MANUSCRIPT THESIS · 2016-12-12 · If the intermolecular potential energy is the same for the ground and excited vibrational states (approximately true), then M(l) is independent

FORM

TO

BE

BO

UND

WIT

H TW

O CO

PIES

OF

PH

.D.

THES

IS

FACI

NG

FR

ONT

CO

VE

RTHE UNIVERSITY OF TORONTO LIBRARY

MANUSCRIPT THESISAUTHORITY TO DISTRIBUTE

NOTE: This form to be signed by those students for whom immediate publication of the thesis by the National Library has been arranged.

The AUTHOR agrees that this thesis may be lent without restriction. A

BORROWERS undertake to give proper credit for any use made of the thesis, and to obtain the consent of the author if it is proposed to make extensive quotations, or to reproduce the thesis in whole or in part.

SIGNATURE OF BORROWER ADDRESS DATE

202A

REVISED NOVEMBER 1 9 6 5

Reproduced with permission of the copyriQht owner. Further reproduction prohibited without permission.

RAMAN SPECTRA OF SOME SIMPLE MOLECULES

IN CONDENSED PHASES

By

S. Morry Blumenfeld

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy at the University of Toronto.

April, 1967.

@ Morry Blumenfeld, 1967

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission

TABLE OP CONTENTS

Page

Chapter I Introduction 1

Chapter II General Experimental MethodA. Introduction : The Growth of

Molecular Crystals 7B. The Low Temperature Cryostat . 9C. The Raman Tube 12D. The Spectrograph 13E. Recording and Measurement of Spectra 15

Chapter III Liquid OxygenA. Introduction 19B. Experimental Procedure 20C. Results and Discussion 21

Chapter IV Methane•A. Introduction 29B. Experimental Procedure : Liquid

Methane 29C. Experimental Procedure : Solid

Methane 30D. Results and Discussion 3

Chapter V EthyleneA. Introduction 39B. Experimental Procedure : Liquid

Ethylene 39C. Experimental Procedure : Solid

Ethylene 40D. Results and Discussion 41


, Page

Chapter VI Formic AcidA. Introduction 50B. Experimental Procedure 51C. Results 54D. Discussion 55

Appendix Calculation of the Second Derivativeof the Intermolecular Potential in Solid Ethylene 62

Summary gg

References g8

Acknowledgements 70


CHAPTER I

INTRODUCTION

Spectroscopic studies of gases at low densities allow the determination of the intramolecular properties of free molecules. To investigate intermolecular properties, the molecules must be allowed to Interact with one another.One way of causing this interaction is to compress the gases to high pressures. The progressive changes which occur in the spectrum as the density is increased can be ascribed to the action of intermolecular forces during collisions.

Another method is to study the condensed states of these molecules. In substances with intramolecular energies which are much greater than the intermolecular ones, the molecules retain their individuality in the condensed states. Consequently, their spectra in the condensed states resemble, in large measure, the spectra of the individual free molecules. Certain definite changes occur which can be ascribed again to the intermolecular forces.

The changes which arise in the vibrational spectrum of the liquid have two causes. The rotational motion of the molecule in most liquids is no longer free. This produces changes in the shapes of the vibrational band profiles, usually sharpening them considerably. Also the selection rules of the free molecule are no longer valid because the molecule is now part of an Interacting system.

In molecular crystals, selection rules, originating in the symmetry of the lattice, and, hence, of the intermolecular crystalline potential, appear. These new selection rules may result in the lifting of degeneracies, or in the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

splitting of the nondegenerate vibrational fundamentals of the free molecule. The changes in the rotational motion in the solid state again affect the shape of the vibrational band profiles. Moreover, a third effect, the appearance of new low frequencies arising from lattice vibrations, may also occur.

The research described in this thesis has continued the investigation of intermolecular forces pursued at this laboratory. The spectra of the condensed states of ethylene, methane, oxygen, and formic acid have been studied through the Raman effect. The experimental technique for studying liquids, even at low temperatures, is relatively simple; for this reason many studies of molecular liquids have been carried out. The situation is quite different, however, in the solid state. Raman spectroscopy demands that the parasitically scattered light be reduced to a minimum, because the intensity of the Raman scattered light is so low. For crystals this means that a transparent sample, free from such defects as cracks, bubbles, and crystallite boundaries which would increase the intensity of the parasitic light, is necessary. Crystals of this type have been very difficult to achieve for most molecular solids. The main experimental innovation of this research has been the development of a method of producing molecular crystals which are suitable for Raman spectroscopy.

All three aspects of the effects of intermolecular forces enter into the results of the present investigation.The effects of the symmetry and periodicity of the crystalline lattice reveal themselves in the research on ethylene described in Chapter V. The appearance of new low frequency bands, lattice vibrations associated with the rotational degrees of freedom of the free molecule, is also detailed in that chapter. A more complicated situation in which new low frequencies arise is described in Chapter VI on formic acid. In this case


the rotational and translational degrees of freedom of the free molecule are transformed into the vibrations of a polymer chain held together by hydrogen bonding.

The changes occurring in the molecular rotation with condensation have been studied extensively. Recently, a new method of analysis of the rotational motion, involving the moments of the spectral intensity distribution, has been proposed by R.G. Gordon. It requires accurate intensity profiles of the spectral bands, particularly in the remote portions of the wings. Chapter III and Chapter IV describe the acquisition of new, improved experimental data on liquid oxygen, and on liquid and solid methane, respectively. The methods described by Gordon have been applied to these results. A short description of the moment analysis of Gordon follows.

MOMENT ANALYSIS OF SPECTRAL BANDSThe problem of molecular rotation in condensed phases

has received considerable attention since the early investigations of Crawford, Welsh, and Harrold (1952), who investigated the Raman spectra of liquid oxygen, nitrogen, and methane, and of solid methane. Prom the shape and the extent of the rotational wings they concluded that these molecules rotated freely in these condensed states.

In a series of articles, Gordon (1963, 1964a, 1964b) has demonstrated a new method of extracting information regarding molecular rotation from the spectra of molecules in their condensed phases. A great deal of information concerning the nature of intermolecular forces and molecular motion is contained in the spectra. However, the detailed features of these bands have proved difficult to interpret, primarily because the complete spectrum has an intensity distribution whose shape is determined by all the N-molecular distribution functions. It is therefore not as simple to analyse the


complete electromagnetic response of a system as it Is to analyze Its thermodynamic behaviour.

If, however, the spectrum is considered in terms of the moments of the intensity distribution, certain quantities which depend on low-order distribution functions may be obtained. In particular, a moment analysis will yield information about the magnitude of the intermolecular torque which hinders the molecular rotation. In the Raman spectrum, the n^h moment of the experimentally determined intensity distribution, I(v), is given by the relation

M(n) “ | (v - vs)n X** I(v) dv , (1.1)

where v is the Raman frequency shift expressed in cm-1,vg is some suitably chosen band origin (called the shiftedbandorigin), X is the scattered wavelength, and the intensity profile is usually normalized so that M(0) equals unity.

If the intermolecular potential energy is the samefor the ground and excited vibrational states (approximately true), then M(l) is independent of the intermolecular forces, and depends only on the molecular constants. The frequency of the shifted band origin is calculated by allowing the first moment to take its theoretical value :

Jv x*» I(v) dvvs a -------------- ~ M0(l) , (1.2)

Jx* I(v) dv

where MQ(1) is the theoretical first moment calculated about the J « 0 -*• J ■ 0 transition in the freely rotating molecule.


The second moment Is essentially the mean square bandwidth of the vibrational transition. This moment is also found to be independent of the intermolecular potential energy in the classical limit (applicable to most gases and liquids). Thus, if the mean square bandwidth is the same in a gas and its corresponding liquid, this need not indicatethat the molecular rotation is free in the liquid.

The fourth moment is particularly useful in the study of the intermolecular torques. In the classical limitit is the sum of contributions from the rotational kinetic energy (independent of the intermolecular potential energy), interference terms depending on the angular correlation between different molecules, and terms containing the explicit dependence of the fourth moment on the intermolecular potential which is assumed to be pairwise additive. These terms consist of the squares and cross terms of the various components of the torques on molecules.

The conclusion of Crawford et al (1952) that the molecular rotation in liquid oxygen, nitrogen, and methane, and in solid methane, was almost free was based on the similarity of the measured contour of the rotational wings to the calculated Intensity distribution of a freely rotating molecule with the individual rotational lines broadened by the intermolecular forces. Because Gordon has shown that a comparison of this nature need not necessarily Indicate that the rotation in the condensed state is free, a reinvestigation of these molecules in their condensed states with improved techniques was undertaken.

Gordon (196*ta, 1965b, 1966a) has also shown recently that the Fourier transform of the spectral band profile will yield dynamical information on the molecular rotation.The Fourier transform of a depolarized Raman band is the second


Legendre polynomial of a correlation function which describes the direction cosine of the angle between vectors describing the anisotropy of the polarizability separated by a time t, averaged over all initial times. It thus represents essentially the decay of our knowledge about the rotational motion of the molecule. An analysis of this type has also been carried out for liquid oxygen, and for liquid and solid methane.


7

CHAPTER II

GENERAL EXPERIMENTAL METHOD

The experimental procedures used in recording the Raman spectra of liquid oxygen, liquid and solid methane, and liquid and solid ethylene were similar; they are described in this chapter. Specifically, the same spectrograph, the same cryostat, termed the low temperature cryostat, and the same general method for photographing and reducing the spectra were used. The growth of formic acid crystalswas governed by the same principles as the methane and ethylene crystals. A different growth environment and a different cryostat were necessary, however, because formic acid crystallizes at a higher temperature (6°C). As well, the spectral region investigated in the formic acid experiments required a different spectrograph; hence, the experimental procedures employed with formic acid are described separately.

Thus, in this chapter the general requirements forgrowing suitable molecular crystals are discussed, the lowtemperature cryostat and the Bausch and Lomb spectrograph are described, and the general procedure for reducing the photographs of the Raman band spectra into profiles of intensity against frequency shift are delineated.

A. INTRODUCTION ; THE GROWTH OF MOLECULAR CRYSTALS

The main feature of this research was the developmentof a method of growing crystals of certain molecular substances that would be suitable for the recording of their Raman spectra, particularly for determining accurately the intensity profiles at the tail ends of weak vibrational bands. For this purpose, the crystals within the Raman tube had to be clear, transparent, and completely free from bubbles or cracks which would tend to scatter parasitic light.It was not necessary for them to be single crystals and no


tests were made to determine whether they were, but it is suspected that the final samples of solid methane and ethylene were single crystals.

A number of different techniques for the growth of molecular crystals (see particularly the review by G.P. Reynolds, 1963) have been described. For the most part these techniques are not satisfactory because of the unique shape of the Raman tube,. It is required to have a plane window at one end of the Raman tube; moreover, it is extremely important that no light scattering faults be present near the window. The method used in this research consisted in slowly passing a temperature gradient up the length of the Raman tube beginning at the window.The rate at which the solid-liquid interface moved up the tube depended on the thermal conductivity of the solid.It was necessary that the interface be kept as plane as possible; therefore, the growth rate had to be slow enough to allow the heat of fusion to dissipate through the solid to the Raman tube walls. In effect, this limited the diameter of the tubes in which it was possible to grow a suitable sample in a reasonable length of time. If the growth rate were too fast the heat of fusion was not dissipated across the interface properly and the interface would become cone-shaped. The normal to the interface would then point in different directions across the surface and misalignments resulting in cracks and crystal grain boundaries would occur.

In the early experiments, a ribbon-like fault was often found running lengthwise through the crystal from the window. Careful examination of the growing process showed that the first layer of solid on the window grew inward from the walls of the tube in a radial direction.The fault began at the junction where different crystal directions intersected. This initial layer was composed of wedge-shaped portions, each of which transmitted light


in slightly different ways indicating slightly different crystal orientations. The fault was eliminated by constructing the heater so that the solid-liquid interface was tipped with respect to the Raman tube window. This ensured that crystallization began at only one point on the rim of the window, and then swept in one direction across the window. As shown in the diagram of the solid Raman tube, Fig, 2.4 below, a nucleating tip at the window provided further Insurance that only a single nucleation could occur.

With this method no cracks, no pie-shaped wedges, or other regions with different optical qualities were noted.It is this fact that makes one assume the solids may have been single crystals.

Certain precautions beyond keeping the interface plane were necessary to ensure that the rest of the Raman tube was filled with suitable crystalline material. These precautions depended on the particular substance and will be outlined in the discussion of that substance.

B. TH1; LOW TEMPERATURE CRYOSTAT

The experiments on oxygen, methane, and ethylene were carried out in the same cryostat. This was designed with three criteria in mind :(a) to allow the crystal to be grown in situ,(b) to allow small adjustments in alignment to be made

during the experiment if necessary, and(c) to allow experiments of one week or more duration

to proceed without undue strain on the experimenter.

A vertical cross section of the Pyrex glass cryostat is shown in Fig. 2.1. The Raman tube was suspended inside an experimental chamber, A, a Pyrex tube 65 cm long and 35 mm i.d


L

E

FIG. 2.1 THE LOW TEMPERATURE CRYOSTAT


55964

10

This tube had a plane Pyrex glass window, B, 3 mm thick fused at one end and a Kovar-to-glass graded seal, C, at the other end. A liquid nitrogen dewar jacket, D, with a second plane Pyrex window, E, at the bottom surrounded the experimental chamber.

The upper section of the dewar widened into a bulb, P, for use as a liquid nitrogen reservoir. With the reservoir, the cryostat held sufficient liquid nitrogen (or air) for about five hours without refilling.

The Raman tube was suspended by means of an 0-ring seal, G, inside a brass vacuum-tight demountable assembly described in Fig. 2.2. This assembly, called the cryostat "head", contained two pulleys, H xand I, for raising and lowering the heater and filter respectively, while the experimental chamber was isolated from the atmosphere. A gas inlet tube, J, and a Pusite seal, K, for the electrical connection were soldered into the wall of the head, A vacuum-tight seal with the experimental chamber was provided by an 0-ring, L, in a sliding cylindrical sleeve arrangement, M. This facilitated the assembly and disassembly of the head and experimental chamber. The inner cylinder, which contained the 0-ring channel, was attached to the Kovar seal, C, of the experimental chamber A through a set of Sylphon bellows, N.

The pulley shafts were sealed by means of 0-ring assemblies, 0, which allowed them to be rotated from outside. The shaft for the filter pulley was rotated by hand. The heater pulley shaft was connected to a variable speed D.C. motor through a universal joint and a speed reducer.

The head was designed so that the 0-ring holding the Raman tube G was centred over the experimental chamber window when the bellows were kept perfectly cylindrical.


Top View

G0

Mto A

Side View

FIG. 2.2. THE CRYOSTAT "HEAD"


Further alignment of the Raman tube could be carried out by means of four set screws, P, held in a tube, Q, above the 0-ring seal and by the adjustment of the bellows.

Because of the requirement of keeping the scattered light to a minimum, it was necessary to keep all the lenses and windows extremely clean. - It was often necessary to clean the inner cryostat window of paint flakes or of a residue left on evaporation of the condensed methane or ethylene.after a Raman tube broke during an experiment.This proved to be a major experlmental.ydifficulty because of the inaccessibility of the window. Wiping the window with any material would invariably leave lint behind, and could scratch the window if, by chance, a small piece of grit was on its surface. Moreover, wiping left an electrostatic charge on the window which attracted even more dust. The best procedure for cleaning the inaccessible window was found to be as follows :

a) A solution of distilled water and a good glass detergent was poured down the experimental chamber and the cryostat was shaken until the solution foamed. It was then rinsed out.

b) A chromic acid cleaning solution, "Chromerge" heated to about 75°C was then poured down the tube. It was kept hot by circulating hot water through the liquid coolant jacket. It was then siphoned out, care being taken that it did not touch any brass surface.

c) The chamber was rinsed many times using distilled water and, for the final rinse, distilled deionized water. The final rinse was allowed to drain off by placing the cryostat in an upside- down inclined position.


12

d) The chamber was dried using a flow of dry nitrogen. The window was carefully examined for drying marks. If any were noted, the process was repeated.

e) The mouth of the chamber was immediately covered so that no dust could enter to settle on the window.

It was found necessary during the crystal experiments to keep the level of the coolant as constant as possible.This was done using an electronic device employing a thermistor as a sensing element. A circuit diagram of this device, essentially an adaptation of the one used by Rosencwaig (1965), is shown in Pig. 2.3.

The thermistor was glued with epoxy resin to a copper tube which extended up out of the cryostat. This decreased the time delay in warming up the thermistor, hence decreasing teh® ohang® in th® liquid ooolanfc l«val between fillings.The particular level at which the liquid coolant was maintained could then be adjusted by raising or lowering the thermistor inside the dewar section of the cryostat.

With this arrangement the level was kept constant to approximately one-half Inch. However, the device was not entirely satisfactory because the cut-in and cut-out point depended on the temperature at the thermistor and not on the precise liquid coolant levels.

C. THE RAMAN TUBE

The dimensions of the Raman tubes used in the experiments varied with the substance and its state; however, the design was essentially similar. A Pyrex glass tube had a 2 mm thick polished Pyrex window fused at one end and an


J V


FIG. 2.3

LIQUID

COOLANT

LEVEL

CONTROL

CIRCUIT

DIAG

RAM

(DESIGNED

BY M.

BARNETT)

13

S-shaped light trap at the other end, as shown in Pig. 2.4.A 10 mm o.d. Pyrex tube was sealed to the other end in such a way that it was perfectly aligned with the Raman tube.The gases were transferred into and out of the Raman tube by means of a polyethylene tube connected ultimately to the gas cylinder and to a pumping system.

The illuminated length of the Raman tube depended on the lens matching arrangement for the particular experiment. The rest of the tube was painted flat black to prevent reflected light from entering the cone of observation of the scattered light.

This paint proved to be a source of considerable experimental difficulty. Lacquer-based flat black paint would flake off the glass and fall down on the inner cryostat window when the temperature was reduced to liquid nitrogen levels. Many different methods of applying paint were attempted, including sand blasting the glass to obtain a rough finish for better adhesion or using a solution of carbon in water called "Aquadac". The most successful application was made using a black block-out paint called "Sta-Zon" manufactured by the A.B. McMahan Co. of St. Paul, Minnesota and used commercially on neon signs. This paint adhered despite many cycles at low temperatures; however, it was not quite as flat black as the lacquer-based paint.

As mentioned above, the Raman tube used in the solid experiments was constructed with a small nucleating tip at the window, as shown in Fig. 2.4(b).

D. THE SPECTROGRAPH

The spectra of liquid oxygen and the condensed phases of methane and ethylene were recorded on a Bausch and Lomb Dual Grating Spectrograph which had been modified somewhat in this laboratory. Instead of the supplied gratings, a


PIG. 2.

A

(a) lb)

RAMAN TUBES(a) DESIGN USED FOR LIQUIDS, AND(b) DESIGN USED FOR SOLIDS SHOWING NUCLEATING TTP


i4

plane grating with 1200 lines per mm, a ruled area of 10 x 10 cm2, and a blaze angle of 17°27’ was Installed.The collimating mirror had a focal length of 200 cm giving the spectrograph an effective numerical aperture of P/14.1. At 4625 8 in the second order the dispersion was about 8.1 cm-1 per mm.

An undesirable feature of the spectrograph for research purposes was its "step-variable slit". It was possible to use one of only four slit widths which had been factory-set to 10, 20, 50, and 1000 microns with the slit jaws closing bilaterally. These widths were not found useful and were changed to 250, 20, 100, and 500 microns respectively. Care was taken to keep the closing of the slit jaws bilateral; however, a slight error was introduced because of the limit of accuracy to which the slit widths could be measured during this operation.

Another unsatisfactory feature was the presence of a number of faint sources of reflected and scattered undispersed light within the spectrograph optics. These were located and masked off.

The most Important modification to the spectrograph was the addition of a half-cylindrical lens. This lens was constructed in the workshop from a "crystal clear" grade acrylic rod and bolted in front of the plate-holder. It was 112 mm long and produced a 2 mm image on the plate; because the slit length was 18 mm, a maximum gain of nine times in intensity could be attained provided the lens matching arrangements were suitable. This increased the effective numerical aperture of the spectrograph 'cone to P/1.6.

The spectrograph was relatively easy to focus and remained in focus over a large wavelength interval. The only change necessary, if different portions of the spectrum


were recorded, was a rotation of the slit to keep the slit images parallel to the grating rulings. The cylindrical lens produced images of very high quality, comparable to those attained with a glass lens. The length of the cylindrical lens limited the spectral region covered by a single exposure to about 900 cm”1 at 4625 8.

An interference filter was placed in front of the slit to prevent Hg 4358 8 and shorter wavelengths from entering the spectrograph. A small transmission region in the interference filter spectrum was eliminated with a Kodak Wratten #2A filter.

E. RECORDING AND MEASUREMENT OF SPECTRA

Exposures for all the experiments in this research were carried out on Kodak 103a-0, 103a-J, IIa-0, and baked IIa-0 spectroscopic plates. It was found in this laboratory .that IIa-0 spectroscopic plates baked for 24 hours at 62,5°C wore considerably faster for long exposures than unbaked IIa-0 and 103a-0 plates, because of the reduction of the reciprocity law failure brought about by the baking process. Moreover, the IIa-0 plates have a better resolving power and better granularity than 103a-0 plates. However, at times, the baking process yielded plates with an extremely high and non-uniform fogged background. Under these conditions it was difficult to perform accurate calibrations for intensity. In addition, the cylindrical lens reduced the exposure times used in the final experiments to less than six hours. For these reasons 103a-0 plates, and when better resolution was necessary, unbaked IIa-0 plates were used extensively.

For frequency calibration, iron lines from a D.C. iron arc were superimposed on the bottom 0.4 mm of the Raman spectrum using the 20 micron slit width, no matter how wide the slit width used for recording the Raman spectrum.


This was done using the illumination control diaphragms to mask off all but one small corner of the grating (either the upper right or the lower left). The shift due to the nonbilateral closing of the slit was measured and found to be negligible in view of the broad features recorded in most spectra. It was less than 8 microns for the 100 micron slit, the most serious case, giving rise to an error of less than 0.1 cm *. This is comparable to the shifts at the spectrum ends due to the tilt of the spectral lines. When an accurate frequency determination of a sharp peak was necessary the 20 micron slit was used to record both the Raman and the calibration spectra.

The wavelengths of the iron lines were obtained from the values tabulated by Crosswhite (1958) for the region h300 - 4962 8 and from M.I.T. Wavelength Tables for the region 4962 - 5200 8. These wavelengths were converted to vacuum frequencies by the application of the dispersion formula of Edlen (1953).The values 24705.350 cm"1 and 22938.133 cm"1 were used for the vacuum frequencies of the Hg 4046,5630 and Hg 4358.3277 lines respectively.

The positions of the iron lines and Raman bands were measured from traces obtained with a Leeds and Northrup microphotometer. The chart positions were then calibrated by a fourth order least squares polynomial of the frequency shift as a function of the chart position.

Intensity calibrations were carried out on a Hilger E.l. glass prism spectrograph fitted with a stepped slit. The widths of the stepped slit were carefully measured yielding values some of which differed appreciably from the values used previously in this laboratory.

Light from a frosted 100 watt bulb was made to fall on the stepped slit after passing through two ground glass screens to produce a suitable intensity and a uniform illumination.


17

The continuous spectrum was recorded on a small piece of the same plate on which, simultaneously, thfe Raman spectrum was recorded. Care was taken to keep the two separate pieces under similar conditions at all times, particularly during development. This procedure minimized the time required for exposures which was a beneficial factor in these experiments.

The densities of the various steps of the spectrum corresponding to the different slit widths were recorded on the Leeds and Northrup microphotometer. A curve of Log (Density) vs Log (Slit-Width) was calculated by fitting the ten values so obtained to a third order polynomial using a least-squares routine on the IBM 7094.

The intensity profiles of the Raman bands were obtained from the microphotometer traces of the densities of the Raman spectrum by using a program which converted the densities to intensities and the chart positions to frequency shifts,The chart heights at given chart intervals were measured using a Benson-Lehner OSCAR model K Oscillograph Analyzer and Reader.The Intervals were chosen to make sure that they represented a distance on the plate less than the value of the slit width.Thus the resolution was kept limited by the spectral slit width. These chart heights were converted to relative intensities by using the third order polynomial calculated from the least squares analysis on stepped slit widths and corresponding densities. The frequency shifts of the chart positions at which chart height readings were made were calculated using a fourth order least squares polynomial obtained from the iron line calibration frequencies and chart positions. A graph of relative intensity against frequency shift was then produced by using the Calcomp Plotter connected with the IBM 7094 installation.

The spectra were reduced in the manner described above. Profiles of the various bands were then constructed using the

R e p ro d u c e d with permission of the copyright owner. Further reproduction prohibited without permission.

low exposures to obtain the peaks and high exposures to obtain the tails of the bands. Portions of the bands that were obscured by other features in one spectral region were obtained from the other spectral region, if possible.


19

CHAPTER III

LIQUID OXYGEN

A. INTRODUCTION

The research outlined in this chapter arises from the Investigation of molecular rotation in condensed phases.As outlined in Chapter I recent theoretical investigations by Gordon (1963, 1964a, 1964b) have provided a tool for analysing spectra in terms of the moments of their Intensity distributions and obtaining information about the intermolecular torques which affect the molecular rotation. Such theoretical analysis was not available for earlier studies of this problem (such as the investigation of. Crawford, Welsh and Harrold (1952) ). Moreover, it requires that the intensities be known to high accuracies, particularly in the tail ends of the spectral bands. Additional information on the molecular rotational motions, related to that obtained from nuclear spin relaxation experiments, can be determined from the Fourier transformation of the depolarized Raman bands (Gordon, 1965a, 1965b, 1966a).

In order to improve the accuracy of the available information a reinvestigation of the anisotropic scattering in the Raman spectrum of liquid oxygen was undertaken, essentially by the method used by Crawfdrd et al. It was hoped that with the equipment used in the present study the band profiles could be determined with sufficient accuracy to allow a moment analysis to be carried out. Liquid oxygen, rather than nitrogen, was chosen for this study because its spectrum, excited by Hg 4358 8, lay In a more suitable region of the spectrum. Moreover, Crawford et al have reported that the intensity of the anisotropically scattered Raman band in liquid oxygen Is more intense than the band in liquid nitrogen. However, this precluded comparison with nuclear spin measurements. A preliminary experiment on liquid carbon monoxide


20

indicated that the anisotropic scattering was too weak to be measured accurately under the present experimental conditions.

The values obtained for the mean squared intermolecular torque using the moment analysis was probably correct only in the order of magnitude, despite the improvement of the experimental results over past studies. Further improvement in the results can be achieved only by a different technique employing a laser source for excitation of the spectrum, together with the elimination of the isotropically scattered Q branch by the use of polarizers. Such experiments are presently under consideration.

B. EXPERIMENTAL PROCEDURE

The experiments on liquid oxygen were performed using U.S.P. grade oxygen obtained from the Linde Company. The major impurity was argon, which would solidify as small pellets and drop to the Raman tube window If the temperature was allowed to fall below -189° C.

The Raman tube used in these experiments was constructed from 17 mm o.d. Pyrex glass tubing and had an illuminated length of ll\. 0 cm corresponding approximately to the height of the spiral mercury arc. A cylindrical section of the Raman tube 13.4 mm in diameter was matched to the spectrograph with two lenses producing an 18 mm image on the slit and filling the aperture of the collimating mirror. This provided the maximum intensity gain possible with this cryostat and Raman tube. No scattered light from the walls of the Raman tube was allowed to enter the spectrograph and so the background was kept to a minimum.

The cryostat described in Chapter II was filled with liquid air at an Initial temperature not less than -l87°C. /


Since the boiling point of oxygen is -183°C, during the experiment, the temperature remained within 2° of -l85°C. Nitrogen gas, at approximately one atmosphere, was used as a heat exchanger within the experimental chamber. The oxygen gas at a pressure of about 500 mm of Hg was allowed to enter the Raman tube. It liquefied quite slowly^ until the level of the top of the liquid stood Just below the painted section of the tube. At this point liquefaction was halted, the discharge in the mercury arc lamp initiated and the alignment of the matching system and the Raman tube carried out. The top of the liquid in the Raman tube scattered light intensely so ' that a bright ring could be seen in the image of the Raman tubethrough the spectrograph optics. This bright ring madepossible a perfect alignment of the Raman tube with the spectro graph axis. After the alignment was carried out liquefaction was resumed and the Raman tube filled with liquid oxygen past the light trap. At this point exposures of the spectrum were begun.

Seventeen useful exposures were made of the Raman spectrum of the vibrational band of liquid 02 excited by Hg 4358 8. The various conditions under which these exposures were carried out are tabulated in Table 3*1. The numbering of the plates in this table indicates the chronological order in which the exposures were carried out.

C. RESULTS AND DISCUSSION

The spectrum of liquid oxygen exhibits a strong isotropic Q branch plus wings due to anisotropic Raman scattering (Crawford et al, 1952). The frequency and half width of the Q branch peak were determined in this study to be 1551.8^ *0.1- cm"1 and 0.44 * 0.03 cm""1, respectively.

The fifteen suitable plates were reduced as outlined in Chapter II with chart height readings taken at intervals of approximately one wavenumber. The spectrum produced by


TABLE 3.1

SUMMARY OF LIQUID OXYGEN SPECTROGRAMS

PLATENUMBER

SLITWIDTHS(microns)

EXPOSURETIME(minutes)

PLATETYPE

10 20 75(a) 103a011 20 360(a) 103a0

13 250 60 103a0m 250 60 103a015 250 60 103a021 250 60 103a022 250 60 Ila0(b)2k 250 90 103a026 250 90 103a027 • 250 90 103a028 250 90 103a017 250 120 103a018 250 120 103a025 250 120 103a020 250 120 Ila0(b)16 250 180 103a0 .23 250 180 103a0

(a) cylindrical lens not used(b) baked plate


this method, a sample of which is shown in Fig. 3.1 exhibits the strong Q branch, quite overexposed, plus the wings due to rotational 0 and S branches, and, as well, scattering in the emulsion and ghost structure. The structure evident in the background results from two different causes. The Hg lamp provides a continuum in this region which is Rayleigh scattered by the liquid oxygen. There is also "grass" arising primarily from the emulsion granularity. The features in the "grass" are comparable in magnitude to the intensity of the continuum features. The shape of these features is therefore difficult to determine with any accuracy, and consequently the background base line is difficult to fix without some ambiguity.

The following procedure was therefore adopted in order to obtain the profile of the anisotropic Raman scattered band. First the background base line was subtracted from the total intensity. To accomplish this a least squares second order curve was drawn through all the background points in the spectral regions 1130 cm-1- 1400 cm-1 and 1680 crrT1- 1890 cm""1 , taking care that those points which could definitely be ascribed to continuum features were not considered. This yielded a background base line curve as shown in Fig. 3.1.The background was subtracted from the total intensity and the resulting curve was normalized using the intensities of the Q branches excited by the satellite lines of Hg 4358 8, at 4348 8 and at 4339 8.

An average profile was then constructed from the profiles so obtained. The fit between this average profile and the individual profiles of the various plates was quite good in almost all the cases. In those cases where the fit was not so good the discrepancy could be ascribed to difficulties in the normalization procedure.

The isotropic scattering, the ghost structure, and the scattering in the emulsion were eliminated from the average


oo(M

•OCO

oCM

OoiH

AiLISN3J.NI 3AIJ.V33H

eoCOLTi<y~i•=rbOWOC£Ph

H&co>Hos.w£5O'wcc;ft.

nwE-<<

COo.J<ooscM6ccCOp-CM%IF■a;CF PIOO HIK ►-'•1EhO P!w c/:Ph •Hico m2 ; nph ««• •o>H b

p :o o

MmQ oH cCO moM>JP.OPIMPHoOh>HE-'MCOwEh2M

rH•

CO

hi)•HP.

Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.

profile by subtracting the properly normalized profile of the Rayleigh line under the assumption that the Q branch was the image of the Rayleigh line, broadened by the slit. This profile is illustrated in Pig. 3-2,

MOMENT ANALYSIS

The first four moments have been calculated for the profile obtained from the anisotropic scattering in liquid oxygen. The peak of the isotropically scattered Q branch was taken as the shifted band origin which is defined as the frequency of the J = 0 -► J = 0 transition. The procedure outlined in Chapter I for finding the shifted band origin could not be followed because the poorly defined scattering geometry does not allow the theoretical value of the first moment of a linear molecule to be calculated. The results of this moment analysis are tabulated in Table 3.2.

TABLE 3.2MOMENT ANALYSIS OP THE ANISOTROPIC BAND OP LIQUID OXYGENShifted Band Origin = 1551-9 cm-1Rotational constant, B = 1.M6 cm-1Average anisotropic band frequency = 1560.9 cm 1

M( 1) = 9.01 cm-1 M(3) - • 34 x 10** cm"3M(2) = 1.37 x 103 cm-2 M(*») * 6.51 x 106 cm”**M(2)/M(l) = 153 cm"1 2kT/hc = 122 cm"1< t 2 > = 8.13 x 10** cm-2 rad-2<02>1/2 = 12.7°

The expressions for the moments of a linear molecule have been given by Gordon (196-4a.) as

M ( 1 ) ■ l » B ( a „ - a ^ ) 2 M ( 2 ) “ 8B ( k T / h c ) ( a u - a ^ ) 2 M ( i ) ) « 256B 2 ( k T / h c ) 2 ( a |( —ot j_) 2 + 8B 2 ( a |( - a x ) 2< t 2 > ( 3 . 1 )


oor-H

OOin

EoEhPHHrew>HoP£3owPCPi

J<scoHEh<ccmMClPc:wE-'Eh<occ>-1<coHP.oc:EnOCOM£2<CW>~r-i*—<, EhP io PI c?

>1 PI X PJ oMPi o O M PC £3 CU O' M >< P3 EhEH £2 CO M £2W O Eh £2 12 < m re

OJonoHP.

AJiiSN ajiN i a A itiva a a

1

Reproduced with permission of the oop,right owner. Further reproduction prohibited without permission.

2k

In these expressions quantum corrections, rotational- vibrational interactions, and cross terms Implying correlations between different molecules have been neglected. All the symbols have their usual meanings in molecular physics, and <t2> is the mean squared torque. The constant of proportionality depends on the scattering geometry of the experiment and is the same for all the moments.

The mean squared torque is given by the ratio between the fourth and second moments,

M(4)/M(2) = 32kTB/hc + hcB/kT <t2> (3.?)

The value determined in this study on’ liquid oxygen is about 8 x 101* cm“2rad“2. An effective root mean square torsional oscillation amplitude can be defined through the relation

,„*,V4 . .-18,0 kT „ (3<r r h c < T2>1'/4

The magnitude of this amplitude in liquid oxygen is about 13°. Similar values of this torsional oscillation amplitude have been found in liquid benzene and in liquid and 8-solid CO (Gordon, 196^b). The variation with density of the mean squared torque in CO-He mixtures has been measured by Armstrong and Welsh (1965), who found that at a density of 800 Agt, comparable to the density of liquid 02, the mean squared torque is about 5 x 101* cm“2rad“2.

These results indicate that the rotational motion In liquid oxygen is highly hindered rather than free as was concluded by Crawford et al. Although the experimental data presented in this study are similar to the results of that investigation, the conclusion Is based on the moment analysis of the results, rather than on the shape of the band.


2 5

Prom the table it is evident that the experimental value of the ratio M(2)/M(l) does not agree well with its classical value, 2kT/hc. The reason for this discrepancy of about 25# is probably the experimental error. The value of the first moment, or the intensity-weighted average band frequency, depends primarily on the intensity distribution near the peak of the band. However, the intensity distribution of this part of the anisotropic band is not well established because of the overlapping isotropic Q branch, the ghost structure, and the. scattering in the emulsion. Moreover, one- quarter of the total anisotropic intensity is in the anisotropic component of the Q branch (Placzek and Teller, 1933).At liquid densities this component may be quite sharp changing the intensity distribution near the peak considerably, and hence, changing the average frequency. (Sharpening of the Q branch will, however, increase the discrepancy.) Fortunately, the dependence of the second and the fourth moments on this part of the band is not so critical. The error in the value of the mean squared torque obtained, which depends on the difference of two large, nearly equal terms, is estimated to be about 30$.

The effect of the rotation-vibration interaction has been neglected in this treatment of the moments, which have been calculated for a classical rigid rotator. This interaction is expected to change the frequencies, intensities, and the statistical averages of the rotational kinetic energies. Gordon has given expressions for the corrections due to the interaction; for liquid Og they are quite negligible (<0.05$).

At low temperatures the quantum corrections, which are inversely proportional to the temperature, may not be negligible. These corrections arise from the classical approximations made during the calculation of the moments, ,and amount to about 7$ for the M(2)/M(l) ratio and about 5$ for the M(;0/M(2) ratio in liquid 0^. They also may be neglected in

R e p r o d u c e d with permission of the copyright owner. Further reproduction prohibited without permission.

26

view of the accuracy to which these ratios have been determined in this experiment.

ROTATIONAL CORRELATION FUNCTION ANALYSIS

.Gordon (1965a, 1965b) has also shown how to recover information about the molecular motion itself from the spectral band shapes. By expressing the scattering cross section as a sum over final states of the matrix elements of the polarizability and applying the Heisenberg equation of motion, the cross section is obtained as an integral of a time developing operator. The cross section, or the measured intensity distribution, is then the Fourier transform of a correlation function, as given by the equation,

A*4 I(v) 1

| A*4 I(v)dv 2tband

where the intensity distribution has been normalized to unit integrated intensity.

For a linear diatomic molecule, such as 02, the correlation function, C(t), can be expressed as

<Tr 6v(0)-Bv(t)>---------------- e c dt (3J1)<Tr 6V(O)*0V(O)>

C(t) = <P2(uz(0).uz(t))> (3.5)

in the classical limit, where uz is the unit vector along the symmetry (z) axis of the molecule, and P2(x) = (3x2-l)/2.

The physical significance of the correlation function,Tr <6vC0)•0v(t)>, is the following. We consider the anisotropy of the polarizability of a particular molecule in a system of molecules in thermal equilibrium at a time t = 0.At a time t later the anisotropy is, in general, in a different direction given by B(t), because of the random thermal motion


of the molecule. We measure the projection of 0(t) on the original anisotropy, £(0), i.e. B(t)*0(O). This measurement is then averaged over all initial times t = 0 to yield the correlation function.

Such a Fourier analysis of a band shape allows the separation of the short and long time behaviour of the molecular motion. At short times the behaviour is displayed by considering the correlation function as a power series in the time. It is found that

\ <3(u(0).u(t))2-l> = 1 - M(2 )t2 + M( 4 )t + ___ (3.6)

where M(2), and M(4) are the second and fourth moments given above. The initial curvature of the correlation function classically depends only on the temperature and the molecular constants and not on the intermolecular forces. The intermolecular forces affect the correlation function through the terms in t**. The hindering of rotation increases the coefficient of t1* by an amount proportional to the mean squared torque which is necessarily positive. Thus the rotational correlation function lies above that for free molecules, and, at least Initially, the decay of the correlation function is slower for hindered rotors than for free rotors.

The correlation function calculated from the experiment ally obtained profile is Illustrated In Fig. 3.3. It is noted that the initial behaviour is similar to that expected for a freely rotating molecule. Departure from this behaviour begins at about 2.5 x 10~13 seconds; it is at this point that the intermolecular torques begin to act on themolecule, hindering its rotation. In the period from about

"•13 *"13 x 10 seconds to about 15 x 10 seconds the rotationalmotion has become so complicated by the intermolecular torques that the correlation function is approximated by a random exponential decay. The time constant of this decay is about

— 1 32.5 x 10 seconds. This time constant has been interpreted


C(t)

o.oi

0.001

PIG. 3.3. ROTATIONAL CORRELATION FUNCTION FOR'LIQUID OXYGEN. DASHED LINE INDICATES SLOPE OF EXPONENTIALLY DECAYING PART


by Gordon (1966a) as the average time between changes in the rotational motion of the molecule. Apparently the 02 molecules rotate freely for an average time 2.5 x 10-13 seconds before a "collision" changes the direction and rate of the rotation.

At the time 15 x 10~13 seconds the correlation function approaches zero rapidly and oscillates about that value with an amplitude which is negligible in terms of the experimental accuracy. At a time greater than

— 1 350 x 10 seconds the curves are no longer reliable because of the finite experimental spectral resolution.

The conclusion of this analysis on the anisotropicscattered Raman band in liquid O2 is that the rotationalmotion of the molecules is highly hindered so that theydescribe a libration with amplitude about 13°. The hindranceis caused by an intermolecular torque whose mean squared

2 2magnitude is about 8 x IQ1* cm" rad" , Apparently, the average time between the changes in the direction of the rotational angular momentum vector of the molecule is2.5 x 10~13 seconds.


29 \

CHAPTER IV

METHANE

A. INTRODUCTION

There has been some disagreement about the nature of the molecular rotational motion in liquid and solid methane. Crawford et al (1952) have stated that both the liquid and solid states exhibit almost free rotation. They based this conclusion on a comparison of the v3 band profile of liquid methane with the envelope obtained by broadening the discrete rotational lines of the freely rotating molecule to a half width of 55 cm *. However, Ewing (1964) has claimed that the v3 band in the liquid exhibits highly hindered rotation.

The analysis of the spectral bands using the band moments and the Fourier transform of the band intensity, as elucidated in the papers of Gordon cited above, promises to shed further light on these questions. A reinvestigation of the Raman spectra of the liquid and solid phases of methane was therefore undertaken in order to improve the accuracy of the information available.

B. EXPERIMENTAL PROCEDURE : LIQUID METHANE

The experiments on liquid methane were performed using the same cryostat and the same Raman tube as were used for liquid oxygen. The methane used was Research Grade with a purity of about 99.99 mol percent CHij obtained from Phillips Petroleum Company through Matheson of Canada, Ltd.

The methane was condensed and the lineup carried out in an exactly similar mariner to the procedure with liquid oxygen. Liquid air was used as coolant and dry nitrogen gas or helium gas used in the experimental chamber as a heat exchanger. With the lamp on, the temperature in the experimental chamber was -l8l * 3°C.


3 0

A number of exposures were taken with a filter to cut out Hg 4047 radiation as an exciting line. This allowed the profile of the v2 band to be measured. The filter was coiled into a cylinder and surrounded the Raman tube within the experimental chamber. Two different filters were used : a Kodak Wratten //2A gelatin filter, which transmits less than 0.1% at 4047 ft and about 805? at 4358 ft, and a Mylar "Greenhouse" Film filter which transmits approximately 1% at 4047 ft and 50% at 4358 ft. The Kodak §2k filter is far superior to the Mylar filter; however, it deteriorates and cracks easily and is difficult to obtain. The Mylar filter was used when a Kodak filter was not available.

The various conditions under which exposures on the Raman spectrum of liquid methane were carried out are tabulated in Table 4.1.

These plates were reduced according to the procedure outlined in Chapter II. In Fig. 4.1 is presented a typical reduced Intensity profile; this one is of Plate 11 and illustrates the spectral region 4525 ft - 4700 ft.

An intensity profile of the Raman spectrum of liquid methane was constructed from the various exposures, and is presented in Fig. 4.2(a). This illustrates approximately the intensity relationship between the various bands. It is not possible, however, to compare the vi band with the other bands because of its extremely high intensity.

C. EXPERIMENTAL PROCEDURE : SOLID METHANE

A Raman tube of similar dimensions to the one used in the liquid oxygen and liquid methane experiments, but with a small nucleation tip pulled out of the tube wall at the window (see Fig. 2.4b), was used in the experiments on solid methane.


TABLE 4.1

SUMMARY OF LIQUID METHANE SPECTROGRAMSr—

PLATENUMBER SPECTRAL REGION SLIT

WIDTH(n)

EXPOSURE TIME (min.)

PLATETYPE

51 5352 50

vi (4047) and

V! (4078)

20202050

180(a)180(a)240(a)90(a)

Ila0(b)Ila0(b)Ila0(b)Ila0(b)

22(c)232425

2 vit(4047) and low frequencies (400-1400 cm""0 excited by Hg 4358 A.

250500500500

307590

180

103a0103a0103a0103a0

2117 1112(c)181920

v3 (4047)

100 100 250 250 - 250 250 500

3075454575120

120

103a0103a0103a0103a0103a0103a0103a0

2829

high frequency tail of v3 (4047) and v2 band (4358)

500500 75180

103a0103a0

35 low frequencies (400 - 1400 cm"1)

500 75 103a0

657323334

v2 (4358)(exciting line Hg 4047 filtered out)

250100250500500500

45150909090

180

103a0103a0103a0103a0103a0103a0

3637404142 3938

*v3 (4358)

#

500500500500500500500

9090

120180240120240

103aJ103aJ103aJ103aJ103aJ103aJ103aJ

(a) cylindrical lens not used(b) baked plate(c) not reduced


o.o•=ror)

OOOJ00

o o • • o oo

o o ■ • CO

CM

oo■ - VO

CM

AJjISNSiLNI 3AI.LVT3H

0-■=ro•=rhO

OKEhPhHmCO>HowcywKpH

Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.

Fin. 4.1

INTENSITY

PROFILE

OF LIQUID

METH

ANE

SPECTROGRAM

§ 11

a

<s

PQ PQ

<N <N

cr

T)(M

X tsua ui 9AHBI3H

oVD

&H<ot—toCO

woCOccEH■a;DH£3o*

cti

WS<KEhWKEt,O‘T4£>KEhOWCL,CO.

C\J

csH

”Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

The cryostat was filled with liquid nitrogen to a point Just above the beginning of the light trap and was kept at this level throughout the whole experiment. It had been found that filling the entire cryostat with liquid nitrogen caused two different difficulties. First, the upper portion of the Raman tube, well above the heater, became too cold and solid methane condensed in the tube, often blocking it. Secondly, filling the cryostat with nitrogen decreased the temperature and hence the pressure inside the tube. When the pressure fell below the vapour pressure of liquid CH^ the liquid began to boil. The latent heat of vaporizationabstracted sufficient heat from the surface of the liquid tofreeze the top layer into a white snowy crust. When this top crust was formed conditions allowing vapour snake formation were present and these were observed.

The vapour snakes were similar to those reported for other substances by Phibbs and Schiff (19*19), Verschingel and Schiff (1955), as well as other investigators. The only difference was that the thin shell surrounding the initial vapour tubule would always break after the snake had propagated for a few seconds. At this point the tubule would rapidly fill with liquid and the snake would disappear almost instantly. After a short delay another snake would begin to propagate downward from the solid crust into the liquid. Within a minute of its formation, white "dendritic"solid would grow from its walls. If allowed to continue,the snake formation would ultimately form a network of tubules throughout the liquid.-

*

Solidification of this- type usually began inside the painted portion of the Raman tube and was not noted until it had grown down into the illuminated portion. Because the vapour snake often passed near or bounced off the clear solid portion, the snowlike growth from the walls of the tubules could take place beside the clear solid. Usually this snowlike portion would "eat" into the clear solid unless measures


32

were taken to halt this type of growth and the formation of vapour snakes.

Prevention of vapour snake formation was accomplished by keeping the level of the liquid nitrogen below the level of the liquid methane in the Raman tube. The heater, described more fully below, was constructed to ensure that the upper portion of the tube was kept sufficiently warm to maintain the methane liquid. In growing the crystal the heater was raised until the solid grew into the painted light trap portion.At this point the heater’s motion was stopped but the current kept on so that a liquid portion remained above the solid portion in the light trap.

The heater was constructed from copper-clad heating wire cable obtained from Pyrotenax Ltd. The copper cladding added weight to the heater and allowed the coils to be constructed easily and permanently. The heater wire was connected to the Fusite seal through enamelled copper wire which was covered with teflon spaghetti. The teflon spaghetti was necessary because it keeps its resiliance at lower temperatures, and this, together with the weight of the copper cladding on the cable, allowed the heater to move downward without sticking.The heater was raised and lowered by means of a fine brass chain connecting it to a pulley in the "head”. A brass chain was used because it was found that nylon, cotton, or silk cord changed in length in a non-elastic way when subjected to changes in temperature and pressure.

At the outset of the experiment, the heater was positioned about 2 cm above the Raman tube window. The cryostat was filled with liquid nitrogen to the proper height; research grade methane gas was then allowed to enter and condense in the Raman tube. With helium as a heat exchanger gas in the experimental chamber, liquefaction proceeded rapidly, and often the bottom portion began solidifying even before the liquefaction was complete. Liquefaction was


stopped just before the liquid level disappeared beyond the painted portion and the lineup described in Chapter III was carried out. The discharge was maintained in the mercury arc lamp and liquefaction was again allowed to proceed until the liquid level was above the light trap. Meanwhile, the methane solidified upward from the window. The current in the heater was then adjusted so that the interface level was just below the bottom heater coil, parallel to it (i.e. tipped with respect to the Raman tube window) and planar. Sufficient current was supplied to ensure that the upper portion remained liquid. The heater was then moved down the tube so that all the methane was liquefied. When the Raman tube was sufficiently filled with liquid methane, crystal growth began by slowly raising the heater at a rate of about 1.0 cm/hour. The interface was carefully watched throughout the growing period to make sure that it was kept perfectly plane. At times, small dips in the interface would occur; if growth was allowed to proceed, these dips would form a bubble. In this case, the solid would have to be melted down again and a somewhat slower growth rate used. Occasionally a dip in the Interface level would occur at a particular point no matter how many times or how slowly this portion was regrown. When this occured, the only thing that could be done was to allow the methane to evaporate, pump out the Raman tube completely, and begin again.

The heater was raised until the solid was grown well into the light trap. The heater motion was then stopped but the current maintained to keep a liquid portion at the top.

Twenty-six useful exposures were made on the Raman spectrum of solid CH^. The various conditions under which they were carried out are tabulated in Table A . 2.

The intensity profile of the Raman spectrum of solid methane was then constructed in a manner identical to that followed for the liquid. Rig. . 3 shows the intensity pi'^flle of a typical plate, //13, and Fig. '1.2(b) presents the Raman spectrum constructed from these intensity profiles.


TABLE 4.2

SUMMARY OF SOLID METHANE SPECTROGRAMS

NUMBER SPECTRAL REGION SLITWIDTH(w)

EXPOSURE TIME

(min.)PLATETYPE

102030313233

\>i (4047) andvi (4078)

202050505050

30(a)30(a)60(a)90(a)

120(a)120(a)

103a0103a0103a0103a0103a0103a0

16 6 ,

18 19 ■9

2 (4047) and low frequencies excited by Hg 4358 (0-300 cm-1) (

500500500500500,

75180180180360

103a0103a0103a0103a0103a0

31213 1514

v3 (4047)

250 • 500 500 500 500

3030303075

103a0103a0103a0103a0103a0

78

high frequency tail of v3 (4047) & v2 (4358)

500500

180360

103a0103a0

272829

v2 (4358)Hg 404? filtered out500500500

90180120

103aQ103a0Ila0(b)

212624 22 2325

v3 (4358)500500500500500500

90150270270360480

103aJ103aJ103aJ103aJ103aJ103aJ

(a) cylindrical lens not used(b) baked plate


ooCMon

ooocn

ooCOCM

OOVOCM

eo■=ro•=rtnoDCfc■ Eh PH MtcCO>Hoswr=>o*KKfo

WPs<WEhW oootH =te fOo sCO <£,

DCfin C5 O DC Eh Ow

M Wfe PhO CODC(C>HEhHCOswEh

mrbO•H

A iis N a jjN i aAiJiVasH

'R eproduced with permission of the copyright owner. Further reproduction prohibited without permission.

34

RESULTS AND DISCUSSIONS

The vl4 v2, and v3 fundamentals and the 2v2 and 2vi+ overtones in liquid and solid CHj( were observed in this study. The intensity distribution in the v2 band, which is very weak and broad, and is overlapped by other bands, could not be obtained with sufficient accuracy, and only qualitative results will be quoted for it.

The frequencies of the band origins in the three states of CHij are listed below. The gas values have been obtained from Thomas and Welsh (i960).

TABLE 4. 3

BAND ORIGIN FREQUENCIES IN CH/, (cm-1)

MODE GAS LIQUID SOLID

vi (Ax) 2916.7 2904.7 * 0.1 2904.05 * 0.06V3 (E) 3018.9 3007.4 * 0.5 3009.7 1 0.52 v 2 ( A ! ) 3065.8 3053.5 1 0.2 3050.0 * 0.22vi, (Aj ) 2573 * 1 2571 * 1

The band origins listed above are the peak frequencies of the sharp peaks, vi, 2v2 , and 2vi, . The band origin of the broad, triply degenerate v3 band is the shifted band origin determined from the moment analysis outlined below.

It is noted that the frequencies of the band origins all shift to lower values by about 12 cm 1 on liquefaction.A similar shift to lower frequency has been noted for the v2 band, as well. On solidification the band origins shift only slightly. The v3 vibration, however, shifts to higher frequencies, as does the v2 band, in contrast with the behaviour of the totally symmetric A^ peaks, which shift down slightly.


The widths at half intensity of the band have been determined from the appropriate spectrograms. In the gas the band has a half width of about 0„9 cm-1 (Thomas and Welsh, i960). This increases to about 2.84 * 0.01 cm-1 in the liquid, but on solidification a decrease of about 25% to 2.13 * 0.03 cm-1 takes place.

The shift of the Q branch frequency can be attributed to the vibrational perturbation by intermolecular forces at high densities; the effect has been discussed in detail for compressed, hydrogen by May, Varghese, Stryland, and Welsh (1964). This shift depends on the intermolecular distance, and there will be a statistical distribution in its value causing an increase in the Q branch width in the liquid. Because of the higher degree ordering in the solid state, the statistical scatter in the shifts would be expected to decrease. This qualitatively explains the decrease observed in the Q branch width on solidification.

The A^ component of the 2 v2 overtone, in Fermi degeneracy with v1, has been observed, as listed above. Thisband thus overlaps v3 and must be subtracted, as must the band, from the total intensity to obtain the profile of the v3 band. Both the A- and F2 components of the 2 vi, band in Fermi degeneracy with v* and v3, respectively, have been observed. As shown in Fig. 4.2(a) and (b) above, the latter component appears as a weak, broad band, with intensity maximum at approximately 2602 cm-1 in the liquid, and at 2599 cm-1 in the solid.

A very weak peak observed at 2764 cm”1 in the liquidand at 2760 in the solid has not been assigned.

Profiles of the v3 band in the liquid and solid phases were constructed by the method outlined in Chapter II, and are presented in Fig. 4.4. In these diagrams the intensities have been normalized to unit integrated intensity . A moment


(A)

w>M

(B)

2800 32003000FREQUENCY SHIFT (cm-1)

FIG. 4.4. PROFILES OF THE v3 BAND IN (A) LIQUID METHANE AND (B) SOLID METHANE


36

analysis has been carried out on the band profiles by the method outlined in Chapter III for the profile of the anisotropic Raman scattered band in liquid oxygen. The theoretical expressions for the moments of the completely depolarized vibrational bands of a tetrahedral molecule are given by Gordon (1966b) as

M(0) = 1M(1) = 6BM(2) = 12B(kT/hc)M(4) = 408 B2(kT/hc)2 + 8B2/(hc)2 <t 2> (4.1)

These formulae are valid in the classical limit and neglect the corrections for the rotation-vibration interaction.

From the above expressions one may form

M(4) - (17/6)(M(2))2 = 8B2/(hc)2 <t2> (4.2)

from which the mean squared torque, < t 2 > , may be calculated.

The results of this moment analysis on the V3 band are shown in Table 4.4. The values of the moments calculated from the band profiles depend strongly on the exact position for the background base line for the profiles. To test the accuracy of the moments obtained, calculations were made with the background base line in different possible positions.The uncertainty found in the second moment of the liquid profile was about 8$ of the value; in the solid profile the uncertainty was somewhat less than 5$. This increased to almost 30$ for the fourth moment in the liquid and about 15$ in the solid.

The mean squared torque is given by a relatively small difference, of the order of about 10$, between large terms,M(4) and (M(2))2. The difference is therefore of the same order as the error in the value of the terms themselves. Only an order of magnitude can, consequently, be properly ascertained


TABLE 4.4

MOMENT ANALYSIS OF THE v 3 BAND IN LIQUID AND SOLID METHANE

LIQUID SOLID

Average Frequency 3038.8 cm-1 3041.2 cm-1Band Origin 3007.4 cm"”1 3009*7 cm"1Band Maximum 3015 cm”1 3031 cm”1Half Intensity

width 110 cm”1 91 cm”1

M(1) 31.44 cm"1 31.44 cm”1M(2) ^5.0 x 102 cm”2 35.2 x 102 cm”2M(3) 36.8 x 106 cm”3 30.5 x 10u cm”3M(4) 60.7 x 10 cm”1* 43.9 x 10 cm”1*

M(2)/M(l) 143 * 10% cm”1 112 * 4% cm”12KT/hc 128 cm” 1 110 cm” 1<t2> 1.5 x 10** cm“2rad“2 4.0 x 101* cm”2rad‘

" Reproduced with permission of the copyright owner. Further reproduction prohibited without permission

37

for the mean squared torque. In order to obtain a torque with an error of *5$ the uncertainty in the second moment must not be more than about 1/H%. Such accuracy in the intensities cannot be achieved by present day experimental conditions.

Even though only an order of magnitude can be established for the mean squared torque, the values obtained follow the trend expected, and compare favourably with those calculated by Gordon (1966b) from the infrared results of Ewing (196*1) :2.2 x 101* cm 2rad 2 in the liquid, and 3*u x lO4 cm“2rad"~2 in the solid. Moreover, from the relatively good agreement between the ratio M(2)/M(l) and its theoretical value, we may conclude that the classical approximation and the neglect of the rotation vibration interaction and the Coriolls interaction are justified.

In addition to the recovery of information from the spectral band shapes regarding the Intermolecular forces and torques acting between molecules, Gordon (1965a, 1965b) has shown how to obtain information about the molecular motion itself.As outlined above (Chapter III), the Fourier transform of the depolarized part of a vibration - rotation Raman band of a

vlinear or a spherical top molecule can be interpreted as the correlation function

C(t) = Tr <gv (o) ■ (3v (t)> = <P2 (u(0)-u(t) ) > (*1.3)where Pp(x) is the Legendre polynomial, (3x2 - l)/2, and 0V is the polarizability tensor of the molecule.

The \>3 band in liquid and solid methane was Fourier analyzed and the resulting correlation functions are displayed in Fig. *1.5. The behaviour of the liquid correlation function is consistent with the behaviour described by Gordon (1965a) from the results of Crawford et al (1952). Initially the correlation function is similar to that •expected for a freely rotating molecule. After about 2 x 10“ 13 seconds the action of the intermolecular torques in hindering the rotation b'ecomcs


0.1 Liquid Solid

C(t)

0.01

o.ooi

Time (10 ",3 sec)

PIG. 4.5. ROTATIONAL RAMAN CORRELATION, FUNCTIONS IN LIQUID AND .SOLID METHANE


38\

evident. At longer times (i.e. greater than about 3 x 10“13 seconds) the rotational motion has become so complicated by the intermolecular torques that the correlation function exhibits approximately exponential decay. The time constant of the exponential decay is about 3.5 x 10“13 seconds, corresponding, in a simple physical picture to the average time between changes in the magnitude and orientation of the angular momentum vector of the molecule. The function drops rapidly to zero after about 7 x 10“13 seconds; this occurs within the time range that the correlation function retains its validity, as determined from the experimental resolution. Liquid methane, therefore, does not conform as well to the model of exponential decay as does liquid oxygen.

The behaviour of the correlation function in the soliddeparts even further from the exponential decay model, and theinterpretation of its behaviour is not as clear as that of theliquid. There is an initial free rotational period, displayed

— 1 3by both bands, lasting about 1.3 x 10 seconds. Following this, the decay can be described as exponential for only a short time, 0.5 x 10“13 seconds, if at all. The slope becomes very steep and the function becomes zero rapidly. Initially, however, the correlation function for the solid lies above that of the liquid, indicating that the mean squared torque for the solid is greater than that of the liquid, as expected.

This study has therefore confirmed the conclusion of earlier experiments (Savitsky and Hornig, 1962, and Ewing, 1964) that the molecular rotation in liquid and solid CHjj at temperatures near its freezing point is hindered. The magnitude of the barrier to rotation has been calculated to be about 125 and 200 cm-1/rad for the liquid and solid, respectively.


CHAPTER V

ETHYLENE

A. INTRODUCTION

Ethylene is a planar molecule of point group Spectroscopic investigations of the gaseous state have determined its structure and dimensions with reasonable assurance. There are twelve normal modes of vibration :3Ag, 2Blg» 1Bxu» 2B2u * and ^B3u * The £erade niodesare Raman-active, the ungerade modes, with the exception of Au, are infrared-active; the Ay mode is inactive in both.

In recent years the Investigation of the condensed phases of ethylene by infrared absorption techniques have begun to yield information on the molecular structure and on the intermolecular interactions in the liquid and solid. However, the Raman spectrum has been investigated only in the liquid state under relatively low dispersion. The principal deterrent to the study of the Raman speotrum of the solid has been the difficulty heretofore experienced in obtaining a suitable solid sample.

The method of growing molecular crystals outlined above was used to prepare a clear sample of solid ethyl'ene.The Raman spectra of liquid and solid ethylene were photographed and intensity profiles of the observed bands constructed.

B. EXPERIMENTAL PROCEDURE : LIQUID ETHYLENE

Research grade ethylene gas, nominal purity 99.9%, obtained from the Phillips Petroleum Co. through MatHeson of Canada, Ltd., was condensed according to procedures similar to those used with liquid oxygen and liquid methane. The only difference was that a small heater was necessary to keep the ethylene from solidifying. For this purpose, about 2 feet of enamelled heater wire about 0.025" in diameter were


40

coiled into a heater about 1" across. The coils were tied together with very fine wire and attached to enamelled copper wires which connected the heater to the Pusite seal in the cryostat head. The heater was placed on the inner cryostat window and a current of 0.25 amp was found sufficient to keep the ethylene liquid. The temperature at the window of the Raman tube beside the heater was -l60°C * 5°C, but this obviously varied up the length of the tube.

The exposures carried out on liquid ethylene are tabulated in Table 5.1. They were all taken with Kodak 103a-0 Spectroscopic Plates. Profiles were constructed according to the method outlined in Chapter II. These are presented In Fig. 5.1, below.

C. EXPERIMENTAL PROCEDURE : SOLID ETHYLENE

A clear crystal of solid ethylene proved to be difficult to grow. The Raman tube employed in the solid methane experiments, which had an i.d. of 14 mm, and an illuminated length of 14 cm, could not be used. In order to maintain a planar interface between the liquid and solid ethylene, the growth rate in this tube would have to be less than 0.5 mm/hour.This meant it would take almost three weeks to grow the entire crystal. The Raman tube actually used had an illuminated length of 66 mm and an i.d. of 8 mm (11 mm o.d. tubing). It was necessary to expose longer for equivalent intensities with this tube; however, the growth rate, 1.5 mm/hour, allowed the crystal to be prepared in little more than two days.

Once the crystal was grown, no changes in temperature could be tolerated, otherwise the crystal would crack and become snowlike. Thus it was necessary to use liquid nitrogen as the coolant. Moreover, it was not possible to raise the filter coil from around the Raman tube without cracking the crystal completely. Whether this was due to the change in the thermal conditions which resulted when the filter was


TABLE 5.1

SUMMARY OF THE LIQUID ETHYLENE SPECTROGRAMS


WIDTH(n)

EXPOSURE TIME (min.)

30 low frequency region 500 6026 excited by Hg 4358 500 6018 (25 - 1100 cm"1) 250 90

27 20 9028 covers spectral region 100 7225 (875 - 1800 cm"1) 250 6029 excited by Hg 4358 100 10822 500 60

13 20 4517 covers spectral regions 100 3010 (850 - 1800 cm"1) 20 18014 and (2625 - 3575 cm"1) 100 457 excited by Hg 4358 and 250 45

12 Hg 4047 respectively 250 4511 250 120


4-1

c

Bwoi

900 950^ Au .1250 140013501300

v) C 0) ojC£•r-»4->.3

• A

*l»w 2t1,IS75 1«00 1625 1650 1675 2625 2625 2850 2675

>s

30!>0

Frequency Shift (cm"’)3150310030002950

FIG. 5.1. RAMAN SPECTRUM OF LIQUID


removed, or to the inevitable jiggling of the Raman tube this process entailed, is unknown. Of course, it was necessary to keep the discharge in the mercury lamp on at all times' during growth.

Care had to be taken as well when the interface disappeared behind the painted portion of the Raman tube. Just before this point, the growth rate was reduced to about 0.5 mm/hr or less, otherwise the change in the thermal conditions could crack the crystal. Because of this possibility, steps were taken to ensure that some useful exposures could be made. The heater was wrapped in black paper which protruded just below the bottom coil. -The solid-liquid interface was maintained just inside'the black paper and the heater was raised until the interface was about to disappear inside the painted portion.A number of exposures were made at this point, and then the heater was raised again at this very slow rate. If the crystal did not crack further exposures were made. This procedure was successfully used in the final experiments,

The successful exposures are tabulated in Table 5.2.Both Kodak 103a-0 and IIa-0 spectroscopic plates were used. Profiles of the spectrum were constructed according to the method outlined in Chapter II and are presented in Fig. 5.2, below. Caution must be exercised in comparing the relative intensities of different bands in these profiles (Figs. 5.1 and 5.2).Three different exciting lines (Hg *10*47, *1078, and 4358) were used to obtain the profiles; moreover, the intensity ratio between different bands may be as high as 1000:1. Although some care was taken to preserve the proper intensity relationship between different bands in presenting the profiles, the accuracy in their relative intensities may not be better than an order of magnitude, particularly if the intensities of the two bands differ greatly.

D. RESULTS AND DISCUSSION

The features observed in the Raman spectra of liquidi


TABLE 5.2

SUMMARY OF SOLID ETHYLENE SPECTROGRAMS


WIDTH(m )

EXPOSURE TIME (mln.)

PLATETYPE

2(a) Low frequency regions 500 60 103a05 (0 - 960 cm"1) 100 300 103a0

1(a)4(a)3(a)

covers spectral region (875 - 1800 cm-1)

20100500

2406060

Ila0(b)Ila0(b)Ila0(b)

11 20 200 Ila0(b)9 covers spectral regions 20 480 JIaO7 850 - 1800 cm-1 and 100 90 Ila0(b)6 2625 - 3575 cm""1 100 120 103a010 100 240 Ila0(b)8 250 300 Ila0(b)

(a) filter used to cut out Hg 4047 exciting line(b) baked plate

Reproduced with permission of the copyright o w ner Further reproduction prohibited without permission

Relati

ve Intensity

Relative

Intensity

Relative

Intensity

Lattice Modes

100 200150 900 950 1000

140013001250 16001550 1650 17 00

2vW» 7 H *7

2600 2650 2900 2950 3000 3050 3100 3200

Frequency Shift (cm'1)

2 » W , ?

3250 3300

PIG. 5.2. RAMAN SPECTRUM OP SOLID


and solid ethylene are listed in Table 5.3, together with assignments and a short description where necessary. The assignments have been proposed on the basis of a comparison with the frequencies of the vibrational fundamentals in the gas (Feldman, Romanko, and Welsh, 1956). The frequencies of the Raman-active fundamental vibrations in all three phases are presented in Table 5 Jl.

LIQUID SPECTRUM

Five of the six Raman-active fundamentals have been definitely identified; it is difficult to ascertain whether the remaining fundamental, v6, has also been seen. It has been reported at 1236 cm-1 in the Raman spectrum of the liquid by Rank, Shull and Axford (1950) and at 1239 cm-1 in the infrared spectrum of the liquid by Brecher and Halford (1961). This position, when excited by Hg fl358 is almost exactly overlapped by the vi band excited by Hg 40^7. A small band was observed at 123$ cm""1 during long exposures with the 10147 ft exciting radiation filtered out by a Kodak Wratten §2k filter. However, whether this band is v6 or is some residual intensity of vi is not certain.

All the first overtones of the vibrational fundamentals are Raman-active in the free molecule; 2v2j 2^3, 2vio> ancl 2vj? fall in the spectral range examined in this study. Of these, all but 2v 3 have been identified at frequencies which are almost double the fundamental frequencies. The anharmonic shift in 2v 10 is negligible, but 2\>2 and 2vi2 display a negat'iv< anharmonic shift of about 8 cm 1. A weak band at 2630 cm 1 may be 2V3 but its anharmonic shift, -^8 cm- 1 , seems too high.

A number of weak bands have been ascribed to combination tones. However, the identifications are not positive and there may be more than one possibility in certain instance:;.

No infrared-active fundamentals were observed in the


TABLE5.3

OBSERVED FEATURES

LIQUID

941.5 m, bd

1238 w?

1339 vs, str.

1559.5 w

1615.5 vw ,1619.0 vs *

1657.5 w

2 616 w 2630 vw

2828 w, bd.

2866.5 m

2996 str.3004.5 vs

3073.5 s, bd.

IN THE RAMAN SPECTRA ETHYLENE (cm- 1)

SOLID40?80 s, bd

108 m936.8 w941.4 s ,949.6 m *

1331.2 vs, bd ,1348.0 vs, shp1382.0 vw.; str,

1597.7 m1602 vw1615.5 VS ,1621.5 VW t1628.0 vw

1647.5 vw ,1658.0 m i

2826.5 m, shp. {

2867.0 m, shp. 2947 vw

2997.0 vs3000.5 str. ,3005.5 str.3015.0 vw3061.0 w, str.3064.0 w, str.3067.3 vs ,3068.8 m, str:

OF LIQUID AND SOLID

ASSIGNMENTlattice modeB 3g lattice modelattice mode ve (isotope)

v8(^2g)

vg (Big)?

v 3

(vi~v2)? v2 (isotope)

v 2 (Ag )

2vj 0 (Ag)

2v10+ v8 (B^)??

2 7 + v 3 (B 3g) ? or

v 2 + v g (Blg)?

2vi2 (Ag)V 4 + V 7 + V g ( A g ) ?

vi (Ag)

V 5 (Big)


TABLE 5.3 (cont.)

L I Q U I D S O L I D

3282.0 v w 3286 v v w '} 3291 v v w

v s v e r y s t r o n g v w

s s t r o n g b d

m m e d i u m s h p

w w e a k s t r

A S S I G N M E N T

v i O v 2 ( A g ) ?

v e r y w e a k

b r o a d

s h a r p

s t r u c t u r e


T A B L E 5 . 4

RAMAN-ACTIVE VIBRATIONAL FUNDAMENTALS OF ETHYLENE

GAS LIQUID SOLIDFREQUENCY FREQUENCY FREQUENCY1

( c m - 1 ) ( c m - 1 ) ( c m - 1 )

MODE SPECIES DESCRIPTION nn^ t,rW v*

v i A C - H s t r e t c h 3 0 2 6 - . 4 3 0 0 4 . 5 2 9 9 7 . 0 3 0 0 0 . 51 S

v 2 A C - C s t r e t c h 1 6 2 2 , 9 1 6 1 9 . 0 1 6 1 5 . 5 1 6 2 1 . 5g

v 3 A C I I n d e f o r m a t i o n 1 3 4 2 . 2 1 3 3 9 . 0 1 3 3 1 . 2 1 3 4 8 . 0d E 2

vk B C-H stretch 3102.5 3073.5 3067.3 3069.3 lg

1236?vc Bi CH0 rock

6 2 1239(IR) 1222(IR)

v8 B 2 C H 2 w a g 9 5 0 9 4 1 . 5 9 4 1 . 4 9 4 9 * 6

X# T h e f u n d a m e n t a l s h a v e t w o c o m p o n e n t s I n t h e s o l i d a s e x p l a i n e d

i n t h e t e x t ( p . 4 5 ) .


'13

Raman effect despite the fact that the selection rules for a free molecule are relaxed in a liquid (Halford, 1946).This is in contradistinction to the infrared spectrum of the liquid in which Raman-active gerade fundamentals were observed by Drecher and Halford (1061).

The frequencies of the observed fundamentals all decreased with liquefaction. The largest shifts, about 25 cm *, occur in the and \>5 fundamentals; they are mainly C-H stretching vibrations. Shifts of about 5 cm-1 are observed in v2, V3, and vg. These vibrations involve C=C band stretches or IICH angle deformations. Most ungerade modes observed in the infrared conform to these observations.The exceptions are V7, an out-of-plane CHg wag, which shifts to slightly higher frequencies with liquefaction, and vl b a C-H bond stretching vibration, which shifts by only 6 cm-1.

The v 1 and V 3 bands in the liquid exhibit some structurewith the appearance of weak, unresolved components. Thestructure cannot be ascribed to the isotopic molecule,

12 13H^C =C I^; either intensity or frequency shift considerations exclude this possibility. Other possibilities, such as accidental overlapping with fundamentals excited by other Ilg exciting lines, or infrared-active fundamentals, can be quickly ruled out. It is noted that the frequencies of the weak, unresolved peaks, at 2996 cm-1 in the vj band and at 1332 cm-1 in the v2 band, correspond to the frequenciesof the most intense components of these bands in the solid.On closer examination, indications of weak auxiliary peaks at 1348 cm-1 in the V3 band and at 1616 cm-1 in the v2 bandare evident. Similar peaks at 3067 cm 1 in the V5 bandand at 9'll cm-1 in the vg band" cannot be resolved because the frequency shifts from the liquid fundamental peaks are too small.

The solidification of ethylene without careful control of the temperature gradient gives rise to snowlike, solid


material. This would reflect light intensely, so that a strong background due to the parasitic light would be present in the spectrum. No such background was evident in the liquid spectra obtained, nor was any solid visually detected in the sample during the exposures. Moreover, the temperature at the Raman tube window was kept above the melting point of solid ethylene. There is the possibility that the liquid in the upper portions of the sample were supercooled, because the temperature did decrease up the length of the tube. In this connection it is of interest to note that there is both a melting point, -l69°C, and a freezing point, -l8l°C, listed for ethylene in some tables (i.e. the 38th edition of the Handbook of Physics and Chemistry) Thus the appearance of low Intensity solid fundamentals in the spectrum of the liquid cannot be due to,the presence of any solid in the sample. However, portions of the liquid may have been at temperatures which are below the melting point of ethylene.

It is proposed that the vibrational fundamentals of the solid are weakly active in the spectrum of the liquid at this temperature. They can be observed in the Raman effect because the gerade vibrational bands are much sharper than the ungerade bands observed in the infrared. Brecher and Halford (1961) have, however, reported components located near the v6 an^ vii bands observed in the infrared in the liquid. They suggest that these bands are associated with the persistence of Uquasi-lattice" modes in the liquid just above the melting point. There must, therefore, be some short-range order in the liquid at this temperature to account for the presence of both "quasi-lattice" modes and solid fundamentals. Such order has been postulated for other liquids notably water.

SOLID SPECTRUM

Some dramatic changes are evident when the spectrum


JI5

of solid ethylene is compared with the spectrum of the liquid. The bands are all narrower than in the liquid; some have halfintensity widths of less than 1 cm As expected, thevibrational fundamentals exhibit factor group splitting due to the unit cell structure. There are two molecules per unit cell and a vibrational mode in one molecule can couple, through the intermolecular potential, with the same mode in the other molecule. The two vibrations must be in phase or exactly 180° out-of-phase with one another in order to produce spectral activity. Thus the vibrational fundamental of a crystal containing two molecules per unit cell will split into two components. In solid ethylene the splitting is most prominent in v3 and vg, but on closer examination evidence of it may be found in Vi, v2, and V5, as shown in Figs. 5.3, 5.,l, 5.5, 5.6,and 5.7. In addition to the factor group splitting some low

10 12intensity structure, not due to the HgC J=C molecule, is associated with the vj, v2, V5, 2v10, 2v3, 2viq + v3, and 2v10 + v2 bands. In the overtones and the combination bands the structure Is most likely due to the lifting of the degeneracies of the symmetry species. In the v2 and V5 fundamentals this structure is very weak compared to the main band. However, the V! band is composed of at least three components and the third component cannot be accounted for.

The presence of the v6 band in the solid could not be conclusively determined for the same reasons outlined in the liquid case. The first overtones, 2v2, 2vi0, and 2v12 have been observed in the solid state, as have certain bands which are again ascribed to combination tones. One of these, at 1382 cm-1, is of particular interest because it has the same appearance as the vj band and is found at exactly the vi-v2 difference frequency. Its relative intensity with respect to the v2 fundamental is of the order of 1:500 and a process which would give rise to such a band with this high intensity is difficult to visualize.

Two intense bands are noted at low frequencies with maxima at 80 cm-1 and at 108 cm"1. There may be another


2 9 8 8 2 9 9 2 2996 3000 3004 3000

Frequency S h ift (cm-1)

PIG. 5.3. THE v! VIBRATIONAL BAND IN SOLID


Rel

ativ

e In

ten

sity

S''1-it

«

1610 1615 1620 1625Frequency S h ift (cm*1)

PIG. 5.M'. THE v2 VIBRATIONAL BAND IN SOLID C2Uk


1320

Fin. 5.5

I _________ I________________I___1330 1340 1350

Frequency Shift (cm*1)1360

THE v 3 VIBRATIONAL BAND IN SOLID


lission of the

copyright ow

ner. Further

reproduction prohibited

without

permission.

73CD-ooQ.CoCDQ.

"OCD

3060 3065 3070Frequency Shift (cm"')

3075

PIG. 5.6. THE v5 VIBRATIONAL BAND IN SOLID CgH^

935 940 945 950Frequency Shift (cm*1)

PIG. 5-7. THE v8 VIBRATIONAL BAND IN SOLID


peak at about *t0 cm 1 but this cannot be decided unequivocally because there is too much ghost structure in this region close to the exciting line. The peak at 80 cm"1 is the more intense and is quite broad compared to the other features in the spectrum of the solid; its half intensity width is approximately 20 cm *. Any comparison with the intensity of the other bands in the solid is not possible. The spectra were recorded with an interference filter in front of the slit of the spectrograph. In the lattice vibration region the absorption of the filter is very high, and is changing rapidly. Moreover, the amount of absorption at a particular wavelength depends critically on the orientation of the filter with respect to the spectrograph axis. Despite the difficulty of estimation it is probably safe to say that these bands were at least as intense as the most intense vibrational fundamentals.

Brecher and Halford (1961) have observed gerade lattice modes at 17 cm-1 and at 7*1 cm"1. These lattice modes are rotatory in origin and represent librations about the molecular figure axis and perpendicular to it. Dows (1962) using the intermolecular hydrogen repulsion potential discussed below has found approximate calculated frequencies for these torsional motions of 90 cm"1 about the figure axis, and *10 cm"1 perpendicular to it. In view of these results it seems likely to ascribe the 80 cm"1 band to the libration about the molecular figure axis.

CRYSTAL STRUCTURE

The crystal structure of ethylene was first studied by Bunn (19*1*1) using single crystal X-ray diffraction. He determined the unit cell to be orthorhombic with the following lattice parameters :

a = *1.87 8 , b = 6.U6 8 , c = *».l*t 8


at -175°C. Each unit cell contained two molecules, one at the cell origin and one at the body center. He was able to determine the carbon positions with certainty, but could not determine the hydrogen atom locations. The carbon- carbon axis is parallel to the ab plane and makes an angle of about 37° with the a axis. The two molecules are tilted in opposite directions around the c axis, making the unit cell primitive. Bunn assumed that the hydrogen atoms were located in a plane containing the £ axis, thus preserving the symmetry of the carbon lattice.

Brecher and Halford (1961) pointed out that the hydrogen configuration proposed by Bunn does not agree with the observed infrared spectra. They, show that a rotation of the plane of the molecules about the C=C axis so that the plane of each molecule is perpendicular to a body diagonal produces a reasonable structure in agreement with the spectroscopic evidence. This structure is no longer truly orthorhombic; ' it is monoclinic with the angle 3 accidentally 90°. Dows (1962) has pointed out that this rotation can yield one of two different space groups, depending on its sense. The two possibilities are designated the a axis case and the b axis case by Dows, to indicate which of the twofold screw axes is left in the resultant structure. Fig. 5.8(b) and (c) show the projections on the ab plane of these two structures.

Dows then attempts to decide between the two cases on the basis of an analysis of the frequency splitting, observed in the infrared spectrum of the solid, using harmonic vibrational coupling theory.

Dows carried out this analysis using both a dipole- dipole interaction potential and a hydrogen repulsion interaction of the form b exp(-ar). His conclusion was that the major cause of band splitting is hydrogen repulsion and that the values of the second derivative of the hydrogen repulsion


<x

FIG. 5.8(a)STRUCTURE OF THE C?Hif MOLECULE SHOWING PARAMETERS USED IN COUPLING CALCULATION '

(bPROJECTION ON ab PLANE OF a-AXIS CRYSTAL STRUCTURE(c)PROJECTION ON ab PLANE OF b-AXIS CRYSTAL STRUCTURE

(AFTER DOWS, HJ62)


4 8

potentials obtained for the two different types of possible crystal structure are :

a axis case |3q = 1100 * 180 dynes/cm

b axis case 8b = 650 1 300 dynes/cm,

where 8 = 32V/3r2.

On the basis of the spread of the standard errors Dows concluded that the a axis is probably a reasonableapproximation to the structure of the ethylene crystal.The value of the second derivative. S., compares favourably

ci *with the value of 1400 d/cm calculated on the basis of a potential derived by de Doer (1942)

„ ' 2.78 e2 / O r , / SV = exp(-l. 87 r/aQ )ao

= 1.20 x, 10"10 exp(-3.52 x 108 r) ergs.This formula, or the formula,

V = 1.44 r~6,18,derived by Amdur, Longmire, and Mason (1961) from scattering experiments, fit equally well the experimental points for 8 obtained at other H...H distances by Snyder (1961) and Dows (1961) in the range between 2.5 and 3*0 ft.

A similar analysis, assuming a hydrogen repulsion potential, was carried out for the Raman active fundamentals. The values of the second derivative of the potentials were calculated from the formula for the frequency splitting, Av>c,

Av>c = ( 1/u 2 C 2 Vq ) 8 ( 3r/8Qj ) ( 8r/DQj j)

where R is the second derivative of the interaction potential between the relevant contacting H atoms in the two molecules, I arid II, of the unit cell, vD is the gas phase frequency of


*19

the particular fundamental, and the partial derivatives are the changes in the IT...II distances with the normal coordinate in each molecule.

The derivatives in the frequency splitting equation were obtained by the calculations outlined in Appendix I. Using the values tabulated in Appendix Table A.6, the calculated values of A',c/R were obtained for each of the two types of the crystal structure and are listed in Table 5.5. The second derivatives, calculated on the basis of the observed splittings, are tabulated in Table 5.6. The average values obtained are :

a axis case B = 1900. ± 1000 d/cm ,““ a

b axis case 3b = 960 ± 320 d/cm .

In this case the b axis values are clearly more consistent with one another. The value of 3 obtained is quite reasonable. In fact, it coincides quite closely with the value obtained by Dows for the a axis case, 980 * 150 d/cm, when he arbitrarily excludes the V7 splittings as being influenced by dipole-dipole interactions.

It is not unreasonable to assume that both crystal structures are possible and that the particular structure obtained depends on the method of crystallization. The infrared spectra were obtained on crystals prepared by vacuum sublimation, whereas the Raman spectra were obtained on samples crystallized from the melt. Different structures in solid formic acid arising from these two different methods of crystalization have been demonstrated by Mikawa, Jakobsen, and Brasch (1966). In this case the point group, i.e. the lattice structure, was the same for both forms but the orientation of the molecules differed, as in the two ethylene structures.


TABLE, 5.5

CALCULATED VALUES OF Avg/B

MODE A 3 (a axis) Avc/3 (b axis)(ore-1 cm-1 x 103) (erg-1 cm 1 x 10 3)

v 1 U l 5 A. 07V2 2.53 12.85v 3 13.69 19.86\>s 2.0*1 4.856 1.98 13.88

2*1.72 6.23

TABLE 5.6

CALCULATED VALUES OF 3

MODE OBSERVED SPLITTINGS (cm 1)

CALCULATED(d/cm) 0a CALCULATf

(d/cin)

vl 3.5 2*110 260

(8.5)* (5860) (2080)

v2 6.0 2370 '170

v 3 16.8 1227 850

v 5 1.7 835 30 0

8.2 332 ] 3 1 5

" Not included in calculation


CHAPTER VI

SOLID FORMIC ACID

A. INTRODUCTION

There is experimental evidence which indicates that molecules of formic acid in all three phases are associated through hydrogen bonds. In the solid the bonding polymerize the molecules into long chains. Because of the comparative structural simplicity of formic acid a number of spectroscopi investigations of the solid phase have been carried out. Despite these studies the low frequency vibrational spectrum has not yet been adequately explained.

The low frequency spectrum was first recorded in the Raman effect under low dispersion by Gross and Valkov (19^9). A re-investigation of the spectrum at high dispersion was undertaken in this laboratory (Blumenfeld, 1961); this gave results which cast doubt on the explanation Gross and Valkov gave for the origin of the observed spectrum. Recently, Carlson, Witkowski, and Pately (1966) and Jakobsen, Mikawa, and Brasch (1967) have studied the low frequency spectrum of the crystals in the infrared and have suggested different explanations for its origin.

This study was undertaken to elucidate the results of the preliminary investigation referred to above. The Raman spectrum of solid HCOOH at -10°C and at -100°C and the spectrum of liquid HCOOH at 0°C were recorded by the author.A similar study of the spectrum of HCOOD including the spectrum of liquid HCOOH and HCOOD at 85°C was carried out together with II. Past. The results obtained are all incorporated in this report. Probable assignments of the bands observed in terms of the normal modes of a vibrating chain with the required symmetry are suggested.


B. EXPERIMENTAL PROCEDURE

The experiment consisted in growing a clear sample of crystalline formic acid and recording its low frequency spectrum in the Raman effect. The procedure for preparing the solid is a modification of the method described above for growing methane and ethylene crystals. The spectrum was recorded using the high dispersion echelle grating during a period when it was not being used for experiments on low pressure molecular gases.

PREPARATION OF THE FORMIC ACID CRYSTALS

The procedure for obtaining relatively large samples of formic acid solid free from defects which would give rise to parasitic light in the cone of observation of the scattered light differed somewhat from the procedure used for the lower temperature crystals, primarily because of the different temperature at which the crystals were grown.

The HCOOH used was Analar grade, obtained from British Drug Houses, or C.P. grade, obtained from Allied Chemicals. The minimum percentage of HCOOH was 9 8%; the major Impurity was acetic acid. The HCOOD used was obtained from Stohler Isotope Chemicals and was 9 8% formic acid with a deuterium content of abdut 92.%.

The formic acid was not processed further except to degas it; previous experiments had shown that this would reduce the tendency to form bubbles of gas in the solid.The apparatus used to degas the sample was adapted from a similar apparatus described by Smaller and Matheson (1955). The liquid formic acid was frozen, the system evacuated, and the acid allowed to reliquify. The cycle was repeated at least five times; the correct amount of formic acid was then distilled into the Raman tubes and the tubes sealed off.


The Raman tubes were made of 1*1 mm o.d. Pyrex glass tubing with a polished Pyrex window fused at one end.Two different illuminated lengths were used : 10 cm for the HCOOH experiments and 5 cm for the HCOOD experiments.A nucleating tip was used on the tubes of HCOOD to ensure that nucleation began at only one point, as in the methane and ethylene experiments. The absence of a tip in the HCOOH experiments did not seem to affect the clarity of the crystal provided that the growth rate was extremely slow initially. The tubes contained an S-shaped light trap, and all but the illuminated portion was painted a flat black.

To grow the solid, the Raman tube containing the liquid formic acid was suspended inside a clear dewar flask kept in a refrigerator maintained at -10°C, about 18 degrees below the melting point of formic acid. A cylindrical heater, similar to the heater used in the growth of the methane and ethylene crystals, encircled the Raman tube.The heater dissipated about 2 watts and maintained the formic acid above the interface liquid. As with ethylene the solid liquid interface was tilted to ensure growth of the crystal in one direction at the window and thus to eliminate the central fault. The heater was raised slowly, not faster than 0.5 mm/hour, after the initial nucleation, in order to obtain a suitable crystal. With care a clear solid sample showing no evidence of bubbles, cracks, or crystalline boundaries could be grown.

After the solid was grown the Raman tube was transferred to a cryostat for the recording of the spectrum.This cryostat was of conventional design; a simple Pyrex glass cylindrical dewar with two polished flat windows fused at the bottom, surrounded by a cold water jacket.The desired temperature was maintained by bubbling dry nitrogen gas through liquid nitrogen, thence out through small holes in a copper tube placed inside the cryostat.The temperature was maintained by regulating the pressure


of the dry nitrogen; it could be kept constant for periods as long as forty hours.

RECORDING THE SPECTRUM OF SOLID FORMIC ACID

The spectrum was excited by a spiral mercury lamp with water cooled electrodes operating at about 13 amp.It was recorded using the echelle grating commonly used for the Raman effect of low pressure molecular gases in this laboratory. This instrument is used with a double prism monochromator to prevent the overlapping of orders, as has been described by Lepard (1964). The grating is blazed so that in the 56th order the blaze wavelength, *B, is 4360.87 8.The grating was moved slightly off its blaze angle and used in the 55th order where = 4440.16 8. It was found that this setting gave the best intensity in the region of interest, particularly around 200 cm-1 from Jig 4358 8. The reciprocal linear dispersion at 4360 8 is 3.B cm-1/mm.

Exposures were taken with spectral slit widths of 0.5 and 0.3 cm-1; the latter slit widths allowed accurate intensity profiles of the spectrum to be recorded to within 45 cm-1 of the exciting line, provided the monochromator band pass slit was adjusted properly.

Kodak 103a0 plates were used instead of the usually superior baked IlaO plates because the backgrounds in the IlaO plates available at the time were spotty and non-uniform.The spectra of HCOOD were recorded on unbaked IlaO plates.

After the apparatus was aligned and adjusted a number of spectrograms for each solid were recorded at -10 C.When these were completed the temperature was lowered to -100 C and a further exposure carried out. This process cracked the crystal severely increasing the resulting background 1 ritensity.


Microphotometer traces of the spectra recorded on the photographic plates were then calibrated for frequency and intensity by the method outlined in Chapter II. Representative intensity profiles of the spectrum of HCOOH and HCOOD recorded at -10°C and at -100°C are presented in Fig. 6.1.

Spectra of the liquid at 0°C and at 85°C were recorded using Raman tubes identical to the ones used in the solid experiments. For 0°C the experimental conditions were similar to those described for the solid, except that the formic acid was maintained as a supercooled liquid during the exposure. The 85°C exposure was carried out by suspending the Raman tube within the mercury'arc without the cryostat. The temperature was maintained to within ± 5°C by blowing a stream of air across the tube.

The microdensitometer traces of the spectrograms of liquid HCOOH and HCOOD are shown in Fig. 6.2. Since the densities of the photographic plates fell on the linear portion of the characteristic curve, these curves may be regarded as intensity vs. frequency profiles.

C. RESULTS

Two broad bands were revealed in the Raman spectrum of the liquid formic acids obtained in this study. The lower frequency peak at 82 cm-1 is the more intense and does not shift significantly with change in temperature or with deuteration. The second band is quite broad, and the frequency of the peak shifts to lower values with increasing temperature and with deuteration. In HCOOH it appears at 200 cm-1 at 0°C and at about 185 cm-1 at 85°C. In HC O O D

the peak is at 185 cm"1 and at 163 cm-1 for the low and high temperature spectra, respectively. According to Jakobm et al (1967) bands of this nature are characteristic of the


Rel

ativ

e In

ten

sity

HCOOD-10°C

HCOOD-lOO'c

HCOOH-10°c

250200100Frequency S h ift (c m 1)

FIG. 6.1. LOW FREQUENCY RAMAN SPECTRA OF CRYSTALLINE FORMIC ACIDS

Reproduced with permission of the copyright owner. Further reproduction prohibited without permiss.on

HCOOD 0*C

HCOOH 0°C

too 200Frequency Shift icm*')

300 4 0 0

PIG. 6.2. LOW FREQUENCY RAMAN SPECTRA OF LIQUID FORMIC ACIDS


spectra observed in liquids of molecules Joined by hydrogen bonds in polymeric chains.

The Raman spectra of solid HCOOH and solid HCOOD observed at -10°C and at -100°C were similar. Six main bands were observed, three in the frequency region 50 cm-1 to 125 cm-1 and three in the region 200 cm-1 to 270 cm-1.The latter three correspond to the "triplet" band observed by Gross (1959). The lowest frequency band at about 60 cm-1 was split into two peaks separated by about 3 cm”1 at -10°C. At-100°C the peaks were separated by about 1 cm-1; however they were narrower and so the splitting was more evident.The intensity of this band was much greater than the intensities of the other bands by about a factor of ten. The exact relationship of the intensities could not be determined accurately in the low temperature spectra.

There was indication of some structure in the l80- 200 cm""1 region. This appeared as a very low intensity band with a peak at about 186 cm”1 and another peak at about 200 cm”1. The noise level in the low temperature spectrograms was too high to determine unequivocally whether or not a similar structure was present; however the feature at 200 cm”1 was apparently there.

It should be noted that the initial band of the higher frequency triplet, at about 225 cm *, has a distinctly different appearance from the other bands. It is much broader and shows some evidence of auxiliary peaks, particularly at low temperatures. As indicated in Table 6.2, or in the spectrograms, there is a main peak at 230 cm 1 in solid HCOOH (225 cm” 1 in solid HCOOD) with another peak about 9 cm”1 lower in frequency.

D. DISCUSSION

In their investigation of the low frequency Raman


spectrum of solid HCOOH, Gross and Valkov (19*19) observed a number of lines at 57, 82, 117, and 1*10 cm-1 which they associated with the intermolecular crystal vibrations. They also observed a group of three intense lines with weaker lower frequency lines situated close to them. Assuming that the molecules were associated as dimers in the solid state, they interpreted these lines, at 255, 235, 212, 19*1, 180, and 170 cm as the vibrational spectrum of the hydrogen bond.The succession of the frequencies and the distribution of intensities they claimed was consistent with the fundamental and "hot band" transitions of an oscillator with a highly anharmonic potential curve. Thus, in their scheme, the line at 255 cm” represents the fundamental vibration of the hydrogen bond, and the lower frequency lines represent the "hot band" transitions between adjacent levels with successively lower frequencies because of the great anharmonicity of the potential.

That Gross's hypothesis regarding the origin of the triplet band is untenable is indicated by the results of this study. It is immediately obvious from an examination of the profile in Pig.6.1 that the relative integrated intensitie do not follow a 1:1/2:1/5 ratio at -10°C nor a 1:1/5:1/20 ratio at -100°C as is theoretically predicted according to his scheme. As has been suggested earlier (Blumenfeld, (1961) ) the triplet band and other observed bands must rather be different modes of vibration of the hydrogen bonded polymer chain.

A number of infrared studies on the low frequencies of solid formic acid have recently been reported (Carlson et al, 1966; Jakobsen et al, 1967). The frequencies observed in these studies are collected in Table 6.1.

Carlson et al (1966) have interpreted the three bands they observed at 283, 232, and 203 cm-1 as the in-plane hydrogen bond stretching mode, analogous to the dimer infrared active


TABLE 6.1

OBSERVED INFRARED FREQUENCIES

SOLID FORMIC ACID

HCOOH HCOOD DCOOHa b c d _b_____d________d

277 261 239

225 228 229 218

197

(a) Miyazawa and Pitzer, 1959.(b) Carlson et al, 1966.(c) Jakobsen et al (1967) - « form(d) Jakobsen et al (1967) - 3 form


283 280 271

227 232 " 239 232

203 200

92 88

DCOODa

mode, V3, (see Fig. 6.3), split by interactions with neighbouring molecules. They suggest that the Raman lines observed are in fact due to the lattice modes.

Jakobsen et al (1967) point out that j.c is unlikely that the three bands observed by Carlson et al are due to splitting by the intermolecular crystal potential because the shifts experienced by each band on deuteration are different. Instead, they suggest that the three bands correspond to different modes of vibration of the polymer chain. These modes are analogous to the normal modes of the dimer which are illustrated in Fig. 6.3. Using the deuteration shifts experienced by the fundamental modes in the dimer they have assigned the three bands as follows :1) an out-of-plane mode, similar to the infrared

inactive mode, v6, at 260 cm-1 in the dimer,2) an in-plane mode, similar to the infrared active

mode, v3, at 248 cm- in the dimer, and3) an out-of-plane mode, similar to the infrared active

mode, at 167 cm-1 in the dimer.

They also assign the band at 90 cm-1, not observed by Carlson, to the twisting mode analogous to v5 at 68 cm 1 in the dimer.

In addition these authors have demonstrated that the formic acid chains can exist in two forms. One polymorph is the same as that reported by the X-ray analysis of Holtz- berg, Post, and Fankuchen, (1953)• it is referred to as the B form and results when the liquid is frozen. This is the form, presumably, found in this experiment, and is illustrated In Fig. 6.4. The other form, a, also illustrated in Fig. 6.4 results from freezing by vapour deposition on a cold window. In this way they have explained differences in the observed mid-infrared spectrum of crystalline formic acid, with different methods of crystallization.


(a)

H

x

3In-plane

2

Out-of-plane.5

<C

(b)

PIG. 6.3. (a) STRUCTURE OF FORMIC ACID DIMER(b) LOW FREQUENCY NORMAL MODES OF VIBRATION

OF THE DIMER (AFTER SLUTSKY AND BAUER, 195J0


H

M

s ? °

OL -Form

's,.04 k1.26

.54A

122

H

N

j3-Form

PIG. 6.4. THE TV/O FORMS FOR THE POLYMERIC CHAINS IN CRYSTALLINE FORMIC ACID


To assign the frequencies to the normal modes the symmetry of the crystalline solid must be examined.Iloltzberg, et al (1953) have determined that formic acid at -50°C has an orthorhombic unit cell containing four molecules. The space group is designated Pna-C2V .However, as Millikan and Pitzer (1958) point out, the presence of hydrogen bonding joining the molecules into a planar zig-zag chain makes the coupling between adjacent chain molecules more important than the coupling between extra-chain adjacent molecules bound together by van der Waals forces. This is particularly true for the low frequency vibrations. The extra-chain coupling is expected to split the inter-chain vibrations.

The space group symmetry of an isolated infinite chain, as depicted in Pig. 6.4 consists of all the symmetry operations which will map the chain into itself. The primitive unit cell of this structure contains two molecules; the entire chain can be generated by translations of this unit cell. These translations form the invariant subgroup of the space group; the coset decomposition consists of two elements, the invariant subgroup and the product of this subgroup with the two-fold screw axis operation. This decomposition generates a factor group isomorphic to Cs, which is the point symmetry of the unit cell group.

Because the only modes that are important in the infrared or Raman effect are those which are totally symmetric with respect to all translations (k = 0 modes), we need only consider the vibrations of the unit cell. Moreover, because the frequencies in which we are interested all fall below 300 cm-1 the internal modes can be effectively separated from the hydrogen bond modes. In the latter modes the two molecules in the unit cell can be considered as two lamallae coupled together by a hydrogen bond. There will be eight degrees of freedom in addition to rotation about the chain axis. Six of the normal modes of the chain unit cell will


be analogous to those of the dimer, and are labelled similarly There will be two additional modes in which the centres of mass of the two lamallae are displaced perpendicular to the chain axis, but the centre of mass of the chain remains motion less. In one the displacement is out-of-plane, in the other it is in-plane. These modes correspond to the rotational modes in the dimer. All the modes will be active in the infrared and the Raman effect under the Cs symmetry, in distinction to the selection rules for the C2v symmetry of the dimer, where the centre of inversion makes the gerade modes Raman active and the ungerade modes infrared active.

The observed frequencies are assigned to the normal modes by analogy with the dimer situation, proceeding in the same way. as Jakobsen et al (1967). Table 6.2 lists the normal modes, the frequencies of the dimer, and our suggested assignment of the normal modes. The correlation with the observed dimer frequencies is quite good except in the case; the frequency in this case is different by about ^5 cm

These assignments'differ from the assignments of Jakobsen et al in the following particulars :1) the band observed in the infrared at 232 cm-1 has

been assigned to the in-plane stretch along the chain axis, instead of the antisymmetric in-plane librational vibration. In this assignment the frequency corresponds to the observation that the frequencies increase with decreasing temperature, and that the modes observed by infrared in the polymer correspond to gerade modes in the dimer.

2) The 8‘8 cm-1 band has been assigned to the symmetric in-plane librational vibration instead of the torsion.The torsional mode has been assigned to the doublet observed at about 60 cm-1. The splitting in this doublet is quite small compared to the width of


TABLE 6.2

OBSERVED FREQUENCIES OF THE NORMAL MODES

MODE DESCRIPTION OF MODE

ANALOGOUS P°LYMER ™QUENCIESDIMER RAMAN RAMAN INFRAREDFREQUENCIES EFFECT EFFECT

20°C -10OC -100°C -150 C

V1 in-planestretch

22*)221*

222216*

230 (221) t 225w(2l6)+

232228*

v2in-planesymmetriclibration

9188*

838*)*

8685*

88

v 3in-planeantisymmetriclibration

2482*10*

23923*)*

2*)72*10*

V,,out-of-planeantisymmetriclibration

16*)167*

118118*

123122*

v 5 torsion 6868*

59, 56. 58, 55*

61,5759,57*

*

6out-of-planesymmetricstretch

2602*»8*

256250*

261259*

271261*

*V If +

v 5combinationmode

-186

N ??185*?

200

* IICOOD observed frequency t auxiliary component?

"Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

6 0

the bands. This splitting is probably due to an interaction with the similar torsional mode in an adjacent chain; it is expected that the torsional vibration would be most affected by interchain potential perturbations.

3) The modes reported as a shoulder in the infrared spectrum at 200 cm-1 and at 186 cm"1 in the Raman effect is probably the result of a combination of V14 + V5. In the Raman effect this band has anextremely low intensity and apparently has anumber of components, the main peaks in HCOOH are at 186 cm 1 and at 199 cm 1. There is some evidence of this band in HCOOD. but the band is not really well resolved over the noise. This combination band would have gerade symmetry in the dim''.*, and so it conforms to the observation that the modes observed in the infrared in the polymer correspond to gerade modes in the dimer.

The two broad bands observed in the liquid result from the coalescence of the peaks in each frequency region.The lack of ordering in the liquid state produces astatistical distribution in the amount of interchain perturbations, broadening each band. This is aided by the (probable) shorter lengths of the polymeric chains in the liquid. As a result, -the condition of translational Invariance breaks down so that the k = 0 selection rule for the vibrational modes of the chain is no longer strictly enforced, further broadening the bands.

The proposed assignment of the vibrational modes is not entirely satisfactory despite the apparent correlation between the dimer and polymer frequencies. It is not clear why the correlation breaks down for the vi* mode. No bands have been assigned to the rotatory modes of the free molecules,


although these bands are expected to develop high Intensities in the condensed states (Halford, 19*16). It is possible that the split 60 cm 1 band represents these two constrained rotational modes instead of the torsional mode. Moreover, because the frequencies of the different bands are similar it is reasonable to expect that there will be considerable degeneracy. Under these conditions it may not be too realistic to assign definite modes to the different observed bands. Despite these shortcomings it is felt that the assignments presented above are reasonable and that the low frequency Raman spectrum of solid formic acid exhibits the vibrational spectrum of a hydrogen bonded polymeric chain.


APPENDIX

CALCULATION OF THE SECOND DERIVATIVE OF THE INTERMOLECULAR POTENTIAL IN SOLID ETHYLENE

The second derivative of the intermolecular potential in a crystal can be obtained from the analysis of the splitting observed in the vibrational fundamentals of the solid by applying harmonic vibrational' coupling theory (Fox and Schnepp, 1955; Craig and Hobbins, 1955; Dows, 1963).The calculation is essentially a first order perturbation calculation, the theory of which is presented below.

The crystal is assumed to be an ordered collection of harmonic oscillators. Zero order- excitation wave functions, reflecting the symmetry of the crystal lattice unit cell (i.e. the factor group of the space group), are constructed from the Bloch functions obtained by applying the Born-von Karmann boundary conditions. Using these wave functions, a first order calculation is performed on the energy. In general, the excitation energy iB found to be

E = e + D + Ma

where E is the energy of the excited state above the ground state, g is the energy of the excited state above the ground state for a harmonic oscillator, D is an energy arising from the motion of one molecule in the static crystalline field

clof the other motionless harmonic oscillators, and M is an energy arising from the exchange resonance between two different molecules. Ma depends on the particular representation of the factor group which describes the transformation of the wave function (hence the superscript a). It is analogous to an exchange integral in the theory of valence, whereas D is analogous to a coulomb integral.

The energy D is independent of the wave vector k (which appears in the Bloch functions) and thus does not


remove the degeneracy of the localized excited states. It contributes a shift to the vibrational energy called the static field shift. P4a can be divided, into two parts; the first part is the sum over molecules that are translatlonally equivalent to the molecule under consideration, and the other is a sum over the molecules which are not translatlonally equivalent (i.e. over the other occupied sites of the unit cells). The two parts of Ma contribute to the shift of the vibrational energy as well. The second part, in addition, splits the vibrational energy (factor group or correlation field splitting).

For ethylene the magnitude of the splitting between two components is given by

A v c = — £ { " 9 ,v " } ( A , 1 ) JPir2 C 2 VQ i i 3 Q j 3 Q j j

where vQ is the gas phase frequency of the mode, and the summation is over all the molecules, II, located at the cell centres. If a repulsive interaction between nonbonded hydrogen atoms of adjacent molecules of the form,

V = b exp(-ar) (A.2)is assumed, then, substituting in equation A.l, and multiplying by a factor of for the four nearest neighbours of type II, yields

i. = — 1----- 6 . -2£- (a .3)"2 c2 vo 3QI 3RII

In this expression 0 has been substituted for the second derivative, 32V/3r2.

The partial derivatives are the changes In the H...II distances with normal coordinates Qj and Qjjj respectively.


The evaluation of these derivatives is outlined below.

Normal coordinate analysis for ethylene and ethylenelike molecules have been carried out by a number of investigators. For our purpose the analysis of Kuchitsu, Oka, and Morino (1965) is most useful. They have, used gerade symmetry coordinates defined in terms of internal coordinates as follow

■s‘(v s ARS2(A„) = 1* S 2

S3(A) = rs

S 5 (E. ) ■g 15 lg 2

s6(n ) rb IS 2

saCB ) = r2 g

{Atfi j + A<pif + + Atjjg}2/J

where R, r and <f> are defined as in Fig, 5.8(a) and is the angle between the C=C bond and the plane.

It is necessary to obtain the cartesian displacementcoordinates of the hydrogen atoms for each normal coordinate. In particular the displacements of atoms 5, and 6 are of Interest, because it is the change in the interatomic distance of the II...H contacts with the normal coordinate that is desired for each possible crystal structure. In the a-axis case (see Fig. 5.8(b)) the change is in the interatomic distance between atom in the molecule at the cell centre and atom 6 in the molecule at the origin. In the b-axis case(Fig. 5.8(c)) it is the change between atom 5 in the molecule at the cell centre and atom 5 in the molecule at the origin of the next higher unit cell.

The s-vectors for the symmetry coordinates given above


are tabulated in Table A.l for the relevant atoms. The composition of the normal coordinates in terms of the symmetry coordinates is given by a matrix L"-1. The normalised elements of this matrix required for this analysis are reproduced in Table A.2. These elements were obtained by Kichitsu et al from the fundamental frequencies of gaseous ethylene.

The general expressions for the cartesian displacement coordinates are presented in the first part of Table A.3.The actual values of the coordinates are given in Table A.3(2) These coordinates are given in the molecule fixed coordinate system. To proceed with the analysis the coordinates must be expressed in the unit cell coordinate system. To accompli: this, the molecules are placed in their positions in the crystal unit cell and the rotational transformations presented in Table A.*t are applied to the molecule fixed coordinates.This yields the coordinates which are tabulated for the various relevant cases in Table A 5» From these coordinates the values of the equilibrium and displaced interatomic distances can be calculated, and hence the values of 8r/3Q can be obtained. These are presented in Table A.6 for both types of possible crystal structure.


TABLE A.1

THE S-VECTORS

si X„ x5 X6

Si 0 0 0

s2 - £ J - f Y2 2 - s ?.2 2 + s2 2-♦*Y

S3 /T /T± sx - i CY 2 2 - 5 SX CY 2 2 sx +*2 2 CY

Sr, p -► q -+- X + % Y 2 2 £5c - | y 2 2C J s 2 “ 2

->■Y

s 5 | X - | Y |X + £ Y2 2S Y C

“ 2 X " 2 Y

o°6 - i - Z2/?

- 1 Z2/2

X 7 2/2

S = sin — 2

C a ac o s -

= sin 58.3° = CO S 58.3°

= 0.8508 = 0.5255

S2 0.4254 ^ S = 0.73^8 | = 0.2627

= 0.4551


TABLE A.2

ELEMENTS OF THE L"1 MATRIX (in AMU)

Qi Si s 2 S 3 S5 S6 s8

Qi - 0 . 0 0 5 9 0 . 9 7 5 2 - 0 . 0 3 5 1 0 0 0

Q2 1.4615 0 . 2 1 9 8 0 . 3 5 2 8 0 0 0

Q 3 2.2090 0 . 0 9 4 4 - 0 . 4 5 8 6 0 0 0

Qs 0 0 0 - 0 . 9 4 9 6 - 0 . 0 0 7 2 0

Qs 0 0 0 0.2028 0 . 7 7 2 9 0

Qe 0 0 0 0 0 0.5889


TABLE A.3(1)

GENERAL EXPRESSIONS FOR THE DISPLACEMENT CARTESIAN COORDINATES for the GERADE NORMAL MODES.,,-l _ . ^

(L U i j

Aig Normal Modes i = 1,2,3

ATOM AX AY AZ

4 A^2( 2) + Ai3C| s> + Ai3^“ 2 0

5 + a 13(-’| s ) Ai3(-’1 ° > 0

6 *!.<!> + Ai3(' 1 S) A \(-)i 2 V + *1,(1°) 0

Bj Normal Modes i = 5,6

ATOM AX AY AZ

II A ( — )i 5 ^ 2 ; + A i s ( !> A, ( - ) 15 2 + A i 6 < - | >

0

5 + * ! . < f> A (--)i 5 2 + A i . < § >0

6 A ( - - ) i 5 2 + A i 6 ^ " 2 ^

A (--) Ai 5 l 2 + Als(l> 0

B2cr Normal Modes QsOATOM AX AY

b 0 0 A 8 8

5 0 0 ~A 0 86 0 0 “A8 8

AZ

1/2'


Reproduced

with perm

ission of the

copyright ow

ner. Further

reproduction prohibited

without

permission.

TABLE A.3(2)

THE MOLECULAR FIXED COORDINATESTop Line Bottom Line

Displacement Coordinate Displaced Position Coordinate

EQUILbMPOSITION

Qi

Q*

Q3

Qs

Qs

Qs

ATOM 4 -0.2387, -0.9240, 0 1.2387,

ATOM 5 -0.9240, 0 1.2387,

ATOM 6 0.9240, 0

-0.2821, -0.3989, 0 0.2821, -0.3989, 0 0.2821, 0.3989, 0-1.5208, -1.3229, 0 1.5208, -1.3229, 0 1.5208, 1.3229, 0+0.2022, -0.2541, 0 -0.2022, -0.2541, 0 -0.2022, 0.2541, 0-1.0365, -1.1781, 0 1.0365, -1.1781, 0 1.0365, 1.1781, 0-0.3627, 0.1685, 0 0.3627, 0.1685, 0 0.3627, -0.1685, 0-1.6014, -0.7555, 0 1.6014, -0.7555, 0 1.6014, 0.7555, 0-0.2526, -0.4021, 0 -0.2526, 0.4021, 0 0.2526, 0.4021, 0-1.4913, -1.3261, 0 0.9861, -0.5219, 0 1.4913, 1.3261, 00.3821, -0.1167, 0 0.3821, 0.1167, 0 -0.3821, 0.1167, 0

-0.8566, -1.0407, 0 1.6208, -0.8073, 0 0.8566, 1.0407, 00 , 00 .2082 0 , 0 ,-0.2082 0 , 0 0.;

-1.2387, -0.9240,0 .2082 1.2387, -0.9240, -0.2082 1.2387, 0.9240,-■0.;

VALUES OF AQ4Qi = 0.4886AQ2 = 0.3247AQ3 = 0.3999

= (AX2 + AY2 + AZ2)1/,

AQsa Q 6AQg

0.47490.39950.2082

TABLE A. 4 ROTATIONAL TRANSFORMATION MATRICES

1. Molecule at Unit Cell Cornera-Axis Case b-Axis Case

GENERAL EXPRESSION 6 = 37.0° * « 63.2° 0 = 37.0° <f> = 61.6°cosB -sin6cos<J> singsin^ 0.7986 -0.2114 0.5372 0.7986 -0.2862 0.5294sinB cos0cos<J>-cos0sin4> 0.6018 0.3600 -0.7128 0.6018 0.3708 -0.70250 sin(|> cos«<i 0 0.8926 .0.4509 0 0.8797 0.4756

2. Molecule at Unit Cell Centre : a-Axis Case

cos 0 sin0cos<J> -sin0sin<f> 0.7986 0.2714 -0.5372-sin0 COS 0COS <j)-cos 0sin<i) -0.6018 0.3600 -0.7128

0 1 sin <f> COSifi 0 0.8926 0.4509

3. Molecule at Unit Cell Centre : b-Axis Case

cosS sinScos<j> sin0sin<|> 0.7986 0.2862 0.5294-sin0 cos0cos<f> cosBsin<)> 0.6018 0.3798 0.7025

0 -sincj) cos<j> 0 -0.8797 0.4756


TABLE A.5 UNIT CELL FIXED COORDINATES

1. a-Axis Case : Atom 6; Molecule at Cell Origin

X Y ZEQUILIB 0.7385 1.0781 0.8248

Ql 0.8555 1.3915 1.1808Q2 0.5080 1.0479 1.0516Q 3 1.0738 1.2357 0.6744

• Qs 0.8310 1.3749 1.1837Qe o.4oi6 0.8901 0.9289Qa 0.6266 1.2265 0.7309

2. a-Axis Case : Atom 4; Molecule at Cell\ Centre

X Y ZEQUILIB 1.1950 3.6428 1.2452

Ql 0.8614 3.6690 0.8892Q2 1.2875 3.4297 1.0184Q3 0.9511 3.9217 1.3956Q5 0.8842 3.6501 0.8863Q6 1.4685 3.3709 1.1411Qe 1.0832 3.4944 1.3391

3. b-Axis Case : Atom 5; Molecule at Cell Next Higher Unit

Origin of Cell

X Y ZEQUILIB 1.2537 0.3945 ■ 3.3272

Qi 1.5931 0.4128 2.9762Q2 1.1649 0.1763 3.1036Q3 1.4951 0.6768 3.4754Q5 0.9369 0.3952 3.6809Q g 1.5254 0.6688 3.4298

Q 8 1.1435 0.5408 3.2281


TABLE A. 5 (Contd)

*1. b-Axis Case : Atom 5; Molecule at Cell Centre

X Y Z

EQUILIB 3.1598 2.1336 2.8829Q i 3.2709 1.8123 3.2337Q2 2.9256 2.1588 3.1063Q3 3. *1977 1.9793 2.7346Qs 3. 2*16*1 1.8289 3.2365Qs 2.8212 2.3193 2.9855Q 8 3.0*196 1.9873 2.7838


TABLE A. 6

VALUES OF 3r/3Q

1. a-Axis Case

3r3Qj in

3QnPRODUCT

Qi -0.722 -0.090 0.065Q2 -0.092 -0.668 0.061Q3 001 0.673 -0.273Qs -0.718 -0.131 0.0 9 *1Q6 -0.608 0.060 0.036Q 8 -0.500 -0.697 0.349

3

2. b-Axis Case

in3 Q jin3Qn

PRODUCT

Qi -0.309 -0.591 0.183Q2 -0.545 0.569 -0.310Qa 0.483 -0.820 -0.396Qs -0.339 0.661 -0.224Qe -0.283 -0.890 0.252Q 8 -0.736 -0.120 0.088


r,6

■SUMMARY

The effects of intermolecular forces on the vibrational Raman spectra of certain simple molecular liquids and crystals have been studied. Accurate intensity profiles of the bands were obtained with a high intensity Raman source and a grating spectrograph giving a reciprocal linear dispersion of 8 cm-1 per mm at 1625 ft. '

In liquid oxygen, a moment analysis of the anisotropically scattered Raman band profile yields a mean squared intermolecular torque of 8 x 104 cm_2rad-2.The rotational motion is thus highly hindered and the molecule may be thought of as performing a'libration with a root mean square amplitude of about 13°. The rotational correlation function obtained by Fourier transformation of this band indicates that the molecule rotates freely for

— 1 3about 2.5 x 10 seconds before a change in the angular1momentum vector is produced by the intermolecular torques.

A similar analysis of the v3 band in the Raman spectrum of liquid and solid methane indicates that the rotational motion of this molecule at temperatures near the freezing point is also highly hindered. The meansquared torques are not as high as for the oxygen molecule :1.5 x 104 cm“2rad“2 in the liquid, and *1 x> 104 in the solid.The rotational correlation function exhibited by methane,particularly in the solid state, does not lend itself to as simple an interpretation as does the correlation function of liquid oxygen, probably because the assumption of infinite smal steps between rotational reorientations leading to an exponential decay in the function is not valid.

The fundamental vibrational bands in the Raman spectrum of solid ethylene exhibit, in the main, two components. This can be explained on the basis of the unit cell structure, which contains two molecules. A calculation


on the magnitude of the splitting indicates that the probable mechanism for the intermolecular perturbation is repulsion between neighbouring hydrogen atoms in the two molecules of the unit cell. The calculated value of the second derivative of the intermolecular potential is about 960 dynes/cm. The conclusions on the crystal structure of the solid do not entirely agree with previous infrared investigations; this may be due to the different methods of preparing the crystals.

Indications of the solid phase vibrational fundamentals have been observed in the vibrational Raman spectrum of liquid ethylene near the freezing-point. This constitute further evidence for the existence of "quasi-la-ttice" ordering in the liquid phase at these temperatures.

The low frequency Raman spectrum of liquid HCOOII and HCOOD at 85°C and at 0°C, and of solid HCOOH and HCOOD at -10°C and -100°C have been observed. An assignment of the observed bands in the hydrogen bonded polymer on the basis of a comparison with the bands in the dimer has been proposed.


6 8

REFERENCES

Amdur, I., Longmire, M.S.(J-and Mason, E.A., 1961. J.Chem.Phys.35, 895.

Dlumenfeld, S.M., 1961. M.A. Thesis, Toronto.Brecher, C. and Halford, R.S. 1961. J. Chem.Phys. 35, 1109.Bunn, C.W. 1944. Trans. Faraday Soc. 40^ 23.Carlson, G., Witkowski, R., and Fately, W. 1966. Spectrochim.

Acta. 22, 1117.Craig, D.P., and Hobbins, P.C. 1955. J.Chem.Soc.(London) 539, 2302Crawford, M.F., Welsh, II.L. and Harrold, J.H. 1952. Can.J.Phys.

30, 81.Crosswhite, C.D. 1958. John Hopkins Spectroscopic Report //13. de Boer, J. 19*12. Physica 9, 363.Dows, D. 1962. J.Chem.Phys. j[6, 2836.------- 1963. Infrared Spectra of Molecular Crystals, in

Physics and Chemistry of the Organic Solid State, Vol.I., ed. by D. Fox, M.M. Labes, and A. Weissberger (John Wiley and Sons, New York).

Edlen, B. 1953. J.Opt.Soc.Am. 43., 339.Ewing, G.E. 1964. J.Chem.Phys. £0, 179.Feldman, T., Romanko, J., and Welsh, H.L. 1956. Can.J.Phys.

34, 737.Fox, D. and Schnepp, 0. 1955. J.Chem.Phys. 23, 757.Gordon, R.G. 1963. J.Chem.Phys. 39., 2788. — ---- 1964a ibid. .40, 1973. ---- 1964b ibid. 4JL, l8l9------------ 1965a ibid. 42, 3658. — ---- 1965b ibid. 13, 1307. 1966a ibid. 44, 1830.-— ---- 1966b private communication.Gross, E.F., and Valkov, V.I. 1949. Dokl. Akad. Nauk SSSR

68, 1013.


Gross, E.P. 1959. Hydrogen Bonding, ed. by D. Hadzi (Pergamon Press, London) 203.

Halford, R.S. 19*16. J.Chem.Phys. lj*_, 8..Holtzberg, P., Post, B. , and Pankuchen, I. 1953. Acta. Cryst.

6, 127.Jakobsen, R.J., Mikawa, Y., and Brasche, J.W. 1967.

Spectrochim. Acta, to be "published.Kuchitsu, K., Oka, T., and Morino, Y. 1965. J.Mol.Spectry. 15Lepard, D. 196*1. Ph.D. Thesis, Toronto.?4ay, A.D., Varghese, G., Stryland, J.C., and Welsh, H.L. 196 .

Can.J.Phys. l»2, 1058.Mikawa, Y., Jakobsen, R;J., and Brasch, J.W. 1966. J.Chem.Phy.

15, **750.Millikan, R., and Pitzer, K. 1958. J.Am.Chem.Soc. 8_0, 3515.Miyazawa, T., and Pitzer, K. 1959. J.Chem.Phys. 30., 1076;

J.Am.Chem.Soc. £l, 7*1.Phibbs, M.K., and Schiff, H.I. 19*»9. J.Chem.Phys. 17, 8*13.Placzek, G., and Teller, E. 1933. Z.Physik 8l_, 209.Rank, D.H., Shull, E.R., and Axford, D.W.E. 1950. J.Chem.Phys.

18, 116.Reynolds, G.F. 1963. Crystal Growth, in Physics and Chemistry

of the Organic Solid State, Vol. I., ed. by D. Pox,M.M. Labes, and A. Welssberger (John Wiley and Sons, New York), 657.

Rosencwaig, A. 1965. M.A. Thesis, Toronto.Savitsky, G.B., and Hornig, D.F. 1962. J.Chem.Phys. 3j6, 263*1. Slutsky, L., and Bauer, S.H. 195**. J.Am.Chem.Soc. 76, 270. Smaller, B., and Matheson, M.S. 1955. J.Chem.Phys. 23, 521. Snyder, R. 1961. J.Mol. Spectry. J_, 116.Thomas, M.A., and Welsh, H.L. i960. Can.J.Phys. 38., 1291. Verschingel, R., and Schiff, H.I. 1955. J.Chem.Phys. 22, 723.


7 0

ACKNOWLEDGEMENTS

I wish to express my gratitude to Professor H.L. Welsh for his guidance and encouragement during this research programme. In particular, his help in the preparation of this thesis is appreciated.

The contributions of Dr. S.P. Heddy and Mr. H. Fast in certain phases of this research is also acknowledged.

Every member of the technical staff, under the supervision of Mr. B. Owen and his predecessor, Mr. B. Clark, has been involved in the preparation of a part of the apparatus employed in this research. I am grateful for the aid and interest they, particularly Mr. B. Brindley and Mr. W. Begg, have given. Much of the success of the experimental work is due to the glassblowing craftsmanship of Mr. J. Legge and his assistant, Mr. J. Rynders.

•Thanks are due to Professor C.C. Gotlieb for enabling me to use the facilities of the computation centre. Discussion with the staff and graduate students of the McLennan Laboratories have helped me many times during this research programme. Moreover, I am indebted to theGovernment of Ontario for their financial assistance.

Finally, without the encouragement of my parents, and my wife and family, this research programme would not have been possible.


Documents

MANUSCRIPT THESIS · 2016-12-12 · If the intermolecular potential energy is the same for the ground and excited vibrational states (approximately true), then M(l) is independent