processes, there is no need to give detailed consideration to the molecular movement of both solution components, since the constant-pressure condition ensures a unique relationship between the changes in their concentrations. We are ultimately interested only in the form of the equation and not in the precise expressions for the coefficients. We will therefore limit ourselves to considering the molecular movement of component A in a continuous medium.

The dissipation of the fluctuations is described by the diffusion equation

(18)

( - ) - Ol'-A where x is the volume concentration x = NA/V , D is the diffusion constant (0 = ~xTx'

where t; is the molecular mobility), and D1 = ~x a;: ~ = Dl2/6. The second term in Eq. (18) results from the fact that the free energy at a given point depends on the concentration gradient [19,20]: the gradient of the modified chemical potential p.~ =iJFjiJNA , where F=Fo++a(x

- x? + + b (VX)2 ,is the motive force of diffusion [12].

We expand the concentration distribution into a Fourier series:

(19)

Substituting this expansion into Eq. (18), we obtain

(20)

where

. 1 'tj = (Df 2 +DIf')

Equation (18) describes the diffusion in a purely phenomenological manner, as directional movement of molecules under the action of the thermodynamic Itforce lt '\111- A' Diffusion is actual­ly caused by random thermal movement, which leads to both dissipation and development of fluctuations. If we assume that there is a totally homogeneous concentration distribution at a given moment, accumulation of fluctuations as a result of diffusive movement of the molecules of component A is the only consequence of thermal movement. The molecular displacement over a time J. is defined by the Brownian-movement equation

where

Oo=~kT. (21)

CONCENTRATION FLUCTUATIONS AND THEIR INFLUENCE ON SOUND ABSORPTION 7

When inhomogeneities appear, the same process is responsible for their dissipation. M:>reover, correlational forces develop in the presence of an inhomogeneity. The Brownian movement becomes partially ordered as a result of these forces and the concentration gradient. It can be represented as a superimposition of the directional movement described by the dif­fusion equation on the purely random movement, which, since the fluctuations are small, can be treated as being the same as in a homogeneous system. The concentration-redistribution process can thus be regarded as the sum of two opposing processes: the accumulation of fluctu­ations described by Eq. (21) and the dissipation of fluctuations described by Eq. (20). The latter equation contains D rather than Do, as a result of the influence of the correlational forces, which result in 8J1A /8 x ¢ kT/x.

We can show that this pattern leads to the correct equilibrium condition. We expand the displacement y (r) into the Fourier series y =! Ylei(/. T), whence y2 = !yj= 6Do {}. As-

I I suming all YI to be identical (rate correlations to be absent), we obtain

The change in concentration is determined from the continuity equation

8x/x= - div y.

Hence,

The rate at which the mean square amplitude rises is

(dcj/dt)I=Cjj{}=X j j2 ~~ .

On the other hand, the amplitude of the f -component of the instantaneous concentration distri-: bution dec~ases in accordance with Eq. (20), Le., (dc'jjdth = - 2cHc'; the mean square_ amp~~de c'j decreases in precisely the same fashion. Neglecting the difference between c'j and cI, we find the total rate of change c'j:

(22)

At equilibrium, dc}/dt = 0, whence the equilibrium value of Cj

ifAF ' iJx2 (I + /2 [2/6)

kT ,(23)

which is in agreement with thermodynamic equation (16).

Substituting Eq. (23) into Eq. (22), we obtain an equation describing fluctuation relaxation

d9 1-- = - - (c2 - Cf) dt ~I I I ,

(24)

8 V.P. ROMANOV AND V.A. SOLOV'EV

We previously proceeded on the assumption that the development of fluctuations is described by an equation of the type (dcf/dt)\ = const [10]. In this case 'tf='tj, so that the esti­mates of the sound-absorption coefficient and its dependence on frequency differ somewhat from those given below. Since the calculation is purely qualitative, this numerical discrepancy is of no real significance.

It is helpful to note that the expansion into a Fourier series employed in deriving Eq. (24) is not used for reasons of convenience but because it is necessary to separate the spatial and temporal variables in the diffusion equation. Expanding x(r, t) into series for functions of the type ~ (r) 'Ij (t), Eq. (18) yields

Tj(t)-ex p (- ~), Rj(r)-expi(fj, r).

Each Fourier component thus decreases by a single exponential rule, regardless of the other harmonics.

m The density p = N/V and temperature T in the sound wave vary periodically. This leads

to a change in the equilibrium fluctuation amplitudes 'C}-CJo=oCJ-eiwt , where c~ is the un-

perturbed value (in the absence of sound). In similar fashion C; = CJo + 0 C; and, in accordance with Eq. (24),

Here,

(25)

(the temperature term for aqueous solutions is unimportant in practice [10]).

The pressure amplitude in the sound wave ot = p - Po equals

(26)

According to Eq.(17) dp/dC; = - -}- aiJv (a+ br) . Substituting this expression into Eq. (26) and

taking Eq. (25) into account, we obtain the following equation for the complex compression modu­lus (see [21]):

= Ko+-}- VkT~[ iJiJv In (a+bf2) r l~i~"f = K(ID) +IID'1j (Il». f

(27)

CONCENTRATION FLUCTUATIONS AND THEIR INFLUENCE ON SOUND ABSORPTION 9

where Ko is the equilibrium compression modulus and K (w) and 1) (w) are the dynamic moduli al).d volume viscosity. Hence it can be seen that relaxation of fluctuations should lead to disper­sion (very slight) and absorption of sound.

Separating the imaginary portion of Eq. (27), we find the dynamic volume viscosity

(28)

In order to make numerical calculations, Eq. (28) must be converted from a sum to an integral. Using the Debye formula for the distribution density of wave vectors f (see [12]), we obtain

(29)

wherefm is the maximum wave number of the Fourier series of fluctuations, which define the applicability limit for a model treating the solutions as a continuous medium. Strictly speaking, these concepts should not be applied to inhomogeneities whose size is comparable to the inter­molecular distance. We are confident, however, that it is permissible to treat associates of molecular size as very small inhomogeneities in a continuous medium in making semiquanti­tative estimates. The limiting wave number of the fluctuations fm must then be regarded as having the same order of magnitude as the average distance between the molecules of one solution component:

(30)

The exact value of fm is actually necessary only for calculating the absorption of sound with very high frequencies w »1!Tmin' For low frequencies, the integral in Eq. (29) converges

rather rapidly when fm - 00, since :t = +(l2 :~ + a :t~) can be assumed to be small.

Actually if 8a/8V > 0, we move further from the stratification point (a= 0) as the solution volume increases. The correlation should become weaker inthis case: 8l2!aV < O. According to Debye [13], b should be independent of V in the general case, since it is governed solely by the interaction potential. This quantity can also be expressed in terms of the Ornstein- Cernik direct-correlation constant [17], which should depend only slightly on the intermolecular struc­ture.

Assuming ab!aV == 0, fm = 00 , we obtain

V2 (I iJa)2 I S~ df V'kT (I iJa)2 I 3n y'6 '1j(O) = 81t2 TIW 7) (1+f2/2/ti)3=s;:;2 7dV 7).---mr- (31)

o

for the case w-O.

We previously obtained a similar result from a purely thermodynamic model without taking into account the gradient terms [10]. In this case, an upper limit of equilibration in Eq. (29) also existed at w-o and, instead of 37r.f6/16l= 1.44;i, the value of fm determined from Eq. (30) was used in Eq. (31). Moreover, the independent variables were p and T

10

(7) tt/v'

1O- 17cm-1Hz· 2

'50

100

Fig. 1

V.P. ROMANOV AND V.A. SOLOV' EV

J(w) '.5r--__ ~

(1) a./V'

- 17 - I - 2 10 em Hz 1.0 70

10 0.5

0 ao!

Fig. 2

(rather than V and T), which was more convenient for comparison with experimental data. As in our earlier study [10], by introducing the quantities v = ( S2V Is c2) p,T, cp =(S2<1>/Sc2)p,T """ a, we obtain

(32)

instead of Eq. (31).

The solid lines in Fig. 1 represent the excess sound absorption !:::. a/ Ii 2 as a function of concentration in aqueous solutions of methanol (1) and acetone (2), as determined from Eq. (32). The value of [was taken from the estimate [.Ja/RT = 10 A (see [13])*; the other values were calculated in the same manner as previously [10]. The results differed little from those ob­tained when the term / 2[2 was neglected (dash -and -dot line) and were in rather good agree­ment with the experimental data (dash lines).

Figure 2 shows the volume viscosity as a function of frequency for different values of /m at Sb/ aV = 0, as determined from Eq. (29). Curve 1 corresponds to/m = 00, curve 2 to /m = 1.75/ [ , curve 3 to/m = Ill, and curve 4 to/m = 1/ 2l ; the latter value was less than that obtained from Eq. (30) by a factor of 2-3 at moderate concentration.

As can be seen from Fig. 2, the value of 1] (w) at w - 0 actually depends only slightly on/m, so that the arbitrary selection of/m is not significant in making a quantitative compari­son with experimental data.

A material contribution is made to 1] (0) by the short-wave fluctuations, to which the theory is probably only qualitatively applicable. However, the initial trend of 1] (0) - 7] (w) as a function of frequency (curve 5) is governed solely by the long-wave fluctuations, and quanti­tative agreement with the experimental data can be expected. The form of this curve at small w is independent of the choice of fm •

For purposes of comparison, Fig. 2 also shows 1] (w) as a function of frequency in the absence of gradient terms for fm = l/l (curve 6). It differs from the corresponding curve in our previous article [10] in the fact that T/ = Tt' /2 .

* The quantity l..[(i1'ff'f serves as the direct-correlation radius in the Ornstein-Cernik function [17].

CONCENTRATION FLUCTUATIONS AND THEIR INFLUENCE ON SOUND ABSORPTION 11

LITERATURE CITED

1. D. Sette, Handbuch der Physik, Vol. 11, Pt. 1, Berlin-Gottingen-Heidelberg (1961), pp.275-359.

2. P. A. Bazhulin and Yu. M. Merson, Dokl. Akad. Nauk SSSR, 24:689 (1939). 3. R. S. Musa and M. Eisner,J. Chern. Phys., 30:227 (1959). 4. R. N. Barfield and W.G. Scheider, J. Chern. Phys., 31:488 (1959). 5. O. Nomoto, J. Phys. Soc. Japan, 11:827 (1956); 12:300 (1957). 6. M. F. Vuks and L. I. Lisnayanskii, Ukr. Fiz. Zh., 1:778 (1962). 7. L.I. Lisnyanskii, Dissertation, Leningrad University (1962). 8. M. Fixman, J. Chern. Phys., 33:1357 (1961). 9. M. Fixman, J. Chern. Phys., 33:1363 (1961).

10. V. P. Romanov and V.A. Solov'ev, Akust. Zh., 11:84 (1965). 11. M. A. Leontovich, Statistical Physics, GTTI (1944). 12. L. D. Landau and E. M. Lifshits, Statistical Physics, GTTI (1951) 13. P. Debye, J. Chern. Phys., 31:680 (1959). 14. M. A. Leontovich, Introduction to Thermodynamics, OGIZ (1951) 15. N. N. Bogolyubov, Dynamic-Theory Problems in statistical Physics, OGIZ (1946). 16. I. Z. Fisher, Statistical Theory of Liquids, (1961). 17. V. P. Romanov and V. A. Solov'ev, Ukr. Fiz. Zh. (in press) (1966). 18. A. Munster, in: Thermodynamics of Irreversible Processes [Russian Translation],

Izd. Inostr. Lit., Moscow (1962), pp. 36-145. 19. M. Fixman, J. Chern. Phys., 36:1965 (1962). 20. I. Z. Fisher, Ukr. Fiz. Zh., 9:379 (1964) 21. I. G. Mikhailov, V. A. Solov'ev, and Yu. P. Syrnikov, Principles of Molecular Acoustics,

Nauka, Moscow (1964) 22. V. P. Romanov and V. A. Solov'ev, Akust. Zh., 11:219 (1965). 23. V. V. Vladimirskii, Zh. Eksperim. Teor. Fiz., 9:1226 (1939).

SPECTRUM OF AQUEOUS UREA SOLUTIONS

IN THE NEAR-INFRARED REGION*

I. N. Kochnev, L. V. Moiseeva, and A. I. Sidorova

The denaturing effect of urea on protein molecules can be attributed to its influence on the structure of the hydrate layer, which surrounds and stabilizes the helical protein strand [1]. Urea has a very large capacity for hydrogen-bond formation and it is apparently for this reason that aqueous urea solutions have a number of unusual properties. Thus, for example, the solubility of urea in water is exceptionally high, reaching 20 M at 25°C; there are data indicating that aqueous urea solutions are close to ideal at all concentrations. The presence of urea in water increases the solubility of all hydrocarbons except methane and ethane and weakens the hydrophobic bonds in proteins.

An interesting survey of the properties of aqueous urea solutions was recently published by Abu-Hamdiyyah [2], who surmises that water and urea are capable of forming joint clusters of advantageous size around hydrocarbons, which facilitates their solution. The spectra we obtained for aqueous urea solutions confirmed the existence of composite urea-water clusters. Our investigations were conducted with a diffraction-grating spectrometer of our own design, which operated on the Hebert- Fast principle and provided a resolution of 2 cm-1 in the 5000 cm -1 region.

We measured the spectra of aqueous urea solutions at different concentrations and temper­atures in the vicinity offour Raman and overtone bands for water absorption, whose frequencies are the sums ofthefundamental-vibrationfrequencies: V2 + JiL",2130 cm-l, V2 + v3 '" 5200 cm-f, "1 + "3 ~6900 cm -1, and" 1 + "2 + "3 ~8500 cm -1 [3,4].

Figures 1a and 2a,b show the water band at 5200 cm -1 for different urea concentrations and different temperatures. Solutions of urea in water produced a maximum at 5120 cm-1,

whose intensity increased with respect to that of the main maximum (5180 cm -1) as the urea concentration rose. The position of the 5180 cm-1 maximum was independent of concentration (Fig. 1a). The new maximum (5120 cm -1) disappeared when the temperature was raised from 20 to 80°C, while the principal maximum was displaced toward higher frequencies, from 5180 to 5215 cm-1 (Fig. 2a,b). The band had the same form as in the spectrum of pure water at the corresponding temperature [3,4,5]. The observed dependance of the displacement of this band on temperature was in good agreement with the data in the literature (e.g., [4]).

We assigned the small maximum on the long-wave slope of the band (at 5000 cm-1; Fig. 1a) in the spectra of the urea solutions to the intrinsic a1;>sorption of urea. For purposes of compa-

* Translated from Struktura i Rot' Vody v Zhivom Organizme 1:66-69 (1966).

12

SPECTRUM OF AQUEOUS UREA SOLUTIONS IN THE NEAR-INFRARED REGION 13

e d

.mo JDDO q 7~O em-I 9000 8500 8000 em-1 1500 2300 2'00 em -1

Fig. 1. Spectra of aqueous urea solutions with different concentrations at room temperature. a) 5200 cm-1 band; b) 6900 cm -1 band; c) 8500 cm -1 band; d) 2130 cm -1 band. The figures indicate the ureaconcentrationinwater: 1) O.OOM; 2) O.l1M; 3) 0.33M; 4) 0.78M; 5) 1.67M; 6) 3.33 M; 7) 4.45 M; 8) 20 M~ The dashed curve represents the absorption of urea emulsified in nujol oil.

a b

5250 50UIJ -1

11750 em

Fig. 2 . Spectra of aqueous urea solution as a function of tem­perature . a) For concentration of 0.11 M; b) for concentration of 4.45 M.

rison, we measured the absorption spectrum of a urea emulsion in nujol oil (represented by the dashed curves in Fig. 1a,b). The literature adequately describes the spectrum of urea, but only in the fundamental-tone region [6,7].

The appearance of a new maximum at 5120 cm-1 in the spectra of the urea solutions can be attributed to formation of composite water-urea clusters. The hydrogen bonds are strength­ened in comparison wi th pure water in this case and the frequency of the O-H valence vibrations of the water is somewhat reduced. The disappearance of the maximum at 5120 cm -1 when the temperature is raised confirms the data in the literature on the reduced thermostability· of water-urea clusters in comparison with pure water clusters [8].

14 I. N. KOCHNEV, L.V. MOISEEVA, AND A. I. SIDOROVA

Similar changes occurred in the 8500 cm-1 band. A new band, which we ascribed to composite clusters, developed at 8350 cm-1 (Fig. lc).

Interpretation of the 6900 cm-1 band (Fig. Ib) is difficult because the intrinsic absorption of urea in this region is superimposed on the water band [4,5,9). However, the indubitable displacement of the maximum of this band toward lower frequencies and the displacement of the maximum of the 2130 cm -1 deformation-libration band toward higher frequencies (Fig. Id) also indicated that hydrogen bonding is stronger in urea solutions.

LITERATURE CITED

1. I. Klotz, "Water," in: Horizons of Biochemistry [Russian translation) Izd. Inostr. Lit., Moscow (1964).

2. M. Abu-Hamdiyyah, J. Phys. Chem., 69:2720 (1965). 3. G. R. Choppin and K. Buijs, J. Chem. Phys., 39:2035, 2042 (1963). 4. H. Yamatera, B. Fitzpatrik, and G. Gordon, J. Mol. Spectr., 14:268 (1964). 5. W. Luck, Ber. Buns. Ges., 67:186 (1963); Angew. Chem., 76:463 (1964). 6. T. Yamaguchi, T. Miyazawa, T. Shimanouchi, and S. Mizushima, Spectrochim. Acta,

10 :170 (1957). 7. Z. Piasek and T. Urbanski, Tetrahedron Lett., No. 16, p. 723 (1962). 8. D. B. Wetlaufer, S.K. Malik, L. Stoller, and R. L. Coffin, J. Am. Chem. Soc., 86:508

(1964) . 9. A. V. Koryakin and A. V. Petrov, Zh. Anal. Khim., 18:1317 (1963).

INFLUENCE OF THE EFFECTIVE (LOCAL) LIGHT-WAVE FIELD ON THE INFRARED ABSORPTION

SPECTRUM OF LIQUID WATER IN THE VICINITY OF THE V ALENCE-VIBRA TION BAND *

V. M. Zolotarev and N. G. Bakhshiev

As was demonstrated previously [1-5], the experimentally observed differences between the spectra of compounds in the vapor and condensed phases can, in some cases, be attributed to effects associated with a change in the strength of the light-wave field acting on the molecules in the condensed medium (in comparison with that in the rarified gas) rather than to intermolec­ular interaction resulting from the phase transition between the gas and condensed phase. The influence of the effective light-wave field on the observed absorption spectra of a number of compounds differing materially in character was illustrated earlier [3-5], using the character­istics of the C-Cl valence-vibration bands of carbon tetrachloride and chloroform. As was shown by these data [3], the spectra of condensed CC14 and CHC13 after introduction of a cor­rection for the effective field were close to those of the gaseous phase in all spectroscopic parameters. As was to be expected, the best agreement was observed for the nonpolar CC14

molecule, which corresponds more closely to the approximations used in the calculations. The spectral differences arising during the vapor-liquid phase transition for polar CHC13 molecules are due both to the influence of the effective light-wave field and to the intermolecular interactions which are more substantial for CHC13 than for CC14•

It is natural to expect that, for polar media with strong intermolecular interactions, the observed spectral differences will be produced in larger measure by the change in molecular properties during the phase transition, i.e., the relative influence of the effective light-wave field on the molecular spectra will be less pronounced in this case. Evaluation of the influence of the effective field thus permits determination of the relative contribution made by these factors to the change in the observed molecular spectrum during the phase transition from the gas to the condensed phase. On this basis, we became interested in evaluating the influence of the effective field on the characteristics of the observed spectrum of liquid water, which is known to differ from the vapor spectrum in all parameters. It is wise first to discuss briefly the basic theoretical assumptions [1,2] that enable us to find a correction for the influence of the effective field on the observed molecular spectra.

As is well known, the vapor-liquid transition is accompanied by changes in the radiation flux density and the effective light-wave field acting on the molecule; however, the recording apparatus does not react to these changes, indicating only the overall weakening of the light flux. As a result, the observed spectrum K (v) can differ from the true molecular spectrum,

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:70-75 (1966).

15

16 V. M. ZOLOTAREV AND N. G. BAKHSHIEV

which is defined by the spectral density of the Einstein factor B(J.i) for all characteristics in the general case. Evaluation of the effective field acting on the molecule enables us to relate the spectroscopic properties of the molecule B(J.i) to its observed spectra K(J.i) [2]. For a condensed medium, this relationship can be written in the form

B (v) = K (v).c 6(v) N·h·v •

(1)

j " ,,/2 where e (J.i) = n (J.i) E av / Eef ' K (J.i) is the experimentally measured absorption constant, N is the number of molecules per unit volume, h is Planck's constant, c is the speed of light, Eav is the average light-wave field in the medium under investigation with a dielectric perme­abilitye = i12(macrofield), Eef is the local (effective) light-wave field (microfield), and n(v)

is the real component of the complex refractive index [fi ( J.i) = n ( J.i) - ik (J.i)]. Equation (1) is simplified for the gaseous phase, since the correction e (v) = 1, which permits direct determina­tion of the molecular spectroscopic characteristics B (v) from the observed spectra. In order to determine B (v) for the condensed medium, it is obviously necessary to calculate the correc­tion e (v) in the spectral region with which we are concerned. The general expression for the correction e (v) was found previously [2], but use of this equation is at present hindered by the fact that we must know and take into account a number of molecular parameters. Solution of the problem is substantially facilitated by resorting to models. In particular, by using the basic assumptions of the Onsager theory [6], we can write an expression for Eef in the optical­frequency region:

(2)

wheref is the reactive-field parameter (f= 2(~2-1).-\-), (lY= O! - iO!'); ~ is the complex 2n2 + 1 r

polarizability of the molecule, and r is the radius of the Onsager cavity, which is correlated with the structural radius of the molecule.

Excluding & from Eq. (2), as was done previously [2], use ofthe expression [(n 2_1) / -411" ] • Eav =

naEef yields

(3)

where a = 27rNr 3.

The problem of determining the correction e (J.i) therefore reduce s to finding the value s of n(J.i) , k(J.i), and r. It should be noted that, although the value of Eq. (3) given above is for a liquid consisting of isotropically polarized molecules, use of this expression for preliminary evaluation of the influence of the effective light-wave field for liquid water is justified as a first attempt at applying the hypotheses considered above to systems with strong intermolecular in teraction.

The optical constants n(J.i) and k(J.i) in the vicinity of the valence-vibration band of liquid water were determined by the DTIR method [7-9], with an SP-122 attachment [10] in a Hilger H-800 apparatus, using a CaF2 prism. The reflection from the interface between the glass (IFS-24) and water was measured with an accuracy .6.R «0.5%. The values of n(v) and k(J.i) were determinedby solving the Fresnel equatiop. system R1. = f( ({1" n, k) and RI( = f( 'P2, n, k) by the graphic method, plotting a series of curves on the coordinates R1. versus RII for two incidence angles and a series of constant values of nand k. The intersection point on this coordinate system, determined from known values of RJ. and Rn ,yielded the pair of optical constants sought

INFLUENCE OF THE EFFECTIVE LIGHT-WAVE FIELD ON THE IR SPECTRUM 17

k n 1.5

0.2 1.3

0.1 1.2

3100 3~OO

Fig. 1

Fig. 1. Optical constants of liquid water.

Fig. 2

Fig. 2. Infrared spectra of water in different physiochemical states. 1) K (v) [II (v) = 1) in B (v) units; 2) B (v), taking into account correction II (v), after Onsanger; 3) K (v) for water in nitrogen matrix at 20° K, for molar concentration ration N2 /H20 of 1012 and 39 respec­tively.

for a given wavelength. In contrast to the graphic method proposed in the literature [8,11], this procedure for determing n ( ~) and k (~) is simple and requires no additional graph s.

Figure 1 shows the optical constants in the vicinity of the valence-vibration band of liquid water found by the method described above. The position of the individual maxima within the band were in good agreement with the data obtained from the infrared absorption and Raman spectra [12, 13]. In conformity with the literature [12], the main bands with maxima at 3280, 3420 and 3490 cm-1 can be preliminarily assigned to the 21lJ2' Vl, and v3 vibrations. A more detailed discussion of the results obtained in investigating absorption and dispersion in the vicinity of the valence-vibration band of liquid water is given by Zolotarev [14].

The next stage in establishing the correction e (v) is determination of the parameter r, which can be found from the Onsager-Betcher equation for the transparency region

(0-1)(21+ I) · (4)

This expression is the equation for a straight line on the coordinates (I _ :~~~ + I) versus

;~: + g ; the slope of the line is defined by the term -1/r3, while the point of its intersection with the ordinate is the value of l/a. The pol ariz ability (a) of water varies with temperature [15,16], but the change is slight over the range 50-70°C, which means that use of Eq. (4) is justified for this temperature region. The graph was constructed from data obtained in precise measurements of the refractive index na and density p over the temperature range 50-70°C [15,16]. The average values of the quantity sought, as determined from the graph, were r = 1.5 A and a = 1.4 A.3. It should be noted that the value obtained for the Onsager radius was very close to the 'x-ray radius of the water molecule R = 1.4 A [17].

18 V. M. ZOLOTAREV AND N. G. BAKHSHIEV

The data given above were used to determine the spectrum B (II) of liquid water in the vicinity of the valence band from Eqs. (1) and (3) (Fig. 2). For purposes of comparison, this figure also gives the observed spectrum of water K(II) [8(11) = 1] and the spectra of gaseous water [18] and of water in a nitrogen matrix at 200K for different molar concentrations [19] (see curves 3,4, and 5). It is readily seen that both the K(II) spectrum and the B(II) spectrum obtained with the correction 8 (II) differ materially from the spectrum of the gaseous phase. Correction of the spectra with 8 (II) , which takes into account the influence of the effective light-wave field, thus causes no material transformation of the K (v) spectrum of liquid water in this case, although it causes substantial differences between the K (II) and B (II) spectra. These changes are manifested, for example, in a slight decrease in integral intensity and in displacement of the center of gravity of the B(II) band by about 70 cm-i in the short-wave direction. In general, the absolute magnitude of the changes caused by introduction of the correction 8 (1/) depends on the model selected, which can be used to investigate a given system only after further development. Use of the "nonmodel" method proposed by Libov [20] eVidently permits more detailed consideration of this problem.

Comparison ofthe spectra of water in different physicochemical states (Fig. 2) thus enables us to conclude that the difference between the spectra of water vapor and condensed water is almost wholly due to a change in the spectroscopic properties of the molecule during the phase transition, which results from the intermolecular interaction. Formation of hydrogen bonds is known to be the principle interaction.

In conclusion, the authors wish to thank V. S. Libov for making a number of valuable suggestions in discussing this work.

LITERA TURE CITED

1. N. G. Bakhshiev, O. P. Girin, and V. S. Libov, Dokl. Akad. Nauk SSSR, 145 :476 (1962). 2. N. G. Bakhshiev, O. P. Girin, and V. S. Libov, Opt. i Spektr., 14:476, 745 (1963). 3. V. S. Libov, N. G. Bakhshiev, and O. P. Girin, Opt. i Spektr., 16:1016 (1964). 4. N. G. Bakhshiev, Opt. i Spektr., 20:976 (1966). 5. N. G. Bakhshiev, Doctoral Dissertation, GOI, Leningrad (1966). 6. W. Braun, Dielectrics [ Russian translation], Izd. Inostr. Lit., Moscow (1961). 7. V. M. Zolotarev and L. D. Kislovskii, Pribory i Tekh. Eksperim., No.5, p. 175 (1964). 8. J. Fahrenfort and W. M. Visser, Spectrochim. Acta, 18:1103 (1962). 9. V. M. Zolotarev and L. D. Kislovskii, Opt. i Spektr., 19:623, 809 (1965).

10. V. M. Zolotarev, Yu. D. Pushkin, and V. A. Korinskii, Opt.-Mekh. Prom., No.8, p. 24 (1966) .

11. 1. Simon, J. Opt. Soc. Am., 41:336 (1951). 12. A. N. Sidorov, Opt. i Spektr., 8:51 (1960). 13. z. A. Gabrichidze, Opt. i Spektr., 19:575 (1965). 14. V. M. Zolotarev, Dokl. Akad. Nauk SSSR (in press). 15. V. P. Frontas'ev and L. S. Shraiber, Zh. Strukt. Khim., 6:512 (1965). 16. N. E. Dorsey, Properties of Ordinary water-Substances, Reinhold, New York (1940). 17. O. Ya. Samoilov and T. A. Nosova, Zh. Strukt. Khim., 6:198 (1965). 18. G. Hertzberg, Vibration and Rotation Spectra of Multiatomic Molecules [Russian

translation], Izd. Inostr. Lit., Moscow (1949). 19. M. Van Thiel, E. D. Becker, and G. C. Pimentel, J. Chern. Phys., 27:486 (1957). 20. V. S. Libov, Candidate's Dissertation, GOI, Leningrad (1965).

RAMAN SPECTRA OF WATER,SATURATED AQUEOUS ELECTROLYTE SOLUTIONS, AND ICE CRYSTALS·

Z. A. Gabrichidze

Study of the vibration spectra of compounds with hydrogen bonds can yield important infor­mation on the nature of the hydrogen bond and on the structure of the substance investigated. Water occupies a special position in this respect, since its basic properties are governed by its hydrogen bonds. Research on the vibration spectra of aqueous electrolyte solutions is also of great interest for determination of the state of individual bonds in water molecules.

Many studies have been made of the spectra of water and aqueous solutions by infrared [1-8] and Raman [9-14] spectroscopy. However, there is as yet no consistent interpretation of the results obtained by different authors, which naturally indicates a need for further research in this area.

This paper presents the results of our investigations of the Raman spectra of water and saturated aqueous solutions of lithium, sodium, calcium and strontium chlorides and lithium and sodium bromides at a temperature of 300°K. The spectrum of water was also investigated

Fig.!. Photomicrographs of Raman spectra of water at tem­peratures of 300 0 K (1) and 350 0 K (2).

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:94-102 (1966).

19

20

Hg 2753.4 I

Z. A. GABRICHIDZE

J~55

I

Fig. 2. Photomicrographs of Raman spectra of sat­urated aqueous solutions of LiCI (1) and NaCI (2) \at 300°K.

"g275JA

2

-u . cm~

Fig. 3. Photomicrographs of Raman spectra of sat­urated aqueous solutions of CaCl2 • 6H20 (1) and SrCl2 • 6H20 (2) at 300°K.

at a temperature of 350 0K. The Raman effect was excited by the 2537 A line of the mercury spectrum and recorded with a quartz spectrograph having a dispersion of 10 A/mm in the 0- H valence-vibration region. The resultant spectra are shown in Figs. 1-4 in the form of photomicrographs while the frequencies of the observed maxima are given in Table 1.

It can be seen from curve 1 in Fig. 1 that the spectrum of water in the O-H vibration region at room temperature consisted of a broad (about 1000 cm -1) band with maxima at 3050, 3210, 3450, and 3620 cm -1. An increase of 50 deg in temperature led to some intensity

RAMAN SPECTRA OF WATER, SATURATED SOLUTIONS, AND ICE CRYSTALS 21

Hg 275J1. I

--- v , cm -1

Fig. 4. Photomicrograph of Raman spectra of sat­urated aqueous solutions of LiBr (1) and NaBr (2) at 300 oK.

redistribution among the maxima and to a characteristic shift in their locations. Examination of curve 2 in Fig. 1 shows that the intensity of the maxima near the long-wave margin of the band was reduced, while that of the maxima near the short-wave margin was increased. The 3210 cm -1 maximum was reduced in intensity and displaced toward higher frequencies by about 30 cm -1, while the 3450 and 3260 cm -1 maxima were increased in intensity and apparently displaced toward lower frequencies.

A pronounced change in the O-H vibration band was observed before formation of a saturated aqueous solution when LiCl, NaCI, CaCl2 • 6H20, SrCl2 • 6H20, LiBr and NaBr were dissolved in water. As can be seen from Figs. 2-4, the spectra of these solutions in the O-H vibration region exibited a band extending roughly from 3000 to 3750 cm -1 and having only a single distinct maximum (at about 3450 cm -1), whose position varied from solution to solution (see Table 1).

At lower frequencies, the Raman spectra of both water and all the aqueous solutions inves­tigated contained intense bands at 170, 500,700 and 1650 cm-t •

Substance

Water

Saturated aqueous solutions of:

LICI NaCI

CaCI2 -6H20 SrCl:/-6H:/O

LiBr NaBr

TABLE 1

ITemperature. Frequency of 0- H valence OK vibrations, cm-1

300

3440 3455 3~40 3450 3450 3465

3610 3620

22 Z. A. GABRICHIDZE

As was pointed out above, the origin of the intense maxima observed in the 100-1700 and 3000-4000 cm-1 regions of the Raman spectra of water and aqueous electrolyte solutions has often been discussed in the literature [9-14]. However, it must be noted that, while there is no question regarding the assignment of the 170, 500, and 700 cm -1 bands to molecular interaction and of the 1650 cm -1 band to deformation vibration of the water molecule, no satisfactory expla­nation has yet been found for the origin of the maxima in the 0- H vibration band.

In our opinion, the two-structure model, which has recently been successfully employed to account for various properties of water and aqueous solutions [15-19], must be utilized to interpret the appearance of the complex band structure in the spectrum of liquid water in the 3000-4000 cm -1 region and the influence of salt solution on this spectrum.

As is well known, the term "two-structure model" refers to the existence of two struc­tures in liquid water in the equilibrium state; the first of these duplicates the structure of ice within the limits of short-range ordering [20), while the second corresponds to denser molecular packing, which results from filling of the voids in the tetrahedral structure by water molecules. Because of their thermal movement, the molecules that enter the voids (whose size exceeds that of the molecules) either have no hydrogen bonds to adjacent water molecules [17, 21) or form distorted hydrogen bonds [22) and are therefore not energetically equivalent to the molecules at the framework points, which have a regular tetrahedral environment. The vibration spectra of these molecules should therefore differ from those of the framework molecules. This assumption permits a natural explanation of the appearance of the complex structure in the 0- H valence-vibration band of the water spectrum and of the changes that occur in the posi­tions and intensities of these maxima when the temperature of the water is raised or various salts are dissolved in it.

As was noted above, the intensity of the maximum at 3210 cm -1 decreased and it was displaced toward higher frequencies when the temperature of the water was raised from 300 to 350°K. This is readily interpreted if it is ascribed to symmetric vibrations of water molecules in a tetrahedral environment bound to the adjacent molecules by four hydrogen bonds, i.e., if we consider the maximum to be produced by symmetric vibration of water molecules with an ice-like structure (such molecules will henceforth be referred to as "water molecules with normal hydrogen bonds "). A rise in temperature undoubtedly weakens the hydrogen bonds, increasing their length and even rupturing some of them. This produces the observed displacement of the maximum toward higher frequencies and the decrease in its intensity. The increase in intensity and displacement toward longer wave lengths observed for the 3450 cm-1 maximum is thus interpreted as resulting from symmetric vibration of water molecules whose tetrahedral environment has broken down and which do not have the maximum possible number of hydrogen bonds or are bound to adjacent molecules by distorted hydrogen bonds (such molecules will henceforth be referred to as "water molecules with defective bonds"). When the temperature is raised, there is an increase in the number of such molecules and in their perturbing effect on the surrounding molecules, since the number of molecules in close coordination at a given molecule in liquid water increases with temperature (17). The combination of these two factors apparently causes the observed intensification of the 3450 cm -1 band in the Raman spectrum and its slight displacement toward lower frequencies. In our opinion, similar considerations regarding the changes in the intensity and position of the 3620 cm-1 maxima with rising temperature (an increase in intensity and a decrease in fre­quency) enabled us to attribute them to the symmetric vibration of water molecules only slightly perturbed by hydrogen bonds ("free water molecules"). We are inclined to treat the 3050 cm-1

maximum as a difference frequency resulting from the interaction of the 3210 cm -1 valence vibration with the intermolecular translation vibration of the water molecules. The correspond­ing resultant frequency, the deformation-vibration overtone, and the asymmetric-vibration

RAMAN SPECTRA OF WATER, SATURATED SOLUTIONS, AND ICE CRYSTALS 23

frequencies for water molecules with a regular tetrahedral environment should lie in the region between 3210 and 3450 cm-1, although they cannot be detected against the background of the continuous band.

Our hypotheses regarding the interpretation of the hydrogen-bond vibration spectrum of liquid water are supported by the fact that the two-structure model can be used to explain the severe change in the structure of the 0- H vibration band observed on moving from the spectrum of water to the spectra of saturated aqueous solutions of LiX and NaX (X = CI, Br), CaCl2 • 6H20, and StCl2 • 6H20 (See Figs. 1-4). Actually, strong electrolytes are known to dissociate into anions and cations when dissolved in water; the ions interact with the water molecules and become centers for translational movement of the latter (moving with them in some cases). If we take into account the fact that ions in solution are arranged like water molecules with respect to the short-range aqueous environment [23] but, in contrast to water molecules, cause reorientation of neighboring molecules, thus disrupting the ice-like structure and increasing the number of water molecules with defective hydrogen bonds, we can explain the disappearance of the 3210 cm -1 maximum, which was ascribed to symmetric vibration of water molecules with normal hydrogen bonds, from the spectra of the solutions and the appearance of a very intense broad maximum at 3450 cm -1 , which can be attributed to symmetric vibration of water mole­cules with defective hydrogen bonds.

The fact that the spectra of the aqueous solutions did not contain the 3620 cm-1 maximum present in the spectrum of liquid water, which we assigned to symmetric vibration of water molecules with no hydrogen bonds, apparently indicates that the number of free water molecules in saturated aqueous solutions, like the number of water molecules with normal hydrogen bonds, is so small that it is virtually impossible to detect the maxima corresponding to their vibration against the background of the broad, high-intensity ° -H vibration band.

The results of our investigation of the Raman spectra of water and saturated aqueous solutions thus demonstrate the validity of the theory that two structures exist in liquid water in the equilibrium state.

In connection with our interpretation of the maxima in the ° -H vibration band of the spectrum of liquid water, we became interested in the spectrum of the ice crystal, on which much research has been done [25, 26]. Specifically, it was to be expected that the number of water molecules with a regular tetrahedral environment would increase on moving from the liquid to the crystalline state. The Raman spectrum should accordingly exhibit an increase in the intensity of the maximum corresponding to symmetric vibration of these molecules and substantial attenuation or disappearance of the maximum corresponding to the vibration of molecules with defective bonds.

Figure 5 shows photomicrographs of the Raman spectra of an ice crystal at temperatures of 260, 200, and 77°K. Curve 1 indicates that the ice spectrum in the ° -H Vibration region consisted of a band with an intense maximum at 3145 cm -1 and weaker broad maxima near 3255, 3350, and 3440 cm- i . When the temperature of the crystal was reduced to 2000K (curve 2), the 3145 cm -1 maximum was displaced toward lower frequencies by 25 cm -1 and the 3243 cm-1

maximum and the broad 3015 cm-1 maximum at the long-wave edge of the band became more pronounced. A further reduction in temperature to 77°K (curve 3) was accompanied by larger changes in the spectrum, which must be regarded as re sulting both from the change in temperature and from the change in the structure of the crystal [27], since ice has a transition point near 193°K (and apparently near 133°K [28]). Thus, for example, the 3145 cm- i maximum was displaced toward longer wavelengths by 34 cm -1 and gave a value of 3086 cm -1; in addition, an intense 3213 cm-1 line and a weak 3255 cm-1 maximum appeared. The bands with maxima at 3320 and 3415 cm-1 were well resolved and weak distinct lines with frequencies of 3290, 3300, 3330, 3390, 3410, and 3440 cm-1 were clearly detected against this background. The space be-

24 Z. A. GABRICHIDZE

o Hg275JA 3145

I I

3120 H

~\

_ v , cm -1

3

Fig. 5. Photomicrographs of Raman spectra of ice crystal at different temperatures. 1) 260oK; 2) 200oK; 3) 77°K.

tween the bands contained a weak maximum at 3355cm -1, while a weak diffuse 3520 cm -1 line ap­peared at the short-wave margin of the band.

In our opinion, the intense maxima at 3086, 3213, 3320, and 3415 cm-1 in the ice spectrum had the same character as the intense maxima in the spectrum of liquid water. Actually, we assigned the 3210 cm-1 maximum in the O-H Vibration band of the liquid-water spectrum to symmetric vibration of water molecules with a regular tetrahedral environment. An increase in the number of such molecules and a corresponding intensification of the 3210 cm -1 maximum is naturally to be expected for crystalline water. Assuming the 3145 cm -1 maximum of the ice spectrum to correspond to the 3210 cm-1 maximum of the liquid-water spectrum [12], the spectrum exhibited a large increase in the intensity of the maximum corresponding to symmetric vibration of molecules with normal hydrogen bonds. Moreover, the ice spectrum contained a band near 3300 cm-1 , which apparently corresponded to the 3450 cm -1 maximum in the liquid-water spectrum. The intensity of this band depended little on temperature. The only effect produced by reduCing the crystal temperature from 260 to 77°K was appearance of a maximum at 3213 cm-1

and of broad maxima at 3320 and 3415 cm-1• On the basis of the foregoing and our interpretation of the maxima in the liquid-water spectrum, we believe that the 3086 and 3213 cm-1 maxima in the ice spectrum must be regarded as resulting from symmetric and asymmetric vibration of water molecules with a regular tetrahedral environment, while the appearance of the 3320 and 3415 cm-1

maxima is spectroscopic proof of the existence of a rather large number of molecules with defec­tive hydrogen bonds in the ice crystal and can be attributed to symmetric and antisymmetric

RAMAN SPECTRA OF WATER, SATURATED SOLUTIONS, AND ICE CRYSTALS 25

vibration of the molecules. It must also be noted that the weak diffuse maximum at 3520 cm-1

detected in the ice spectrum may indicate the existence of a very small number of water mole­cules free or almost free of hydrogen bonds in the ice crystal.

LITERA TURE CITED

1. J. W. Ellis and B. W. Sogre, J. Chern. Phys., 2:559 (1934). 2. D. Williams and W. Millet, Phys. Rev., 66:6 (1944). 3. V. Liddel., J. Chim. Phys., 45:82 (1948). 4. V. M. Chulanovskii, Dokl. Akad. Nauk. SSSR, 93:25 (1953). 5. R. D. Waldron, J. Chern. Phys., 26:809 (1957). 6. M. O. Bulanin, Opt. i Spektr., 2:557 (1957). 7. Yu. P. Syrnikov, Dokl. Akad. Nauk SSSR, 118:760 (1958). 8. L. D. Shcherba and A. M. Sukhotin, Zh. Fiz. Khim., 33:2401 (1959). 9. G. S. Landsberg, Izv. Akad. Nauk SSSR, Ser. Khim., 2:273 (1938).

10. J. H. Hibben, The Raman Effect and Its Chemical Applications, New York (1939). 11. P. K. Narayanaswamy, Proc. Ind. Acad. Sci., 27A:311 (1948). 12. V. 1. Val'kov and G. L. Maslenkova, Opt. i Spektr., 1:881 (1956); Vest. Leningr. Gos.

Univ., 22:8 (1957). 13. J.W. Shultz and D. F. Hornig, J. Phys. Chern., 65:2131 (1961). 14. G. F. Walrafen, J. Phys. Chern., 36:1035 (1962). 15. L. Hall, Phys. Rev., 73:775 (1948). 16. K. Grojotheim and J. Krogh-Moe, Acta Chern. Scand., 8:1193 (1954). 17. O. Ya. Samoilov, Structure of Aqueous Electrolyte Solutions and the Hydration of Ions,

Consultants Bureau, New York (1965). 18. 1. G. Mikhailov and Yu. P. Syrnikov, Zh. Strukt. Khim., 1:12 (1960). 19. A. Yu. Namiot, Zh. Strukt. Khim., 2:408,476 (1961). 20. J. D. Bernal and R. H. Fowler, J. Chern. Phys., 1:515 (1933); Usp. Fiz. Nauk, 14:586 (1934). 21. G. H. Haggis, J. B. Hasted, and T. J. Buchanan, J. Chern. Phys., 20:1452 (1952). 22. J. A. Popie, Proc. Roy. Soc., 205A:163 (1951). 23. J. Beck, Phys. Z., 40:474 (1939). 24. O. A. Osipov and 1. K. Shelomov, Dokl. Akad. Nauk SSSR, 122:428 (1958). 25. N. Ockman, Adv. Phys., 7:199 (1958). 26. M. J. Taylor and E. Walley, J. Chern. Phys., 40:1660 (1964). 27. A. I. Stekhanov and Z. A. Gabrichidze, Opt. i Spektr., 11:359 (1961). 28. M. Blackman and N. D. Lisgarten, Adv. Phys., 1:189 (1958).

THE GERMANIUM-WATER INTERFACE*

V. M. Zolotarev

Study of the state of the interface between semiconductors with a lattice of the diamond type and polar media is of definite interest for solution of a broad range of problems. The pressing need for research on the surface properties of semiconductors is specifically related to determination of the physicochemical nature of impurity centers, which will permit establishment of the correlation between the properties of these centers (concentration, capture cross section, etc.) and the experimentally measured electrophysical parameters [1].

The present work was undertaken as an investigation of the germanium -water interface. It should be noted that the results obtained had the same qualitative character as for the silicon­water interface. Investigation of the surface-interaction effects of these materials by the ciassical method of infrared spectroscopy, using perpendicular transmission and reflection, is very cumbersome. We were able to avoid such difficulties by employing spectrophotometry based on deflected total internal reflection (DTIR) [2,3,4].

The DTIR method requires that optical contact be created between the material (germanium), which must be transparent in the spectral region to be investigated and have a high refractive index (n = 4), and the test medium (water), which must have a lower refractive index (nHzo < nGe). Op­tical contact is automatically achieved for a liquid medium. The angle of incidence (cp) of the radia­tion on the interface under investigation should exceed the critical angle (sin (/J > sin (/Jcr = nH20/ nGe)' The angle of incidence in our apparatus was 45°, which was materially greater than (/Jcr; the divergence of the incident beam did not exceed 1°. Since there are no losses due to reflection outside the absorption bands with this method [2,5], multiple reflection was used to increase the contrast of the DTIR spectrum, with a set of special germanium plates [6] as the reflecting surfaces. DTIR spectra obtained under such conditions are virtually identical to the correspond­ing absorption spectra with respect to band position, form, and intensity recalculated for passage through an equivalent thickness of the test specimen [3,6]. This is due to the fact that, in DTIR spectrophotometry, the incident beam penetrates the optically less dense medium to a certain depth that depends on the angle of incidence and polarization state of the incident radiation [7]. The "depth of penetration" is an arbitrary concept defined as the distance from the surface of the optically dense medium at which the energy density of the incident beam is reduced by a factor of e [6]; the optically less dense medium is assumed to be transparent. The depth of penetration in our experiment was about 0.1 jJ..

Specimens of the n-type germanium with a resistivity of 48 Q. cm were cut from single

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:108-113 (1966). This article is based on a paper presented at the 16th All-Union Conference on Spectroscopy, Moscow, 1965.

26

THE GERMANIUM- WATER INTERFACE 27

crystals along the LHll and LHO] planes; they were oriented to within 30 minutes of arc with an x-ray apparatus. The deviation from planularity over the entire surface of the polished specimen did not exceed 0.1 wavelength. Substantial energy losses occur with lower surface precIsIOn. The DTIR spectra were determined in a Hilger H-800 double-beam infrared spectrophotometer with LiF and CaF2 prisms, using the simple attachment shown in Fig. 1. The multiple-reflection liquid cell was made of a fluoroplast (teflon) and permitted determi­nation of the DTIR spectra with 100-fold reflection of the beam from the test surface. A reflec­tive filter based on Sn02' which cut off all radiation shorter than 1.5 J.l, was used to prevent heating of the specimen. The composite polarizer shown in Fig. 1 was constructed from layers of fluorite and polyethylene by the method described in the literature [7].

R,'. 100 --- R.L

so

lJ , cm -1

Fig. 1. Diagram of attachment to H-800 spectrophotometer for determination of DTIR spectra. 1) Source (Nernst glower); 2) heat filter based on Sn02j 3, 6, 7) ele­ments of H-800 illumination system;

o~~ __ ~~ ____ ~~ __ ~ __ WlOO 3000 2000 1000

Fig. 2. DTIR spectrum of wa­ter at interface with polished germanium ([111] plane).

4) polarizer; 5) multiple-reflection cell; 8) entrance slit.

Fig. 3. Diagram of interaction of water mole­cules with polished germanium surface. I, II) Double and single 4ydrogen bonds to surface hydroxyls; A) highly perturbed complex of m-associated molecules near surface; B) weakly perturbed complex of molecules far from surface.

28 V.M.ZOLOTAREV

Figure 2 shows the DTIR spectra obtained from a germanium-water interface with the attachment described above. The center of the valence-vibration band of water in the DTIR spectrum was displaced toward lower frequencies by 20 cm-1 (in comparison with the absorption spectrum, where the center of this band lies at 3360 cm -1 ), while calculations based on the known optical constants of liquid water [13] showed that the displacement should amount to about 35-40 cm-1• The center of the valence-vibration band for water in contact with a germanium surface is thus displaced by approximately 15 cm -1 in the short-wave direction. Calculation shows that the position of the deformation-vibration band for water in the DTIR spectrum precisely coincides with the position of this band in the absorption spectrum of liquid water, at 1640 cm-1• As can be seen from Fig. 2, the experimental data were in complete agreement with the calculations for this band. The results obtained can be explained on the basis of adsorption theory [8,9,10].

A real.germanium or silicon surface is always hydrated in a damp medium and sorbed structural water is present at the surface in the form of hydroxyl groups, which serve as centers for further polymolecular water adsorption [8,9,10]. According to the literature [11], the area of the atomic surface of germanium occupied by a single hydroxyl depends on the crystallographic orientation and amounts to 8, 11.3, and 13.8 A2 for the [100], [110], and [111] planes respectively. Since a real polished germanium surface consis ts of a set of microregions with greatly differing crystallographic orientations, the distance between the structural hydroxyls can be markedly less than for a pure atomic surface. The increased hydroxyl density should promote occurrence of a large number of surface structural defects in the crystal lattice. The presence of an oxide film on the germanium surface leads to a decrease in its adsorption capacity [12], apparently as a result of a decrease in the number of hydroxyl groups and possibly of a change in the activity of the remaining adsorption centers. The interaction of the molecules of liquid water with a germanium surface probably takes place principally by formation of hydrogen bonds with the surface structural hydroxyls [11], following the pattern shown in Fig. 3.* Interaction of the water molecule with the surface hydroxyl by formation of two hydrogen bonds (type I) is quite probable, since, according to Ellis [14], the distance between the germanium

I I 0

atoms in the -Ge-O-Ge- system is about 3 A, although it can be less, as a result of I I

structural defects, which is favorable for formation of a double hydrogen bond [9]. As can be seen from Fig. 3, other interaction mechanisms are also possible. Interaction with the surface hydroxyls promotes a decrease in the mobility of the interacting molecules and probably facili­tates rupture of the system of hydrogen bonds in the boundary layer of the liquid water, which leads to displacement of the valence-vibration band of water toward higher frequencies in the DTIR spectrum (see Fig. 2). Contributions to the integral band intensity in the DTIR spectrum are made both by molecular complexes of type A, which occur near the germanium -water inter­face and form hydrogen bonds with the surface hydroxyls, and by molecules of type B, which are comparatively remote from the interface. The main contribution to the band intensity is made by the weakly perturbed molecules of type B complexes. The deformation-vibration band of water is less sensitive to structural changes and the band position in the spectrum shown in Fig. 2 remains unchanged during weak interactions. In order to verify that the structured surface layers of water participate in displacement of the valence band, it is necessary to vary the thickness of the layer undergoing spectrophotometry. We conducted an experiment in which the depth to which the beam penetrated the surface water layer was materially reduced. The perpendicular and parallel components of plane-polarized radiation are known to have different

* A similar pattern was used by Kiselev [9] to explain the changes that occur in the spectrum of water during its adsorption on silicate gel, where' a broad band with a maximum in the vicinity of 3400 cm-1 and an intense band at 1640 cm-1 were observed at a relatively high vapor pressure (pip = 0.6).

THE GERMANIUM-WATER INTERFACE 29

penetration depths; the perpendicularly polarized component of the incident radiation penetrated to a smaller depth under our experimental conditions. The valence-vibration band obtained for the water with perpendicular-polarized radiation was markedly displaced toward high frequencies in relation to the band obtained with unpolarized or parallel-polarized radiation; as can be seen from Fig. 2, the position of the deformation-vibration band of the water remained unchanged. We believe that this experiment confirms the presence of a perturbed layer of liquid water, with a structure differing from that of liquid water, near the germanium surface. The results obtain­ed were for the [111] surface.

On the basis of crystallographic data [1, 15] on the surface structure of semiconductors with a lattice of the diamond type, it is to be expected that the interaction with a polar medium will differ in character for different main surfaces. A surface atom in the [111] plane is coordinated with the three atoms below it, while an atom in the [110] plane is bound to two surface atoms and only one atom in the lower layer [15]. There is a larger number of active adsorption centers when the lattice contains defects in the [110] plane than when it contains the same number of defects in the [111] plane. Research on the low-temperature oxidation of a germanium surface has confirmed that the main planes have different reactivities. We noted a tendency toward displacement of the valence band of the water toward higher frequencies for the [110] plane in comparison with the [111] plane.

Brattain and Boddy [11] noted that there is a difference in the number of structural hydrox­yls on the principal planes of germanium; similar results have been obtained for quartz [10]. It can be concluded from these data that the [110] surface has a larger number of adsorption centers (the main centers for interaction of water molecules with the germanium surface) than the [111] surface or that the adsorptive capacity of the centers at the [110] surface is greater than that of those at the [111] surface. The results obtained are for an oxidized surface, which probably has only a small predominance of microregions with appropriate orientation. More pronounced spectral changes should be observed for atomically pure and unoxidized surfaces.

In conclusion, the author wishes to take this opportunity to express his deep gratitude to L. D. Kislovskii, A. N. Sidorov, and A. E. Stanevich for the valuable advice and observations they offered in discussing this work.

LITERA TURE CITED

1. G. E. Pikus, Physics of Semiconductor Surfaces [Russian translation], Izd. Inostr. Lit., Moscow (1959).

2. J. Fahrenfort, Spectrochim. Acta, 17 :698 (1961). 3. v. M. Zolotarev and L. D. Kislovskii, Pribory i Tekh. Eksperim., No.5, p. 175 (1964). 4. V. M. Zolotarev and L. D. Kislovskii, Opt. i Spektr., 19:623 (1965). 5. V. M. Zolotarev and L. D. Kislovskii, Opt. i Spektr., 19:809 (1965). 6. N. J. Harrick, J. Phys. Chem., 64:1110 (1960). 7. E. Ya. Yakovlev and F. M. Gerasinov, Opt. i Mekh. Prom., 10:28 (1964). 8. A. N. Terenin, in: Surface Compounds and Their Role in Adsorption Phenomena, Izd.

MGU, p.206 (1957); A. N. Sidorov, Dokl. Akad. Nauk SSSR, 95:1237 (1954). 9. A. V. Kiselev, Kall. Zh., 2:17 (1936); A. V. Kiselev and V. 1. Lygin, Kall. Zh., 21:581

(1959); 22 :403 (1960). 10. s. P. Zhdanov, Zh. Fiz. Khim., 32:669 (1958); s. p. Zhdanov and A. V. Kiselev, Zh. Fiz.

Khim., 31:2213 (1957) 11. W. N. Brattain and P. J. Boddy, Proc. Nat. Acad. Sci. USA, Vol. 48, No. 12 (1962). 12. J. T. Low, J. Phys. Chem., 59:67 (1955). 13. L. D. Kislovskii, Opt. i Spektr., 7:312 (1959) 14. S. G. Ellis, J. Appl. Phys., 28:1262 (1957). 15. H. C. Gatos, Science, 137, (3527) :311 (1962).

STA TE OF WATER IN CERTAIN PERCHLORATE CR YST AL HYDRATES FORMED BY ELEMENTS

OF PERIODIC GROUP 11*

T. G. Balicheva and T. I. Grishaeva

The structure and many properties of electrolyte solutions depend on the interaction between the ions and the solvent molecules. The strongest influence for typical complex­forming ions is exerted by the nearest solvent molecules, which form the solvate shell of the ions. However, the state of such molecules and the directly related problem of the composition and structure of their solvate shells in solution. are still among the least studied and most dif­ficult problems of solution chemistry. It is difficult to solve them merely by study of the prop­erties of solutions, since such chemical processes as complexing, polymerization, hydrolysis, etc. are superimposed on the phenomenon in question. The lack of reliable data on the short­range environment of ions in solutions of moderate and high concentration is therefore one of the main obstacles to research on the state of coordinated particles.

The recent rapid development of the theory and technology of such spectral methods for studying the composition and structure of materials as nuclear and electron magnetic resonance and electron and vibration spectroscopy makes it possible to obtain the requisite information on both the composition and three-dimensional structure of the solvate shells of ions in solu­tion, regardless of the solvent.

Despite the high sensitivity of these methods to the symmetry and field strength of the ligands around the complex-forming cation, however, the data obtained by these methods are still very limited.

One of the simplest ways to solve the spatial problem is apparently to study the proper­ties of water in solid crystal hydrates, since the composition and structure of the ionic hydrate shells and the interatomic 0 .. ·0 distances can be reliably established from x-ray data, while neutron diffraction data provide information on the interatomic O-H distances.

Use of infrared spectroscopy to study the state of water in isostructural crystal hydrates [1-3] has permitted both direct evaluation of the change in the microparameters of the coordi­nated water molecules under the influence of the cation field (its charge and radius) and deter­mination of the factors responsible for the influence of the anion and other proton-containing particles in the outer sphere of the complex. In conformity with Sokolov's theory [4] of inter­molecular interaction and proton-transfer processes, it was established that formation of donor­acceptor bonds between coordinated water molecules and anions can lead to a quite substantial

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:114-125 (1966).

30

STATE OF WATER IN CERTAIN GROUP II PERCHLORATE CRYSTAL HYDRATES 31

polarization of the O-H bond in water molecules comparable in magnitude to that caused by an increase in the charge on the complex-forming cation [3].

The present investigation was conducted to obtain additional information on the influence of the radius and structure of the electron shells of complex-forming cations on the polarization of the O-H bond in coordinated water molecules, using perchlorate crystal hydrates formed by elements of periodic group II.

We decided to investigate crystal hydrates of the Me(C104h . 6H20 type, where Me+2 is Mg+2, Ca+2, Zn+2, Cd+2, and Hg+2, which belong to the isostructural series of perchlorates studied by West [5-7].

According to the x-ray diffraction data obtained by West, the short-range environment of the cation in these crystal hydrates is composed of six water molecules that form a regular Me (H20) 6 +2 octahedron. This symmetric arrangement of the water molecules around the central ion is due to the identical character of the ligands and to the exceptional symmetry of the central-ion field, which results from the electron-shell filling that occurs in group II cations. The symmetric positioning of the ligands around the central ion reduces the dipole-dipole repulSion between the coordinated water molecules to a minimum [8] and it should therefore have no effect on the acidic functions of the coordinated water.

The fact that the group II cations belonged to different periods thus enabled us to make a more thorough study of the influence of changes in the radius and structural characteristics of the electron shells of the cations on the state of the coordinated particles. A nonmonotonic change in ionic radius with increasing atomic number and a similar nonmonotonic change in total polar­ization potential, which is manifested in secondary periodicity [9,10] (Fig. 1), is observed for the elements of group II (Zn, Cd, and Hg). A similar periodicity in the change in acidity in iso­molal solutions of the perchlorates of group II elements was noted by Lilich and Mogilev [11]. U was found that Hg(CI04h solutions had the highest hydrogen ion concentration, followed in order of decreasing acidity by the perchlorates of Zn +2> Be +2> Cd+2> Mg+2> Ca +2> Sr+2> Ba +2.

l,keal 300

~OO

800~~~~~ __ ~~ __ ~ __ z Be Mg- Ca Zn Sr Cd & Hir

Fig. 1

180n J6IIO J~OO .1100 3000 1800

Fig. 2

3,515 log 10 /1 J~O J~6~

0.6 J.l50! b~lO 0..1 I I J160

o. O.J 0.1 O}

I _ l

lI. em "!'

3600 J~QO J1O{) )000 1800

Fig. 3

Fig.!. Sum of two ionization potentials of group II atoms as a function of atomic number.

Fig. 2. Infrared absorption spectra of aqueous solutions of perchlorates of Cd+2 and Hg+2.

1) CCd(CI04)2· 6H20 = 3 moles/liter; 2) CHg(C104)2'6H20 = 3.8 moles/liter; 3) CHg(ClO) .6HO= 1.3 moles/liter. 42 2

Fig. 3. Infrared absorption spectra of aqueous perchloric acid solutions. 1) C HC104 = 10.5 moles/liter; 2) CHCI04 = 4 moles/liter.

32 T. G. BALICHEVA AND T. I. GRISHAEVA

We assumed that the cause of the high acidity of aqueous solutions of the perchlorates of Hg+2, Cd+2, Zn+2, and other elements, although the same as that of aqueous perchloric acid solu­tions and substantially exceeding that of solutions of salts of these cations with other anions [12], must be sought both in the severe deformation of the water molecules in the cation field and in the very weak proton-acceptor properties of the CI0'4 ion. It is obviously for this reason that soi ions, which bind H+ ions more strongly, accelerated the hydrolysis of hydrated Fe+3 salts [13], while CIO:; ions inhibited it [14].

Our study of the infrared absorption spectra of concentrated aqueous solutions of the perchlo­rates of Mg+2, Ca+2, Mn+2, Fe+2, Co+2, Ni+2, Zn+2, Fe+3, Cr+ 3 [15], Cd+ 2, and Hg+ 2 (Fig. 2) showed that a change in the characteristics of the cation (charge, radius, or electron-shell structure) caused only very slight changes in the spectrum.

The great similarity of the infrared spectra of the aqueous perchlorate solutions and those of the corresponding aqueous perchloric acid solutions (Fig. 3) indicates that the position of the absorption bands in such solutions is governed primarily from the change in the number and strength of the hydrogen bonds between the water molecules and between the water molecules and the CI04' ions resulting from the change in solution concentration.

Since it is a very large inorganic anion (having an ionic radius of 2.36 A.), ClO4' is distin­guished by a small negative-charge density on the oxygen atoms [16]; according to quantum­mechanical calculations, the charge on the oxygen atom of the CIO:; ion is -0.359 e and is substan­tially lower than the charge on the oxygen atom of other oxy anions [17]. Production of such a large anion with a weak capacity for formation of hydrogen bonds disrupts the quasi-crystalline structure of liquid water and results in replacement of the H20 ... H20 bonds by H20 ... OCI0S' bonds as the perchlorate ion concentration increases; the absorption bands for the water are accordingly displaced toward higher frequencies, to 3530 cm-i . A similar effect, i.e., displace­ment of the absorption (and reflection) maximum of water towards higher frequencies with increasing anion radius, has also been noted in the literature [18-24]. A change in the nature of the cation had no effect on the water spectrum.

It was thus very difficult to detect the absorption bands of the cation-coordinated water molecules in the infrared spectra of the concentrated salt solutions because of the severe masking caused by the absorption bands of the solvent itself. In order to determine the influ­ence of the nature of the cation on the state of the coordinated water molecules comprising the short-range cation environment in aqueous solutions and to verify our hypotheses regarding the factors responsible for the high acidity of concentrated perchlorate solutions, we therefore decided to study the infrared spectra of solid perchlorate crystal hydrates.

Since very thin single tabular crystals with an area of no less than 1 cm2 are necessary for investigation of the infrared absorption spectra of solid crystal hydrates [1-3], we grew large single crystals of perchlorate hexahydrates both by the high-speed planetary [25] and vertical-displacement [26] methods and by the slower static method, gradually reducing the solution temperature in order to obtain continuous crystal growth. The resultant crystals were large six-sided prisms, with a rhombic cross section for the Ca (CI04 )2 • 6H20 crystals and somewhat. shortened along the c axis for the Cd (CI0 4h . 6Hp crystals. Chemical analysis of the single crystals obtained showed their composition to be in complete conformity with the formula Me (CI04h . 6H20. Thin single-crystal plates about 10-20 J1 thick and suitable for infra­red spectroscopy were produced by grinding thicker plates or even intact crystals and polishing them under vaseline oil, using the method described previously [3]. When the crystals were hygroscopic they were polished and the cells for determination of the infrared absorption spectra were assembled over P 20s in a manipulator, in which all the necessary material was placed no less than a day beforehand. The infrared absorption spectra of the single crystals

STATE OF WATER IN CERTAIN GROUP II PERCHLORATE CRYSTAL HYDRATES 33

log loll

1.5

1.2

O.

0.6

0.3

1.5

1.2

Q9

3600 3QOO 3100

Fig. 4. Infrared absorption spectra of single crystals. 1) Zn(CI0 4h . 6H20; 2) Ca(C104) 2 •

6H20; 3) Mg(CI04)2 • 6H20.

log Io! I 0.7 0.6

0.5

0.11

0.3

0.2

0.1

10 10 II 3265

I

3800 )600 3QOO 3100 3000

Fig. 5. Infrared absorption spectra of Cd (CI04 ) 2 • 6H20 single crystals.

3800 3600 31100 32(}{1 3000 1800 2500 21100 2200 Fig. 6. Infrared absorptio~ spectrum of Hg (C104)2'

6H20 single crystals .

were studied in IKS-14 and IKS-6 (LiF prisms) infrared spectrometers. The instruments were checked for constancy of calibration with polystyrene film, The spectral width of the slit for the IKS-14 spectrometer was 4.5 cm -1 in the 3500 cm -1 region and 3.6 cm -1 in the 3000 cm-1

region, while that for the IKS-6 spectrometer was 2 cm-1 in the 4000-3100 cm-1 region.

The infrared absorption spectra of the crystal hydrates, which were repeatedly determined for several specimens, are shown in Fig. 4-6, while the observed absorption-band maxima and their assignments are given in Table 1.

Comparing the infrared absorption spectra obtained, the follOWing patterns can be noted.

The spectrum of the perchlorate hexahydrates of Mg +2, Ca +2, Zn +2, Cd+2 exhibited two distinct absorption maxima.

According to West [5,6], two types of hydrogen bonds are possible in the structure of Mg(CI04h . 6H20 and other perchlorate crystals isostructural with it: between the coordinated water molecules (with an H20 Of' H20 distance of 2.91 A) and between a water molecule and the closest oxygen atom of a CI04' ion (with an H20 ... OCI0S" distance of 2.98 A).

On the basis of the x-ray diffraction data given above and the weak tendency of Clot ions toward hydrogen-bond formation, we attributed the high-frequency absorption-band maximum in the infrared spectra of the perchlorate crystal hydrates of Mg+2, Ca+2, Zn+2,

and Cd+2 to the valence vibrations of the O-H bond of coordinated water molecules

34 T. G. BALICHEVA AND T. 1. GRISHAEVA

TABLE 1

Bond v, cm-1 - -,~ f·IO". ~ A' , 6v, cm yn. cm- rO_ H' kcal/mole

H2O gas 3750 - 7.68 0.958 -Mg+LH20·, .OCIO; . 3515 235 6.74 0.988 3.7 Mg+2- H20 ... H2O 3460 290 6.54 0.991 4.5 Ca+2-H20·· .OCI03 . 3660 90 7.31 0.981 1,4 Ca+2-H20·. ·H2O 3590 160 7.04 0.984 2.5 Zn+2-H20·· .OCIO; . 3530 220 6.80 0.987 3.4 Zn+2-H20· .. H2O 3440 310 6.46 0.992 4.8 Cd+2-H20·· .OCI03 . 3640 110 7.23 0.982 1.7 CdH -H20· .. H2O 3265 485 5.82 1.001 7.6 rIg+2-H20·· .OCI03 . 3775 -25 7.78 - -Hg+2 - H20 ... H2O 2460 1290 3.30 l.u43 20.2

Notes. 1) The strength constant of the bond was calculated from the frequency

M equation derived for a plane triatomic molecule of the type m/ ""'m [27]:

41tllvrnc2

f = (1 + ~ s1n2 (l) L '

where 20: is the angle between the m - M bonds ( < HOH) and is assumed to be 106.5 ±1.5°, this being the average value obtained from neutron-diffraction data for several crystal hydrates [29,28]. 2) The interatomic rO_H distances in the water molecules were determined by interpolation from the direct rela­tionship between the displacement of the O-H vibration frequency and the interatomic rO-H distance obtained from neutron-diffraction data described by Pimentel and McClellan [30]. 3) The approximate hydrogen-bond energies (e)

were calculated from the relative displacement of the O-H valence-vibration

band with the equation [31]~ ~v = _ pis, where p/D equals 0.017 kcal-1•

Vo

hydrogen-bonded to the ClOi ion (Me+2- H20 ... OClO; ) and the low-frequency maximum to the valence vibrations of the O-H bond of coordinated water molecules hydrogen-bonded to one another (Me+2-H20 ... H20).

The distance between the two aforementioned absorption maxima successively increased on moving from Mg(CI04h . 6H20 to the corresponding perchlorates of Ca+2, Zn +2, and Cd+2, giving values of 55, 70, and 90 cm -1 and reaching 370 cm -1 for Cd(CI04)2 . 6H20 (see Table 1). The absorption bands in the infrared spectrum of the Hg(C104h . 6H20 single crystals were therefore expected to be displaced by larger amounts toward low and high frequencies respec­tively. As can be seen from Fig. 6, the infrared spectrum of the Hg(CI04 )2 . 6H20 actually exhibited a very intense absorption band greatly displaced toward low frequencies, with its principal maximum at 2640 :!: 10 cm -1 and weak subsidiary maxima at 2900 and 3315 cm-1, which indicates anomalously strong polarization of the 0- H bond in water molecules coordina­ted by the Hg+2 ion. The high polarizing capacity of the Hg+2 cation can be attributed to its very high ionization potential. In this case, one might expect a parallelism in the changes in the ionization potential and in the degree of polarization of the O-H bond of the water molecules in the cation hydrate shells, which is reflected in both the intensity and the long-wave frequency displacement of the O-H valence vibrations resulting from elongation of the O-H bond under the influence of the cation field. In order to determine this relationship, we plotted the observed frequency displacement ~v of the O-H valence vibrations of water under the influence of the cation field (the Me+2- ~O ... H20 bond) from the frequency for isolated water molecules (3750 cm-i ) as a function of the atomic number of the cation forming the crystal hydrate (Fig. 7, curve 1).

STATE OF WATER IN CERTAIN GROUP II PERCHLORATE CRYSTAL HYDRATES 35

~ -1 t; I) . em

Fig. 7. Observed frequency displacement of O-H valence vibrations of coordinated water molecules under the influence of cation field (1)

and hydrogen bond to CI04-

ion (2) as a function of atomic number of element.

Comparison of Figs. 1 and 7 (curve 1) shows that the decrease in the frequency of the O-H valence vibrations of the water molecules in the Me +2 -H2 ° ... H2 ° group for Ca +2, Mg+2, Zn +2 and Hg+2 paralleled the increase in their ionization potentials. The intensity of the displaced absorp­tion band increased over the same series. However, the larger increase in the intensity of the absorption band and greater displacement toward low frequencies for water in the Cd+2-H20 ... H20 group than for water in the Zn +2-H20 ... H20 group does not conform to the lower ionization potential for Cd+2 than for Zn +2.

The Cd+2 ion has a crystal-chemical radius very sim­ilar to that of the Ca +2 ion but differs from it in the struc­ture of its electron shell. Comparison of the frequencies of the O-H valence vibrations of water molecules in close proximity to Ca +2 and Cd+2 should therefore reflect the difference in the polarizing force of these cations, which is due solely to the difference in their electron shells.

A typical donor-acceptor 1r - bond is formed between the hybrid d2 sp3 -orbital of the central ion and the un shared p­electron pair of the oxygen atom of the water in the perchlo­rate crystal hydrate of Cd+2, as in the corresponding com­pounds of other d-elements. This should result in a greater residu::tl charge on the hydrogen atoms of the water and an increase in their capacity for hydrogen bonding. There should also be an increase in the probability of protolytic

association of the water. The substantial decrease in the frequency of the O-H vibrations in the Cd+2-H20 ... H20 group in comparison with that in the Ca+2-H20 0" H20 group observed in the infrared spectrum of Cd (CI04)2 . 6H2 ° single crystals confirms that water molecules are more strongly protonized in the hydrate shell of Cd+2 than in that of Ca +20

The Me - OH2 bond is known to be rather highly ionic for Ca +2 and especially for Mg +2, which have electron shells of the inert-gas type [8,32]. The polarizing effect of the Ca+2 and the Mg +2 cations should therefore decrease proportionally as the ionic radius of the cation increases. It is for precisely this reason that there is a linear relationship between the displacement of the 0- H valence-vibration frequency of water molecules coordinated with Mg+2 and Ca +2 and their ionic radii. Their abrupt deviation from this relationship represented by the anomalously large decrease in the O-H vibration frequency of the water in the Cd+2_ H20 ... H20 and Hg+2-H20 ... H20 groups and the substantial increase in the relative intensities of the displaced absorption bands result from the substantial increase in the covalency of the Me-O bond for Cd+2 and Hg+2 [8, 33, 34]. The very slight observed decrease in the vibration frequency of the coordinated water in the Zn+2-H20 ... H20 group in comparison with that for the water in the Mg+2- H20 ... H20 group can be attributed to a very slight increase in the co­valency of the Me-O bond moving from Mg +2 to Zn +2. The large difference in the covalency of the Me+2-0 bond for Cd+2 and Hg+2 on one hand and Zn+2 on the other hand results from the fact that the filled 3d valence orbitals of Zn+2 and the other ions of its series, like their 4s­and 4p-orbitals, are too small to provide the requisite overlapping with the p-orbitals of the oxygen atoms of water [33, 34]. A change in the electron configuration of the cation within the series in question therefore had only a very slight effect on the strength constants of the O-H bond in the coordinated water molecules of the perchlorates of the Zn+2, Mn+2, Fe+2, Co+2, and Ni+2 [2,3].

36 T. G. BALICHEVA AND T. 1. GRISHAEVA

It was quite natural to expect the nature of the cations to have a substantially weaker influence on the strength of the hydrogen bonds between the coordinated water molecules and the CI04' anions in the outer sphere, since the water molecules should screen the anions from the cations. Theimer's study [35] of the Raman spectra of a large number of crystal hydrates and powdered anhydrous salts showed that the effect of the cation on the frequency of the wholly symmetric vibration of the anion (for 80'4"2, NO'r, N:i", CO':i"2) completely disap­peared when a large amount of water of crystallization (six molecules or more) was present.

Investigation of the position of the high-frequency absorption band, which we attributed to the O'-H vibrations of the water in the Me+2- H2O' ." O'CIO'3- group, showed that the O'-H vibrations of the water in this group were actually displaced toward higher frequencies when we moved from the perchlorate of Mg+2 to the perchlorates of Zn+2 and Cd+2(see Table 1). There was a parallel decrease in the intensity of the absorption band, which indicates weakening of the H2O' ... O'CIO'3- hydrogen bonds.

Pr . e m -! 3700 3300 3~OC z,,~.~

ca:o~ )70 /. 3800 / oHg-"l r.A

I.Y 1.3 1.7 1,1 W 0.9 0.60.7 0.6 o.j O.q 113

Fig. 8. Relationship between position of absorption maximum for coordinated water in Me-H2O' ... O'CIO'S" group and crystal-chemical radius of cation.

The similarity of the crystal-chemical radii of Ca +2 (1.06 A) and Cd+2(1.03 A) and the observed frequencies of the O'-H vibrations of the water in the Ca+2-H2O' ... O'ClO'S" (3660 cm -1) and Cd+2 - H2O' ... O'ClO's (3640 cm -1) groups enabled us to hypothesize that the strength of the hydrogen bonds between the water molecules and the anions in the outer coordination sphere may depend on the radius of the complex-forming cation. As can be seen from Fig. 8, a linear relationship was actually observed between the frequency of the O'-H vibrations of the water in the Me+2-H2O' ... O'CIO'3" group and the cation radius for the perchlorate hexahydrates of Mg+2, Ca +2, Zn +2, and Cd+2•

Using the relationship obtained and the graph in Fig. 8, the frequency of the O'-H vibrations of the water in the Hg+2 - H2O' •.. O'ClO'3 - group can be evaluated by interpolation, yielding a value of 3695 cm -1. Examination of the infrared

spectra of the Hg(CIO'4 h . 6H2O' single crystals confirmed that, in addition to the aforementioned very intense absorption band greatly shifted toward low frequencies (with a maximum at 2460 cm -1), there was alsoa separate, substantially weaker absorption band with a maximum at 3775 ± 10 cm-1

(see Fig. 6). This high value for the frequency of the O'-H vibrations of the water in the Hg+2_ H2O' ... O'CIO'3 group is obviously due to the fact that the Hg+2 field has no effect on a CIO'; ion in the outer sphere. Mathews [36] investigated the Raman spectra of the perchlorate hexahydrates of Mg+2, Zn+2 and Cd+2 near the vibration frequencies of the CIO'; ion and reached a similar solution regarding the decrease in the polarization of the CIO'; ions as the cation radius increases.

The observed fact that the weakening of the hydrogen bonds between water molecules in the immediate vicinity of the cation and CIO'4" anions depends on the cation radius can thus be directly attributed to the decrease in the ionic component of the Me-O' bond of the water in the crystal hydrates studied and can be used to make a rough estimate of this factor.

As can be seen from Fig. 7, the displacement of the frequency of the 0'- H valence vibra­tions of the coordinated water molecules under the influence of hydrogen bonding to CIO'i (curve 2) parallels the change in the ionization potential of the cation, which confirms our hypothesis that the ionic component of the Me-O'H2 bond decreases as the ionization potential of the metal increases.

STATE OF WATER IN CERTAIN GROUP II PERCHLORATE CRYSTAL HYDRATES 37

The negative value of A. v calculated for the Sr+2-H20 ... OClO3' and Ba+2-H20 ... OCI03' bonds with the graph in Fig. 8 presumes a high percentage of ionic character for the Me-OH2 bonds in these compounds. Only Sr(CI04h . 4H20 and Ba(CI04h . 3H20 therefore crystallized from aqueous solutions of Sr+2 and Ba+2 perchlorates as the higher hydrated form.

The results obtained in studying the infrared spectra of the perchlorate crystal hydrates of Mg+2, Ca+2, Zn+2, Cd+2, and Hg+2, which are presented in Table 1 and compared in curves 1 and 2 in Fig. 7, thus confirm our hypothesis regarding the factors responsible for the high acidity of concentrated aqueous solutions of heavy-metal perchlorates. The strong polarization of the O-H bonds of the water molecules in the hydrate shell of Zn+2, Cd+2, and Hg+2 and the formation of hydrogen bonds between the coordinated water molecules that are substantially stronger than H20'" OCI0S" bonds pave the way for formation of H30+ ions in the solid phase. Some water molecules are already present in the form of H30+ ions in Hg(CI04)2 . 6H20, so that its spectrum exhibits O-H valence vibrations of H30+ at 3315 and 2900 cm -1 [37,38]. This result. provides a good explanation for the increase in the degree of hydrolysis (a H+ / m) of the perchlorates of Cd+2 and Hg+2 [11,39] with increasing salt concentration, as well as for the very high content of H30+ ions in concentrated solutions of these compounds.

CONCLUSIONS

1. We studied the infrared absorption spectra of Me(CI04)2 . 6H20 single crystals, where Me+2 is Mg+2, Ca+2, Zn+2 , Cd+2, or Hg+2, inthevicinityoftheO-Hvalencevibration.The observed frequencies were assigned on the basis of existing x-ray diffraction data. A supplemen-tal study of the frequency of the O-H vibrations in aqueous solutions of these metal perchlorates and of perchloric acid as a function of concentration confirmed that our frequency assumptions were correct.

2. We discovered a relationship between the degree of polarization of the O-H bond in the coordinated water molecules and the nature of the Me-OH2 bond, which is governed by the electron-shell structure of the cation. The cation radius has a substantially smaller effect.

3. There is a severe decrease in the frequency of the O-H valence vibrations of water molecules constituting the short-range environment of a cation in contrast to the corresponding frequency for water molecules in the gaseous phase. This result indicates that there is an increase in the proteolytic dissociation of the coordinated water in the direction Ca+2 < Mg+2 s Zn+2 « Cd+2 <<< Hg+2.

4. A linear relationship was found to exist between the strength of the hydrogen bonds of coordinated water molecules to CIO; anions in the outer sphere and the ionic radius of the cation.

5. Our results show that, in discussing the acidic properties of coordinated water, One cannot limit oneself merely to considering the nature of the isolated aquoion [Me +n(H20)ml + n; the intermolecular interaction of the coordinated water with the particles of the outer coordina­tion sphere (anions or water molecules of a more remote hydrate shell) must also be taken into account.

LITERA TURE CITED

1. S. N. Andreev, S. A. Shchukarev, and T. G. Balicheva, Zh. Strukt. Khim., 1:183 (1960). 2. s. N. Andreev and T. G. Balicheva, in: The Hydrogen Bond [in Russian], Nauka (1964),

p.144. 3. T. G. Balicheva and S. N. Andreev, Zh. Strukt, Khim., 5 :29 (1964). 4. N. D. Sokolov, Doctoral Dissertation, Leningrad University (1952). 5. A. F. West, Z. Krist. , 88:98 (1934).

38 T. G. BALICHEVA AND T. I. GRISHAEVA

6. A. F. West, Z. Krist., 91:480 (1935). 7. A. F. Wells, Structural Inorganic Chemistry [Russian translation], Izd. Inostr. Lit.,

Moscow (1948), p. 428. [English edition: Oxford University Press (1950), second edition.} 8. I. B. Bersuker and A. V. Ablov, Chemical Bonding in Complex Compounds [in Russian],

Izd. Shtinitsa, Akad. Nauk Moldav. SSR, 25:88 (1962). 9. E. V. Biron, Zh. Russk. Fiz.-Khim. Obshch., 47:964 (1915).

10. S. A. Shchukarev, Zh. Obshch. Khim., 24:584 (1954). 11. L. S. Lilich and M. E. Mogilev, Zh. Obshch. Khim., 26:312 (1956). 12. L. S. Lilich and Yu. S. Varshavskii, Zh. Obshch. Khim., 26:317 (1956). 13. A. B. Lamb and A. J. Jacques, J. Amer. Chem. Soc., 60:967, 1215 (1938). 14. R. Olson and Simonson, J. Chem. Phys., 17:348 (1949). 15. S.o A. Shchukarev, S. N. Andreev, T. G. Balicheva, and L. N. Nechaeva, Vestn. Leningr.

Gos. Univ., 16:120 (1961). 16. G. Bedtker and O. Hassel, Zbl. Chem., 1:3404 (1933). 17. E. L. Wagner, J. Chem. Phys., 37:751 (1962). 18. T. Dreisch and W. Trommer, Z. Phys. Chem., 37:37 (1937). 19. T. Dreisch and O. Kollschauer, z. Phys. Chem., 45:19 (1939). 20. A. M. Buswell, R. Gore, and W. Rodebush, J. Phys. Chem., 45:543 (1941). 21. D. Williams and W. Millet, Phys. Rev., 66:6 (1944). 22. R. D. Waldron, J. Chem. Phys., 26:809 (1957). 23. G. E. Walrafen, J. Chem. Phys., 36:1035 (1962). 24. J. W. Schultz and D. F. Hornig, J. Phys. Chem., 65:2131 (1961). 25. O. M. Ansheles, V. B. Tatarskii, and A. A. Shternberg, High-Speed Growth of Homogeneous

Single Crystals from Solution [ in Russian], Lenizdat (1945). 26. T. G. Petrov and E. B. Treivus, Kristallografiya, 5:425 (1960). 27. K. W. F. Kohlrausch, Raman Spectra [Russian translation], Izd. Inostr. Lit., Moscow

(1952), p. 81. [German edition: Vol. 9, Part 6 of Hand- und Jahrbuch der Chemischen Physik, Euken, A. (ed.), J. W. Edwards, Ann Arbor, Mich. (1943).]

28. R. Chidambaram, J. Chem. Phys., 36:2361 (1962). 29. W. C. Hamilton, Ann. Rev. Phys. Chem., 13:19 (1962). 30. G. C. Pimentel and A. L. McClellan, The Hydrogen Bond [Russian translation], Mir,

Moscow (1964), p. 226. [English edition: W. H. Freeman & Co., San Francisco (1960).] 31. N. D. Sokolov, Usp. Fiz. Nauk, 57:247 (1955). 32. J. Nakagawa and T. Schimanouchi, Spectrochim. Acta, 20:429 (1964). 33. R. S. Nyukhol'm, Usp. Khim., 32:354 (1963). 34. L. Orgel, Introduction to Transition-Metal Chemistry [Russian translation], Mir (1964),

p. 145. [English edition: J. Wiley & Son, New York (1966), second edition.]

35. O. Theimer, Monatsh. Chem., 61(3):301 (1950). 36. J. P.Mathews, Compt. Rend., 238:2510 (1954). 37. R. Teylor and G. Vidale, J. Amer. Chem. Soc., 78:5999 (1956). 38. S. A. Shchukarev, S. N. Andreev, and T. G. Balicheva, Dokl. Akad. Nauk SSSR, 144:606

(1962) • 39. I. Newbery, Trans. Electrochem. Soc., 69:17 (1936).

INVESTIGA TION OF AQUEOUS NONELECTROLYTE SOLUTIONS BY THE SPIN ECHO METHOD'"

Yu. I. Neronov and G. M. Drabkin

Investigation of molecular self-diffusion in solutions can add materially to our knowledge of the structure of water solutions. The spin echo method is one of the most direct procedures for determining self-diffusion. If a spin echo is observed for proton resonance, the self-dif­fusion determined from the amplitude of the spin echo as a function of the magnetic-field gra­dient characterizes the mobility of the protons that participate with the molecules in Brownian movement:

A=Aoexp{-f.!02't3 Dp}, (1)

where A is the amplitude of the spin echo, Ao is the amplitude of the spin echo in the presence of a homogeneous magnetic field, 'Y is the gyromagnetic ratio of the proton, G is the linear magnetic-field gradient in the specimen, T is the time between the exciting pulses, and Dp is the proton self-diffusion.

Fig. 1. Proton self-diffusion and viscosity as functions of x (propor­tion by weight of 3-methylpyridine for solutions of 3-methylpyridine and water at 9.5°C).

The calculated proton self-diffusion for pure liquids whose molecules contain protons is also the molecular self-diffusion. Proof of this assertion for water was pro­vided by Graupner and Winter [1], who established that the self-diffusion figures for deuterium and oxygen in water agree within the limits of experimental error (5 %). The proton self-diffusion determined for solutions by this method is close to the self-diffusion of those molecules whose protons make the greatest contribution to the am­plitude of the spin echo Signals.

The observation time for self-diffusion by the spin echo method is governed by the lag time between the 90° and 180° pulses. If the average translational displacement of the molecules is evaluated from the Einstein equation

(AX)2=2'tDp,

we obtain ~ ~ 6 . 10-4 cm for the customary values T = 0.01 sec and Dp = 2 • 10-5 cm2 • sec-1• As when tagged

*Translated from Struktura i Rol' Vody v Zhivom Orga­nizme 1:132-137 (1966).

39

40 Yu. I. NERONOV AND G. M. DRABKIN

atoms are used [2], the proton self-diffusion is therefore a macrocharacteristic of the medium, in contrast, for example, to the proton self-diffusion measured with the aid of cold neutrons [3].

The proton self-diffusion can be represented by the Stokes-Einstein equation

(2)

if r is used to represent the effective radius of the proton-carrying article and 1/ to represent the microviscosity to which the proton-carrier is subject during progressive movement.

Figure 1 shows Dp and the viscosity as functions of concentration in a mixture of 3-methyl­pyridine and water. The value of Dp was determined to within ± 3%. The results qualitatively confirm Eq. (2) and are typical of aqueous solutions.

According to Eq. (2), a decrease in proton mobility in solutions may result from an in­crease in the effective radius ofthe proton-carrying particles. An increase in effective proton-car­rier radius in liquids with intermolecular hydrogen bonds is most probably caused by partici­pation of complexes in progressive Brownian movement.

If we know that a given substance contains only particles of one type, we can use the cubic­cell model for self-diffusion [4] to determine the mass of the proton-carriers from the relationship

M = 7 36. 10-2; p. P (_1_) p' '(IDp , ' (3)

where Mp is the mass in atomic units, p is the density of the medium, and 1/ is the viscosity.

Determination of the proton-carrier mass from Eq. (3) for acetic acid yields a value of 101 (for this liquid Dp = 1.12 . 10-5 cm2 • sec- t , 1/= 1.13 cP, and p = 1.045 glml at 25°C). This result indicates that most of the protons in acetic acid are transported with dimers. Another example is a solution of triethyl amine and chloroform. Determination of the proton-carrier mass from Eq. (3) for a solution containing 50 mol.% triethyl amine yields a value of 195 (for this solution, Dp = 1.29 • 10-5 cm2 • sec- t , 1/= 0.769 cP, and p = 1.066 glml at 17°C). This result, together with the data yielded by the high-resolution nuclear magnetic resonance method [5], indi­cates formation of complexes of triethyl amine and chloroform molecules by hydrogen bonding.

Investigation of the product 1JDp as a function of concentration is of interest for research on complex formation in solutions of water and nonelectrolytes. However, it must be kept in mind that the macroviscosity can exceed the microviscosity. This is possible when complex polymer associates develop in the medium. The viscosity to which the particles are subject during progressive movement in such a medium depends on their size. Since the macrovisco­sity is greater than the microviscosity, the Stokes-Einstein equation is "unsuitable" for deter­mining the molecular self-diffusion in a medium containing large molecules, as was established by Osborne and Porter [6]. Investigation of alcohols [7], ethylene glycol [3], glycerol, and oleic acid [8] with cold neutrons showed that the self-diffusion manifested during neutron scattering exceeds the corresponding value calculated from the Stokes-Einstein formula to a greater and greater extent as the temperature is reduced. This demonstrates that the movement of individual alcohol molecules between polymer associates is more rapid than would be expected from the macroviscosi ty.

Figure 2 shows the product 11Dp for the 3-methylpyridine-water system. Proton transfer in solutions with a high 3-methylpyridine content is effected by individual 3-methylpyridine mole­cules. The preferential increase in macroviscosity rather than microviscosity and the character­istics of the infrared absorption spectra are readily explained by formation of short-lived polymer associates by hydrogen bonding at these concentrations. Hydrogen bonds are apparently produced

INVESTIGATION OF NONELECTROLYTE SOLUTIONS BY THE SPIN ECHO METHOD 41

!.2L-_~_~_-+::---:-:----' 0.2 o.~ 0.6 0.8

I-

Fig. 2. Product 1JDp as a function of x (proportion by weight of 3-methylpyridine) for solutions of 3-methyl­pyridine and water at 9.5°C.

0.8 0.6 0." 0.2 - - x

Fig. 3. Product 1JDp as a function of x (proportion by weight of wa ter) in solu tions of acetone and water at 20°C (1) and triethyl amine and water at 17°C (2).

between the 3-methylpyridine molecules and those water molecules at the surface of the water tetrahedra. The minimum in the product 1JD p may be a consequence of another characteristic of proton self-diffusion (Fig. 2). At moderate concentrations by weight, the complexes have maximum distribution over the system and make a perceptible contribution to the total proton transfer, increasing the effective mass of the proton carriers.

The isotherms for 1JDp (Fig. 2) exhibit a maximum at large water concentrations, whose appearance is due to the characteristics of the water structure. The effect of 3-methylpyridine molecules on this structure is similar to that of a rise in temperature. Proton transfer is ef­fected mainly by those water molecules not capable of forming a sufficiently stable tetrahedral structure under these conditions.

Comparison of the infrared absorption spectra of the O-H group in water and in solutions with 3-methylpyridine shows them to be similar, which indicates that the water-molecule as­sociates persist on solution [9]. The maximum viscosity and minimum proton self-diffusion (see Fig. 1) correspond to the concentration at which the number of water molecules is twice the number of 3-methylpyridine molecules. It can be hypothesized that the complex is a dodeca­hedron of twelve water molecules [10,11] stabilized by ten 3-methylpyridine molecules. Such a complex contains forty hydrogen bonds. The improvement in micromiscibility at reduced temperatures can be attributed to an increase in the number of complexes [12]. However, this approach does not seem as interesting as certain other working hypotheses.

Figure 3 shows the 1JDp isotherm for solutions of acetone and water and triethyl amine and water. The trend of the curves shows that the characteristics of proton self-diffusion described above for solutions of 3-methylpyridine and water are even more characteristic of solutions of triethyl amine and water but less pronounced for solutions of acetone and water. Triethyl amine has the strongest disruptive effect on the water structure, since its molecules are large and have stronger electron-donor properties than those of 3-methylpyridine, acetone, or the alcohols investigated [13]. The diffusion cons tant for triethyl amine molecules during infinite solution in water is twice the self-diffusion constant for water molecules in water [14]. Displacement of triethyl amine molecules apparently takes place outside the tetrahedral as­sociates in water. The abrupt decrease in the diffusion of triethyl amine molecules in water when the triethyl amine concentration 'is increased results both from development of concentra­tion fluctuations and from binding of the triethyl amine molecules to one another through water molecules.

42 Yu. I. NERONOV AND G. M. DRABKIN

Acetone molecules are evidently similar to methanol molecules in their capacity to influ­ence the structure of water [13]. According to the data of Fratiello [15], the isotherms for 1JDp in solutions of methyl formamide and water and diethyl formamide and water resemble those in Fig. 3.

All our data are in good agreement with the two-structure model of water [16, 17]. How­ever, they cannot be used as a basis for evaluating the stabilization of the water structure by fill­ing of the voids in the tetrahedral structure by the nonelectrolyte molecules.

Concentration fluctuations were quite extensive in the aqueous solutions investigated, but they had no material influence on molecular mobility. As was pointed out by Neronov and Drab­kin [18], no peculiarities are observed near the stratification temperature in determining proton self-diffusion for a mixture of triethyl amine and water of critical concentration.

Our investigation of solutions of 3-methylpyridine and water at 72.5°C established that the viscosity was increased as a result of the large concentration fluctuations, but we detected no unusual features in the proton self-diffusion. The maxima in the corresponding 1JDp isotherms in these cases are also caused by the discrepancy between the macroviscosity and microviscosity.

Our proposed approach to explanation of the trend of the 1JDp curves (taking into account the fact that the macroviscosity exceeds the microviscosity and giving consideration to the mass of the proton carriers) is sufficiently general. The influence of these factors readily accounts for the trend of the 1) Dp isotherms for mixtures of alcohol with carbon tetrachloride [19]. The hypothesis that there is a minimum in the alcohol association in such solutions is difficult to reconcile with the data yielded by the high-resolution NMR method [20]. In conclusion, the authors wish to express their gratitude to Prof. D. M. Kaminker for his consistent interest in this work.

LITERATURE CITED

1. K. Graupner and E. R. Winter, J. Chem. Soc., 1145 (1952) 2. P. A. Johnson and A. L. Babb, Chem. Rev., 56:387 (1956). 3. V. V. Golikov, I. Zhukovskaya, F. L. Shapiro, A. Shkatula, and E. Yanik, in: Inelas tic

Scattering of Neutrons in Solids and Liquids, Vienna (1965). 4. C. Houghton, J. Chem. Phys., 40:1628 (1964). 5. C. M. Huggins and G. C. Pimental, J. Phys. Chem., 60:1311 (1956). 6. A. D. Osborne and G. Porter, Proc. Roy. Soc., Vol. A284, No. 1396 (1965). 7. D. H. Saunderson and V. S. Rainey, in: Inelastic Scattering of Neutrons, Vienna (1963),

p. 413. 8. K. E. Larsson and V. Dahlborg, Physica, 30(8):561 (1964). 9. G. M. Drabkin, Yu. I. Neronov, and A. I. Sibilev, Proceedings of the 7th Conference on the

Thermodynamics of Nonequilibrium Processes and Transfer Phenomena in Liquids [in Russian], Ukr. Fiz. Zh. (1965).

10. G. G. Malenkov, Dokl. Akad. Nauk SSSR, 137:1354 (1961). 11. G. G. Malenkov, Zh. Strukt.. Khim., 3:220 (1962). 12. M. V. Vuks, and L. I. Lisnyanskii, in: Hydrogen Bonds [in Russian], Izd. AN SSSR,

Moscow (1964). 13. K.A.Valievand M. I. Emel'yanov, Zh. Strukt. Khim., 5:1 (1964). 14. N. R. Krichevskii and Yu. V. Tsekhanskaya, Zh. Fiz. Khim., 30:2315 (1956). 15. A. Fratiello, Molec. Phys., Vol. 7, No.6 (1964). 16. Z. Hall, Phys. Rev., 73:775 (1948). 17. O. Ya. Samoilov, Ukr. Fiz. Zh. 9(4):387 (1964) 18. Yu. I. Neronov and G. M. Drabkin, Zh. Fiz. Khim., 39:2691 (1965). 19. K. A. Valievand M.l. Emel'yanov, Zh. Strukt. Khim., 5:814 (1964). 20. E. D. Becker, V. Ziddel, J. N. Shoolery, J. Mol. Spectr., 2:1 (1958).

TEMPERA TURE-RELA TED CHANGES IN THE INFRARED ABSORPTION SPECTRUM OF WATER IN THE

CEREBRAL AND MUSCLE TISSUES OF THE FROG*

A. I. Sidorova and A. I. Khaloimov

Ambient temperature is one of the most important factors affecting the life of animals.

A large number of recent experimental investigations of the influence of severe chilling on living organisms has established that there is a close relationship between the resistance of a living organism to cold and the extent to which it is dehydrated. Numerous articles were published during the 1950's by Becquerel [1], Smith [2], and Ray [3] on the resistance of biolog­ical systems to cold and on the physicochemical processes that occur during freezing of various solutions and biological systems. These authors believe it to be self-evident that water, with its complex and variable structure, plays a decisive role in the decrease in physiological activity and retardation of metabolic processes that take place during chilling of the organism and even in the blocking of all physiological functions that develops at very low temperatures.

In his monograph, Ray described a method for microscopic observation of freezing and thawing processes in the cells of living tissues and gives several illustrative photographs taken at a magnification of 560X, which show crystallization of both intercellular and intracellular water at definite temperatures under certain experimental conditions.

The research described in this article, in which similar temperature-related changes in animal tissues were traced by spectroscopic methods, can be regarded as additional experimental material on this problem.

Lacking physical facilities for observing temperature-related changes in the spectrum of water in the intact organism, we became interested in following the spectral changes in a section of biological tissue isolated from the organism but to some extent retaining the characteristics of life.

The temperature-related changes in the spectra of pure water are well known [4-7]. Since water is always present in solutions rather than in pure form in the living organism, there arises the problem of comparing the spectra of biological tissues with those of salt solutions. However, the proportion by weight of all compounds dissolved in water in the body does not exceed 1% and impurities in such a concentration have no effect whatsoever on those spectral characteristics of the absorption bands of water that can be established by determining the spectra of biological tissues. In all our experiments, we attempted to determine only the position of the absorption­band maximum and the band width, to within ± 5 cm -1.

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:146-150 (1966).

43

44 A. I. SIDOROV A AND A. I. KHALOIMOV

Fig. 1. Cell for measuring absorp­tion spectra of biological tissue at different temperatures. 1) T.lermocouple inserted into biolog­ical tissue; 2) tubes connecting cell to heating element; 3) hol­low shell of cell, through which heat-transfer liquid circulates; 4) fluorite windows and inserts; 5) solid metal plate.

Fig. 2. Absorption band of frog brain at different temperatures,

In this investigation, as in our previous work, the great heterogeneity of biological tissue severely restricted our choice of absorption bands suitable for study. In order to avoid damage to the cells in preparing the specimens, it was necessary to take samples of such thickness that it was generally more reliable to work in the overtone region. Because of its heterogeneity, however, any biological tissue dissipates radiation so badly that preference must be given to the fundamental-tone region for good reproduction of even the gross outline of an absorption band. The band most suitable for investigation is the "2 + "L deformation­libration band, whose absorption maximum lies at 2130 cm-1

for pure water at room temperature. This band is readily recorded in the spectral curve with a specimen thickness of 50 /1.

We measured the spectra of the brain, muscles, kidneys, and blood of the frog rana temporaria, a cold­blooded animal whose tissues undergo substantially less severe changes when isolated from the organism than the tissues (especially the brain) of warm-blooded animals.

The cell depicted in Fig. I, which makes it possible to vary the specimen temperature over a broad range above and below room temperature, was designed for the measurements.

The procedure used to prepare the test specimens and the details of the spectrometric method were the same as those described previously [8,9]. An additional condition in the present experiments was the fact that the rate of temperature change was kept constant. The temperature was measured with a copper-constantan thermocouple to within ± 3°C and varied smoothly throughout the experiment in such fashion that it increased or decreased by one degree during the time required to record a single curve (5-6 min).

Formation of ice in the specimens during chilling was established from the appearance of the ice band in the ab­sorption spectrum of the water. There was an abrupt dis­placement of the absorption band and a decrease in specimen transmission when ice was formed, as can readily be seen from the curves recorded (Fig. 2).

Table 1 gives the freezing points of pure water and water in different frog tissues. Each value was obtained from the data for no less than three experiments.

The fact that pure water did not freeze at O°C in our experiments was partially due to the orientation of the water molecules near the cell surface. The existence of

such superficial water layers has been demonstrated, for example by Palmer et al. [10], who studied the dielectric properties of water films between mica plates. They established that water behaves not as an ordinary liquid but as "liquid ice" near mica plates. The thickness

TEMPERATURE-RELATED CHANGES IN THE IR SPECTRUM OF WATER IN TISSUES 45

TABLE 1. Freezing Points of Pure Water and Water in Different Frog Tissues, DC

Substance Experimental data Calculated values

H20 •••••.•.••.•.•

Blood •...•........

~lusc1e •.•....•....

Brain .••..........

Kidney ...•........

- 1.6 - 2.1 - 2.3 - 2.9 - 3.5

o - 0.5 - 0.7 - 1.3 - 1.9

TABLE 2. Temperature Displacement of Absorption-Band Maximum, DC

HzO . Blood . l--.lusc1e Brain . Kidney

Substance

40 2112 2119 211\1 2119 2119

Frequency, cm - 1

20 2128 2134 2134 2134 2138

o 2156 2164 2:64 2170 2178

-5 2226 2226 2126 2226 2226

of the superficial layers reaches several microns. The orientation of the water molecules reduces their mobility and this is reflected in the freezing point, which decreases. The reduced freezing point of the pure water was also due to infrared heating of the specimens (the mica naturally also contributes to the experimental error). All these considerations are also applic,.­able to the freezing of water in tissues.

Considering the foregoing, we took the freezing point of the pure water, -1.6°C, as the zero point for the readings. Subtraction of -1.6°C from each freezing point yielded the figures given in the right-hand column of Table 1.

The freezing point given in the literature [11] for frog blood is -0,45°C, i.e., very close to our data.

In addition to determining the freezing point from the spectral curves, we also established certain spectral characteristics: the temperature displacement of the absorption-band maximum for pure water and water in tissues (Table 2), the change in optical density at the absorption maximum, and the band half-width at different temperatures. All these characteristics were in good agreement with the data in the literature for pure water.

The low freeZing points for the water in the brain and kidney indicates that ice formation is more difficult in these tissues than in the blood or muscle. We also observed a more pro­nounced temperature displacement of the absorption maximum and a greater temperature-related difference in absorption intensity over the temperature range from 0 to 20°C for the brain and kidney. The most probable explanation for these phenomena is the hypothesis that the water in the brain is highly ordered [6]. Binding of wa ter in the kidney apparen tly results from hy­dration of ions, whose content is substantially higher in the renal tissue than in other tissues.

LITERA TURE CITED

1. P. Becquerel, Compt. Rend., 231:1392 (1950); 287:1473 (1953); Scientia, 87:242, 485 (1952) .

46 A. 1. SIDOROV A AND A. 1. KHALOIMOV

2~ A. U. Smith, Biological Effects of Freezing and Supercooling, Williams and Wilkins, Baltimore (1961).

3. L. Ray, Preservation of Life by Cold [Russian translation], Medgiz (1962). 4. E. Ganz, Ann. Phys., 28:445 (1937). 5. J. J. Fox and A. E. Martin, Proc. Roy. Soc., 174:234 (1940). 6. N. Ockman, Adv. Phys., 7:199 (1958). 7. P. A. Giguere and K. V. Harvey, Canad. J. Chem., 34:798 (1956). 8. N. A. Verzhbinskaya and A. I. Sidorova, Biofizika, 9:349 (1964). 9. A. I. Sidorova and I. N. Kochnev, Vestn. Leningr. Gos. Univ., 16:38 (1964).

10. L. S. Palmer, A. Cunliffe, and J. M. Hough, Nature, 170:796 (1952). 11. A. G. Ginetsinskii, Physiological Mechanisms of Water-Salt Equilibrium [in Russian],

Izd. Nauka (1964).

A MASS-SPECTROMETRIC STUDY OF DISTURBANCES OF WATER EXCHANGE THROUGH THE

PULMONARY BARRIER IN ANIMALS*

L. A. Kachur and A. N. Shutko

Heavy hydrogen isotopes, deuterium and tritium, are widely used for studying water ex­change and the permeability of various water barriers in animals and man [1).

In early research on animals with deuterium-tagged water, we showed that ionizing radiation affects the permeability of certain water barriers, the rate of water displacement from the extracellular and cellular fluid, and the total water content of the body [2,3].

In order to extend these observations and refine our conclusions, which may be significant for determining the physiological effect of radiation, it seemed wise to investigate the action of radiation on water exchange through the lungs and to establish whether there is a change in the permeability of the pulmonary barrier and a disruption of the water balance shortly after whole­body x-irradiation of animals in different doses.

The literature contains almost no data on this problem. It has been reported [4] that rapid exchange of water vapor between the tissue fluids and alveolar air takes place in both directions during the respiratory cycle and that comparatively complete equilibrium is achieved between D20 and H20 in different tissues.

We employed deuterium-tagged (99.88%) heavy water as a tracer in studying water exchange; the heavy water was injected into the marginal vein of the ear of a rabbit in a dose of 2 cm3 per kg of body weight. Hevesy et al. [5,6] showed that deuterium-tagged heavy water, mixing with the water in the body, readily exchanges with the hydrogen of the latter and forms a solution (HPO) which has almost the same physicochemical properties as ordinary water and has no effect on metabolic processes in concentrations not exceeding 1-2%. Our experiments were conducted on 60 rabbits of roughly the same weight. Irradiation was carried out in an RUM-3 apparatus at a voltage of 180 kV and a current of 20 mA, using a filter consisting of 0,5 mm copper and 0.5 mm aluminum; the dose rate was 24.5 R/min. The air supplied for the animal to breathe was first thoroughly dried with silica gel. The water from the exhaled air, which was drawn off through a tube inserted in the trachea, was frozen and samples were taken for analysis of its deuterium content at different intervals. In a number of experiments, blood samples were taken from the marginal vein for an additional check on the rate at which the heavy water concentration reached equilibrium in the body.

The water and blood were analyzed for deuterium content by mass spectrometry. A commercial mass-spectrometer (MI-1305) intended for determination of average masses was

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:151-155 (1966).

47

48 L. A. KACHUR AND A. N. SHUTKO

Uamp J1J Mass 2

20

10

[mag

Fig. 1. Curves representing inten­sity of mass-lines 2 and 3 as a func­tion of electromagnet current.

1.0 t,min

O~~~~~~~~_ 60 1'/0 180 '/110

Fig. 2. Kinetics of water exchange through lungs in control.

t,min

60 120 180

Fig. 3. Comparison of kinetics of water exchange through lungs in control animals and animals x­irradiated in different solutions.

used in this work, havirip; been specially adapted for deuterium -hydrogen analysis. In analyzing a mixture of gaseous isotopic hydrogen (deuterium content of no more than 3 %), the intensities of mass-lines 2 and 3, which correspond to the maximum ionic currents produced by the single-charge ions Ht and HD+, are compared [7J. Unfortunately, in addition to HD+ ions, the ion source for analysis of hydrog;en with a low deuterium content also produces Hi ions which have a mass of 3, in amounts that noticeably distort the analytic results. Since the Ht ions are formed as a result of a bimolecular reaction [7J and their concentration is consequently proportional to the square of the pressure, while the concentration of the HD+ ions to be analyzed depends on the first power of the pressure, a decrease in the relative proportion of Ht ions can be obtained by reducing the pressure of the gas mixture in the ion source. Hence it is necessary to conduct the analysis at as Iowa pressure as possible (no more than 10-6 mm Hg), which in turn necessitates an increase in the in­tensity of the ionic current.

In our case, the intensity of the ionic current was increased by the simplest possible method, enlarging the output slit of the ion source by a factor of 10. The input slit for the ion selector was also enlarged by a corresponding amount. This enabled us to obtain peaks for ions of mass 2 and 3 with sufficiently broad apices, corresponding to a range of electromagnet currents of several tens of milliamperes as can be seen in Fig. 1. The decrease in resolving power resulting from enlargement of the slits is obviously unimportant for hydrogen analysis, since the difference in the masses to be analyzed (2 and 3) is large, while the masses of 3 for the HP+ and H t ions cannot be resolved in instruments of the type used [8].

The hydrogen-deuterium gas mixture was pro­duced in a special vacuum apparatus by decomposition of liquid water and blood samples (0.3-0.5 ml) with magnesium amalgam. This gas was kept under the viscosity regime employed for isotopic analysis. The analysis was made by the relative method in the deuterium-concentration region most common in biological investigations (from 0.05 to 0.50% by volume). The instrument was calibrated with

standard specimens, which were also used for systematic mOnitoring of the state of the spectrometer. The reproducibility of the results over the deuterium-concentration range in ques tion was ::I: 2%.

The average kinetic curve for water exchange with the ambient atmosphere through the lungs for the unirradiated rabbits (control), which is shown in Fig. 2, had a complex exponential form resulting from summation of a number of metabolic processes in the body.

DISTIJRBANCES OF WATER EXCHANGE THROUGH THE PULMONARY BARRIER 49

Figure 3 presents the results obtained in measuring the kinetic curves for water exchange through the lungs of the rabbits in the control (curve 1) and after whole-body x-irradiation in doses of 500 R (curve 2), 900 R (curve 3), 1250 R (curve 4), and 1500 R (curve 5). The mea­surements were made one day after irradiation, since we were interested in the early radiation damage and since it is known that there is a substantial increase in the changes in permeability in an irradiated animal toward the end of the first day [9]. Each of the curves in Fig. 3 repre­sents an average for 10 experiments.

Examination of the data in Fig. 3 revealed the following characteristics of the effect of radiation on the kinetics of pulmonary water exchange. The initial rate of the process was markedly higher after x-irradiation in doses of 500 and 900 R than in the control, and equilibrium was accordingly reached earlier. Thus while achievement of equilibrium required three days in the control it only required 1 h after irradiation in a dose of 500 Rand 30-45 min after irradiation in a dose 900 R. A further increase in irradiation dose to 1200 or 1500 R did not cause a further decrease in the time needed to reach equilibrium, which remained at 30 min as for irradiation in a dose of 900 R. However, the equilibrium involved higher deuterium concentrations in the latter case.

The fact that there is a substantial increase in the rate of pulmonary exchange of heavy water injected into the blood stream after whole-body irradiation of rabbits in a dose of 500 R and that the time required to reach equilibrium is markedly reduced enables us to assume that the permeability of the pulmonary barrier is increased by irradiation and that subsequent displacement of water vapor from the alveolar air is accelerated. A similar increase in the rate of the exchange process was observed for water intake through the gastrointestinal tract, where exchange took place with substantial differences in the heavy water concentrations in the gastrointestinal tract and the blood plasma and resulted from diffusion, as was shown by calculation [2]. The observed effect might also take place when the external respiration rate is increased (and the rate of water vapor evolution is accordingly accelerated) under the action of radiation. However, this hypothesis contradicts our observations and the data in the litera­ture indicating that external respiration is inhibited under the action of ionizing radiation in the doses we employed [10].

The fact that, according to the data in Fig. 3, there is no further increase in the perme­ability of the pulmonary barrier when the irradiation dose is increased to 1200 or 1500 R can be attributed to the relatively small size of the water molecules, which cannot provide informa­tion on any increase in permeability markedly exceeding their dimensions. In this case, one must resort to studying larger molecules.

It can also be seen from the data in Fig. 3 that equilibrium occurs at higher deuterium concentrations for the animals x-irradiated in doses of 1200 and 1500 R than in the control or after irradiation in smaller doses. This might indicate that the doses in question reduced the total water content in irradiated animals by 10-20%, since the total water content in animals and man is more accurately calculated from the dilution of tagged water [11]. However, obser­vation of the change in the animal's weight during the first day after irradiation showed that there were average increases of 10 and 20% after x-irradiation in doses of 1200 and 1500 R, which indicated that the percentage water content in the body remained almost unchanged for the irradiated rabbits.

We thus traced the changes in the kinetics of water exchange through the lungs of rabbits shortly after x-irradiation in different doses, using deuterium-tagged water and conducting the subsequent analysis in a specially adapted commercial mass spectrometer. It was shown that irradiation leads to an increase in the permeability of the pUlmonary barrier and has virtually no effect on the percentage water content of the body.

50 L. A. KACHUR AND A. N. SHUTKO

LITERA TURE CITED

1. E. Pinson, Physiol. Rev., 32:123 (1952). 2. L. A. Kachur, P. N. Kiselev, and A. N. Shutko, in: Problems of Radiobiology [in Russian],

VoL3, TsNIRRI (1960) p. 124. 3. L. A. Kachur, P. N. Kiselev, and A. N. Shutko, in: Problems of Radiobiology [in Russian],

Vol. 3, TsNIRRI (1960), p. 138. 4. J. Campbell, D. White, and P. Paane, Brit. J. Radiol., 24:682 (1951). 5. G. Hevesy and E. Hofer, Klin. Wochenschr., 13:1524 (1934). 6. G. Hevesy and C. Jacobson, Acta Physiol. Scand., 1:11 (1940). 7. P. Kirschenbaum, Heavy Water [Russian translation], Izd. Inostr. Lit., Moscow (1953). 8. N. E. Alekseevskii, G. P. Prudovskii, G. N. Kosourov, and S. 1. Filimonov, Dokl. Akad.

Nauk SSSR, 100 (2) :229 (1956). 9. P. N. Kiselev and Z. N. Nakhal'nitskaya, Med. Radiol., 2:73 (1960).

10. R. M. Rabinovich, Med. Radiol. Vol. 5, (1958). 11. P. Scholoer, B. Fries-Nansen, J. Edelman, A. Solomon, and F. Moore, J. Clin. Investig.,

29:1296 (1950).

POSSIBLE ROLE OF WATER IN NEUROMUSCULAR EXCIT A TION*

Yu. V. Dubikaitis and V. V. Dubikaitis

More and more attention has recently been paid to the significance of water in neuro­muscular excitation. Many researchers hold the view that the water in the cytoplasm is in a structured state and its structure varies in accordance with the functional state of the cell. Thus, Szent-Gyorgyi, a founder of the theory of muscle contraction, writes [1]: "Above all else, I am convinced that half the contractile apparatus of muscle consists of water and that contraction itself is a disruption of its structure induced by actomyosin."

Not all researchers support this view, however, and, as before, water is not given suf­ficient importance in considering excitation; moreover, there are almost no theories regarding the mechanism by which the structure of water affects this process.

Since our theory of neuromuscular excitation assigns great importance to the structure of the water-protein component of the cytoplasm [2], the present investigation was conducted to study this process as a function of temperature. This approach to the problem was selected because there are no direct methods for studying the influence of water structure on the activity of biological subjects. Knowing the qualitative characteristics of the change of the structuring of water as a function of the change in temperature (t), we can indirectly evaluate the influence of the structuring of water on the activity of a given biological subject by studying the influence of of t on it.

There are many experimental data showing that quantitative and qualitative changes take place in biological subjects when t is varied over the range 24-27°C. This is supported by the following facts.

1. The protein content and composition of the blood plasma is constant under normal conditions; during hypothermia, the protein content first increases and then decreases, especial­ly at t = 26-24 °C (the albumins decrease by 13-15%) [3].

2. The K+ content of the blood plasma decreases by 10-l2% and Ca++ content increases by 8-9% when animals are chilled to 26-22°C [3].

3. The blood vessels of the liver and pancreas do not react to chilling to 27-25°C, but they constrict on further cooling [3].

4. Analysis of the contraction of myosin fibrils in smooth muscle as a function of temper­ature has shown that a reduction in t to below 25°C causes an abrupt decrease in the contractile capacity of myosin [41.

*Translated from Struktura i Rol' Vody v Zhivom Organizme 1:161-167 (1966).

51

52 Yu. V. DUBIKAITIS AND V. V. DUBIKAITIS

5. Three types of discharges are recorded in the neurons of the median nucleus of the thalamus at normal t; the number of discharges increases in parallel with t during hypo­thermia and all discharges disappear at 25°C [5].

6. The lowest air temperature at which a naked man can maintain resting gaseous inter­change without a reduction in body temperature is 27°C [6].

7. Experiments on 83 mice showed that there is an increase in the latent period of the convulsive spasms evoked by strong phonostimulation during hypothermia. No spasms occurred in any of the mice when their rectal temperature dropped belOW 27°C [7].

8. When the temperature of the brain reaches 27-26°C, cold narcosis sets in and its bioelectric activity ceases, i.e., the electroencephalogram becomes isoelectric [8].

This is, naturally, a far from complete list of the phenomena that occur when biological systems are chilled through this temperature region.

The facts described above give rise to the question of which component of a biological system is responsible for the changes that occur at temperatures of 25-27°C. In attempting to answer this question, even in first approximation, we thought it best to determine whether there is any specific feature characteristic of protein or water at these temperatures.

It was natural to begin by considering the properties of pure water and solutions. In 1926, Tamman [9] studied ice and concluded that water contains molecules of large volume, so-called type I molecules, which fill the lattice Mice and have the physical properties of water. Using Tamman's data, we constructed it graph representing the difference t::. V between the volume of water at P = 1 atm and the volume of water without type I molecules as a function of temperature (along ideal isobars). As can be seen from Fig. I, this linear relationship has an inflection at 26.6°C. In other words, the derivative dV/dt is discontinuous at this t, decreasing by a factor of 2.5 when the temperature is further raised. This discontinuity indicates a change in the structure of water at 26-27°C.

Later data [10] obtained in evaluating the coordination numbers of ions in dilute solutions by the thermochemical method showed that the ice structure persists in water at t = 25°C.

Bergman and Vlasov [11]

AV, ml

0.022

0.017

V,012

0.008 0.006

t;c o 10 70 30 ~O

Fig.!. Dependence of t::. V on temperature.

found that the solubility curve for KCl in water has an inflection at t = 27°C. According to other authors, the inflection occurs at t = 22°C. This means that the product of the solubility and t is discontinuous at the temperature in question. According to the molecular theory of solutions, this phenomenon is due to a type II phase transition. One factor responsible for the discontinuity in the product of the solubility and t is therefore the abrupt change in the solution properties that accompanies the transition from a more ordered to a less ordered state.

The data given above show that, when the temperature is varied, the structure of water is altered in the vicinity of t = 27°C. They thus indicate that the actual matrix of the biologi­cal system, i.e., water, has the specific characteristic of un­dergoing a change at 27°C. Hence it can be concluded that the change in water structure is responsible for the change in the activity of biological subjects when they are chilled to below 27°C.

POSSIBLE ROLE OF WATER IN NEUROMUSCULAR EXCITATION

a

b d

c e

. . ~ flr.~~( I _ v.' I I - . -/

. ~ 1 ~ • it . -

. \ ft. ·

~ - ; 'If L ~- : ..

~. -~. ~ .. --- . , ,

Fig. 2. Mechanogram of atrium at temperatures of: a) 2SoC; b) 27°Cj c) 22°Cj d) 19°Cj e) 17°C. The time marker cor­responds to 20 msec.

53

We studied the guinea pig atrium and striated muscle in order to obtain detailed data on the influence of t on the activity of biological subjects. Our investigations were conducted over the temperature range 16-45°C; special attention was paid to the interval between 25 and 27°C.

The experimental data showed that the atrium retained normal rhythmic activity over the range 40-28°C (Fig. 2a). A drop in temperature to below 28°C led to disruption of normal contractile activity, which was accompanied by alternation of contractions of large and small amplitude, although the rhythm was maintained at temperatures down to t = 22°C (Fig. 2b). A further reduction in temperature caused arrythmia and still greater changes in the contractile capacity of the atrium (Fig. 2c and d). Complete cessation of atrial activity occurred at 16-1SoC, but it was restored when the temperature was again raised, the oscillograms passing through the same stages in reverse order (Fig. 2d, c, b, and a).

Study of the rise time of the contraction-pulse front showed that there was an inflection at t = 25-2SoC in the graph representing front duration as a function of temperature (Figs. 3 and 4).

Let us now consider how the structure of water can influence cytoplasmic structures of the d~oxyribonucleoprotein (DNP) type, which are mainly responsible for the structuring of cytoplasmic water and are in turn affected by it.

A decrease in temperature is known to cause an increase in the structuring of water . Chilled DNP molecules elongate [12] and unfold, exposing a larger number of anionic groups at their sur­face. The mechanism by which increased structuring of water affects macromolecular elonga-

54 Yu. V. DUBIKAITIS AND V. V. DUBIKAITIS

Fig. 3. Mechanogram of muscle att=38°C (a) and t=20°C (b). The time marker is 20 msec in the up­per oscillogram, and one square on the grid in the lower oscillogram is 200 msec.

T,msec

500

Fig. 4. Rate of atrial (1) and muscular (2) contrac­tion as a function of temper­ature.

tion is still unclear. It seems to us that the phenomenon may be caused by the decrease in the dielectric constant [. of water as its structuring increases, since the structural temperature of a subject at a normal temperature of 25-27°C may lie below zero. A decrease in the £ of water intensifies the coulombic interaction (F =ql . q2/ [.. r2) of the anionic groups at the lateral surfaces of the nucleoproteins, which causes them to elongate. An increase in the number of anionic groups capable of forming hydrogen bonds promotes still greater structuring ofthe water. If this process continues without any additional factors acting on the DNP or water, it leads to breakage or irreversible deformation of the DNP, i.e., such a process with positive feedback under normal functional conditions or with possible compensation under pathological conditions does not exist in nature, since it always leads to death of the system in question. We must therefore seek a factor that would convert this process to one with negative feedback. In our case, this factor is apparently a decrease in the solubility of KCI as the structuring of the cytoplasm increases. It must be assumed that the newly exposed anionic groups bind additional K+ (which is already insoluble in the cytoplasm) both by covalent bonding and as a result of the increased electrostatic interaction of the fields of the negative charges and the K+ ions (since the number of charges increases and £ decreases). This evidently results in a decrease in the mobility of the K+ ions and they accumulate and are held around the neucleoprotein structure. The latter phenomenon in turn reduces the dissociation of the anionic groups, which either prevents further elongation of the DNP molecules or causes them to contract as a result of intermolecular bonding. The negative feedback in the process is therefore produced by the influence of K+ ions on the structure of the DNP, which i~ turn affects the structuring of the water.

Let us consider the effect of cold narcosis. According to Pauling's theory, blocking of excitation as a result of formation of clathrate compounds occurs when the brain is cooled to t = 27°C . It has been established that protein molecules are capable of forming clathrate compounds at body temperature through the side chains of their amino acids. The stability of these compounds

POSSIBLE ROLE OF WATER IN NEUROMUSCULAR EXCITATION 55

A

20

o 10 20 30 ~O 50 60 t,OC

Fig. 5. Solubility of NH4CI, KCI, and NaCI as a function of temper­ature. A) C, g of compound per 100 g of water.

is known to depend on temperature, and two factors can be noted in this respect. First of all, the higher the boiling point of the substance forming a clathrate compound, the more stable is the latter at high temperatures. Secondly, solution of salts reduces the stability of clathrate compounds. These two factors are simultaneously operative when the temperature is reduced, both acting in the same direction to increase the stability of clathrate compounds.

It is interesting that the same narcotic effect can be pro­duced either by anesthesia or by a reduction in temperature. In the first case, a substance that promotes formation of clathrate compounds is administered at normal body temperature; because of increased structuring of the water, its ability to serve as a solvent is reduced. In this case, the decrease in salt solubility

is a consequence of clathrate-compound formation. In the second case, there is a decrease in salt solubility when the temperature is reduced, without introduction of narcotics into the body . The decrease in salt solubility and the reduction in temperature provide greater stability for both the previously formed but rapidly decomposed and the newly f9rmed clathrate compounds. If the transmission of natural excitation is blocked by formation of clathrate compounds (probably as a result of the increase in excitation threshold), there still remains the question of whether this occurs precisely at t = 27°C. On one hand, there is a change in the structure of water, as was pointed out above, while, on the other hand, the characteristic ionic asymmetry of K + and Na+ between the cytoplasm and the intercellular plasma must be taken into account in considering the problem from the standpoint of cell physiology. At this level, it is extremely important that, when curves representing the solubilities of KCI, NaCI, and N~CI as functions of temperature are plotted (Fig. 5),they intersect, i.e., KCI and NaCI have the same solubility at a temperature of 26.6°C, while NH4CI and NaCI have the same solubility at 16°C. The absolute solubilities at temperatures below 26.6 and 16°C vary in such fashion that KCI and NH4CI are less soluble than NaCl. Since, according to the literature and our experimental data, the normal activity of a biological subject is first disrupted when the temperature reaches 25-27°C, this can be regard­ed as a unique "critical" temperature, while the rearrangement of the solubilities of KCI and NaCI is of great biological importance and is the main factor responsible for the changes in biological activity observed on chilling to below 27°C. The second temperature point (16°C) is interesting because it is also "critical," a further decrease in temperature completely arresting automatic cardiac contraction.

LITERA TURE CITED

1. A. Szent-Gyorgyi, Introduction to Submolecular Biology, Academic Press, New York (1960). 2. V. V. Dubikaitis and Yu. V. Dubikaitis, Biofizika, 9:204 (1964). 3. L. I. Murskii, Physical Hypothermia [in Russian], Yaroslavl' (1958). 4. M. M. Zaalishvili and G. V. Mikadze, Biokhimiya, 29:801 (1964). 5. J. Hori, J. Hayasi, and Kh. Takeguti, J. Physiol. Soc. Japan, 25:185 (1963). 6. P. Scholander, K. Andersen, J. Krog, F. Lorentzen, and J. Steen, J. Appl. Physiol., 10:231

(1957) . 7. W. Essman and F. Sudak, Exptl. Neurol., 9:228 (1964). 8. L. Massopust, M. Albin, H. Barnes, R. Meder, and H. Kretchmer, Exptl. Neurol., 9:249

(1964) . 9. G. Tamman, Z. Anorg. Allg. Chem., 158:1 (1926).

10. N. I. Lipilina and O. Ya. Samoilov, Dokl. Akad. Nauk SSSR, 98:99 (1954). 11. A. G. Bergman and I. A. Vlasov, Dokl. Akad. Nauk SSSR, 34:64 (1942). 12. D. M. Snitkovskii, Biofizika, 7 :96 (1962).

THE TWO-STRUCTURE MODEL AND THE HEAT CAPACITY OF WATER*

Yu. P. Syrnikov

According to current theories, the structure of liquid water can be described in the following manner. When ice melts, some of the water molecules enter the interstices of the ice lattice, this being responsible for the decrease in volume on melting. The molecules that do not enter the interstices form an ice-like lattice, which is in thermodynamic equilibrium with the molecules moving in the interstices. In general outline, these are the present concepts of the structure of liquid water on which the two-structure model is based.

A whole series of articles has appeared in which the two-structure model is used to calcu­late the thermodynamic characteristics of water. The first and best known of these was one by Hall [1], who believed that water can be treated as an ideal mixture of the ice-like and densely packed structures. Thus, according to Hall's model, passage of molecules into the interstices is equivalent to some degree of excitation. The ratio of the "excited" and unexcited molecules is defined by the Boltzmann constant. A similar model was proposed by Grjoetheim and Krogh­Moe [2] and a number of other authors.

Frank and Quist [3] made a substantially more correct calculation of the two-structure model. They derived the condition for thermodynamic equilibrium between the lattice and the molecules in the interstices in the following manner. Having calculated the entropy of mixing for molecules that do not enter the lattice from the interstices, they wrote the thermodynamic potential of the system, taking this entropy into account, and minimized it. The relative number of molecules composing the lattice was used as the variable for differentiation.

Frank and Quist used the relationships thus obtained to calculate a number of the thermo­dynamic characteristics of water. However, their model yields overly low values for the heat capacity and the entropy of diffusion, even if the molecules in the interstices are assumed to rotate in total freedom.

The heat capacity of water was not considered in the survey of the two-structure model by Vdovenko et al. [4].

This article proposes a method for calculating the two-structure model that takes into consideration not two but three possible states of the molecules in liquid water. Actually, the two-structure model of water is an n-state model, where n 2:: 2. The following states must be taken into account in calculating the thermodynamic potential: a) the "free" state, occupied by water molecules in the interstices; b) the "lattice" state, occupied by the molecules in the lattice if the nearest interstices are empty; c) "boundary" states, occupied by lattice molecules that interact with the molecules in the interstices.

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2:11-15 (1968). 56

THE TWO-STRUCTURE MODEL AND THE HEAT CAPACITY OF WATER 57

The simplest hypothesis is that only one boundary state exists.

Let the total number of molecules equal N. The number of molecules in the lattice is then IN and the number of molecules in the interstices is N(1 -f). We designate the number of mole­cules in the "boundary" state as v (1 - j) N, where lJ is the numberof "boundary" molecules for each molecule in the interstices. The number of molecules in the "lattice" state is then N[j - v (1-j »). The thermodynamic potential of the system, calculated per mole, can now be written in the form

A A A. A

<1> = (1 - f) <1>1 + [f - v (1 - f)] <1>2 + V (1-f) <1>3 - TIlSc• (1)

The entropy of mixing is calculated in the usual manner:

A N!

~-Sc = k In fA 1 [A 1 [A 1 N(1-I)! N(f-v(l-j»)! N~(l-f) I

= - R {(1- f)ln (1- f)+ [f - v(1- f)] In [f - v(1- f)] + v (1- f)ln [v(1- I)ll· (2)

The quantities ~1' ~2' and ~3 in Eqs. (1) and (2) are the thermodynamic potentials per mole for the first, second, and third states respectively.

Equation (1) must be minimized in order to find the thermodynamic eqUilibrium condition. We will assume that both I and v are variables" i.e., that the number of molecules in the boundary state depends both on the lattice geometry and on the thermodynamic parameters.

Solving Eqs. (1) and (2) jointly, we obtain

(3)

(4)

Equation (3) gives the ratio of the number of molecules in the "lattice" state to the number of molecules in the interstices, while Eq. (4) gives the ratio of the number of molecules in the "lattice" state to the number of molecules in the boundary region.

The relationships obtained can be used to calculate a whole series of thermodynamic quantities, but numerical values must be found for ~<I>21 and A<I>23 in order to do so. We proceed in the following manner. The volume of one mole of water can be represented by the expression

(5)

where Vt is the volume of one mole in the first state and AV21 and AV23 are the differences in the volume between the second and first and second and third states respectively. If we assume that the molar volume of the lattice at O°C equals that of ice, while the molar volume of the first state corresponds to dense molecular packing, and take the average volume of the first and second state as the molar volume of the boundary state, we obtain

It is still necessary to make an assumption about the value of lJ. We will assume that lJ

equals 4 at O°C. This corresponds to the coordination number in the structure of ice, which is determined by the four possible modes of directional-bond formation for the water molecule.

58 Yu. P. SYRNI KOV

TABLE 1

1". K I 273 277 :283 I 293 I 303 I 313 I 323 t 333 I 343 I 353

f I U.870 0.867 0.859 I 0.~471 0.835 1 0.H24 I 0.813/ 0.801 10.790/0779

\I 1

4.00 3.87 3.60 13.26 12.98 12.71 12.51 12.31 12.15 /2.01

Using the values given above and Eqs. (3), (4), and (5), we obtain the following values for the two thermodynamic potential differences:

Knowing these quantities, we can calculate the values of jand v for any temperature. The resul­tant values are given in Table 1.

Using the relationships derived above, let us calculate the structural compressibility of water, which is an important thermodynamic characteristic. Differentiating Eq. (5) for pressure and assuming that ~4>21 and ~4>23 depend on pressure in the usual manner

(6)

we obtain the expression

(7)

for the structural component of the compressibility. Calculations made with this formula yield a value of 17.8 . 10-12 cgs units for the structural compressibility, which is quite reasonable.

It is also interesting to calculate the heat capacity of liquid water from the relationships obtained.

The expression

(8)

is readily found for the enthalpy of one mole where H1, H2, and H3 are the molar enthalpies of the first, second and third states respectively. We therefore obtain

(9)

for the heat capacity at constant pressure.

In order to make numerical estimates, we must know the values of ~H12 and ~H23' These can be found in the following fashion. The entropy of fusion for ice is 5.26 eu per mole. Assum­ing that molecules in the second and third states have the same entropy (~s23 = 0), the entropy of fusion can be written as

(10)

Calculating ~c from Eq. (2), we obtain ~12 = 27.5 eu per mole.

Since ~4> = AH - ~ T, we obtain the following values for ~H12 and ~H23: ~H12 = 7540 cal/mole and AH23 = 210 cal/mole. Calculation of 'OJ/'OT and 'Oll /'OT yields _1.1.10-3 deg- 1 and

THE TWO-STRUCTURE MODEL AND THE HEAT CAPACITY OF WATER 59

-4 . 10-2 deg-1 respectively at O°C. We therefore obtain a value of 8.5 cal/mole . deg at O°C for the structural component of the heat capacity

(11)

This value is far more reasonable than that found by Quis t [3], who obtained a total of 0.55 cal/mole. deg for the structural component of the heat capacity and could not account for the anom­alously large increase in heat capacity during the melting of ice. The value we found for the structural heat capacity shows that the main increase in heat capacity during melting is in the structural component.

If we take CP2 and CP3 to be equal to the heat capacity of ice, 9 cal/mole . deg (which is a somewhat too low but quite reasonable estimate, since the molecules in the second and third states form an ice-like lattice), and follow Frank and Quist [3] in assuming that entry of a mole­cule into the interstices increases its heat capacity by 3 cal!mole . deg, we obtain a value of about 18 cal! mole· deg for the heat capacity of liquid water at O°C, which is in agreement with the experimental value.

Our proposed model thus makes it possible to obtain reasonable figures for a whole series of thermodynamic characteristics of water and to account for the anomaly in its heat capacity.

LITERA TURE CITED

1. L. Hall, Phys. Rev., 73:775 (1948). 2. K. Grjotheim and Krogh-moe, Acta Chern. Scand., 8 :1193 (1954). 3. H. S. Frank and A. S. Quist, J. Chern. Phys., 34:603 (1961). 4. V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin, in: Structure and Role of Water in the

Living Organism [in Russian], Vol. I, Izd. LGU (1966).

STUDY OF THE STRUCTURAL CHARACTERISTICS OF WATER FROM THE INFRARED ABSORPTION SPECTRA

OF AQUEOUS ACETONITRILE SOLUTIONS *

B. N. Narziev and A. I. Sidorova

When an aqueous solution contains small concentrations of any solute, the structure char­acteristic of pure water is almost totally retained and the solute molecules have hardly any distorting effect on it. A greater or lesser disturbance of the water structure occurs when the concentration or temperature of an aqueous solution is raised. This structural change is mani­fested in a change in the interaction between the solute and water molecules. The nature of the interaction depends on both the physicochemical properties and geometry ofthe solute molecules.

In this connection, our choice of acetonitrile as a research subject for studying aqueous solutions was not accidental. Acetonitrile and water molecules are polar (j..tCHsC N == 3.94 D and f.l water == 1.84 D), they have comparativE':ly large static dielectric constants (£'CH 3CN == 39 and £. water == 80), similar boiling points (t~~~CN == 82°C), which is very important in temperature­related studies, and almost identical refractive indices (n22HsCN == 1.3416 and ~ater == 1.3325), and they resemble each other in a number of other physicochemical properties, particularly their high mutual solubility. Proceeding from the geometric parameters of the acetonitrile molecules [1, 2] and the dimensions of the voids in the water framework [3, 4], we can assume that dissolved CH3CN molecules are readily displaced through the channels in the water structure and form hydrogen bonds of the -C ==: N '" H type with the framework molecules.

Infrared Absorption Band of the C ==: N Bond

Our spectroscopic studies of acetonitrile solutions revealed certain special features of aqueous solutions in comparison with nonaqueous solutions.

First of all, in studying the width and position of the absorption band of the C ==: N bond (~, 2254 cm- i ) in the CH3CN molecule as a function of concentration in aqueous solution, we observed a large change in band width with varying concentration [5], in addition to displacement of the band toward higher frequencies, which reached 8-9 cm-1 at small acetonitrile concentra­tions (a molar proportion xa == 0.010-0.005). The greatest band width (12 cm- i ) corresponded to equimolar acetonitrile and water concentrations; an increase in the concentration of either component caused the band width to decrease almost symmetrically to 7-8 cm-1 (Fig. 1). This effect was not observed when CH3CN was dissolved in other solvents (CCl4• CsHs. or CHCl3):

the band width remained almost unchanged when the concentrations were varied [6].

The anomalous change in band width with varying concentration in aqueous solution is due to the structural properties of water. A large variety of interactions apparently takes place

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2:15-25 (1968).

60

WATER STRUCTURE FROM IR ABSORPTION OF ACETONITRILE SOLUTIONS 61

-1 l::J.1I112 . cm

J2,O

11.0

100

.8.0

a.O 02 % 06 08 1.0 Molar proportion of acetonitr ile

Fig. 1. Half-width of absorption band of C == N bond in acetonitrile molecule as a function of concen-tration in aqueous solution.

between the acetonitrile and water molecules when the medium contains one water molecule for each CH3CN molecule. The number of different types of interactions is minimal when the medium contains an excess of either acetonitrile or water molecules. It would seem that the elongated acetonitrile molecule must fit into elongated voids in the water framework [4]. The acetonitrile molecules thus singly arrayed will interact in like manner with the neighboring molecules and the band half-width will be small, as is observed at low concentratiqns. When CH3CN concentration is very high, the molecules interact principally with one anbther, almost never encounter­ing a water molecule. This also causes a small band width, virtually the same as for pure acetonitrile. A maximum number of different combinations should be observed when the two types of molecules are present in equal numbers: some of the CH3CN molecules fit

precisely into the voids in the water structure without disrupting the integrity of the tetrahedral lattice and form hydrogen bonds of the == N ... H type with the water. Introduction of other mole­cules distorts the structure in different ways and the strength of the hydrogen bonds is somewhat altered; finally some acetonitrile molecules interact only with one another. As a result of these various interactions, which entail distortion of the water structure, the absorption band becomes broader at moderate concentrations.

The displacement of the absorption band is due to the dipole~ipole interaction between the acetonitrile and water molecules, since comparatively large displacement was observed for aqueous CH3CN solutions. The shift in the absorption band is small or totally lacking when aceto­nitrile is dissolved in nonpolar solvents [6].

Secondly, investigation of the spectra of aqueous acetonitrile solutions as a function of temperature showed that water exhibits another type of anomalous behavior as a solvent [7]. It is well known that, because of the thermal movement of the molecules, the orientation-relaxation time in a liquid Tor can be represented by the exponential formula

+ U/kt Tor == TO e

where U is the activation energy of molecular reorientation. If we change from T == 1/7TC~lJ 1/2 to the band half-width ~lJl/2' the de~endence of ~1I1/2 on the temperature T can be represented by the similar formula ~1I1/2 == Ae - /kt, i. e., the dependence of log ~Vl/2 on liT should be linear. Actually, as we have shown, this rule is satisfied for acetonitrile solutions in carbon tetrachloride, acetone, ether, chloroform, and other solvents. However, it is violated in aqueous solutions. There is an inflection in the straight line representing log ~vll2 == j(l/I'} at all acetonitrile concentrations in aqueous solution (we investigated concentrations of 1: 1, 1 : 3, and 1: 7): this occurs at 90-100°C for solutions in ordinary water [7] and at 135-145°C for solutions in heavy water [5]. The activation energy U calculated from the slope tangent of the line for log AV1/2 == j (liT) above the inflection point is 1.5 kcal/mole for solutions in H20 (as for pure acetonitrile) and about 3 kcal/mole, i.e., about twice as high, for solutions in D20.

Proceeding from theories of the change in the structure of water with rising temperature, it can be said that the presence of an inflection in the line representing the width of the absorption band of the C == N bond as a function of temperature (log ~v1/2 versus liT) indicates a complete

62 B. N. NARZIEV AND A. 1. SIDOROVA

reorganization of the tetrahedral structure of water, beginning at temperatures and pressures corresponding to the inflection region. The fact that this region lies at higher temperatures for solutions in heavy water than for those in ordinary water conforms to hypotheses about the water structure. The structures of H20 and D20 are known to be almost identical [8-10], but liquid D20 has a greater degree of structuring than H20 and the deuterium bond is stronger than the hydrogen bond. It is therefore natural that a higher temperature is required to break down the structure of CH3CN solutions in heavy water than in ordinary water.

In order to clarify the influence of the structure of H20 and D20 on the formation of aceto­nitrile-water associates, we investigated the dependence of log ~v1/2 on l/T for CH3CN solu­tions in semiheavy water HDO [11]. The ratio of H20 to D20 was 1: 1, i.e., such as to yield the maximum amount of semiheavy water [8]. The inflection in the straight line plotted on the coordinates log ~V1/2 versus l/T characteristic of aqueous solutions was also observed in this case, but the temperature corresponding to the inflection region was approximately 80°C, i.e., lower than for CH3CN solutions in H20 or D20. The activation energy of molecular reorientation was 1.3 kcal/mole, i.e., even less than for pure acetonitrile. Judging from these data, a mixture of light and heavy water is substantially less structured than either type of water separately.

Other Absorption Bands of Acetonitrile

We became interested in determining the influence of the structure of water on the spectral parameters of the other absorptive vibration bands of acetonitrile, since the literature contains almost no reports on studies of the complete infrared absorption spectrum of liquid CH3CN and its solutions, particularly in water. There are a number of articles [12-15] on the infrared spectra of gaseous acetonitrile, but only Venkatesvarlu [12] gives and interprets the complete spectrum of liquid CH3CN. Neelakantan [16] recently gave a rather complete description of the Raman spectrum of acetonitrile. Of the twelve lines he observed in the Raman spectrum, we will consider ten in this paper.

The acetonitrile absorption bands in aqueous solution were investigated only at room temperature. We measured six of the eight fundamental-vibration bands (the V3 and Vs bands with frequencies of 1376 and 1443 cm -1 were not studied because of their extensive overlapping and the strong absorption of water in this region), one overtone band (2 vs), and five combination bands. The solution concentration ranged from pure acetonitrile (xa = 1) to a molar proportion xa = 0.005 CH3CN. In order to avoid (as far as possible) superimposition of water bands on each specific acetonitrile band under investigation, the acetonitrile was dissolved either in ordinary water or in heavy water, depending on the relative locations of the bands. Table 1 presents the results obtained in measuring the width and position of the absorption-band maxima in aqueous solutions with different concentrations. The type and symmetry of the vibrations and the assignments of the frequency and relative intensity of the band at the absorption maximum are also given. More precisely, the ratio of the molecular absorption coefficient £a at the maximum of each absorption band, calculated from the formula £a = Dmax / Cl (where Dmax is the optical density, C is the acetonitrile concentration in moles/liter, and 1 is the specimen thickness in centimeters), to the value of £a for the C == N bond, which is taken as 100, is given in parentheses. The observed frequencies in the pure liquid were in good agreement with Venkatesvarlu's data [12] and differed from the frequencies in the Raman spectrum of pure acetonitrile [16] by 3-4 cm -1. As can be seen from Table I, the half-widths of these bands for pure CH3CN ranged from 7.5 cm-1 for the symmetric valence-vibration band of the C-C bond to 37 cm-1 for the asymmetric valence-vibration band of the C- H bond; none of the bands was very wide, so that the changes they underwent with varying solution concentration could readily be traced. Because of the strong absorption of water in the libration-vibration region [17], the v8 (E) band corresponding to scissors vibration of the C-C== N bond could be investigated only at high acetonitrile concentrations.

WATER STRUCTURE FROM lR ABSORPTION OF ACETONITRILE SOLUTIONS 63

TABLE 1. Half-Widths and Positions of Maxima in Infrared Absorption Bands of Aqueous Acetonitrile Solutions

Type of vibrations

W- -- ~

'" W- -- <: :r: 00 <. W- e: , z'" +~ I.) U 0::

I.) ~O:: ~ 0:: ~o:: I.) I.) <: ~o:: xa ,....111 (5 u u ~.~ .... ~ ",.~ u u ~.~ e':I'-! ~o --::: 0:: .- '5.0-. ~z~- ;> .0,.... ;>.0,.... ;>.0 ,.... 0:: ,....:I:O:: .,..0 ;>.0

UJU~~ $5~ <UI.),.... ~ 00<- $I:!~g +8C! + Ell:! +8"'" <:I:~,.... r.t.lu$S ;> 8-- +8--- 1 '..-IUj

_I~O _<':$-: oC'! -U~r--: -t o~ .... O~ t5e i (Ij • 0<'1 00 - I ~ •

~U~~ ;,u>e ;t'"~:::.. ~U>:::.. ~U~ ~u-::... ;.~U::.. ;- r1 >~ ;f~>~ ~U'2! ~Ue

1.000 I 9

I 18.5

I 7.0

I 24 8.0

I 10.5

I 28 12 20 37 11.5 15

375 750 918.5 1043 2253.5 2293..'i 2411.5 2626.5 2945 3004 3162 3200

i 10

I 19.0

I 7.0

I 24 9.0

I 10.5

I 29 13.0 19.5 37 12.5 16

0.860 I 376 752.5 918.5 1042 2253.5 2293.5 2411.5 2626.5 2945 3003 3163.5 3201

0 .. 576 1 16

1

20.0 1

7.0 I

22 11.3

I 10.5

I 25 18.0 17.5 38 15.0 15

375 753 918.5 1041.5 225:i 2294.5 2411.5 2628 2945 31102.5 3164.5 3203 I 17

I 20.0

1

7.0 I

22 11.5 I

10.0 I

25 18.5 17.0 38 15.5 16 0.500 I 376 754 919 1042 2255.5 2295 2411 2628 2945 30u3 3165 3203

I 225 1

7.0 I

22 11.5 1

9.5 I 20.0 17.0 38 16.5 0.445 1 377

1 755 919.5 1041 2256 2295 2410 2629 2945 3004 31655

0.2551 1 I

6.5 I

24? 11.0 I

9.5 I

20.5 16.5 41 17.5 16 751 920 1041.5 2257.5 2295.5 2409.5 2631 2945 3004 3169 3208

{l.080 1 I I 6.8

1 21 9 .. 5 I 9.5

1

20.0 16.5 43 13.5 923 1043 2259 2296.5 2637 2947.5 3006 3170.5

0.038 1 I I I I I 17.0 44

2947 3008.5

0.010 I I I I 9.0 I I 2259 2296 2948

0.005 1 I I I 8.7 I I 2260 2299 2952

The observed bands can be divided into three groups on the basis of the manner in which their spectral parameters changed when the concentration of the aqueous acetonitrile solution was gradually reduced.

1. Vibrations in which the C == N group participates: va, 2 va, V2, V2 + va, and 1'2 + 1'4,

In all these cases, we observed an almost parallel broadening and displacement of the bands toward higher frequencies; the change in the width of two bands (v2 and v2 + V 4) passed through a maximum as the concentration was varied, while the displacement increased with rising water concentration. The greater the extent to which the C == N group participated in the vibrations, the ,greater was the broadening and displacement of the absorption bands (e.g., the V2 + Va band).

2. Vibrations in which the C-C group participates: V4, v3 + v4, and 2v4 + v3' Gradual displacement of the absorption band toward higher frequencies without marked broadening was observed in these cases.

3. Vibrations of the CH3 group: V7, v3 + V7t 1'10 and V5' Here we observed a slight dis­placement ofthe band maximum toward lower (V7 and v3 + v 7) or higher (VI and V5 ) frequencie sand a relatively small change in band width (V7 and Vi became narrower, while V5 became broader). Since the v3 (Ai) and v6 (E) frequencies of 1376 and 1443 cm-1 respectively, which were not investigated because of the overlapping of water absorption, are also due to deformation vibration of the CH3 group [12], it can be assumed that they will exhibit the same behavior in solutions of different concentrations as the V7 (E) and v3 + Voz frequencies.

Let us consider each group separately. We pointed out above that the geometric parameters of the acetonitrile molecules are such that it fits well into the channels of the water framework.

64 B. N. NARZIEV AND A. 1. SIDOROVA

According to data on Rayleigh scattering, strong associates are formed between the CHaCN and water molecules in the acetonitrile-water system [18], resembling the associates of pyridine or a-picoline molecules with water molecules [19]. Weak hydrogen bonds of the == N ... H type are formed between the solute and framework molecules. In addition to this interaction, dipole­dipole interactions can take place between different polar molecules through the hydrogen bonds. Since the main dipole moment of the acetonitrile molecule is concentrated at the C-C == N group [1] (!lCN = 1.66, !lcc = 1.48, !lCH = 0.25 D), it can be assumed that the more polar C == N group plays the basic role in the intermolecular dipole-dipole interaction, the latter being somewhat intensified when this group is combined with the C-C group. We previously noted [11] that the slight displacement of the absorption band of the C == N bond in aqueous solutions results pri­marily from the intermolecular dipole- dipole interaction and not from formation of hydrogen bonds. The H bonds between the acetonitrile and water molecules are weak and their formation energy is 2.6 kcal/mole [20]. while the energy of an ordinary hydrogen bond is 5-6 kcal/mole [21]. Filimonov and Bystrov [22] attributed the displacement direction for the maximum of the CN band, which is atypical for a hydrogen-bonded system, to hybridization of the nitrogen or­bitals during the interaction of the CR3CN and water molecules.

The mechanism by which acetonitrile interacts with water, as manifested in the behavior of the CN band, depends to a large extent on the solution concentration. As was pointed out above, acetonitrile fn small concentrations (a molar proportion below 0.16) enters the water framework without disturbing it and forms weak hydrogen bonds, mostly with the framework molecules. At moderate or large concentrations. where the water structure is disrupted, the dipole-dipole interaction plays a larger role and is the principal factor governing the spectral parameters of the absorption bands. Freely dissolved water molecules [23] form water-aceto­nitrile complexes at high acetonitrile concentrations. The C - C group in the acetonitrile mole­cule does not take a direct part in the intermolecular interaction, e.g., does not participate in formation of hydrogen bonds with the molecules of the water framework, since it is restricted on two sides by CRa and CN bonds. The dipole moment of this group differs little from that of the C == N group and it can therefore be hypothesized that a change in the dipole moment of the latter bond will be accompanied by a change in !l for the C-C group. It has been demonstrated [1] that the vibrations of the C == N groups are related.

The following statements can be made about the vibration of the CRa group. The deforma­tion-vibration bands of this. group were slightly displaced toward lower frequencies when the acetonitrile concentration of the solution was reduced (as was to be expected). while the valence­vibration bands were displaced toward higher frequencies; the absorption band for both types of vibration became narrower [with the exception of the 1)5 (E) asymmetric vibration band for the C- R bondJ. The CRa group is surrounded by water molecules at low solution concentrations and the frequencies of the absorption bands are governed by the interaction of this group with the ambient medium. This is especially true for the I) 7 (E) band, whose frequency in pure aceto­nitrile is dictated by the deformation vibration of the Ra == C-C group (oscillation of the CHa group as a whole around the C-C bond).

Experimental Method

Figure 2 shows the absorption spectra obtained for acetonitrile (A) and its aqueous solu­tions (B). The intensity of certain composite frequencies and overtones was apparently increased at the expense of that of adjacent fundamental tones. The measurements were made in an IKS-12 infrared spectrometer ~ith an LiF prism (for the spectral region from 2200 to 3500 cm -1) equipped with an OAP-1 optical-acoustic pickup and with an IKS-21 spectrometer with KBr (for the spectral region from 650 to 1200 cm-1) and CsI (for 250-450 cm-1) prisms. In working with the KBr and CsI prisms, we used KRS-5 plane-parallel plates with a transmission of about 70% in

WATER STRUCTURE FROM IR ABSORPTION OF ACETONITRILE SOLUTIONS 65

D~--~----~----------~--~---------r----------~ C Ira o a255 I xa-o.OBO 'x,. ' o.Of 0, ::r~oO. 080 I r.-o.038 - -- ... _______ 1- ______ - - - -1-- ---+- --- ---- ---r--------- -- ---

1.0

Fig. 2. fufrared absorption spectra of liquid acetonitrile and its aqueous solutions in the 300-3300 cm -1 region. The optical density D is plotted along the ordinate and the wave number in cm-1 along the abscissa. A) Pure CH3CN (xa = 1); B) xa = 0.50; C)

different x a' whose values are indicated at the top. The figures above the absorption bands indicate the specimen thickness in mm.

in the 300-1000 cm -1 region at a thickness of 2.4 mm. The total cell thickness was about 9 mm, which resulted in a still greater decrease in transmission. We were therefore forced to operate with wide slits over the 300-1000 cm -1 region. which reduced the accuracy of the results obtained in determining the true half-widths of the absorption bands. The spectral slit width lWe for the IKS-12 instrument was 3 cm-1 and that for the IKS-21 spectrometer was about 30-50% of the observed absorption-band half-width. No less than three measurements were made and the results were averaged to yield satisfactory reproducibility. The error in the position of the maximum was ± 1 cm-1 for the 2 v4 + 113. v2 + V4. and V5 bands and ± 0.5 cm -1 for the other bands; the errorinthehalf-width was ±lcm-1 for the 2v4. + v3. V5. ~ + V7, and ll7 bands and ±0.3-0.5 cm -1 for the other bands.

Table 1 gives the true absorption-band half-widths measured at the half-height of the optical density. taking the equipment function of the monochromator into account [24, 25]. The formula given by Chulanovskii et al. [24] is suitable for narrow slits and for symmetric and almost symmetric (slightly asymmetric) bands. It permits determination of the quantitative ratio of the true and observed values for broad slits at AVe < A1/ 2/2. Russel and Thompson [26], who used a Perkin-Elmer 12C spectrometer with a diffraction grating, found the half-width of the 2vs (750 cm-1) absorption band of acetonitrile to be 15.6 cm-1• The discrepancy between this figure and our data (AVI/2= 18.5 cm-i ) resulted from our use of a broad slit in working with the KBr prism. The value AV1/2 = 8 cm-1 for the v4 (918 cm-1) band is almost identical to the value A lJ1/2 = 7 cm -1 we obtained. Russel and Thompson were among the first to study the relationship between vibration-band width and spectrometer slit width and showed that the band width increases with the slit width, narrow bands undergoing the largest changes.

The following conclusions can be drawn from the material presented above.

1. The spectrum of aqueous acetonitrile solutions clearly reflects the characteristics of the intermolecular interaction. which are related to the structural characteristics of liquid water.

2. The molecular mechanism of the acetonitrile-water interaction differs for different solution concentrations.

3. High-temperature spectroscopic investigations revealed that aqueous solutions have unusual properties in comparison with nonaqueous solutions.

66 B. N. NARZIEV AND A. I. SIDOROVA

4, The main role in the intermolecular interaction is played by the C == N group, as a result of its high dipole moment, the electronegativity of the nitrogen atom, and the convenient marginal position of the latter in the acetonitrile molecule.

5. The C-C group plays a secondary role in the intermolecular interaction. The changes in the C-C band are apparently due mainly to the dipole moment of this bond and to the partici­pation of the CN group in this vibration.

6. Valence vibrations playa larger role than deformation vibrations in the composite vibrations.

7. The CHa group also takes part in the intermolecular interaction. Its geometric dimen­sions are such that it fits conveniently into the voids in the water framework [27]. This factor is the principal one responsible for its interaction with the ambient medium.

LITERATURE CITED

1. E. M. Popov and V. N. Roshchupkin, Opt. i Spektr., No.2 (1963). 2 •. B. L. Crawford and S. R. Brinkley, J. Chem.Phys., 9:69 (1941). 3. O. Ya. Samoilov, Structure of Aqueous Electrolyte Solutions and the Hydration of Ions,

Consultants Bureau, New York (1965). 4. G. G. Malenkov, Dissertation, Institute of General and Inorganic Chemistry, Academy of

Sciences of the USSR (1966). 5. A. I. Sidorova and B. N. Narziev, Ukr. Fiz. Zh., 12:320 (1967). 6. A. I. Sidorova and B. N. Narziev, Proceedings of an All-Union Conference on the Physics

of Liquids [in Russian] Samarkand (1966). 7. A. I. Sidorova, I. N. Kochnev, and E. N. Shermatov, in: Optical Investigation of Liquids and

Solutions [in Russian], Tashkent (1965). 8. A. I. Brodskii, Isotope Chemistry [in Russian], Izd. Akad. Nauk SSSR (1957). 9. Yu. V. Gurikov, Zh. Strukt. Khim., 6:817 (1965).

10. V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin, in: Structure and Role of Water in Living Organism [in Russian], Vol. I, Izd. LGU )1966).

11. B. N. Narziev and A. I. Sidorova, Dokl. Akad. Nauk Tadzh. SSR, 10 (11) :30 (1967). 12. P. Venkatesvarlu, J. Chern. Phys., 19:293 (1951). 13. F. W. Parker, A. H. Nielsen, andW. H. Fletcher,J. Mol. Spectr., 1:107 (1957). 14. J. Nakagawa and T. Shimanouchi, Spectrochim. Acta, 18:513 (1962). 15. H. W. Thompson and R. L. Williams, Trans. Faraday Soc., 48:502 (1952). 16. P. Neelakantan, Proc. Indian Acad. ScL, A60(6):422 (1964). 17. A. I. Sidorova and L. V. Moiseeva, this volume, p. 70. 18. M. F. Vuks, L. I. Lisnyanskii, and F. Kh. Tukhvatullin, in: Physical Problems in Spectro­

scopy [in Russian], Vol. 2, Izd. Akad. Nauk SSSR (1960). 19. M. F. Vuks and L. I. Lisnyanskii, Critical Phenomena and Fluctuations in Solutions [in

Russian], Izd. Akad. Nauk SSSR (1960). 20. I. S. Perelygin and N. R. Safiullina, Proceedings of an All-Union Conference on the Physics

of Liquids [in Russian], Samarkand (1966). 21. G. C. Pimentel and A. L. McClellan, The Hydrogen Bond, W. H. Freeman & Co., San

Francisco (1960). 22. v. N. Filimonov and D. S. Bystrov, Opt. i Spektr., 12:66 (1962). 23. L. D. Shcherba, in: Structure and Role of Water in the Living Organism [in Russian], Vol.

1, Izd. LGU (1966). 24. V. M. Chulanovskii, I. V. Peisakhson, and D. N. Shchepkin, Opt. i Spektr., 7:763 (1959);

8:57 (1960).

WATER STRUCTURE FROM IR ABSORPTION OF ACETONITRILE SOLUTIONS 67

25. G. G. Petrash, Opt. i Spektr., 9:121 (1960). 26. R. A. Russel and H. W. Thompson, Spectrochim. Acta, 9:133 (1957). 27. A. 1. Sidorova and I. N. Kochnev, Proceedings of an All-Union Conference on the Physics

of Liquids [in Russian], Samarkand (1966).

CONCENTRATION-RELATED CHANGES IN THE SPECTRAL CHARACTERISTICS OF THE LIBRA TION BAND

OF LIQUID WATER IN ACETONITRILE AND ACETONE SOLUTIONS·

A. I. Sidorova and L. V. Moiseeva

Acetonitrile is highly soluble in water, in contrast to other nitriles. All the molecular pa­rameters of acetonitrile (bond lengths, force constants, dipole moments, etc.) are well known [1). Spectroscopic investigation of aqueous acetonitrile solutions is therefore a convenient pro­cedure for studying the spectral characteristics of water. In particular, the acetonitrile absorp­tion band corresponding to the valence vibration of the C == N triple bond is very sensitive to changes in temperature and solvent properties. The structural characteristics of liquid water are manifested in the anomalous behavior of this band in aqueous solutions [2,3).

The intermolecular interactions in aqueous solutions should be more directly reflected in the low-frequency spectrum of water, where a very intense, broad absorption band ascribed to the libration vibrations of liquid water molecules (the I/L band) occurs in the 200-1000 cm-1

region.

There is at present no generally accepted interpretation of the libration spectrum of liquid water. This band was first experimentally observed in the infrared spectrum at the beginning of the century (4) and in the Raman spectrum in the 1930's [5). Nevertheless, there are very few data in the literature and those available are contradictory [6, 7). This is apparently due to experimental difficulties associated with the large width and considerable intensity of the band. A recently published article by Shcherba [8] describing a detailed investigation of the libration spectrum of water is therefore of great interest. In addition to pure water, Shcherba studied very dilute solutions in acetonitrile and ternary systems containing salts, which enabled him to calculate the force constants for hydrogen-bonded molecules in pure water, ion-coordinated molecules, and molecules freely dissolved in an organic solvent. Proceeding from the asym­metric contour of the H20 band in the infrared spectrum and following Walrafen's work [9] on the Raman spectrum, he divided the ilL libration band of water into two components correspond­ing to two possible molecular vibrations about the two principal axes of inertia, i.e., vibrations with the frequencies vA and Vc (the vB vibration appears only in the Raman spectrum; see Fig. 1). Other component ratios specifically related to the structure of water are possible, however. In this article, we will not separate the maxima and will discuss only the behavior of the band as a whole. The broad width and asymmetry of the band introduce a substantial error into determi­nations of the position of the overall maximum.

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2:25-\30 (1968).

68

CONCENTRATION-RELATED CHANGES IN THE LIBRATION BAND OF LIQUID WATER 69

I I

--A-- +AO +/ "\,+ ./ : ~-

H H H H H Ii

Fig. 1. Libration vibrations of molecules in liquid water.

The maximum of the vL band in ordinary water is located at 700 cm -1 and the band has a wid th of the order of 350 cm-t • The maximum is displaced to 520 cm-1 when the hydrogen atoms are replaced by deuterium atoms, while the width of the heavy-water band is 280 cm-1 •

The libration band of liquid water is very sensi­tive to temperature and to the influence of sol­utes. As will be shown below, it is displaced by 300-400 cm -1 in concentrated acetonitrile solu-

tions. It is interesting that the position of the maximum of this band in ice at O°C differs com­paratively little from its position in the liquid at O°C (790 cm -1 for ordinary water and 605 cm- t

for heavy water). This can be regarded as a spectroscopic manifestation of the structural sim­ilarity of ice and water.

We made a thorough study of the concentration-related shifts in the libration bands of ordinary and heavy water during solution of acetonitrile and acetone. Acetone was selected for comparison with acetonitrile, also being a molecule that has been investigated in detail. Acetone, like acetonitrile, contains methyl groups. The former is highly soluble in water and has a substan­tial dipole moment (2.76D). Figure 2 shows the spectrum of acetonitrile. Several narrow solute bands are superimposed on the broad libration band of the water in each spectral curve. These bands were subtracted in measuring the displacement of the vL band maximum. As can be seen from Fig. 3, the concentration-related displacement of the band was very large and nonuniform. The acetonitrile (Fig. 3a) or acetone (Fig. 3b) concentration is plotted along the abscissa as a molar proportion. The position of the maximum of the v L libration band of water is plotted along the ordinate.

The trend of the graphs characterizes the introduction of acetonitrile and acetone molecules into the water structure. The libration band was displaced to a substantially greater extent during solution of acetonitrile and acetone in light water than during their solution in heavy water. The maximum displacement, which was observed at small solute concentrations, amounted t0250 cm-1

for acetonitrile and 220 cm -1 for acetone in ordinary water and to 130 and 120 cm- l respectively in heavy water. This means that both compounds severelydisrupt the structure of ordinary water and cause considerably smaller changes in that of heavy water. All four curves were horizontal at small solute concentrations, since the position of the absorption maximum was displaced by almost the same amount as in pure water. The length of the horizontal segment differed for the four graphs, as a result of the differences in solution structure.

We were most interested in the curve for acetonitrile dissolved in ordinary water. The absorption maximum retained the same position as in the spectrum of pure water (700 cm-1) to a concentration of 16 mol.%. This is in agreement with our hypothesis that acetonitrile molecules should move freely through the channels in the water structure, not disturbing its integrity.

The graph in Fig. 3a can be used to evaluate the proportion of the voids in the water structure filled by acetonitrile molecules. Let us assume that, at small acetonitrile concentrations, the solute molecules occupy all the free voids in the water structure without disturbing the framework. If we designate the degree to which the voids are filled as Y, it is readily shown that, since the number of voids in ice I is half the number of lattice points, the proportion of unfilled voids is (1 - Y )/( 2 + y) [10]. According to our graph, the maximum of the vL band retains its position at 700 cm-1 to a molar proportion of 0.16. This concentration corresponds to five H20 molecules for each CH3CN molecule, which should probably occupy two voids. In this case, (1 - Y )/( 2 + y) = 2/5, so that y = 0.14. This figure falls into the range of most typical values at room tempera­ture (according to Fisher [10]).

70 A. 1. SIDOROV A AND L. V. MOISEEV A

Fig. 2. Libration spectra of acetonitrile solutions in H20. Acetonitrile concentra­tion, mol. %: 1) 0; 2) 0.125; 3) 0.17; 4) 0.25; 5) 0.33; 6) 0040; 7) 0.50; B) 0.60; 9) 0.66; lOr 0.75; 11) 0.B3; 12) 0.B7.

cm- 1

100

600

A

5000-0'0<_

400

B

as 1.0 as t.o

Fig. 3. Concentration-related displacement of vL libration band of water in acetonitrile (A) and acetone (B) solutions. The two upper curves are for solutions in ordinary water, while the low-er curves are for solutions in heavy water.

The framework apparently breaks up at acetonitrile concentrations above 0.16 mol. %. The libration-band maximum is rapidly displaced toward lower frequencies, the extent of the displacement beingpropor­tional to the increase in concentration. The frequency and hence the energy, of libration rapidly decreases and librational movement is impeded. The water molecules enter into a strong interaction (probably of the dipole-dipole type) with the acetonitrile molecules. Finally, at high acetonitrile concentrations (above BO mol. %), where the concept of retention of the framework structure of liquid water loses its meaning, the concentration-related displacement of the libration-band maximum ceases and its position becomes stable at about 4BO-460 cm -1, which is probably characteristic of the water-acetonitrile complex; this complex has been considered in detail by such authors as Shcherba [B].

Figure 3 clearly shows the structural difference between D20 and H20. The hori­zontal segment of the graph is longer for D20 solutions than H20 solutions, which cor­responds to the greater structural strength of heavy water than light water. The ~O framework contains a larger number of unfilled voids, so that more acetonitrile molecules can enter it without materially disrupting it: the position of the libration­band maximum remains constant to almost 30 mol. ~&. At the same time, comparison of the curves in Fig. 3 shows that the dif­ference between aqueous acetonitrile and acetone solutions lies in the fact that the water framework begins to break down at a lower concentration for the latter. G. G. Malenkov, who considered the geometric aspect of the "insertion" of acetonitrile mol­ecules into the water framework, regards these two compounds as having different introduction mechanisms. According to his calculations, acetonitrile molecules are

similar to those of ethanol and fit conveniently into dodecahedra of water molecules, which they reorganize from the ice-like framework. Acetone molecules organize more complex polyhedra, which have hexagonal facets.

The spectra were measured with three spectrometers (IKS-21, IKS-14, and UR-20) using NaCI, KBr, and CsI prisms. The specimen thickness ranged from 2-5 J.1. (free-spreading drop) to 65 J.1., depending on the water concentration in the solution.

CONCENTRATION-RELATED CHANGES IN THE LIBRATION BAND OF LIQUID WATER 71

LITERA TURE CITED

1. E. M. Popov and V. P. Roshchupkin, Opt. i Spektr. No.2, p. 166 (1963). 2. A. I. Sidorova, I. N. Kochn~v, and E. N. Shermatov, in: Optical Investigation of Liquids

and Solutions [in Russian], Tashkent (1965) p. 22. 3. A. 1. Sidorova and B. N. Narziev, Ukr. Fiz. Zh., 12:320 (1967). 4. H. Rubens and E. Ladenburg, Verh. Deut. Phys. Ges., 11:16 (1909). 5. G. Bolla, Nuovo Cimento, 9:290 (1932); 10:101 (1933); 12:243 (1935); M. Magat, Annal.

Phys., 6:108 (1936). 6. D. A. Draegert, N. W. B. Strone, B. Curnutte, and D. Williams, J. Opt. Soc. Amer.,

56 :64 (1966). 7. G. C. Pimentel and O. McClellan, the Hydrogen Bond [Russian translation], Izd. Mir.

(1964) . 8. L. D. Shcherba, in: Structure anf Role of Water in the Living Organism [in Russian],

Vol. 1, Izd. LGU (1966), p. 76. 9. G. E. Walrafen, J. Chern. Phys., 40:3249 (1964).

10. I. Z. Fisher and 1. S. Andrianova, Zh. Strukt. Khim., 7:337 (1966).

INVESTIGA TION OF AQUEOUS ELECTROLYTE SOLUTIONS BY THE DEFLECTED TOTAL INTERNAL

REFLECTION (DTIR) METHOD*

L. V. Ivanova and V. M. Zolotarev

Use of infrared spectroscopy to investigate systems with an absorptive index 0.004 < k2 <

0.4 is hampered by the fact that high-contrast reflection spectra can be obtained for almost perpendicular incidence angles only when the absorptive index k2 > 0.4. Materials for which k2 lies in the region 0 < k2 < 0.4 yield reflection spectra of insufficient contrast. Thus, aqueous systems, which are characterized by the value n2 = 1.35 outside the absorption region (k2 = 0), have the reflection coefficient R = 2.2%, while R = 3.9% at the maximum of the 0- H valence­vibration band (k2 = 0.31), i.e., the contrast of such spectra is very low [here n2 is the refractive index of the solution under investigation, k2 is the absorptive index of the solution (110 = n2 - ik), k = kdnl is the relative absorption index, and nl is the refractive index of the DTlR prism. On the other hand, use of classical (transmission) spectrophotometric methods for systems with k » 0 .004 makes it necessary to employ a cell with an optimum thickness of no more than 0.002 mm. Fabrication and quality control of so thin a cell is difficult. Moreover, it should be noted that use of such thin layers causes the structure of the test material to break down in a number of cases [1, 2].

A new method has recently been developed that makes it possible to obtain high-contrast infrared reflection spectra for substances with an absorptive index 0.002 < k < 0.2. It has come to be called the deflected total internal reflection method [3, 4, 5]. The basic features of this procedure, the selection of experimental conditions, and the design of the DTIR equipment have been described in the literature [3, 4, 6-8].

The principal advantage of the new procedure lies in the fact that, when the DTIR method is used, the depth of penetration of the incident radiation, or the corresponding "effective cell thickness," can be regulated by changing the material from which the DTIR prism is fabricated and thus the relative refractive index, or by varying the angle at which the radiation impinges on the specimen, which is especially important in the differential version of the DTIR method.

As can be seen from Fig. I, the effective thickness of the layer under investigation teff is maximal at incidence angles CfJ close to the critical value (CfJcr' where sin CfJcr = n2/nl)' It would there­fore be necessary to operate at CfJ ~ CfJ cr in order to obtain high-contrast DTIR spectra, but this choice of conditions causes substantial distortion of the contour of the band under investigation. Figure 2 shows an absorption band with a Lorentz contour and the contour of the same band in the DTIR spectrum [8]. It can be seen from this figure that the greatest distortion of the band contour

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2 :30-39 (1968).

72

INVESTIGATION OF AQUEOUS ELECTROLYTE SOLUTIONS BY THE DTIR METHOD 73

6}"

f>.. =====~ / -'- - - - .-.- ~

'-'-'-{

o 29(X) 3000 3100 3200 3300 31,00 ]5()() 3500 1'. em-1

Fig. 1. Change in effective thickness of test layer of aqueous solutions in vicinity of OH valence-vibration band. 1) f{J = 26°10'; 2) cp = 31°; 3) cp = 33°; 4) tp = 46°. Data on the optical con­stants of water from the literature [12] were used in the calculations.

Fig. 3. DTIR spectra of water with radiation impinging on specimen at different angles. 1) cp = .45°; 2) cP = 40°; 3) cp = 35°; 4) cp = 33°; 5) cp = 29°30'.

o~~ ____ -=~ ____ ~ 1 1500 f(X)(} SOO 1'. em-

Fig. 2. Calculated band kvm

= 0.1, n = 1.5, AVL = 0.1 I'm). 1) DTIR, nprism = 1.723, cp = 65°; 2) absorption (thick­ness ~ /I. ).

74 L. V. IVANOVA AND V. M. ZOLOTAREV

occurs on the long-wave slope; the band maximum is displaced toward lower frequencies, which accounts for the specific change in effective layer thickness (teff ) within the absorption band (see Fig. 1). The value of teff is governed by both the refractive index and the wavelength of the incident radiation. [9, 10]. As the refractive index increases in the vicinity of the band, the value of teff rises, a phenomenon that is especially pronounced at 'P == 'P- • This characteristic of the er method is well illustrated in Fig. 3, from which it can be seen that the greatest agreement with the transmission spectra occurs at large incidence angles ('P > 'Per). However, the contrast of the spectrum is reduced in this case (as a result of the decrease in teff). Contras t can be mater­ially improved by utilizing the parallel component of the electrical vector of the incident radia­tion or by employing the MDTIR (multiple deflected total internal reflection) technique [5, 11], which makes it possible to increase teff by a factor of from 5 to 300 without introducing any additional distortion into the contour of the band. Another advantage of the DTIR method is the fact that, by using DTIR spectra recorded at twodifference incidence angles and special nomo­grams plotted on the coordinates R ('P1) versus R ('P2) with nand k constants, one' can calculate the optical constants of the system (n2 and k2) with a rather high degree of accuracy [4, 11,13, 14J .

The accuracy with which the optical constants can be determined by the DTIR method is not the same for different values of nand k. The relative error in determining n2 can amount to 0.01-0.1 %, while that in determining the absorptive index for a strong band (k2 == 0.3) can only be reduced to 2-5%. The relative error in determining the absorptive index k2 ~ 0.3 by the classical methods of transmission or reflection spectrophotometry is 20%. This convincingly shows that the DTIR method has considerable advantages for determination of optical constants and absolute intensities over the region 0.002 < k < 0.2. The high reproducibility of the spectra obtained in studying liquid systems must also be regarded as an advantage of this method.

As a result of its distinctive features, the DTIR method has found broad application to a number of different problems involved in studying the structure of a wide range of objects, including biological materials ill rim. It has been used to determine the infrared spectra of human erythrocytes under normal and pathological conditions [14J, the rat brain before and after anesthesia [14], bacteria [15], aqueous amino acid solutions [16], and the water in the hemoglobin of the white rat [14]. DTIR and MDTIR spectra are widely employed for qualitative and quantitative analysis of liquid [3, 4, 17, IS, 19], solid [20], and dispersed [11, 17] systems. The DTIR method has opened up new prospects for research on water and aqueous solutions, since it makes it possible to obtain quantitative data from the infrared spectra of such solutions [17, 21, 22]. Studies have now been made of the D TIR spectra of a number of aqueous nonele c­trolyte solutions (particularly of the interactions in water-alcohol solutions [IS]), the water in hemoglobin [14], that in the hydrate shell ofthe A13+ cation [23J, and that in uranyl nitrate hexa­hydrate [24].

We attempted to use the opportunities afforded by the DTIR method to study the state of the ions in aqueous electrolyte solutions. The measurements were made with an SP-122 attach­ment [6] to a Hilger H-SOO apparatus. We determined the spectra near the valence vibrations of H20 and calculated the optical constants of the aqueous solutions whose compositions are shown in Table l.

It can be seen from Fig. 4 that all the bands in the spectra of the perchlorate solutions studied were displaced toward higher frequencies by about 30 cm -1. Considering that a similar shift occurs in the spectrum of pure H20 when the temperature is raised from 20 to SO°C and that the CI04- ion is one of the strongest destructuring ions, the displacementofthe bands toward higher frequencies can be attributed to weakening of the hydrogen bonds in the water framework. Examination of the spectrum of the Ca(CI04h solution (Fig. 4) leads us to conclude that the effect of Ca(CI04h on water reduces merely to an increase in its" structural temperatures," since the spectrum of the Ca(CI04h solution was very similar to th'at of pure H20 at elevated temperatures.

INVESTIGATION OF AQUEOUS ELECTROLYTE SOLUTIONS BY THE DTffi METHOD 75

Electrolyte

Be(C104h Mg(CI04)2 Ca(CI04)2 Sr(C10,h Zn(CI04)2 Cd (CI04). Hg(U04)S

NaCI NaBr

NaNOa NaCIO.

AICla• pH=0.8 AICI3• pH=2,3

NaCI

o -----:3-:.200:::----::-J4:':OO=---3::-:WO':-:-V-:-.-c m -1

Fig. 4. Absorption spectra of 2m aqueous electrolyte solutions, calcu­lated from DTffi spectra determined at two different incidence angles (cpt = 22°, CP2 = 321. 1) Be (CI04)2;

I

2) Mg(C104h; 3) Ca(CI04h; 4) H20.

TABLE 1

Concen-

I tration nD

2m 1.3612 2m 1.3643 2m 1:3671 2," 1.3705 2m 1.3665 2m -2m 1.3855 3m 1.3590 3m 1.3675 3m 1.3570 3m 1.3511 3M -3M -3M -

I 'I"

-------

3400 3443 3470 -

3370 3375 3400

1 100

~'

3029 3186 --

3169 3129 3073 ----

2993 3010 -

O~-~ ___ ~L-___ J-____ _

JI,.OO 3000 2600 v. cm - 1

Fig. 5. Differential spectra of 3M so­lutions (DTffi method). 1) AICla, pH = a.8; 2) AICla, pH = 2.3; 3) NaCI; 4) zero line (cpt = CP2 = 33°). The inci­dence angles CP1 in the first channel and ({J? in the second were 30 and 33° respec­tively.

However, if we move on to the spectra of Mg(CI04h and, particularly, Be(CI04h, we cannot help but see that they differed markedly from the spectrum of pure HzO, principally in a decrease in the intensity of the maximum near 3420 cm -1, an increase in band half-width, and severe deforma­tion of the low-frequency slope. These differences between the spectra of Ca(CI04h on one hand and Mg(CI04h and Be(C104h on the other, are due to the increase in the covalency of the Me-O bond as we move from Ca2+- to -Be2+, which 'leads to weakening of the O-H bonds in the coordinated water molecules and hence to strenghtening of the hydrogen bonds between the water molecules in the first and second hydrate shells of the cation. This should entail an increase in band half­width and displacement of the band toward lower frequencies. This was precisely the effect we observed in the spectra of the solutions investigated.

76 L. V. IVANOVA AND V. M. ZOLOTAREV

It is interesting to note that Karyakin et al. [25], who investigated the infrared spectra of dilute aqueous electrolyte solutions in the overtone region (7300-5000 cm-1), concluded that posi­tively hydrated ions cause additional absorption to develop at frequencies lower than those cor­responding to the absorption maximum for pure water, while destructuring ions (i.e., ions with negative hydration) have the opposite effect: absorption is reduced in the low-frequency region but somewhat increased at frequencies higher than that of the absorption maximum for pure water. These authors attribute the observed effects to a change in the bonding energy of the OH groups of the water molecules constituting the short-range environment of the ion to the molecules of the second hydrate layer, i.e., to the "long-range effect of the ion field."

Fripiat et al. [23] arranged the cations they studied in the following series on the basis of their influence on the spectrum of water: A13+ > Cr3+ > Be2+ > Cd2+ > Zn2+ > Mg2+ > Na+; the cor­responding series for anions was CIO; > 1- > NO; > CI-.

The spectra of solutions containing a strongly positively hydrated cation (Mg2+, Be2+, A13+ , etc.) and a strongly negatively hydrated anion (I -, CI04") exhibit an ordering effect (development of additional absorption in the low-frequency region) and a disordering effect (deformation of the high-frequency slope of the band), which indicates that rather large areas in whic h the structure of the water is altered exist around the ions.

We observed a similar phenomenon (displacement of the band maximum toward higher frequencies and deformation of the low-frequency slope of the band) in studying the spectra of Be(CI04bCd(CI04)2' and Zn(CI04h. However, the absorption spectra of the solutions studied (Fig. 4) did not enable us to draw any definite conclusions regarding the intensities and frequencies corresponding to the bands for the structurally altered water, since it was difficult to distinguish individual maxima in the valence band. Karyakin et al. [25] reached the same conclusion, although they investigated the overtone region.

In the present investigation, we attempted to isolate the individual valence-vibration bands corresponding to water structured and destructured under the influence of dissolved-salt ions. The differential version of the DTIR method was employed for this purpose.

Proceeding from the hypotheses advanced by Frank [26], it can be assumed that there is an equilibrium in dilute aqueous electrolyte solutions among the water structured under the action of the ions, the destructured water, and the water whose normal structure remains intact.

As was pointed out above, the DTIR method permits regulation of the effective thickness of the layer under investigation by variation of the angle at which the radiation impinges on the specimen. This makes it possible to compensate for the band produced by the water with an undisrupted normal structure and to obtain undistorted differential spectra for solutions; Fig. 5 shows the most characteristic spectra of this type.

The technique for determining the DTIR spectra by the differential method was described in detail previously [14]. Table 1 gives the frequencies of the bands in the DTIR spectra of all the salts studied, as determined under optimum conditions (411 = 31°,412 = 33° for all the 2m solutions and 41t = 30°, 412 = 33° for all the 3m or 3M solutions; the DTIR prism was fabricated from silicon and had a radius of 16 mm, t:p = 26j.

cr

Examination of the data obtained leads us to conclude that the following bands were present:

1) a broad band in the 3200-3000 cm-1 region (v'). All the solutions studied can be divided into three series in accordance with the character of this band: The NaCI, NaBr, NaN03,

NaCI04, Ca (CI04b and Sr (CI04h solutions exhibited no band at 3200-3000 cm-1, the Mg(CI04b Zn (CI04b and Cd (C104h solutions exhibited a weak band in the 3200-3100 cm-1 region, and the Be (CI04b Hg (C104h, and AICl3 solutions exhibited a strong band in the 3100-3000 cm-1

region;

INVESTIGATION OF AQUEOUS ELECTROLYTE SOLUTIONS BY THE DTIR METHOD 77

2) a broad weak band near 3400 cm-1 (v") in the spectra of the 3m NaCI, NaBr, and NaCI04

solutions. The 3600-3400 cm-1 region of the spectra of the perchlorate solutions contained one slope of a band with a frequency of about 3600 cm-1• We did not establish the precise position of the maximum of this band, since it was masked by the 3600 cm-1 band of atmospheric water, which could not be eliminated under our conditions because of the difference in the ray paths in the first and second channels.

We assigned the band at 3400-3600 cm-1 to the OH valence vibrations of the destructured water, since the capacity for hydrogen-bond rupture over the salt series NaCI, NaBr, NaN03,

and NaC104 increases from NaCI to NaCI04 [15], while it can be seen from Table 1 that the fre­quency of the band under investigation increased in the same direction.

Fripiat et al. [23], who used the differential method to determine the DTIR spectra of dilute aqueous solutions of AICI3, AlBr3. and AI(N03h at different pH's, assigned the 3480 cm- t band to the OH valence vi brations ofthe hydroxyl bridge in the polynuclear aluminum hydroxo complexes. This attribution is based on the fact that the intensity of the 3480 cm- t band increases when alkali is added. However, we observed a similar band near 3400 cm-:1 in 3MNaCI solutions, where no polynuclear hydroxo complexes are formed (Fripiat considered the spectra of Al3 solutions with different alkali concentrations against a background of 3M NaCI). Moreover, consideration must be given to the fact that, on the basis of absorption data [27], the intrinsic OH vibrations of the alkali hydroxyl in the DTIR spectrum should lie in the same region (3550-3450 cm- t). The assignment made by Fripiat [23] for the 3480 cm- t band therefore does not seem fully justified to us.

The band in the 3200-3000 cm-1 region can be ascribed to the OH valence vibrations of the water molecules lying in the first coordination sphere of the cation and hydrogen-bonded to the H20 molecules of the second coordination sphere. This attribution is based on the fact that the intensity and frequency of the band depends in a well-defined manner on the type of bonding between the cations investigated and the water molecules. Actually, as is well known, the inter­action of water molecules with the cations of the salts of the first series above is principally electrostatic, while their interaction with the cations of the salts in the second series has a substantial covalent character. The cations of the salts in the third series form strong coval­ent bonds with the oxygen atoms of the coordinated water molecules, which leads to strong hydrolysis of the salts. It can be surmised that this difference in the bonding of the cations in­vestigated to water molecules should lead to an increase in intensity and displacement of the band in question toward the long-wave region over the series A13+ > Be2+ > Cd2+ > Zn2+ > Mg2+ > Ca2+; this was observed experimentally (see Table 1).

The data obtained are in good agreement with those of Karyakin et al. [25], who discovered the relationship described above between the deformation of the low-frequency slope of the 5700 cm- t band and the nature of the dissolved-salt cation. and with those of Balicheva and Grishaeva [28J. who studied the infrared spectra of crystal hydrated of the Me(C104h . 6H20 type (Me = Be2+, Zn2+, Cd2+. etc).

Our results thus indicate that the ions in the aqueous electrolyte solutions studied are sur­rounded by a large region of water with a severely altered structure (structured and destruc­tured) , which conforms well to the data in the literature [26. 29]. On the whole. it can be con­cluded that the DTIR method is very promiSing for quantitative study of absorption in aqueous systems; the differential version of this method can be used to obtain data that permit evalu­ation of the state of the ions in aqueous electrolyte solutions and the structure of such solutions.

78 L. V. IVANOVA AND V. M. ZOLOTAREV

LITERA TURE CITED

1. V. M. Zolotarev, this volume, p. 26. 2. P. A. Griguere and K. B. Harvey, Canad. J. Chem., 34:798 (1956). 3. J. Fahrenfort and W. M. Visser, Spectrochim. Acta, 17:698 (1961). 4. J. Fahrenfort, Spectrochim. Acta, 18:1103 (1962). 5. W. N. Hansen and J. A. Norton, Anal. Chem., 36:783 (1964). 6. V. M. Zolotarev, V. A. Karinskii, and Yu. D. Pushkin, Opt.-Mekh. Prom., 8:24 (1966). 7. v. M. Zolotarev and L. D. Koslovskii, Opt. i Spektr., 19:623 (1965). 8. V. M. Zolotarev and L. D. Koslovskii, Opt. i Spektr., 19:809 (1965). 9. N. J. Harrick, J. Appl. Phys:, 33:2774 (1962).

10. N. J. Harrick and K. du Pre, Appl. Optics, 5:1739 (1966). 11. N. J. Harrick and N. H. Riederman, Spectrochim. Acta, 21:2135 (1966). 12. V. M. Zolotarev, Prikl. Spektr., 5:62 (1966). 13. W. N. Hansen, Spectrochim. Acta, 21:209 (1965). 14. V. M. Zolotarev, Candidate's Dissertation, GOl, Leningrad (1967). 15. R. W. Hannah and J. L. Dwyer, Anal. Chem., 36:2341 (1964). 16. F. P. Robinson and S. N. Vinogradov, Appl. Spectr., 18:62 (1964). 17. B. Katlafsky and R. E. Keller, Anal..Chem., 35:1665 (1963). 18. c. P. Malone and P. A. Flournoy, Spectrochim. Acta, 21:1361 (1965). 19. N. A. Puttnam, Report at 11th Colloq.Spectr. Intern., Belgrade (1963). 20. R. Bent and W. R. Lardner, Fuel, 44:243 (1965). 21. v. M. Zolotarev, Dokl. Akad. Nauk SSSR, 170:317 (1966). 22. W. N. Hansen, Anal. Chem., 35:765 (1963). 23. I. I. Fripiat, F. van Caurvelaert, and H. Bosmans, J. Phys. Chem., 69:2458 (1965). 24. A. M. Deave, E. W. T. Richards, and I. G. Stephen, Spectrochim. Acta., Vol. 22, No.7

(1966) . 25. A. V. Karyakin et al., Zh. Teor. Eksperim. Khim., 2:494 (1966). 26. H. S. Frank and W. Y. Wen, Disc. Faraday Soc., 24:133 (1957). 27. G. V. Yukhnevich, Usp. Khim., 32 :1937 (1963). 28. T. G. Balicheva and T. A. Grishaeva, this volume, page 30. 29. O. Ya. Samoilov, Structure of Aqueous Electrolyte Solutions and the Hydration of Ions,

Consultants Bureau, New York, (1965).

CONCENTRATION FLUCTUA TIONS AND LIGHT SCATTERING IN AQUEOUS SOLUTIONS

OF PROPYL ALCOHOLS *

M. F. Vuks, L. I. Lisnyanskii, and L. V. Shurupova

The characteristics of intermolecular interaction in solutions are reflected in both their thermodynamic properties and their light-scattering behavior. The additional light scattering in solutions is due to concentration fluctuations, which are related to the Gibbs excess thermo­dynamic potential in the following manner:

F:2-BI-1 [1 + X 1X2 (iJ2QE

) ] V X - N RT ox2 P. T ' (1)

where ~ is the mean square fluctuation in the molar concentration in an element of volume v, X1 and x2 are the molar proportions of the first and second components, GE is the Gibbs excess molar thermodynamic potential, and N is the total number of molecules per cm3 of solution.

The intensity of the light scattering in the concentration fluctuations (the Rayleigh number Rk) is expressed by the formula [1-3]:

--- n·- .--R - .. 2 (2 dn)2 XIX2 K 2i.4NA dx g' (2)

where A is the wavelength, NA is Avogadro's number, n is the refractive index, and g is the non­ideality factor, which can be expressed by the activity a1 or a2:

(3)

This quantity represents the stability of the solution with respect to stratification into two phases. Its reciprocal, l/g, can serve as a measure of the extent of the concentration fluctuations.

Study of alcohol-water solutions is of particularly great importance for determining the details of the structure of water. Roshchina [4] investigated light scattering in a number of alcohol-water solutions. The present investigation was conducted to compare light scattering in the isopropanol-water system with that in the propanol-water system. The latter was previ­ously studied by Roshchina. In order to refine her data, we reinvestigated the propanol - water system. Figures 1 and 2 give curves representing the intensity ofthe scattered light as a function

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2:39-43 (1968).

79

80 M. F. VUKS, L.I. LISNYANSKII, AND L. V. SHURUPOVA

l is 0.8

0.7

0,6

as

0.'

0,3

• I

62 ° 3

~2o~--~a2~---O~,4----~O~,6----0~,8~--~~OXZ

Fig. 1. Intensity of isotropic light scat­tering in mixture of water (1) and isopro­panol (2). 1) T = 22°C; 2) T = 35°C; 3) T = 45°C.

g

Fig. 3. Nonideality coefficient g for mixture of water (1) and isopropanol (2) at T = 35°C. 1) From scattering intensity; 2) calculated for water from ther­modynamic data; 3) calculated for alcohol from thermodynam­ic data.

16

1.2

to

08

Q6

ot,.

02

O~--L---L---~~~~

02 a4 06 08 1.0 Xz

Fig. 2. Isotropic light scatter­ing in mixture of wa ter (1) and propanol (2) at T = 22°C.

g

Fig. 4. Nonideality coefficient g for mixture of water (1) and propanol (2) at room tempera­ture. 1-3) the same as in Fig. 3.

CONCENTRATION FLUCTUATIONS AND LIGHT SCATTERING 81

of concentration in these two systems. The intensity of the parallel component in benzene was taken as the intensity unit lis' In order to convert to absolute units (:\ = 5460 A), lis must be multiplied by 3.78 . 10-6 cm- t • The first system was studied at three temperatures. Compari­son of Figs. 1 and 2 shows that: 1) the maximum intensity of the concentration-related scatter­ing in the n-propanol-water system was more than twice that in the isopropanol-water system; 2) the maximum scattering in the first system occurred at substantially lower alcohol concentra­tions than that in the second system. The maximum occurred at x2 = 0.06 in the former and x2 = 0.15 in the latter. It should also be noted that the maximum in the first system occupied a very narrow concentration region (X2 = 0.02-0.11), but it was broader in the second system (x2 = 0.07-0.35).

The scattering intensity does not fully reflect either the deviation from ideality or the concentration fluctuations, since Eq. (2) for the scattering intensity also includes the term dn/dx. We measured the refractive index of isopropanol-water solutions with different concentrations at 35°C. Data from the literature were used for the n-propanol-water system. Figures 3 and 4 show the nonideality coefficients g for the two systems, as calculated from the scattering data given above.

Belousov [5] studied the thermodynamic properties of the isopropanol-water system, mea­suring the activities for different solution concentrations. Fig. 3 also gives two curves calcula­ted for g from Belousov's data, one for water and the other for the alcohol. The two curves should theoretically coincide and the fact that they do not is due to errors in the measurement. It can be seen that the calculated curve for water lies quite close to the curve we derived from the scattering data.

The thermodynamic data for the n-propanol-water system [6] are apparently not particu­larly accurate. The nonideality coefficients g calculated for water and the alcohol do not differ very substantially. The general trend of the two curves differs little from that of our curve plotted from the scattering data. The calculated curve for the alcohol almost exactly coincides with our curve (1). The thermodynamic stability minimum or fluctuation maximum lies at x2 = 0.15 in both cases.

Comparison of the values of g for the reciprocals l/g obtained from the scattering data for our two systems shows that the concentration fluctuations are substantially less extensive in the isopropanol-water system than in the n-propanol-water system. The region of large concentration fluctuations (X2 = 0.02-0.06) is very narrow in the first system when 1/ g >4 (the narrow minimum in Fig. 3), but it is rather broad in the second system (X2 = 0.05-0.55). The concentration-fluctuation maxima (the minima in g) accordingly occur at different points: x2 = 0.04 in the first system and x2 = 0.15 in the second. For the first system, gmin = 0.163; for the second, gmin = 0.041. This means that the maximum concentration-fluctuations in the second system exceed the corresponding fluctuations in the first system by a factor offour. The explan­ation for this difference in the properties of aqueous solutions oftwo homologous alcohols must be sought in the different shapes of their molecules. The normal propanol molecule is elongated, while the isopropanol molecule is shorter and rounder. This shape probably enables it to freely enter the voids in the ice-like water framework without disrupting its structure. The normal propanol molecule apparently has a more difficult time entering these voids and therefore dis­turbs the water structure to a greater extent.

LITERATURE CITED

1. L. I. Lisnyanskii and M. F. Vuks, Ukr. Fiz. Zh., 7:778 (1962). 2. L. I. Lisnyanskii and M. F. Vuks, Vestn. Leningr. Gos. Univ., 4:67 (1962). 3. M. F. Vuks and L. I. Lisnyanskii, Akust. Zh., 9:23 (1963).

82 M. VUKS, L. I. LISNYANSKI, AND L. V. SHURUPOVA

4. G. P. Roshchina, in: Critical Phenomena and Fluctuations in Solutions [in Russian]. Izd. Akad. Nauk SSSR (1960).

5. Y. P. Belousov, N. A. Buzina, and V. Ponner, Zh. Fiz. Khim. (in press). 6. J. A. V. Butler, D.W.Thomson, and W. H. Maclennan, J. Chern. Soc., 674 (1933).

INTERPRET A TION OF THE SPECTRUM OF ICE AND WATER IN THE V ALENCE­

AND DEFORMATION-VIBRATION REGIONS *

B. A. Mikhailov and V. M. Zolotarev

Use of infrared spectroscopy for quantitative studies in the fundamental-vibration regions for H20 molecules in the condensed phase is hampered by the fact that specimens with a thickness of about 1 jJ. must be prepared and that the interference within the layer, as well as the selective reflection, must be taken into account. Raman spectroscopy is therefore generally employed to study the vibration spectra of ice, water, and aqueous solutions. However, the deflected total internal reflection (DTIR) method [1-4), makes it possible to overcome a major portion of the difficulties inherent in infrared absorption spectroscopy. Using this technique, we were able to obtain high-contrast spectra for H20, D20,and HDO and to calculate their optical constants.

Inspection of the data on the optical constants of ordinary (H20) and heavy (D20) water obtained by the DTIR method shows that the J.is, as valence-vibration band of H20 and D20 consists of more than three bands [5) (Fig. 1). Together with the Raman data, this leads us to conclude that the generally accepted interpretations of the band as comprising only vs ' vas' and 2v6 com­ponents must be reexamined and refined. Similar conclusions were drawn by Taylor and Wallei [6), who observed a complex structure for the valence band (in the Raman and infrared spectra) of different isotopic modifications of ice obtained at different pressures. Gabrichidze [7), who also observed a complex structure for the valence band of water and ice, attempted to interpret its structure in the Raman spectrum from the standpoint of the two-state model, on which much work has recently been done. However, there are a number of objections to the frequency assign­ment made by Gabrichidze [7). Thus, it is difficult to imagine the existence ofa large number of molecules with ruptured H bonds, particularly since, according to the same author [7), the number of defective bonds in the ice lattice increases as the temperature is reduced. Moreover, Gabri­chidze did not always observe the condition that the corresponding lines in the Raman spectrum be depolarized in assigning frequencies to the symmetric and antisymmetric vibrations of the H20 molecule. Gurikov [8], who investigated the Raman spectra obtained by Gabrichidze [7], gave a different assignment for the fundamental band of water and ice, proceeding from the theory that there is a similarity in the structures of ice and water.

Similar theories were first successfully utilized in studying the low-frequency region of the spectrum, employing data on slow-neutron scattering by water molecules [17). Gurikov [8) assigned the 3210 cm -1 band to proton vibrations along the stronger mirror-symmetric (m.s.) bonds and the 3450 cm -1 band to vibrations along centrosymmetric (c.s.) bonds. However, the substantial difference in the molecular absorption coefficients of the m.s. and c.s. bonds in the

*Translatedfrom Struktura i Rol' Vody v Zhivom Organizme 2:43-51 (1968)

83

84 B. A. MIKHAILOV AND V. M. ZOLOTAREV

nk

(6 0.3

{ t. 0.2

HH {t

I ' I ,

: ,h I II, , I I \

I I \ , ~"\ n . .... - \:

~ J .... n J

('I I \ k ' J I J \

'000 v. em-1

H20 molecule remains unexplained. We previously noted [9] that the infra­red spectrum of water can be interpre­ted from such a standpoint, but Sidor­ov's data [] 0] on the infrared spectra of semi heavy water (HDO) did not permit a simple band attribution, since the hypothesis that the ice-like framework is maintained in liquid water required that the HDO spectrum show a difference between the m.s. apd c.s. bonds, i.e., the structural similarity of liquid lIDO, H20,and D20 had to be borne out spectro­scopically. Recent research on lIDO [11] has shown that the valence band of lIDO is asymmetric (Fig. 2) and that the asymmetry increases with rising temperature. Hence itcan be concluded that the vs,as band of HDO consists of at least two bands. This enabled us

Fig. 1. Optical constants (n and k) of light (H20) and heavy (D20) water in the fundamental­vibration regions.

to attempt an interpretation of the in­frared spectrum from the standpoint of the two-state model, using x-ray diffraction data on the structure of ice and water.

The ice structure is known to permit formation of two types of hydrogen bonds (mirror­symmetric and centrosymmetric [12]), with the corresponding distances Ro ... o = 2 . 76 and 2.77 A; the quantitative ratio of the m.S. and c.s. bonds is 1/3. It is to be expected that the difference in bond lengths will be reflected in the vibration spectra. Actually, as was noted by Taylor and Wallei [6), who gave the Raman spectra of ordinary and heavy water at a number of temperatures, the existence of a complex structure has been demonstrated (Fig. 3). The frequency assignment for the m.s. and c.S. bonds was made with the aid of a curve representing the valence-vibration frequency as a function of the R 0 ... 0 distance in crystals [13]. It was found that the m.s. bonds should correspond to a frequency of 3190 cm -1 and the c.s. bonds to a frequency of 3230 cm-1

(the accuracy of the frequency determination from the graph was ± 30 cm-1). These data are in good agreement with the experimental results of Ockman [14], who found frequencies of 3180 and 3252 cm-1 (at a temperature of -27°C). Using Ockman's data on the depolarization ratio [14), we assigned the 3180 cm-1 band to symmetric vibration along the m.s. bonds and the 3252 cm-1 band to symmetric vibration along the c.s. bonds; the 3380 cm- I band must be attributed to antisym­metric vibrations of the m.s. and c.s. bonds. The vas frequencies for these types of bonds dif­fer only slightly [25). The spectra of heavy ice (D20) obtained by Taylor and Wallei [6] are shown in Fig. 3, where three strong maxima with frequencies of 2283, 2416, and 2489 cm-1 can be seen; these must be interpreted in the same fashion as for ordinary ice, as is confirmed by the fact tha t the frequency ratios remain cons tan t after isotopic subs ti tu tion (Table 1).

There is as yet no direct proof that the qualitative difference in the bonds persists during the ice-water phase transition. However, Danford and Levy [15] give an asymmetric radial-dis­tribution curve for water, obtained from x-ray diffraction data, that is described by two contours corresponding to Ro ... o distances of 2.77 and 2.94 A at 25°C, i.e., two types of bonds are ascribed to the water structure. The position of the central maximum in the radical-distribution curve corresponds to a distance of 2.90 A. These data evidently require further refinement, since they do not agree very well with the spectroscopic results and since the radial-distribution curve can also be described by a different set of Ro ... o distances [16). It should be noted that Gurikov [16)

INTERPRETATION OF THE SPECTRUM OF ICE AND WATER

Frequency 'I H•O --'- Ice

',1DJO

vs•m •s• 1.39

us•c .s 1.35

vas•c .s. 1.36

v.s. m •s. V.s .c .s.

3'00

2300 2500 2700 1' . cm -!

Fig. 2. Absorption of semi­heavy water (lIDO) in valence­band region.

Frequency ratio

\ 'H,O , 'd --- LlqUl 'ID,O

~ Liquid I 'I 'IHDO

\.34

1.36

1.35

1.10 1.12

2600 2t.()() 2200 1'. cm -!

Fig. 3. Spectrum of ice, from data of Taylor and Wallei [6J.

85

gives two structural models that account for the form of the radial-distribution curve and the change in coordination number with temperature, but his Ro ... o distances differ from those given by Danford and Levy [15J. In the first model, both bonds have a distance of 2.885 A. The second model assumes two distances, 2.88 and 3.2 A, with an average distance of 2.93 A. Never­theless, Gurikov's results [16J do not show good agreement between the intensities and the fre­quencies in the water spectrum.

Taking the foregoing into account, proceeding on the assumption that the tetrahedral coordi­nation is retained in water during the ice-water phase transition, and giving consideration to the similarity in the spectra of water and ice near O°C and to the aforementioned relationship observ­ed by Nakomato and Margoshes [13J, we attempted to make an attribution of the individual maxima in the valence band of the infrared spectrum of water (by analogy with the interpretation of the ice spectrum).

Since the literature contains no reliable quantitative data on the optical constants of water, we measured these characteristics by an independent method [9J. The determinations were made by the DTIR technique, for which liquid water is a subject with optimum optical characteristics. The measurements were made in a Hilger spectrophotometer (H-800) with LiF and NaCI prisms and an SP-122 attachment [18J, which is used for determining infrared spectra by the DTIR method. Crystals of Si and Ge, as well as oxygen-free IKS-25 glass, were employed for the high-refractive prisms in determining the DTIR spectra. The measurements were made with polarized radiation and the optical constants were calculated by the method described in the literature [19, 20J. The accuracy with which the absorption coefficient (k2) was determined in the vicinity of the maximum for the vs,as and Vo bands was 5%.

86

k 0 15

01

aDs

B. A. MIKHAILOV AND V. M. ZOLOTAREV

Fig. 4. Valance band of water, described as sum of Gaussian curves.

a

1650

k 009

008

007

006

005

ao~

a03

b

1750 v. em -I 02'---'-:-:'400'::::-----""",50':-:0,....-V-. -em -1

Fig. 5. Absorption of light (a) and semiheavy (b) water in deformation-band (1'6 ) region.

Figure 4 shows that the Vs as bandofH20consistsoffivecomponents,at3080,3280, 3420, 3490 , 'tnd 3620 em -1, as was known p:r~viously [5, 7, 21). Assuming that the difference in the bonds per­sists during the ice-water phase transition and using the data on the depolarization ratio [14). we made the following frequency assignments for the individual maxima. The 3280 cm-1 band was attributed to symmetric vibration along the m.s. bonds (J.ls.m.s.) and the 3420 cm-t band was attributed to symmetric vibration along the c .s. bonds (J.I s.e.s.). The 3490 cm-t band was ascribed to anti symmetric vibration along the· c.s. bonds, as well as to anti symmetric vibration along the m.s. bonds; this is similar to the interpretation of the ice spectrum given above. The fre­quencies of these vibrations apparently are very difficult to distinguish by infrared spectroscopy (25) •

The band with a maximum at 3620 cm -1 was attributed to vibrations of the molecules in the voids of the ice-like framework, proceeding from the fact that the hydrogen bonding of such ~O molecules to neighboring molecules is substantially weakened but still exists. The vibration frequency for these molecules should therefore be displaced toward lower frequencies with re­specttothemaximum for H20 in the gaseous phase (3756 cm-1). The weak band with a maximum at 3080 cm-t was treated as a difference frequency (3280-170 cm-1). A similar view has been advanced by a number of other authors [7, 22J.

INTERPRETATION OF THE SPECTRUM OF ICE AND WATER 87

k

0.4

0.3

0.2

/' ,

( \.

I \ / ' , C . / \

I /\ .. ,/ \ I / ....... /\ ..... -.-\

(... '. \ r.' '- \ J If

If / 1/ . F / l-

f i f / ,(.{

// .(.-.. ,

°2800 3200 ]400 3600 II , cm"-'l Fig. 6. Absorption of liquid water at different temper­atures. 1) Ice, -70°C [14]; 2) water, +2°C; 3) wa­ter, +25°C; 4) water, +80 °C.

Proceeding from the above inter­pretation and data on the integral inten­sities of the individual maxima in the band, we also estimated the number of molecules in the framework voids. At 25°C, this figure amounted t020 % (± 10%) of the total number of molecules, which is in good agreement with the data of other authors [27] .

The valence-vibration band of heavy water (D20) was also structured. We detected strong maxima with fre­quencies of 2440, 2510, and 2580 cm -1.

These can be interpreted in the same manner as for D20 ice and liquid wa­ter, i.e., the 2440 cm -I band was as­signed to v s. m . s ' the 2510 cm-I band to Vs.c.s., and the 2580 cm-1 band to Vas.c.s. and Vas.m . s .• The fact that the frequency ratios remain constant after isotopic substitution (see Table 1) shows that the frequency assignments for D20 are correct if the assignments of corresponding bands for H20 are valid.

The deformation band (lieS) of water, which is shown in Fig. 5a, is asymmetric. The asymmetry of the high-frequency slope of the VeS band can be described by two curves with frequencies near 1640 and 1690 cm -1, which are assigned to the c.s. and m .s. bonds respectively [28]. This attribution was made On the basis of our data on the deformation band of semiheavy water (HDO), where a similar structure is more clearly visible (Fig. 5b). The constancy of the frequency ratios (see Table 1) enabled us to refine the position of the Vii maximum for the m.s. bonds of H20 (1690 cm-1). The distor­tion of the low-frequency slope of the deformation band can be attributed to superimposition of the high-frequency slope of the strong libration-vibration band (~760 cm-1) on this region. Moreover, a va band corresponding to vibration of the water molecules in the framework voids can be observed at 1610-1600 cm -1.

In order to verify the above attribution, we measured the infrared spectrum of water in the vicinity of the valence-vibration band as a function of temperature; the results obtained are pre­sented in Fig. 6. As can be seen from this figure, the band half-width increased and its intensity decreased as the temperature was raised, which is in qualitative agreement with the data in the literature [24, 26] . However, we are interested in the behavior of the individual maxima corre­sponding to different bonds in the above attribution. A rise in temperature should probably act primarily to weaken the less strong c.s. bonds. This was observed experimentally. The inten­sity of the 3420 cm-1 band (c.s.) decreased more rapidly than that of the 3280 cm-1 band (m.s.) over the temperature range 2-25°C. A further increase in temperature (to 80°C) led to propor­tional attenuation of both bands, since the probability of weakening or rupture is the same for both bonds in this case.

The above interpretation of the valence and deformation bands from the standpoint of the two-state model thus permits description of the complex structure of the fundamental absorption

88 B. A. MIKHAILOV AND V. M. ZOLOTAREV

bands of water. It should be noted that the results obtained by infrared spectroscopy confirmed the structural differences in water molecules in the solid and liquid phases detected by direct x-ray diffraction measurements.

LITERA TURE CITED

1. J. Fahrenfort and W. M. Visser, Spectrochim. Acta, 18:1103 (1962). 2. w. J. Harrik, J. Chern. Phys., 64:1110 (1960). 3. v. M. Zolotarev and L. D. Kislovskii, Opt. i Spektr., 19:623 (1965). 4. v. M. Zolotarev and L. D. Kislovskii, Pribory i Tekhn. Experim., No.5, p. 175 (1964). 5. v. M. Zolotarev, Dokl. Akad. Nauk SSSR, 170:317 (1966). 6. M. J. Taylor and E. Wallei, J. Chern. Phys., 40:1660 (1964). 7. Z. A. Gabrichidze, this volume, p.19. 8. Yu. V. Gurikov, ibid., p. 103 9. V. M. Zolotarev, Opt. i Spektr., 23:816 (1967).

10. A. N. Sidorov, Opt. i Spektr., 8:51 (1960). 11. T. D. Wall and D. F. Hornig, J. Chern. Phys., 43:2079 (1965). 12. N. Bjerrum, Dan. Mat. Fys. Medd., Vol. 27, No.1 (1951). 13. K. Nakamoto and M. Margoshes, J. Amer. Chern. Soc., 77:6480 (1955). 14. W. Ockman, Adv. Phys., 7:199 (1958). 15. M. D. Danford and H. A. Levy, J. Amer. Chern. Soc., 84.:3965 (1962). 16. Yu. V. Gurikov, Zh. Strukt. Khim., 9:944 (1968). 17. Yu. V. Gurikov, Zh. Strukt. Khim., 4:824 (1963). 18. V. M. Zolotarev, V. A. Karinskii, and Yu. D. Pushkin, Opt. Mekh. Prom., 8:24 (1966). 19. V. M. Zolotarev, Candidate's Dissertation, GOI, Leningrad (1965). 20. V. M. Zolotarev, Zh. Strukt. Khim., 5:1 (1966). 21. V. M. Chulanovskii, Dokl. Akad. Nauk SSSR, 93:25 (1953). 22. V. I. Val'kov and G. A. Maslenkova, Vestn. Leningr. Gos. Univ., No. 22 (1957). 23. L. D. Kislovskii, Opt. i Spektr., 7:315 (1959). 24. J. Fox and A. Martin, Proc. Roy. Soc., 174:234 (1940). 25. A. V. Petrov, Candidate's Dissertation [in Russian], Inst. Geokhim. i Anal. Khim., Moscow

(1965) . 26. G. E. Walrafen, J. Chern. Phys., 47:114 (1967). 27. Yu. N. Neronov. Zh. Strukt. Khim., 8:999 (1967). 28. G. C. Pimentel and O. McClellan, The Hydrogen Bond [Russian translation], Mir (1964),

p. 107. [English edition: W. H. Freeman & Co., San Francisco (1960)].

CHEMICAL PROTON SHIFTS IN H20-D20 SOLUTIONS·

V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin

Investigation of the high-resolution proton NMR spectra of water and aqueous solutions makes it possible to obtain additional information on their structure and on the nature of their intermolecular interactions. It is now thought that the displacement of the proton signal toward higher yield strengths when the temperature is raised is due principally to weakening or complete rupture of the hydrogen bonds [1, 21. This affords new opportunities for selection of reliable models of the water structure [3-5]. It has been found that the best agreement with NMR data is achieved with the two-structure model [6-9]. In this model, the chemical shift in the water pro­tons (ow) is additively composed of the shifts in the protons in the ice-like (s-) and disordered (h-) structures:

(1)

where ~ and nh are the molar proportions of the water molecules in the ice-like and disordered structures.

Direct experimental determination of the structural chemical shifts is impossible because of the rapid molecular exchange in liquid water. Even if we assume that the properties of the ice-like structure and of ice are identical, the broad width of the line for the proton signal of ice makes measurement of Os impossible. Estimates of Os and Oh are therefore made with certain arbitrary assumptions. Muller [3] assumes that the structural chemical shifts are independent of temperature, i.e.,

d~w _ dn, 0 + dn,. 0 dT - dT S dT /t' (2)

Using the data from the literature [7, 10, 11] for ns and nh and solving Eqs. (1) and (2) jointly, we calculated the values of Os and <'>h (see Table 1). The bottom line ofthis table gives the values

of Os and 0h calculated with the estimates of nh and dnh/dT made in our previous investigation [9]. Hindman [4] deter­

Os. parts per million

--6.4 -4.6 -5.5 -5 -6,6

TABLE 1

parts per million

-2.54 -2.11 -0.39 -0.43 -3.3

Reference

[101 [11 (7) (4)

Present article

mined Os and Oh with a simplified model of the hydrogen bond, assuming that the water molecules in the disordered structure do not partic ipate in bonding and rotate freely.

This paper is intended to explain the characteristics of the shifts in the PMR spectra of water when small amounts of D:!O are added. Bergqulst and Eriksson [12] found that the proton signal is displaced toward higher field strengths

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2 :51-56 (1968).

89

90 V. M. VDOVENKO, Yu. V. GUR1KOV, AND E. K. LEGIN

in accordance with a linear rule when D20 is added to ordinary water:

OH,O-D,O - 8w = O.02x. molar proportion (3)

where Xa is the molar proportion of D20 in the solution. It is difficult to account for this result when one recalls that replacement of the protons in water with deuterons leads to strengthening of the hydrogen bonds [8, 13] and hence to stabilization of its structure. It would therefore be expected that addition of D20 would act on water like chilling, i.e., displace the proton signal toward weaker field strenghts.

Let us consider in greater detail the energy and structural changes that occur in ordinary water when a small amount of D20 is added to it. The entire discussion that follows is based on the theory of solution in a two-structure solvent which was presented in previous articles [9, 14] and is limited to very dilute solutions, where no more than one solute particle is present in the nucleus of a given structure. This approach permits a determination, albeit qualitative, of the direction of the changes in the properties of an aqueous solution under the influence of addi­tives.

Turning to dilute solutions of D20 in H20, it is necessary to take into consideration the ra­pid isotopic exchange* [15]

(4)

Since this equilibrium is almost wholly displaced to the right in dilute solutions, we obtain a dilute solution of 2xa moles of HDO in 1- x mole of H20 rather than Xa moles of D20 in 1 mole of H20. The HDO molecules formed dissolve in the nuclei of both the ice-like and disordered structures. The proportions of the HDO molecules dissolved in the s- and h-structures are defined by the equations [9, 14]

(5)

where n~ and n~ are the concentrations of the s- and h- structures in pure water (H20) and

( L1fL~ - L1fL~ .)

Wa = exp RT • Here D.J.' r and AJ.'~ are the changes in the chemical potentials of the s- and h-structures when HDO molecules are introduced into them. They are negative, because of the high strengths of the deuterium bond. The numerical values of 6.J.'~ and ~J.'~ can be estimated by using the previously calculated differences () J.'s and () J.'h [9] in the thermodynamic potentials of the s- and h-structures of D20 and H20.

Since the HDO molecule contains only one deuteron and there is an average of two bonds for each water molecule, we can write

w. = exp CfLs2Rih ) = 0.95 at 32° C. (6)

The concentrations of s- and h- structure nuclei in the solution (ns • lltJ) differ from the concen­trations in pure water by

*1t will henceforth be assumed that the equilibrium in Eq. (4) is independent of whether the reac­tion takes place in the s- or h-structure.

CHEMICAL PROTON SHIFTS IN H20-D20 SOLUTIONS 91

2x 1-'" 0_ __._ ° 0. • n,,-fl,,-- l+x qn/l" n0...Lnow '

a. S I h C1

(7)

where q is the number of molecules in the nucleus. *

In view of Eq. (6), it can be seen that solution of HDO molecules in water increases the concentration of the ice-like structure, i.e., stabilizes the water structure.

Since the chemical PMR shift for water depends on the number of protons in the ice-like and disordered structures, we determined the manner in which the proton concentrations in the s- and h-structures are altered by addition of heavy water to H20. The total number of sites available for protons in a solution consisting of2xo: molesof solute (HDO) in 1 - Xo: moles of solvent (H20) is 2 + 2xa: moles. The number of moles of protons in the s- structure nuclei is made up of the protons belonging to the H20 molecules and the protons in the HDO molecules and equals 2ns (1 - xa:) + nO:, where no: is the number of moles of HDO in the s-structure nuclei. The proportion of the protons in the s-structure is then

and similarly

while

Instead of Eq. (1), we now write

y~=

1 • ns(l-x.)+"2ns

1 +x.

y~ = ----,--,-----1 +x.

n~ = 2x.ts'

n~=2x.th'

(8)

(9)

(10)

for the chemical proton shift in the solution. Substituting in Eqs. (8) and (9) and taking Eq. (5) into account, we obtain (retaining only those terms linear for the concentration xa:)

(11)

or, if we neglect the terms of power (1- W 0:)2,

(12)

*We assume that the number of water molecules is the same in the nuclei of the s- or h-struc­ture. This is valid if the structural reorganization of an s- structure nucleu s into an h- structure nucleus or vice versa takes place more rapidly than self-diffusion of the water molecules. If we assume that the average lifetime of a given structural nucleus is governed by the dielectric relaxation time [18], it is readily computed from the Einstein formula for the self-diffusion coef­ficient [19] that the water molecules will be displaced through a distance of about 3 A over this period, which is comparable to the distance between nearest neighbors, and hence do not have time to leave the nucleus, whose size substantially exceeds the length of the hydrogen bond at q»1.

92 V. M. VDOVENKO, Yu. V. GURIKOV, AND E. K. LEGIN

The first factor in the brackets is of structural origin. It is negative and corresponds to displacement of the proton signal toward lower field strengths as a result of stabilization of the water structure after solution of the D20. The second term appears as a result of the de­crease in the proton concentration in the solution. It is positive, i.e., corresponds to a chemical shift toward stronger fields. The experimentally observed displacement of the proton signal toward higher field strengths [12] indicates that the second contribution is dominant.

Using numerical estimates of the structural characteristics of water and the isotopic ef­fects in the chemical structural potential [9], the value of q can be calculated from Eq. (11). In making calculations with Eq. (11), we used the following estimates for a temperature of 32°C (the temperature at which 0HP-DP was measured) [12]: n~ = 0.69, n~= 0.31 [9], dnh/dT= 3.10-3

[9], Ow = 4.28, and dow/dT = 0.01 parts per million/deg [1). Table 1 gives the coresponding values of Os and 0h. We found that q = 60 at 32°C.

The above discussion of the chemical proton shifts in H20-D20 mixtures is readily extend­ed to the chemical deuteron shifts in dilute solutions of H20 in D20. Since the hydrogen bond is weaker than the deuterium bond, oJJ. s > oJJ. h > 0 and, consequently Wex > 1. Both factors in Eq. (11) are therefore positive. This means that there should be a strong chemical deuteron shift toward higher field strengths. Experimental study of the character of the chemical deuteron shifts in H20 solutions in D20 is accordingly of interest.

It should be noted that the approach developed for analysis of the chemical PMR shifts in H20 solutions in D20 is general in character and can easily be extended to additives of any type. We previously established [9) that the effect of a solute on the structure of water depends on the sign of the difference 1- wo:. The solute stabilizes the water structure atw a < 1 and destroys it at Wo: > 1. Let us consider the two limiting cases.

1. wa« 1. Equation (11) then takes the form

(13)

Substances that act to stabilize the structure of water should therefore shift the proton signal toward lower field strengths.

2. W 0:» 1. In this case,

(14)

Substances that act to break down the structure of water should therefore shift the proton signal toward higher field strengths.

It must naturally be kept in mind that this approach describes only that component of the chemical shifts which is of structural origin. Itisalsonecessarytotakeintoaccountthechange in the screening of the water protons that results from formation of new bonds between the solvent and solute molecules. Qualitative agreement between our proposed theory and experiment is therefore to be expected only when the structural effects are dominant. Such systems include solutions of normal alcohols (methyl, ethyl, propyl, and butyl), whose molecules strengthen the water structure, according to a number of researchers [16, 17].

Some research has recently been done on the PMR spectra of alcohol-water solutions [5]. The water-proton signal was found to be displaced toward lower field strengths, in accor­dance with Eq. (13), when methyl, ethyl, or propyl alcohol was added to water.

CHEMICAL PROTON SHIFTS IN ~O-D20 SOLUTIONS 93

LITERA TURE CITED

1. Schneider, H. J. Bernstein, and J. A. Pople, J. Chern. Phys., 28:601 (1958). 2. H. G. Hertz and W. Spalthoff, Z. Electrochern., 63:1096 (1959). 3. N. Muller, J. Chern. Phys., 43 (6):2555 (1965). 4. J. C. Hindman, J. Chern. Phys., 44(12):4582 (1966). 5. H. Ruterjans and H. A. Scheraga, J. Chern. Phys., 45(9):3296 (1966). 6. L. Hall, Phys. Rev., 73(7):775 (1948). 7. C. M. Davies and T. A. Litovitz, J. Chern. Phys., 42(7):2563(1965). 8. V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin, Zh. Strukt. Khirn., 7:819 (1966). 9. V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin, in: Structure and Role of Water

in the Living Organism [in Russian], Vol. I, Izd. LGU (1966). 10. G. Nernethy and H. A. Scheraga, J. Chern. Phys., Vol. 36, No. 12 (1962). 11. R. P. Marchi and H.Eyring, J. Phys. Chern., 68(2):221 (1964). 12. M. S. Bergquist and L. E. G. Eriksson, Acta. Chern. Scand., 16(9):2308 (1962). 13. G. Nernethy and H. A. Scheraga, J. Chern. Phys., 43(3):680 (1964). 14. V. M. Vdovenko, Yu. V. Gurikov, and E. K. Legin, Dokl. Akad. Nauk SSSR, 172:126 (1967). 15. P. Kirschenbaum, Heavy Water [Russian translation], Izd. Inostr. Lit. (1953). 16. O. Ya. Sarnoilov and M. N. Buslaeva, Zh. Strukt. Khirn., 4:502 (1963). 17. A. Ben-Nairn, Israel J. Chern., 2(5):278 (1964). 18. H. S. Frank, Proc. Roy. Soc., A247:481 (1958). 19. Yu. V. Gurikov, Zh. Strukt. Khirn., 5:188 (1964).

SELF-DIFFUSION IN AQUEOUS SOLUTIONS OF AMINO ACIDS, PEPTIDES, AND PROTEINS·

L. K. Altunina, O. F. Bezrukov, N. A. Smirnova, I. A. Moskvicheva, and V. P. Fokanov

Much research has recently been done on self-diffusion in liquids and solutions, as a result of the development of a convenient and sufficiently precise method for measuring self­diffusion constants on the basis of the spin echo phenomenon [1, 2]. The most fruitful investi­gations of aqueous solutions have been those of K. A. Valiev et at. (e. g., [3]) and the work of Douglas and McCall [4], who measured the self-diffusion constants of water in electrolyte solu­tions. These authors attempted to obtain information on the influence of ions on the structure of water and to calculate the quantitative characteristics ofthis influence from data on the self-dif­fusion constants of water as a function of concentration. The criteria used to evaluate the influ­ence of the solute on the structure of water in aqueous nonelectrolyte solutions [5] are less con­clusive and require thorough theoretical and experimental verification.

We previously reported the results obtained in measuring the self-diffusion constants in aqueous solutions of tertiary butanol, dioxane, acetonitrile, and a number of aliphatic amino acids [6-7]. The present investigation was a continuation of our research on self-diffusion constants in solutions of amino acids, peptides, and proteins.

~ 1. Solutions of Amino Acids and Peptides

1. We measured the self-diffusion constants in aqueous solutions of glycine, a- and {3 -alanine, a-aminobutyric acid, leucine, valine, a-isoaminobutyric acid, y-aminobutyric acid, proline, diglycine, triglycine, a-alanyl-a-alanine, and /3-alanyl-{3-alanine over the temperature range 25-50°C and in glycine solutions at different medium pH's. Figures 1,2, and 3 and Tables 1-4 present the results obtained.

As is well known, the decrease in spin-echo amplitude resulting from molecular self-dif­fusion in solution is defined by the expression

(1)

where nt is the number of protons in a molecule of the i-th component, Xt is the molar propor­tion of the i-th component, g is the magnetic-field gradient, T is the time between the 90° and 180 0 impulses, y is the gyromagnetic ratio, and Di is the self-diffusion constant of the i-th component. It follows from Eq. (1) that the self-diffusion constant Drel in a binary system mea-

* Translated from Struktura i Rol' Vody v Zhivom Organizme 2:57-69 (1968).

94

SELF-DIFFUSION IN AQUEOUS SOLUTIONS 95

as "'-=----------- {"

1.0 2,0 J.O mol. "/0 ami no acid

Drel

('

2'

4.0

, 2

a 5 ~--~~--~~--~----~ f.O 2,0 3.0 4,0

mo l. '"/0 ami no acid

Fig. 2. Relative self-diffusion constants in solutions of amino­butyric acid isomers as a func­tion of concentration. 1) y­

Aminobutyric aCid; 2) a -amino­butyric aCid; 3) a-isoaminobu­tyric acid.

5.0

Fig. 1. Relative self-diffusion constants Drel in amino acid solutions as a function of concentra­tion. 1) Glycine; 2) !3-alanine; 3) a-alanine; 4) a-aminobutyric acid; 1',2',3',4') relative self­diffusion constants of amino acids in solution; 1") product of self-diffusion constant of glycine by relative solution viscosity as a function of con­centration.

D reI

2

aSo~-----~------2~---~3

mol. "/0 amino aci d

Fig. 3. Relative self-diffusion constants in solutions of a-alanyl-alanine (1), glycyl-glycine (2) !3 -alanyl-alanine (3), and triglycine (4).

sured by the spin-echo method is an average of the self-diffusion constants of the individual components D1 and D2•

We were able to determine the contribution made by the amino acid molecules and the self-diffusion constants for water in the solutions of glycine, two types of alanine, and a-amino­butyric and O!-isoaIhinobutyric acids. We made use of the fact that the mutual diffusion constant D~uin an infinitely dilute solution should equal the self-diffusion constant of the amino acid [8), as well as of the fully justified assumption that the product of the self-diffusion constants of the amino acid by the solution viscosity is independent of concentration [7). As was to be expected,

96 L. K. ALTUNINA ET AL.

TABLE 1

Glycine B-Alanine (X-Alanine (X-Aminobutyric (X- Isoaminobutyric Proline

acid acid

Concen- NS I il NS lil N IU NS lil N IU S OJ S OJ

tration, U w U w U w U w U w

'" '" '" '" '" mol."/o <::> <::> <::> <::> <::> - - - - <:

~ '<: 0 v <: 0 ~ '<: 0 v '<: 0

~ <: 0 ~ <: c:. <: ':£ Q .... <: £ <: ':£ ....

Q<: ':£ <: ':£ * *:r: Q Cl Q Q Q Q Q Q Q Q Q Q Q Q Q Q

0.0 1.00 1.06 1.00 1.00 0.918 1.00 1.00 0.946 1.00 1.00 0.831 1.00 l.00 0.$15 100 1.00 0.5 0.97 1.02 0.98 0.96 0.86 0.97 0.95 OJi8 0.96 0.94 0.755 0.95 0.91 0.74 0.92 0.92 1.0 0.94 0.98 0.96 0.92 0.81 0.94 0.91 0.82 0.93 0.89 0.69 0.91 0.85 067 0.88 0.88 2.0 0.89 0.90 0.92 0.84 0.71 0.89 0.R2 0.71 0.86 0.79 0.58 0.84 0.76 0-56 0.82 0.817 2.5 0.86 0.86 0.91 0.81 0.68 0.86 0.78 0.66 0.83 073 0.51 0.78 0.67 -3.0 0.83 (J.83 0.89 0.77 0.63 0.8.~ 0.73 0.58 079 0.68 0047 0.74 0.71 3.5 0.80 0.79 0.87 0.73 0.60 0.81 0.63 0041 0.70 4.0 0.78 0.76 0.85 0.69 0.57 0.78

concen-I r -Aminobutyric I tratlOn, I acid

Valine G lycil- glycine

I Triglycine (X- Alanyl-alanine . B - Alanyl- alanin

mol. "/0

0.0 1.00 1.00 1.00 0.796 100 1.00 0.665 1.00 1.00 0.5 0.97 0.90 0.98 0.73 l.00 087 0.\19 0.91 1.0 0.93 0.80 0.92 0.67 0.95 0.98 0.83 2.0 0.80 0.8! 0.56 0.87 0.68 2.5 0.75 0.73 3.0 069 0.68

'The values of DAA and DHp were not calculated for some ami[]o acid solutions.

TABLE 2

Compound I Glycine (X-Alanine B-Alanine (X- Aminobutyric I (X- Isoam~nobutyric I y-Aminobutyric acid aCld acid

mol. 0/0 I 3 3 3 3 2.5 I 0.9 1.9

UD I 0.87 0.86 0.89 0.85 0.87 0.87 0.91 1,05 0.95 0.98 I

0.89 0.93

Compound I G lycyl- glycine (X-Alanyl- (X-alamne

mol."/o I 0,2 0.5 0,7 1.0 1.5 2.0 2.5 2.9 0.16 0.50 0.71 1.00 l.51

UD I 1.00 0.97 0.90 0.91 0.95 0.95 1.00 1.08 0.9 0.93 0.88 0.91 0.94

the self-diffusion constants for water DH20 in the solutions differed little from the average Drel at amino acid concentrations of 1-1.5 mol.% ; however, the difference reached 8% in solutions containing 3 mol.% a-aminobutyric acid.

e

Table 1 gives the experimentally measured relative self-diffusion constants in the solutions Drel • the relative self-diffusion constants for water in these solutions DH 0 calculated with the

2

SELF-DIFFUSION IN AQUEOUS SOLUTIONS 97

amino acid contribution taken into account, and the absolute self-diffusion constants ofthe amino acids D AA calculated on the assumption that

D~u DAA =-- .

1] reI

The self-diffusion constant of pure water at 25°C was assumed to be 2.2 . 10-5 cm/sec2•

The literature gives data on the mutual diffusion constants. at infinite dilution for a number of amino acids and peptides, but there are no data on this viscosity as a function of concentra­tion. We were therefore unable to calculate the contributions made by these compounds to DreI ,

We noted the following phenomenon in analyzing the self-diffusion constants of water in the amino acid and peptide solutions as a function of concentration. The self-diffusion constants of the water decreased as the size of the amino acids increased or, more precisely, decreased in proportion to the drop in the self-diffusion constants of the amino acids in the solutions. A similar relationship was observed for the peptide solutions. However, with peptides and amino acids having the same mobility (e. g., glycil-glycine and 'Y-aminobutyric acid), the self-diffusion constants of the water were higher in the peptide solutions than in the amino acid solutions, which indicates that the peptide group has a destructive effect on the structure of water.

The mobility of the water molecules in the a-alanyl-alanine solutions was anomalously high in comparison with solutions of the ,B-isomer or any other amino acid or peptide. The viscosity of the a-alanyl-alanine solutions also differed little from that of pure water. More­over, differences in the shape of the molecules and the relative positioning of the hydrophobic and hydrophilic groups have little effect on the mobility of the water. Thus, the difference in water mobility in the a-alanine and ,B-alanine solutions did not exceed 3%. The water mobility in the a-aminobutyric, a-isoaminobutyric, and y-aminobutyric acid solutions was also very low,

2. We measured the self-diffusion constants as a function of temperature over the range 25-50°C for solutions of glycine, different alanine and aminobutyric acid isomers, and a number of peptides. The accuracy with which the activation energy of self-diffusion was measured was no less than 4-5%. Table 2 gives the values of UD for solutions of a number of amino acids and peptides (the activation energy of self-diffusion for pure water was assumed to be 1). The data obtained show that the amino acids and peptides investigated reduced the activation energy of self-diffusion for water.

The contribution made to U D by the solute molecules is slight until a concentration of the order of 2 mol.% is reached, since the proportion of these molecules is small and the activation energy of self-diffusion is close to that in pure water. Thus, UD = 4.275 kcal/mole in an infinite­ly dilute solution between 1 and 25°C [9]. According to other data [24], UD amounts to 4.625 kcal/mole for glycine and 4.783 kcal/mole for alanine. The activation energy of self-diffusion for pure water is 4.2-4.6 kcal/mole between 1 and 50°C.

Similar patterns have been established for the activation energy of viscous flow U II [12] and are explained by breakdown or stabilization of the water structure. It was found that UI1 is lower for solutions of glycine, diglycine, triglycine, and other compounds than for water and higher for solutions of proline and leucine than for water, despite the general increase in solu­tion viscosity in comparison with pure water.

+ 3. Our experimental results showed that amino acids exist in the form of dipolar ions HaN-R-COO- in the crystalline state and in solution at pH's between 4.4 and 7.7. They behave as bases in an acidic medium and as acids in an alkaline medium:

+ + H2N-R-COO-~ H3N-R-COO-~ H3N-R-COOH.

pH>7 pH<7

98 L. K. ALTUNINA ET AL.

Figure 4 presents the results obtained in measuring the self-diffusion constants D reI in glycine solutions at pH's of from 2 to 10, as well as in aqueous control solutions of HCI and NaOH. The value of Drel was found to increase in an acidic medium and remain almost unchanged in an alkaline medium.

4. The data obtained indicate that the influence of amino acids and peptides on the structure of water is very complex. The most interesting phenomena are the decrease in the activation energy of self-diffusion for water, which occurs despite a decrease in the self-diffusion constant itself, and the increase in solution macroviscosity with rising concentration. A similar phe­nomenon was detected in measuring the activation energy of viscous flow in solutions of amino acids [12J and ions [13].

Tsangaris and Martin [12] surmised that the increase in solution macroviscosity was due to the contribution made by the ions and molecules dissolved in the water. When the particles are sufficiently large, this contribution exceeds that made by the breakdown of the water struc­ture, which also leads to an overall increase in solution viscosity. These authors therefore consider the activation energy of viscous flow to be a direct indication of the character of the change in the water structure.

The change in the self-diffusion constants of water in our case may have resulted from a number of factors.

1. A specific interaction between the water molecules and the NH2, NH;, COOH, and COO- groups. If some of the water molecules were bound comparatively strongly to a solute molecule, so that they participated in translational movement with it (the lifetime of the water­amino acid complex is longer than the "sedentary" life of an amino acid molecule), this would lead to a decrease in D.

2. A change in the structure of the water. The decrease in the activation energy of self­diffusion of water that occurred in the amino acid solutions investigated is difficult to account for solely on the basis of the aforementioned interaction.

As is well known, the activation energy of self-diffusion for water decreases with tempera­ture, from 5 kcal/mole at O°C to 3-3.5 kcalhnole at 90-100°C. Within the framework of the two­structure model of water, this is obviously associated with displacement of the structural equi­librium toward disordered water. A simple calculation shows that, if the ratio of the two struc­tures is the same at 25°C as at 90-100°C (Un = 3-3.5 kcal/mole) the self-diffusion constant of the water will be higher at 25°C, as was observed experimentally. The molecules of disordered water therefore ha ve a higher mobility than those of ice-like water.

Amino acid molecules apparently displace the structural equilibrium toward water of the disordered type, so that the activation energy of water self-diffusion decreases. The expected increase in the diffusion constant of the water does not occur, since the increase in the mobility resulting from the shift in the equilibrium is more than compensated for by the decrease in the mobility of the water molecules in direct contact with the solute molecule.

An interesting peculiarity among the systems investigated was exhibited by the Q!-alanyl­a-alanine solutions, whose self-diffusion constants and viscosity differed little from those of pure water. This behavior can be explained either by the strong destructive effect of these molecules on the water structure or by the fact thay they contain no free polar groups, forming

- + intramolecular bonds of the - COO ... H3N- type. The second hypothesiS is more reason-able, although we found no data in the literature confirming the existence of such rigid bonds in peptides. Comparison of the self-diffusion constants of water in solutions of y-aminobutyric acid and glycyl-glycine shows that the peptide group does not cause a decrease in the mobility of the water molecules in contact with it.

SELF-DIFFUSION IN AQUEOUS SOLUTIONS 99

TABLE 3

Concen-

I h';RS h;AS ...

Compound tration, hA hlJ hR' h ultrasound mol. ,,!e

Glycine 1 5.4\ 1°,6-2,6\ 1 4-6 1-2 3 5.5

j3-Alanine 1 i:g 1 3,8-4.51 1.0 I 1 3

a-Alanine 1 g 1 5.1- 5.7 1 1.6 I 1 6-8 2-4 3

a- AminobutyriC! 1 ~.~ !6.4-S.J I 1.2 1 acid

:)

·See [18]; • ·See [17]; • • ·See [15, 16].

D reI 1.0 It is customary in the literature on electrolyte

solutions to characterize the capacity of ions to un-

0.9 o 0

o

0.8

f

I 0 00 o

dergo hydration by the hydra tion number h. It is as­

o.7~--~--~--~--~~~ 2 4 6 8 fOpH

sumed that, during displacement, each water mole­cule moves for some time in a complex with an ion and assumes its self-diffusion constant. This pattern is equivalent to the one in which h water molecules move together with an ion throughout the entire ob­servation period. The number h is called the hydra­tion number. The literature contains estimates of Fig. 4. Relative self-diffusion con­

stants as a function of medium pH in 3% glycine solution (1) and con­trol solutions of Hel and NaOH (2).

h for amino acid solutions calculated by different methods [15-17]. Our data also permit us to make similar formal estimates. Table 3 presents the results of calculations made by two methods.

A. The decrease in the amplitude of the spin echo in a solution resulting from self-dif­fusion of water molecules and hydrated amino acid molecules is described by the expression

(2)

Equation (2) is identical to Eq. (1) if we assume that some of the water molecules diffuse with the self-diffusion constant of the amino acid and the rest diffuse with the self-diffusion con­stant of pure water. We thus presume the change in the self-diffusion constants in the solutions studied to be caused solely by hydration. The hydration numbers hA determined by this method have similar values for different amino acid concentrations.

B. The hydration numbers given in Table 3 were calculated from Eigar's formula [18], with (hB') and without (hB) the relative solution viscosity taken into account:

v (dln~) [ (DHO ')] J) = DO ,dTiim (1 - O.0l8hm) 1 + O.018m -&- h 'tlrel' (3)

where DV is the mutual diffusion constant of the amino acid in solution at a given concentration, DO is the mutual diffusion constant of the amino acid at infinite dilution, and yand m are the activity of the unhydrated compound and the solution molality respectively.

100 L. K. ALTUNINA ET AL.

TABLE 4

Compound Concentra tion

mg/cm 3 Drel Notes

Bovine serum albumin •• 50 1.0 Austria Trypsin ••.••...•••• Saturated 1.0 Hungary Chymotrypsin •••..••• Saturated 1.0 Hungary Chymotrypsinogen .•••• Saturated 1.0 Hungary Equine y -gobulin ••••• Saturated 1.0 Isolated and purified by

the usual method Equine hemoglobin 10 1.0 Hungary

Recrystallized four times Diphtheria toxin 46 0.99

140 0.8 Diphtheria anatoxin Saturated 1.0

110 0.9 Ribonuclease 20 0.95 Hungary

40 0.92 60 0.9

Human fibrinogen 16 1.0 Isolated and purified at 70 0.9 the Leningrad Institute

of Blood Transfusion

The hydration numbers calculated by different methods can be divided into two groups: those with "low" values (h ~ 1-3) and those with "high" values (h ~ 4-11).

Without analyzing the factors responsible for the discrepancy in the estimates of h, we will merely note several conclusions common to many methods:

a) the hydration number of an amino acid increases as its molality decreases and is in­dependent of its dipole moment;

b) branched amino acid isomers have higher hydration numbers;

c) the presence of the peptide group in diglycine causes it to have a lower hydration num­ber than aminobutyric acid isomers, which are similar in size and shape.

§ 2. Protein Solutions

The self-diffusion constants of water measured by the spin echo method in biopolymer solutions are lower than for pure water for three reasons. First of all, biopolymer molecules, which are of large size and have a very low self-diffusion constant, are "obstacles" to some water molecules. The avetage particle displacement over the observation time should be less than in the pure liquid when such obstacles are present. This effect was first considered by Wang [20] in an investigation of water self-diffusion in protein solutions conducted by the tag­ged-atom method. The decrease in the self-diffusion constant of water resulting from the pres­ence of obstacles for dilute solutions of globular proteins is expressed by the formula

D=Do (1 - (XV),

where Do is the self-diffusion constant of pure water, V is the proportion of proteins in the solu­tion by volume, and O! is a constant that depends on the shape of the molecule.

Secondly, the water molecules are bound to the protein molecules (hydration) and there­fore undergo almost no displacement over a certain time interval.

SELF-DIFFUSION IN AQUEOUS SOLUTIONS 101

A third effect, stabilization or breakdown of the water structure, occurs in aqueous elec­trolyte and nonelectrolyte solutions and causes a change in the mobility of the water molecules. This effect is undoubtedly also operative in aqueous protein solutions, as is indicated by the decrease in entropy and the increase in partial molar heat capacity that occurs when proteins are dissolved in water [21]. It has also been hypothesized that the change in the structure of the water surrounding the nonpolar groups of a biopolymer plays an important role in producing hy­drophobic bonds, which determine the molecular conformation in solution. Robinson and Stokes [19] neglect this effect, however, on the basis of the fact that D01Jo /T = const in protein solutions, where DO is the self-diffusion constarlt of the protein,1Jo is the viscosity of pure water, and T is the absolute temperature.

The present investigation was devoted to the feasibility of using the spin-echo method to measure the self-diffusion constants of water in biopolymer solutions.

The first measurements of this type were made by Douglass et al. [22] in a tobacco mosaic virus solution. At a virus concentration of 26.9 m2/ em3, the self-diffusion constant of water was found to equal that of pure water to within 3%. The authors therefore asserted that water is not in the "ice-like" state around virus particles, despite the rather short times for spin-lattice and spin-spin relaxation (Ti = 0.75 sec, T2 = 0.02 sec). They therefore failed to detect any effect exerted by the three aforementioned factors, despite the fact that a large mass of water mole­cules was in direct contact with the virus surface at so high a concentration.

Table 4 presents the results of our measurements of the self-diffusion constants of water in globular protein solutions at 25°C. We used commercial protein specimens, which almost al­ways contain a certain amount of inorganic salts; these can only act to reduce the self-diffusion constant of the water.

The equipment condition Hi »Gd must be strictly satisfied in measuring the self-diffusion constants in systems with short relaxation times Ti and T2• In our opinion,' the absence of a de­crease in spin-echo amplitude in glycerol (T2 = 0.03 sec) over the entire range of magnetic-field gradients provides a good check on the satisfaction of this condition. If it is not strictly satis­fied, the measured self-diffusion constants can only be too low.

Another factor that must be kept in mind is that a biopolymer-water system is a hetero­phase, i.e., consists of at least two ensembles of nuclear spins with different Ti and T2. The over­whelming majority of proteins do not yield high-resolution spectra. This means that their proton spin-spin relaxation times are short (T2 < 10-3 sec) and their contribution to the amplitude of the spin echo can be neglected at 2T > 10-2 sec. Ribonucleaseistheonlyproteinwithahigh-reso­lution spectrum and therefore has a longer relaxation time T2. In this case, it is necessary to investigate the logarithm of the spin-echo amplitude In A(2 T, G) as a function of the square of the magnetic-field gradient G2 and to measure the self-diffusion constants at different values of 2 T. The relatronship between· In A and G2 is linear in pure liquids, whose molecules have the same self-diffusion constant. The deviation from linearity in ribonuclease solutions is 3-5%.

( - ~ - 2 1,0'D<') Le., the contribution made by the second term in Eq. (1) A02 e T, 3 is small. The self-diffusion constants measured at different 2 T also differ little from one another.

Keeping these factors in mind and observing the equipment conditions, we obtained the following results.

1. The self-diffusion constants of water in saturated solutions of most globular proteins (the protein concentration in a saturated solution is generally less than 10-15 mg/cm3) are usual­ly the same as in pure water (to within no less than 3%) at 25°C and 3-4% lower than in pure water at 45°C. The activation energy of self-diffusion UD is 2-4% lower in protein solutions than in pure water.

102 L. K. ALTUNINA ET AL.

2. The self-diffusion constant begins to undergo a marked decrease, in direct proportion to the volumetric percentage of biopolymer, at protein concentrations above 30-40 mg/cm3•

3. Addition of 0.1% formaldehyde to a ribonuclease solution reduces the self-diffusion constant 01 water almost to the level for pure water. The presence of formaldehyde in solutions of diphtheria toxin causes no changes in the self-diffusion constant.

We employed gel-filtration through Sephadex G-100 to establish that ribonuclease aggre­gates in solution under the action of formaldehyde. Formaldehyde has no such effect on toxin molecules.

The decrease in the self-diffusion constant of water in true solutions of globular proteins therefore lies within the limits of experimental error, with rare exception~ (for highly soluble proteins). On the other hand, it is clear that the scale of the changes in water structure in pro­tein solutions is small and is limited by hydration effects [23].

The "obstacle" effect evidently plays the decisive role in reducing the self-diffusion con­stants of water. This is shown by our measurements in protein solutions containing formalde­hyde. However, further research is necessary before definite conclusions can be drawn.

In conclusion, the authors wish to express their deep gratitude to M. F. Vuks, O. Ya. Samoilov, Yu. V. Gurikov, and G. G. Malenkov for their valuable advice and the criticisms they offered in discussing this work.

LITERA TURE CITED

1. H. Y. Carr and E. M. Purcell, Phys. Rev., 94:63 (1954). 2. D. Douglass and D. W. McCall. J. Phys. Chern., 52:1102 (1958). 3. K. A. Valiev and M. I. Emel'yanov, Zh. Strukt. Khim., 5:1 (1964). 4. D. W. McCall and D. C. Douglass, J. Phys. Chern., 69:2001 (1965). 5. K. A. Valiev and M. I. Emel'yanov, Zh. Strukt. Khim., 5:6 (1965). 6. o. F. Bezrukov, D. K. Toropov, and V. P. Fokanov, Abstracts of an All-Union Conference

on the Liquid State [in Russian], Samarkand (1966). 7. O. F. Bezrukov, N. A. Smirnova, V. P. Fokanov, and A. I. Chebaevskii, Abstracts of an All­

Union Conference of the Liquid State [in Russian] Samarkand (1966). 8. H. Y. Johnson and A. L. Babb, Chern. Revs., 56:387 (1956). 9. M. S. Lyons and J. V. Thomas, J. Amer. Chern. Soc., 72:4506 (1950).

10. M. W. Aaron and E. H. Grant, Trans. Faraday Soc., 59:85 (1963). 11. J. Conner and E. Smith, J. Amer. Chern. Soc., 64:1870 (1942). 12. J. M. Tsangaris and R. Br. Martin, Ar~h. Biochem. Biophys., 112(2):267 (1965). 13. E. R. Nightingale, J. Phys. Chern., 66:894 (1962). 14. O. Ya. Samoilov, Structure of Aqueous Electrolyte Solutions and the Hydration of Ions,

Consultants Bureau, New York (1965). 15. Yu. A. Petrenko, L. A. Petrenko, and V. K. Tkach, Biophysics and Radiobiology [in Russian],

Naukova Dumka (1966). 16. V. B. Kazanskii, L. D. Stepin, and P. M. Onishchenko, Biophysics and Radiobiology [in Rus­

sianj, Naukova Dumka (1966). 17. A. G. Pasynskii, Zh. Fiz. Khim., 11:606 (1938). 18. I. G. Orlov, V. S. Markin, Yu. V. Moiseev, and U. I. Khurgin, Zh. Strukt. Khim., 7(5):796

n·966). 19. R. A. Robinson and R. H. Stokes, Electrolyte Solutions, Butterworth, London (1966). 20. J. M. Wang, J. Amer. Chern. Soc., 76:4755 (1954). 21. H. A. Scheraga and L. Mandelkern, J. Amer. Chern. Soc., 75:179(1953). 22. D. C. Douglass, H. L. Frisch, and E. W. Anderson, Biochem. et Biophys. Acta, 44:401

(1960) •

SELF-DIFFUSION IN AQUEOUS SOLUTIONS

23. S. E. Bresler, Introduction to Molecular Biology [in Russian), Izd. Akad. Nauk SSSR (1963), pp. 120-123.

24. L. G. Longsworth, J. Phys. Chern., 56 :770 (1954).

103

USE OF INFRARED ABSORPTION SPECTROSCOPY TO INVESTIGATE THE INFLUENCE

ON WATER STRUCTURE OF A NUMBER OF COMPOUNDS WITH A PROTECTIVE ACTION DURING FREEZING

OF HUMAN ERYTHROCYTES·

A. I. Sidorova and A. I. Khaloimov

The lethal effect of freezing on animal cells and tissues can be avoided if they are prelimi­narily treated with protective substances. It is for this reason that most researchers who have studiedthe effects of low temperatures on biological systems have directed their efforts at seek­ing compounds that will protect tissues against the action of cold. A number of valuable prac­tical results were obtained in using glycerol as a protective substance [1].

Lovelock [2] investigated the protective action of 15 compounds, including mono-, di-, and poly­atomic alcohols, mono- and disaccharides, and amides. He established that some compounds, particularly ethylene glycol and glycerol, taken in appropriate concentrations protected human erythrocytes from hemolysis after freezing at any temperature between -3 and -80°C. Such com­pounds as methanol, ethanol, and formamide in small concentrations protected cells at tempera­tures between 0 and -30 or -40°C but no lower. These compounds have a toxic effect in high con­centrations, which may account for the hemolysis of erythrocytes frozen below -30 or -40°C. Both groups of compounds readily penetrate the erythrocyte. Compounds of the third group, such as glycose, erythrite, andxylose,did not completely protect the erythrocytes from damage during freezing at any temperature. These substances only partially penetrate the cell. The compounds of the fourth group, sucrose and polyethylene glycol, provided little or no protection against cell damage during freezing at different temperatures. They do not penetrate erythrocytes at all [2].

Since the cells are in contact with dilute aqueous solutions and the effect of freezing is to a substantial extent governed by the behavior of water and aqueous media at below-freezing tem­peratures, it can be assumed that the effectiveness of protective substances is in some measure associated with their influence on water structure. In order to determine the mechanism of the protective effect, we investigated the infrared absorption spectra of aqueous solutions of ethylene glycol, glycerol, glucose, and sucrose. The influence of methanol and ethanol on the structure of water had previously been studied in our laboratory [3].

Our investigation was made in a spectrometer with a diffraction grating operating in the near infrared region, in the "2 + "3 band at 5200 cm -1. The instrument has a resolution of 4 cm-1 in the 5000 cm-1 region. This band is almost the only one suitable for studying aqueous solutions of molecules containing hydroxyl groups, since there is no superimposition of the OH

* Translated from Struktura i RoP Vody v Zhivom Organizme 2:69-71 (1968).

104

INFLUENCE OF COMPOUNDS WITH PROTECTIVE ACTION DURING FREEZING 105

TABLE 1

Molecular C, 6v. cm-1

Compound Formula weight Penetration g/100 ml of solution max 3011/0

Methanol CHpH 32 Complete 2.8 59 22 Ethanol CzHsOH 46 Complete 4.2 40 19 Ethylene glycol C2HsO z 62 Complete 4.5 35 17 Glycerol C 3Hs03 92 Complete 5.4 27 13 Triethylene glycol CsH1404 150 Complete 8.0 13 5 Glucose CSH120S 180 Partial 15 7 7

Sucrose C12H2Pu 342 None 3 3

vibration bands of the solute molecules on the water absorption band. Our investigations of alco­hol-water systems were conducted with this band for the same reason [3].

The spectra of aqueous solutions of the aforementioned compounds were measured at dif­ferent concentrations. Methanol, ethanol, ethylene glycol, triethylene glycol, and glycerol are highly soluble in water. The maximum of the water absorption band in the spectra of aqueous solutions of these compounds was displaced toward lower frequencies, the extent of the displace­ment gradually increasing and reaching the value shown in the right-hand column of Table 1 at a concentration of 95%. Glucose and sucrose are substantially less soluble in water. The right­hand column of Table 1 gives the maximum band displacement obtained in our experiments; for glucose and sucrose, this occurred at a concentration of 30% by weight. The largest shift was thus -59 cm-1 for methanol solutions, followed by -40 cm-1 for ethanol, -35 cm-1 for ethylene glycol, -27 cm -1 for glycerol, -13 cm -1 for triethylene glycol, -7 cm-1 for glucose, and -3 cm-1

for sucrose. Table 1 compares the concentrations necessary to prevent hemolysis of erythro­cytes during freezing at -lO°C,asdeterminedby Lovelock, with the maximum displacement of the water absorption band observed in our experiments. For ease of comparison, the last column of the table shows the displacement of the water absorption band at a concentration of 30 wt. % for all the compounds investigated.

As can be seen from Table 1, the maximum displacement of the water band decreased from compound to compound in parallel with the increase in the concentration necessary to prevent hemolysis. The observed correlation is naturally still a preliminary result, but it indicates that the correct direction has been taken in seeking the factors responsible for the effect of com­pounds that prevent cell damage during freezing.

By analogy with the influence of alcohols on the structure of aqueous solutions, glycerol, glucose, and the other compounds should somehow rearrange the water framework. There is as yet no solidly established theory regarding the configuration of the glycerol molecule [4], not to mention more complex molecules such as glycose and sucrose. It would therefore be premature to discuss the structural details of their aqueous solutions.

LITERA TURE CITED

1. L. Hey, Preservation of Life by Cold [Russian translation], Medgiz (1962). 2. J. E. Lovelock, Biochem. J., 56:265 (1954). 3. A. I. Sidorova and I. N. Kochnev, Abstracts of an All-Union Conference on the Liquid State

[in Russian], Samarkand (1966). 4. R. Cetina and J. L. Mateos, Bol. !nst. Quim. Univ. Nal. Auton. Mex., 17:49 (1965).

ACCESSIBILITY OF WATER IN MUSCLE FIBERS TO MOLECULES OF DIFFERENT SIZES·

N. N. Nikol'skii

The state and properties of intracellular water has long been a matter of dispute. Use of modern physical techniques to evaluate the state of water in the living cell has not yet provided an unambiguous solution to the problem, because of the complexity of the subject.

A knowledge of the properties of intracellular water is absolutely necessary for correct evaluation of the concentrations (activities) of the substances dissolved in the cell sap. On the other hand, research on the distribution of material between the cell and its medium provides information on the properties of the intracellular water as a solvent. The most widely held the­ory is that the water in the cell does not differ materially from that in an ambient solution, so that it is assumed in calculating intracellular concentrations that all the intracellular water is a solvent.

Formulation of experiments to investigate the solvent power of intracellular water in living subjects is complicated by biochemical processes, which can alter the intracellular compound concentrations. It has now been demonstrated that many substances enter the cell by means of specific transport systems localized in the superficial cell membrane. Some of these systems utilize metabolic energy to produce an accumulation of a substance in the cell in comparison with the medium or to gradually eliminate a substance from the cell. These processes are referred to as active transport. The coupling of flows of materials that are transported against the concen­tration gradient with those of other materials can lead to a nonequilibrium distribution of groups of compounds that are not themselves transported against the gradient. It must be emphasized that we are speaking only of the transfer of a material from the medium into the cell or in the opposite direction and not of the transformations that take place during intracellular metabolism. Com­pouudsthatarenotmetabolized, Le., that undergo no changes in the cell, are usually employed to investigate the mechanisms by which compounds are redistributed between the cell and the me­dium. Thus, for example, glucose uptake can be studied with galactose, methyl glucose, or xy­lose, which enter the cell by the same pathway as glucose but are not phosphorylated in most cells. However, as was noted above, the concentrations of these nonmetabolized sugars can differ sub­stantially from those in the medium if their transport into the cell is coupled with a system for active transport of another compound or itself entails expenditure of energy. The above "purely biological" characteristics of the living cell hamper investigation of the properties of intracel­lular water as a solvent from the steady-state material distribution. It should be added that the precise potential difference between the cell and the medium must be known in studying the ion dis tribu tion.

*Translated from Struktura i Rol' Vody v Zhivom Organizme 2:92-99 (1968).

106

ACCESSIBILITY OF WATER IN MUSCLE FIBERS TO DIFFERENT MOLECULES 107

In studying the properties of intracellular water from the steady-state material distribu­tion, it is most convenient to conduct experiments with low-molecular nonelectrolytes, selecting compounds and experimental conditions such that the material distribution between the cell and the medium depends solely on the solubilit,y of a given nonelectrolyte in the intracellular water. However, because of the heterogeneous structure of the cell, it is always necessary to make the unproved assumption that all the intracellular organoids are equally indifferent to a given compound and that the cell membrane and organoid membranes are equally permeable to it. Experiments on the material distribution in nonliving cell models and in killed cells therefore provide one procedure for evaluating the properties of intracellular water. Such experiments give an idea of the minimum restrictions imposed on compound solubilit,y by the characteristics of the mater­ial composing the cell. Many experiments on the material distribution between the cell and its medium have been performed with muscle tissue and the data in this article pertain only to this subject.

Muscles isolated from the body can live in artificial media for rather long periods, which makes it possible to investigate the distribution of compounds added to the medium after a steady state is reached. As a rule, 20% of the total crude weight of a muscle consists of dry residue. Since 10-20% of the muscle volume is composed of the interfiber (extracellular) space, only 60-70% of the crude weight is intracellular water.

Among low-molecular fat-insoluble nonelectrolytes, muscle fibers arepenetratedcompar­atively rapidly by monoatomic alcohols (methanol and ethanol), amides (formamide and acetamide), glycerol, urea, and urea derivatives. The fiber membrane is almost impermeable to hexaatomic alcohols (mannitol and sorbitol) and certain sugars (fructose, d-arabinose, and sucrose for frog muscle). The available experimental data lead us to conclude that substances with a molecular radius of more than 3 A can enter muscle fibers only by means of specific transport systems.

Very little research has been done on the steady-state distribution of alcohols, amides, and urea between muscles and the ambient medium. Interpretation of experiments with urea is complicated by the fact that it is absorbed on the cellular structures. The distribution of alcohols has been investigated with only one alcohol concentration in the medium, but it is as­sumed that alcohols are not adsorbed. With a steady-state distribution, the alcohol concentra­tion in the intracellular water of frog muscle is lower than that in the medium. According to Linderberg and Gary-Bobo [1], the ratio of the intracellular concentration to the concentration in the medium (the distribution constant) was 0.92 for methanol and 0.89 for ethanol; on the other hand, Fenichel and Horowitz [2] obtained distribution constants of 0.79 for methanol, 0.81 for ethanol, and 0.92 for formamide. According to Bozler's data [3], the distribution constant for glycerol in the same tissue is 0.90. Despite the discrepancies in the distribution constants, these data enable us to conclude that a minimum of 10% of the water in muscle fibers is not a solvent, even for methyl alcohol, or that the properties of all the intracellular water are altered in such fashion that the solubilit,y of alcohols in it is reduced by 10%. Similar values for the limitation of solubility in muscle-fiber were obtained for sugars. These experiments were con­ducted with nonmetabolized sugars and the sugar uptake was stimulated with insulin. It was found that 10-15% of the water in frog muscle fibers is inaccessible to penetratinghexoses andpentoses [4, 5, 6]. Some experiments were conducted at different sugar concentrations [4, 6] and the agreement of the distribution constants served as proof that there was no adsorption or active sugar accumulation, since the rate of these processes depends nonlinearly on concentration. A distribution constant of 0.8 was obtained for l-arabinose in the rat myocardium with sugar transport Similarly stimulated by insulin, i.e., 20% of the intracellular water was inaccessible to the sugar [7].

Experiments on nonliving models, such as polymer gels or tissues that have been killed or specially treated in such fashion that they lose their "biological" characteristics with respect to

108 N. N. NIKOL'SKII

material transport but retain the structural features of living tissue, can aid in interpreting the possible factors responsible for the inaccessibility of some of the water in living cells to low­molecular nonelectrolyte molecules. Glycerinized muscles are convenient subjects for such research.

Experimentation has shown that some of the water in nonliving tissues and polymer gels remains inaccessible to molecules of certain nonelectrolytes. The inaccessible volume depends on the size of the nonelectrolyte molecule. Thus, almost all the water in alcohol-killed muscles is accessible to sucrose, galactose, and fructose [8, 9], but polysaccharide and inulin molecules occur in only 70% of the tissue water [9]. It can be concluded from these data that the amount of water of hydration for proteins and other biopolymers in killed muscles* is small and has al­most no effect on sugar solubility in the tissue water. It should be noted that the method employed in these investigations permits evaluation of the amount of water available for solution to within only 5%.

Experiments on glycerinized muscles showed that neither inulin nor fructose is distributed throughout the tissue water [9]. Only 60% of the water is accessible to inulin, while 84% is acces­sible to fructose.

Most of a muscle fiber is composed of myofibrils, so that it might be surmised that inulin does not penetrate the myofibrils at all in killed or glycerinized muscles. However, experiments on isolated myofibrils have shown that only 35% of their water is inaccessible to inulin and 10% to sucrose [9]. In terms of the entire muscle, 35% of the myofibril water is 17% of the muscle water. This figure is substantially lower than the proportion inaccessible to inulin molecules in killed and glycerinized muscles. It must therefore be assumed that additional restrictions on the distribution of inulin molecules are created when myofibrils are packed into a muscle fiber.

Results similar to the data for glycerinized muscles and myofibrils have been obtained with gels of gelatin [6, 9] and hyaluronic acid [10, 11]. About 20% of the water in a 10% gelatin gel is inaccessible to inulin, while 10% is inaccessible to sucrose; experiments on the inulin distri­butionshowedthatthe percentage Of inaccessible water was independent of the solution pH, i.e., was not correlated with changes in the amount of water. It was also found in experiments with hyaluronic acid gel that a considerable percentage of the gel water was inaccessible to inulin. The inaccessible proportion remained unchanged when the pH and ionic strength were varied but depended on the gel concentration.

All the above data on the inulin distribution can be explained if we assume that the restric­tion imposed on the solution of this compound in the water of gels and nonliving tissues is steric in nature. That portion of the water enclosed in cells formed by the polymer chains is inacces­sible'to sUfficiently large molecules. The smaller the size of the molecule, the lower is the probabilityofa steric restriction. According to calculations made by Ogston [11], the volume V accessible to a given molecule in a homogeneous polymer gel or solution is defined by the equa­tion V = exp [-rr L (rs + r t ) 2], where rs is the molecular radius (assuming that the molecule is spherical), r t is the polymer-chain radius (assuming that the polymer consists of straight rod­like chains), and L is the polymer concentration expressed as the polymer-chain length per cm3•

This equation descrioes the experimental data (see Fig. 1). The volume inaccessible to sucrose in 1.45% hyaluronic acid gel was found to be 4%, while that inaccessible to glucose was 1% [11]. No experiments with inulin were conducted, but it can be determined from the curve in Fig. 1 that the inaccessible volume for inulin would be about 25%. In the experiments of Ogston and Phelps [11], the inaccessible volume of inulin was grouped with that of polyglucose and serum albumin, whose molecular radii exceed 20 A. The molecular radius of inulin is 10.6 A when de-

*The water content of alcohol-killed muscles is 90%.

ACCESSIBILITY OF WATER IN MUSCLE FIBERS TO DIFFERENT MOLECULES 109

10

8 10

Fig. 1. Relationship between size of molecules and volume accessible to them in 1.45% hyaluronic acid gel [11]. The molecular radius (in 10-7 cm) is plotted along the abscissa and the accessible volume along the ordinate. The curve was calculated from the equa­tion given in the text, while the dots represent experimen­tal data. 1) Glucose; 2) su­crose; 3) raffinose; 4) myo­globin; 5) cyanomethemoglo­bin; 6) transferrin; 7) serum albumin; 8) ceruloplasmin; 9) gamma globulin; 10) QI­

crystallin.

o

termined from a compact spherical model and about 16 A when determined from its diffusion constant. However, investigation of the physicochemical properties of inulin solutions leads to the conclusion that the inulin molecule has the form of a rod consisting of individual helical seg­ments with a radius of 6 A and a total length of the order of 100 A. The probability that such rigid rod-like mole­cules will enter the cells of a gel depends both on the actu­al volume of the molecule and on the volume it occupies during rotation.

The hypothesis of straight polymer chains arrayed randomly in space is the simplest but does not necessari­ly comform to reality. The deviations from the calculated accessible volumes can therefore be substantial for gels, while it makes no sense at all to evaluate data obtained for nonliving muscles by this method. However, the idea of a steric restriction imposed on water in nonliving tis­sue seems quite well justified. For example, it is difficult to assume that glycernized muscles contain far less water of hydration than killed muscles, so that the accessibil-ity of their water to fructose is substantially altered. It is more logical to attribute the difference in the accessi­bility of water to inulin and fructose in these subjects to an increase in structure disorganization in killed muscles.

Experiments on gels and nonliving tissues lead to the conclusion that the steric restriction imposed on wa­ter in living cells should have a similar mechanism. Inu­lin molecules are incapable of penetrating the cell under normal conditions, but, if they could do so, probably no

more than 60% of the intracellular water would be accessible to them. Definite restrictions should also exist for sugars (hexoses and pentoses).

The current available data on the steady-state distribution of sugars and alcohols, which were given at the beginning of this paper, show that the intracellular water is almost equally accessible to the two classes of compounds. Unfortunately, we are unable to find any articles on the alcohol distribution in nonliving models. However, proceeding solely from molecular size, the volume inaccessible to alcohols should be negligibly small. We can therefore assume that the inaccessibility of a small amount of water in muscle fibers to alcohols is a specific property of the living fiber structure. It is most probable that this water consists mainly of the water in the membrane structures of the cell. The protein and lipid layers of the membrane are tightly packed structures, while the total water content of the membrane is estimated at about 50% [14]. The water molecules in the membranes are probably enclosed in very small spaces bounded by both hydrophilic and hydrophobic surfaces. The structure of the water in these spaces should differ greatly from that of ordinary water. The membrane structures in nonliving cells are disorganized. The living structure is retained to the greatest extent in glycerinized muscle fibers, but we found no published works on the alcohol distribution in muscles so treated.

As was noted above, the amounts of water inaccessible to alcohols and sugars in living muscle fibers are approximately equal. However, there is a striking and unexplained discrepancy in the alcohol-distribution data. The most reliable figures seem to be those given by Linderberg and Gary-Bobo [1] and by Bozler [3]. Their data showed the amount of water inaccessible to su-

110 N. N. NIKOL'SKII

gars to be greater by 2-10% (of the total water content). Consideration must also be given to the possibility that sugars accumulate in small volumes of the cell in concentrations higher than in the medium. In any event, it is hard to assume that the percentage of inaccessible water in liv­ing cells is less than that in glycerinized cells; according to Vasyanin et al. [10] 16% of the wa­ter in the latter remains inaccessible to fructose. It is therefore quite probable that the inacces­sibility of part of the water in muscle fibers to sugars is due to steric factors.

Nasonov and Aleksandrov [16] advanced a similar view regarding the possibility of steric restrictions imposed on a portion of the intracellular water. Related ideas were discussed by Bozler [3, 17], who believes that the intracellular solubility of a compound is greatly reduced because most of the water is enclosed in very narrow channels (slits). He assumes that this factor can make 60-70% of the total water in muscle fibers inaccessible to sugars. However, his hypotheses agree poorly with experimental data.

Comparison of all the data considered above leads to the following conclusions regarding the properties of the water in muscle fibers.

1. About 10% of the water in the fibers does not serve as a solvent for any substance.

2. Most of the intracellular water is accessible to compounds whose molecular radius differs only slightly from that of water, but a definite proportion of the water is inaccessible to some extent for molecules of larger size, as a result of steric limitations.

LITERA TURE CITED

1. A. B. Linderberg and C. Gary-Bobo, Arch. Sci. Physiol, 14:303 (1960). 2. J. R. Fenichel and S. R. Horowitz, Acta Physiol. Scand., 60 (Suppl.):221 (1963). 3. E. Bozler, Am. J. PhysioI., 200:651 (1961). 4. N. T. Narahara and P. C)zand, J. BioI. Chem., 238:40 (1963). 5. L. G. Leibson, E. M. Plisetskaya, and L. G. Ogorodnikova, Zh. Evolyuts. Biokhim. i Fiziol.,

1:374 (1965). 6. N. A. Vinogradova, N. N. Nikol'skii, am A. S. Troshin, Tsitologiya, 9:658 (1967). 7. H. E. Morgan, D. M. Regen, and C. R. Park, J. BioI. Chem., 239:369 (1964). 8. T. P. Tezhelova, Kolloidn. Zh., 3 :631 (1937). 9. I. I. Kamnev, Arkh. Anat., Histol. i Embriol., 19:145 (1938).

10. S. I. Vasyanin, N.A. Vinogradova, S. A. Krolenko, and N. N. Nikol'skii, Tsitologiya, 9:51 (1967).

11. A. G. Ogston and C. F.Phelps, Biochem. J., 78:827 (1961). 12. T. C. Laurent, Biochem. J., 93:106 (1964). 13. A. G. Ogston, Trans. Faraday Soc., 54:1754 (1958). 14. c. F. Phelps, Biochem. J., 95:41 (1965). 15. J. B. Finean, J. Biophys., Biochem., CytoI., 3:95 (1957). 16. D. N. Nasonov and V. Ya. Aleksandrov, Reactions of Living Matter to External Factors

[in Russian], ONTI, Moscow-Leningrad, (1940). 17. E. Bozler, Am. J. Physiol., 197 :505 (1959).

CALCULATION OF BINAR Y DISTRIBUTION FUNCTIONS AND THERMODYNAMIC CHARACTERISTICS OF

AQUEOUS SOLUTIONS OF STRONG ELECTROLYTES BY THE MONTE CARLO METHOD*

P. N. Vorontsov-Vel'yaminov and A. M. El'yashevich

An aqueous solution of a strong electrolyte is a system consisting of positive and negative solute ions distributed among the polar water molecules. In attempting to give a theoretical de­scription of the thermodynamic properties of such a system, one is confronted with difficulties resulting from the extreme mathematical complexity of the statistical problem, in which consid­eration must be given to all the different types of interaction in the system (ion- ion, ion- dipole, and dipole-dipole), the repulsive forces over short distances, and the specific interaction of the water molecules with one another, which entails formation of hydrogen bonds. Most theories of electrolyte solutions (the Debye-HUckel theory [1] and theories based on the Bogolyubov-Born­Green-Ivon or Kirkwood equations [2-6]) therefore utilize a simplified model of the system, in which the solvent is treated as a continuous medium with a dielectric constant £, filling the space between the ions; in the simplest case, that of an electrolyte with 1-1 valence symmetry, the po­tential of the interionic interaction is described by the equations:

r<a

, {1,iX=~ o.~= 0, iX =1= ~ (iX, ~ = 1, 2), (1)

where 1 represents a positive particle, 2 represents a negative particle, and a is the ion diame­ter; this is the simplest way to take into account the ionic interaction forces over short distances. However, even within the framework of this simple model, the thermodynamic properties of highly concentrated aqueous electrolyte solutions cannot be described by the aforementioned theories, while the results obtained in describing the properties of moderately concentrated so­lutions contain errors that are difficult to evaluate.

In a previous article [7], we proposed a variant of the Monte Carlo method [8], which has been used for thermodynamic description of other particle systems (see the survey by Fisher [9]), for development of a theory of strong electrolyte solutions within the framework of the coulombic solid sphere model [a system of particles with the interaction potential given by Eq. (1)]. The unusual feature of this numerical method is the fact that investigation of a system consisting of a small number of particles No (of the order of tens or hundreds) can yield inform a-

*Translated from Struktura i RoP Vody v Zhivom Organizme 2:99-106 (1968).

111

112 P. N. VORONTSOV-VEVYAMINOV AND A. M. EL'YASHEVICH

TABLE 1

Ml N!!4 MJ N!! 23 N!! 29 N!! 44 M 61 N!! 66 2-2- val. N!! 67

Ar·N C=O.OIM C=0.05 M C=O.l M C=0.5 M C= 1.0 M C= 1.5 M C=2.5M C=5,OM C=5.0M C=6.5 M Ar= Ar= Ar= Ar= 4r= !1r= Ar= !1r=

Ar = 4.33 A. !1r=2.54 A. = 2.015A = 1,178 A =0.993 A =0.816 A =0.6Sl8A. =0.546 A =0.546 A =0,500 A

1 '2 (gll + g22)

0.5 0 0 0 0 0 0 0 0 0 0 1.5 0.398 0 0 0 0 0 0 0 0 0 2.5 0.660 0.524 0.397 0 0 0 0 0 0 0 3.5 0.805 0.671 0.583 0 0 0 0 0 0 4.5 0.830 0.781 0.712 0.572 0 0 0 0 0 0 5.5 0.917 0.R23 0.820 0.716 0.623 0.618 0 0 0 0 6.5 0.924 0.879 0.886 0.784 0.716 0.696 0.745 0 7.5 0.912 0.907 0.909 0.867 0.799 0.787 0.784 1.060 0.75\ 0 8.5 0.936 0.935 0.908 0.927 0.887 0.894 0.830 0975 0.844 1.250 9.5 0.957 0.935 0.944 0.937 0.933 0.890 0.884 0.911 0.927 1.133

10.5 0.972 0.970 0.975 0.972 0.93\ 0.942 0.891 0.921 0.950 1.054 11.5 0.975 0.967 0.966 0.984 0.961 0.97~ 0.949 0.920 1.013 0.956 12.5 0.987 0.969 0.975 0.980 0.963 0980 0.994 0.990 1.099 0.928 13.5 0.977 0.975 0.985 0.987 0.973 0.990 0.988 1030 1.089 0.890 14.5 0.989 0.976 0.970 0.966 0.980 0.992 1007 1.030 1.030 0.901 15.5 0.973 0.982 0.996 0.994 0.979 1.017 1.007 1.020 1.071 0.966 16.5 0.99\ 0978 1.006 0.992 0.986 0.981 0.987 0.967 1.089 1.042 17.5 0.983 0.977 0.991 0.991 0.989 0.989 1.000 1.020 1.043 1.065 18.5 0.992 0.977 0.980 0.978 0.993 1.001 1.003 1.010 0.970 1.038 19.5 0.983 0.986 0.994 0.985 0.993 0.973 1.000 0.980 0.957 1.012 20.5 0.992 0.990 0.989 0.999 0.991 0.990 0.987 0.990 0.91\ 1.0n8 21.5 0.982 0.986 0.979 0.990 0.987 0.985 0.999 0.924 0.996

1 '2(gl.2 + gIl)

0.5 0 0 0 0 0 0 0 0 0 0 1.5 2.635 0 0 0 0 0 0 0 0 0 2.5 1.585 2.063 2.347 0 0 0 0 0 0 0 3.5 1.375 1.617 1·701 0 0 0 0 0 0 4.5 1.212 1.332 L399 1.725 0 0 0 0 0 0 5.5 1.178 1.189 1.253 1.472 1.664 1.970 0 0 0 0 65 1.110 1.123 1.176 1.237 1.352 1.446 1.886 0 7.5 1.073 1.095 1.140 1.143 1.160 1.237 1.456 1.919 2.178 0 8.5 1.077 1.066 1.089 1.117 1.120 1.170 1.298 1.458 1.500 2,584 95 1.060 1.037 1.019 1.110 1.053 1.071 1.100 1.122 LI86 1.793

10.5 1.035 1.047 1.022 1.050 1.027 1.026 1.059 1.035 0.934 1.331 11.5 1.041 1.036 1.050 1.019 1.024 1.021 1.014 0.964 0,860 1.088 12.5 1.011 1.010 \.020 0.999 1.008 1.009 1.014 0.954 0.807 0.997 13.5 1.020 1020 1.011 1.008 1.001 0.993 1,003 0.982 0.845 0.896 14.5 1.017 1.002 1.000 1.017 1.002 0.993 0.991 0.990 0.887 0.923 15.5 1.005 1.004 1.020 1.010 0.993 1.016 0.978 0,970 0.934 0.935 16.5 1.017 0.9~6 1-005 1.000 1.000 1.014 0.980 0,996 0.948 0.984 17:1; 0.996 1.002 1.017 0.985 0.981 1.007 1.000 0.984 0.994 1.036 18.5 1.005 0.998 1.002 0,990 1.000 1.007 0.982 1.018 1.048 1.012 19.5 1.000 0.995 0.984 0.989 0.989 1.003 0.990 1.015 1.063 1.012 20.5 1.000 0.996 1.001 1.009 1.002 1.003 0.999 1.001 1.086 0.983 21.5 0.995 0.995 0.998 0.993 0.934 0.991 0.993 0,988 1.022 0.994

tion on a system containing a macroscopic number of particles. The smaller system is related to the macroscopic system by imposing selected periodic boundary conditions on the latter.

This paper presents the results obtained in calculating the internal energy, free energy, osmotic constant, activity constant, and binary distribution functions. The calculations were made by the Monte Carlo method for a system comprising No/2 negative ions and No/2 positive ions placed in a cubic cell whose size depended on the system concentration (No = 32, 48, 64, or 128) and interacting in accordance with Eq. (1) over the concentration range 0.01-6.5 M. The temperature of 300 0 K and the dielectric constant e = 80 correspond to those for an aqueous elec-

CALCULATION OF BINARY DISTRIBUTION FUNCTIONS 113

TABLE 2

'" 2

N! I

-} ~ g.p(a+O) C.M S No --u -A II -In-: X "-l .,p=i

1 O.oI 22 128 0108 0.084 0.0329 0.117 3.8

2 0.05 10 32 0.215 0.182 0,0565 - -3 11 128 0.210 0.136 0.0538 0.190 -4 31 128 0,207 0.163 0.0511 0.214 4.4

5 0.1 10 32 0.273 - - - -6 20 32 0.267 0.215 0.0578 0.273 3.8 7 12 128 0.266 0.229 0.0640 0293 3.1

8 0,2 10 32 0.346 - - - -9 6 128 0.348 0.252 0.0780 0.330 -

10 0.3 10 32 0.389 0.349 0.0693 0.418 2.5 11 10 128 0.387 0,329 0.0586 0.388 2.9

12 0.4 14 128 0.427 0348 0,0437 0.391 3.1 13 0.5 26 32 0.453 - - - -14 \0 32 0.468 0.382 0.0197 0.402 3.3 15 25 32 0.462 0.362 00315 0.394 3.0 16 25 32 0.451 0.368 00384 0.407 2.8 17 22 48 0.462 0.388 0.0345 0,421 3,0 18 22 48 0,456 0.378 0.0541 0.432 2.4 19 20 16 128 0.454 - - - -21 17 128 0.458 - - ~ -22 31 128 0.458 0.389 0.0391 0.429 2,8 23 12 128 0.459 0.411 0.0317 0.443 3.0 24 0.8 10 32 0.533 0.634 -0.00824 0.425 2.9 25 1.0 20 32 0.578 0.359 -0.0194 0.340 2.6 26 18 32 0.563 0.458 --0.0143 0.471 2.5 27 7 128 0.567 0.499 -0.05K8 0.440 3.0 28 26 128 0.550 0.487 -0.0328 0.454 2.7 29 28 128 0.548 0.478 -00566 0.421 2.9 30 15 45 32 0.627 - - - -31 18 32 0,624 - - - -32 31 32 0,629 -- - - -33 37 32 0.629 - - - -34 18 48 u.626 - - - -35 18 48 0,624 0.552 -0.113 0.438 2.7 36 15 48 0.620 0.543 -0.141 0.401 2.9 37 13 64 0.616 - - - -38 14 64 0.619 - - - -39 17 64 0.616 - - - -40 31 128 0,618 - - - -41 26 128 0.611 0.553 -0.131 0,423 -42 25 128 0,606 0.548 -0.141 0.407 2.8 43 15 128 0,610 - - - -44 26 128 0.608 0,545 -0.145 0.399 2.8 45 10 128 0.620 0.569 -0.154 0.415 2.9 46 2.5 16 32 0.717 0609 -0.310 0,298 2.7 47 20 32 0.703 0612 -0.344 0.267 2.9 48 29 32 0.713 0.6.5 -0.314 1).290 2.7 49 20 32 0.722 062u -0.'08 0.111 2.7 50 13 48 0.717 0643 -0.372 0.270 3.1 51 9 48 0.721 0.627 --0,386 0.241 3.1 52 12 48 0.720 0.629 -0.341 0.287 2.9 53 18 48 0,703 0.563 -0335 0.227 2.8 54 18 48 0.7114 0,616 -0,415 0.200 il.2 55 10 48 0.700 0630 -0.411 0.219 3.2 56 13 64 0700 0.617 -0.377 0.240 3.0 57 6 64 0.694 0.544 -0.282 0.261 2.5 58 23 64 0.704 06 '3 -0.386 0.236 3.1 59 27 128 0.701 0.626 -0.357 0.269 2.9 60 28 128 0.698 0.642 -0.41.') 0.207 3.3 61 26 128 0.698 0.643 -0.409 0.237 3.2 62 7 128 0,694 0.657 -0.389 0.267 3.1 63 10 128 0.713 - - - -64 23 128 0.703 0.640 -0.359 0.280 2.9 65 5.0 28 32 0.820 0.720 -1.210 -0,480 3.7 66 9 128 0,821 0.810 -1.257 -0.446 3.8 67 6.5 19 128 0.872 0.817 -2,05 -1.233 4.4

114 P. N. VORONTSOV-VEVYAMINOV AND A. M. EVYASHEVICH

trolyte solution at room temperature. The ionic diameter of 4 A corresponds to the size of hy­drated ions in real electrolyte solutions. The calculations were made in an M-20 computer.

1. Distribution Functions

Table 1 gives the values obtained for the binary distribution functions at No == 128 and C == 0.01,0.05,0.1,0.5,1.0,1.5,2.5,5.0, and 6.5Mfor an electrolyte with a 1-1 valence symmetry and C == 5M for an electrolyte with a 2-2 valence symmetry (the temperature was 300"1(, the dielectric constant was 80, and the ionic diameter was 4 A in all cases). Since the functions gl1 (r) and g22 (r) as well as g12 (r) and g21 (r) should coincide for a symmetric electrolyte, Table 1 gives the half-sums 112 (gl1 + g22) and 1/2 (g12 + g2V calculated by the Monte Carlo method. The values of the functions are compared with those of the argument r in terms of ~r; the latter de­pends on the concentration that is given in the table in each case. The numbers in the cblumns of the table correspond to the individual Markov chains in Table 2.

Analysis of the data shows that the dependence of the functions on distance has a mono­tonic character from small concentrations (O.OIM) to 2.5M; the functions reach saturation (i.e., values close to one) with increasing C at small values, which corresponds to intensification of the electrical screening in the system with riSing concentration. This intensification of screen­ing ceases when C exceeds 2 .5M and a new type of correlation appears in the system, as a re­sult of the fact that the ion size (short-range forces) begins to playa relatively more important role than the coulombic forces at high densities. Moreover, the g 11 function for an electrolyte with 1-1 valence symmetry exhibits a reversal of its trend from that of short distances, initially decreasing rather than monotonically increasing. This behavior on the part of gl1 indicated the existence of an unusual type of short-range ordering in the system with the physical parameters' in question, probably corresponding to the formation of individual groups of ions of the tripole or quadripole type predicted by Fuoss [10] for electrolyte solutions. The functions gl1 and g12 for an electrolyte with 2-2 valence symmetry at C == 5 Mcorrespond to the short-range ordering characteri-stic of a regular ionic lattice. This difference is understandable, since the electrical interaction in a 2 - 2 valence system is four times stronger than in a 1-1 valence system. Ac­dording to rough estimates, the error in the distribution-function values given in Table 1 is 3-5% in most cases for Markov chains with 15-30 thousand steps.

2. Thermodynamic Functions

Table 2 gives the values of the following factors:

the excess internal energy of the system (in kT units) per particle: 3

E-TkT

u= NkT

the excess free energy (in kT units) per particle:

- A-Auo A= NkT ;

the osmotic constant II, determined from the osmotic pressure in the system under in­vestigation with the formula

pv ll= 1- kT

(where v is the volume of a single particle in the system);

the activity constant 'Y which is related to the excess chemical potential,

I'--I'-uo In l' = ------=­kT

(2)

(3)

(4)

(5)

CALCULATION OF BINARY DISTRIBUTION FUNCTIONS 115

The internal energy was calculated by averaging the potential electrical energy of the indi­vidual configurations of a system of No particles Uj (No) over L steps of a Markov chain, taking into account the periodic boundary conditions imposed on the system:

(6)

The free energy Awas determined by averaging the values of exp {Uk(;ol} along the Markov chain:

L

A = ~ In~ ~ exp {Ui(No)} No L ~ kT'

(7)

1=1

The osmotic constant was calculated from the general statistical expression for pressures, which takes the form

2

~~ = 1 - +ID I + 1t6a: ~ g_~(a+O). (8) _. ~-l

for the potential given in Eq. (1). Here gcxe(a + 0) is the value of the function gexs(r) at the point where the ions are closest together. The value of In y was determined from the relationship

Inl=A-n. (9)

The chain length L, which is shown in a separate column of Table 2, was 10,000 to 30,000 steps, which provides an accuracy of the order of 1 % in calculating the internal energy, 5% in calculating the free energy and activity constant, and 5-10% in calculating the osmotic constant; a rough estimate of the error was made by comparing the data obtained for different chains with the same parameter values and different initial conditions (e.g., the chains for concentrations of 0.5, 1.5, and 2.5M).

The data presented in this article are the results of a mathematical experiment. They can be treated as accurate for the model adopted within the aforementioned limits of error and used to check different approximate theories of strong electrolytes and for direct comparison with experimental data on specific electrolyte solutions.

LITERA TURE CITED

1. D. Debye and E. Hiickel, Phys. Z., 185:305 (1923). 2. N. N. Bogolyubov, Dynamic-Theory Problems in Statistical Physics [in Russian], Gostekh-

izdat (1946). 3. J. G. Kirkwood and J. C. Poirier, J. Phys. Chern., 58:591 (1954). 4. S. V. Tyablikov and V. V. Tolmachev, Dokl. Akad. Nauk SSSR, 114:1210 (1957). 5. V. G. Levich and V. A. Kirlyanov, Zh. Eksperim. Teor. Phys., 36:8 (1962). 6. G. R. Martynov, Usp. Fiz. Nauk, 91:3 (1967). 7. P. N. Vorontsov-Vellyaminov, A. M. El'yashevich, and A. K. Kron, Elektrokhimiya, 2:708

(1966) • 8. N. Metropolis, M. Rosenbluth, A. Rosenbluth, A. Teller, and E. Teller, J. Chern. Phys.,

21:1087 (1953). 9. I. Z. Fisher, Statistical Theory of Liquids [in Russian], Fizmatgiz (1961).

10. J. OIM. Bockris (ed.), New problems in Modern Electrochemistry [Russian translation], Izd. Inostr. Lit., (1962).