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Rochester Institute of TechnologyRIT Scholar Works
Theses Thesis/Dissertation Collections
7-1-1988
A simple solubility theory combining solubilityparameter and Lewis acid-base conceptsLan Tuyet Evans
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Recommended CitationEvans, Lan Tuyet, "A simple solubility theory combining solubility parameter and Lewis acid-base concepts" (1988). Thesis. RochesterInstitute of Technology. Accessed from
A SIMPLE SOLUBILITY THEORY COMBINING SOLUBILITY
PARAMETER AND LEWIS ACID-BASE CONCEPTS
by
Lan Tuyet Evans
July, 1988
THESIS
SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE
APPROVED:
Project Advisor
Project Co-advisor
Department Head
Library
Rochester Institute of Technology
Rochester, New york 14623
Department of Chemistry
Title of Thesis "A Simple solubility Theory Combining
Solubility Parameter and Lewis Acid-Base Concepts"
I, Lan Tuyet Evans, hereby grant permission to the
Wallace Memorial Library, of R.I.T., to reproduce my
thesis in whole or in part. Any reproduction will not be
for commercial use or profit.
Date
Dedication
To Bill, who gave me support and encouragement when I
needed it most.
ii
ACKNOWLEDGEMENTS
I would like to express my sincere thanks to my research
advisors, Dr. L. Paul Rosenberg and Dr. William B. Jensen,
without whose guidance and encouragement this thesis
would not have been possible. I wish to thank my
graduate committee, especially Dr. Laura Tubbs and Dr.
Joseph Hornak, for their suggestions. I wish to thank
Peter Michelsen for his assistance. I also wish to thank
Nancy L. Wengenack for her help with the computer. The
financial assistance from the Department of Chemistry in
the form of a teaching assistantship is gratefully
acknowledged .
iii
TABLE OF CONTENTS
ABSTACT 1
GENERAL IMPORTANCE OF SOLUBILITY PHENOMENON 3
SOLUBILITY PARAMETER THEORY 5
Introduction 5
Definition of Solubility Parameter 6
Evaluation of Molar Cohesive Energy 7
Evaluation of 8 in Terms of Heat of Vaporization . . 8
Empirical Methods for Evaluation of Solubility .... 9
Hildebrand's Model with Dispersion Term only 11
Models with Dispersion and Polar Terms 12
Hansen's Model with Dispersion, Polar and H-bonding.14
Model Incorporating Proton Donor-Acceptor
Properties 19
LEWIS ACID-BASE CONCEPTS IN SOLUBILITY THEORY 23
Definitions 23
Lewis Acid-Base Donor-Acceptor Term 23
A concept Combining Dispersion and Donor-Acceptor
Terms 24
Determination of Acceptor and Donor Numbers 25
EXPERIMENTAL 32
Materials 32
Correlations 33
Miscibility Determination 35
Construction of Miscibility Sorting Maps 36
IV
RESULTS AND DISCUSSION 38
Research Objectives 38
Correlation of AN and Ey(30) 39
Error Analysis of Schmid's Equation 39
Correlation of AN and Ej(30) for Alcohols
and Chlorinated Hydrocarbons 43
Error Analysis of Correlation Equation for
Alcohols and Chlorinated Hydrocarbons 45
Correlation of AN, DN and Dielectric Constant 47
Miscibility Sorting Maps 51
Benzene-Solvent Binary Mixtures Sorting Map 54
Analysis of Benzene Sorting Map 54
Benzene Sorting Map- Miscibility Experimental . . 61
Benzene Sorting Map- Error Analysis 64
Benzene Sorting Map to Predict Miscibility
of Mixtures 67
Hexane- Solvent Bianary Mixtures Sorting Map 70
Evaluation of Hexane Sorting Map 70
Hexane SortingMap- Miscibility Experimental ... 75
Hexane Sorting Map- Error Analysis 79
Hexane Sorting Map to Predict Miscibility
of Mixtures 79
CONCLUSION 84
REFERENCES 88
APPENDIXES 91
LIST OF TABLES
1 . SOLUBILITY OF NAPTHALENE 5
2. ERROR ANALYSIS FOR SCHMID'S CORRELATION EQUATION. 41
3. ERROR ANALYSIS OF CORRELATION EQUATION FOR
ALCOHOLS AND CHLORINATED HYDROCARBONS 46
4. CORRELATION OF AN, DN, AND e FOR DIFFERENT
CLASSES OF SOLVENTS 50
5. DATA FOR SORTING MAP FOR BINARY LIQUID SYSTEM ... 55
6. REFRACTIVE INDEX AND MISCIBILITY OF
BENZENE-SOLVENT MIXTURES 63
7. ERROR ANALYSIS OF BENZENE-SOLVENT SORTING MAP ... 66
8. PREDICTING MISCIBILITY OF MIXTURES WITH
BENZENE SORTING MAP 68
9. REFRACTIVE INDEX AND MISCIBILITY OF
HEXANE-SOLVENT MIXTURES 74
10. MISCIBILITY OF HEXANE-METHANOL MIXTURES 78
11. ERROR ANALYSIS OF HEXANE-SOLVENT SORTING MAP .... 80
12. PREDICTING MISCIBILITY OF MIXTURES WITH
HEXANE SORTING MAP 83
A-l. LIST OF E_(30), AN (experimental and calculated),
AND DIELECTRIC CONSTANT ( 6 ) 92
A-2. LIST OF AN VALUES CALCULATED FROM EITHER SCHMID
OR ALCOHOL CORRELATION 99
A-3. LIST OF DN VALUES AND DN ERROR 106
A-4. LIST OF AN, DN, AND 8 109
VI
LIST OF FIGURES
1 . Structure of phenolate dye 27
2. Reichardt's correlation of AN and ET(30)
for pure organic solvents 29
3. Schmid's correlation of AN and ET(30) 30
4. Correlation of AN and Ej(30) for alcohols,
5. Benzene-Solvent Sorting Map 57
6. Benzene-Solvent Sorting Map(Beerbower's DN Values). 62
7. Benzene-Solvent Sorting Map (Final Map) 65
8. Benzene-Solvent Sorting Map (Predictions) 69
9. Hexane-Solvent Sorting Map 71
10. Hexane-Solvent Sorting Map (Beerbower's DN Values). 72
11. Hexane-Solvent Sorting Map (Final Map) 76
12. Hexane-Solvent sorting Map (Predictions) 82
vii
ABSTRACT
A simple model of liquid / liquid solubility has
been developed. The existing solubililty parameter
theory which tries to explain solvent-
salute
interaction in terms of dispersion ,polar
, and hydrogen
bonding interactions is discussed. The current theory
has been widely used qualitatively but can not be used
quantitatively due largely to incorrect modeling of the
hydrogen bonding interactions.
This research proposes modifications to the
current solubility parameter theory that are designed to
overcome the problems encountered with hydrogen bonding
interactions in which the hydrogen bonding interactions
are described as a special case of more general Lewis
acid- base or donor acceptor interactions. The specific
electron-
pair acceptor- donor properties themselves
are quantitatively characterized using acceptor numbers
( AN ) and donor numbers ( DN ) .
This modified model predicts that the enthalpy of
mixing of two liquids can be represented using the
equation :
AH [mix] - V 02
( S. -S)2
+ k ( AN - AN > ( DN - DN )2 2 1 2 1 2 *
where V2 is the molar volume of the solute, 0] is the
volume fraction of the solvent and Sj is the dispersion
solubility parameter. AN and DN are electron-
pair
acceptor number and electron pair donor number
respectively. Research discussed in this thesis includes
development of empirical relationships to extend the
limited range of available AN and DN values for liquids,
and the experimental testing of the model using
qualitative sorting maps. These maps consist of a plot
of the acceptor- donor term against the dispersion term
of the above equation to empirically determine areas of
miscibility and immiscibi 1 i ty using liquids of known
AN,
DN and known miscibi 1 i ties . Once these regions are
established, the maps can be used to predict the
miscibility of other liquid pairs via interpolation.
GENERAL IMPORTANCE OF SOLUBILITY PHENOMENON
The importance of solvents is their ability to
dissolve different solutes. Solvents can act as an inert
carr ier for solutions, chemical reactions and seperation
processes. Solutes may also form complexes or react with
the solvent. If solubility can be predicted for a given
solute combination or for the change of one solvent for
another, then solvents can be used more effectively-
Solubility of organic compounds may be estimated
by many methods (1). One is a simple trial and error
method of attempting to dissolve a compound in a variety
of different solvents. This random process is
inefficient and can take a long time. More experience
leads to the use of the "like dissolved like"
rule of
thumb to estimate the solubility of organic compounds in
selected solvents (2). It is generally expected that a
compound with properties and structures similar to a
solvent would be soluble in that solvent. However, this
rule is very limited. A major problem is determining
when two compounds are alike when there is no
quantitative measure of"
likeness ".
A better way of predicting solubility is to use
the solubility parameter concept proposed by
Hilderbrand nearly 70 years ago. This theory provides a
means of measuring the likeness between solute and
solvent. Maximum solubility occurs when there is little
or no difference in the nonspecific dispersion forces of
the salute and solvent. Dispersion forces or London
forces, arising from the fluctuating dipoles which result
from a positive nucleus and negative electron"
cloud"
in each atom, occur in all molecules whether polar or
not .
In contrast, the Lewis acid- base concepts
predict solubility in term of highly specific electron
pair donor acceptor interactions (3). This theory
defines an acid as an electron pair acceptor and a base
as an electron pair donor. Maximum interaction of solute
and solvent occurs not with similar acid- base
properties, but with complementary properties.
This present research seeks to a develop a simple
solubility concept which combines the nonspecific
interaction of the solubility parameter concept with the
specific interactions of the Lewis acid- base theory.
SOLUBILITY PARAMETER THEORY
Introduction:
The solubility parameter, 8 , as originally
proposed, is related to nonspecific dispersion forces
present in liquids (2). Mixing of two liquids is
favorable when there is little or no differences in
theses forces. Thus Hildebrand found that a good solvent
has a solubility parameter, 6 , that is close to the 6 of
the solute. This is illustrated for the solubility of
napthalene in Table 1.
Table 1
SOLUBILITY'
OF NAPTHALENE
6 AS (cal/cm3)^
Napthalene 9.9
Hexane 7.3 9.9 - 7.3 = 2.6
Toluene 8.9 9.9 - 8.9 = 1.0
Water 23.4 23.4 - 9.9 - 13.5
Diethylether 7.5 9.9 - 7.5 = 2.4
Methyl iodide 9.9 9.9 - 9.9 = 0.0
Ethanol 12.9 12.9 - 9.9 = 3.0
The absolute difference in 6 values of 1 . 0 for napthalene
and toluene indicates that toluene is a good solvent for
napthalene. Other values in Table 1 predict that methyl
iodide is a very good solvent for napthalene, while
hexane, ether, and ethanol are not quite as good. Water
is not a solvent for napthalene, as can be seen by the
large difference in 6 values. These predictions are
experimentally verified ( 2 ) .
Definition of Solubility Parameter:
The basic assumption in the solubility parameter
concept is that there is a correlation between the
cohesive energy density ( potential energy per unit
volume ) and mutual solubility (4). The solubility
parameter, S , can be defined as the square root of the
cohesive energy density of a liquid:
( -E / V )^( cal/cm3)^ [1J
where -E is the cohesive energy and V is the molar
volume. The solubility parameter, 8 , is usually
3 ^expressed in units of ( cal/ cm ) but may also be
expressed in units of ( MPa 2) . Since the molar volume of
a liquid is easily determined at any temperature, the
evaluation of 8 is mainly dependent on the determination
of the molar cohesive energy, -E. The molar cohesive
energy is the energy associated with the net attractive
interactions in a mole of substance. These include
dispersion forces, polar interactions and hydrogen
bonding interactions. Hildebrand originally proposed the
solubility parameter concept for nonpolar, regular
solutions where dispersion forces dominate (4). Concepts
of solubility parameters which include polar and
hvdrogen-bonding interactions will be discussed later.
Evaluation of Molar Cohesive Energy:
The molar cohesive energy (-E) is the energy of a
liquid relative to its ideal vapor at the same
temperature ( assuming that the intramolecular properties
- those associated with individual molecules-
are
identical in gaseous and liquid states, which may not be
true in the case of a complex organic molecule) . It can
be seen that -E consists of two parts: the energy ( L . E )
required to vaporize the liquid to its saturated vapor
and the energy required to isothermally expand the
saturated vapor to infinite volume:
-E- A?E + \V=0(^E/'2>V) dV
[2]
At a temperature below a liquid's boiling point, the
second term is small and may be neglected to give
equation [ 3] .
- E =
A^ E [3]
If ideal gas behavior is assumed, then this expression
may be rewitten as:
E =
A^ H - RT [4]
where A H is the heat of vaporization.
Evaluation of S in Terms of Heat of Vaporization:
The solubility parameter may be witten in terms
of AH by :
( -E / V V - [(AH - RT ) / V] [5]
The heat of vaporization may be determined experimentally
by calorimetry or by the temperature dependence of the
vapor pressure through the use of the Clausius-Clapeyron
equation:
d In p AH
dTRT2
r6]
The heat of vaporization of nonpolar liquids may also be
estimated by using Hildebrand "s rule
2
AH (cal/mol) = -2950 + 23.7 Tfa + 0.020 T"b [7]
where T. is the boiling point of the liquid,D
Empirical Methods for Evaluation of Solubility Parameters:
Various empirical methods have been used to
estimate S values (5). For a series of compounds having
a common functional group, plots of S versus V are
linear. Therefore, S values of other compounds in the
same series can be determined by interpolation or
extrapolation of the plot (6).
The surface tension of nonpolar substances has
been suggested to have a close relation to the heat of
vaporization. Experimental data gives the relation of
surface tension, Y , to cohesive molar energy density (7):
Y/AE\M6
[8]
v "3 Vv I
Beerbower combined equations [1] and [8] and obtained a
relationship where S may be determined from the surface
tension, t , by the empirical equation (7):
u, 0. 4 s, ,
5 = k ( Y / V/2) [9]
where V is in cm /mole, Y is in dyne/cm 5 is in
(cal/cm3/2and k is a proportionality constant with a
numerical value of 4.1 at25
C.
Equations of state for gases do not fit liquids
well. However, for many liquids the following expression
has been used as a workable approximation
-E/V = ( "&E / *V ) = [10]
where a is the Van der Waal constant for the gas and
( "& E / *&V) is the internal pressure of a liquid (8).
Thus S can be expressed as:
S = ( -E /v'/2
) = a'/2/ V [11]
The internal pressure can also be related to the thermal
pressure by:
l E \ U'
= T
& V ) \W ,
E12J
T V
For nonpolar liquids at low pressure, the pressure P is
10
small and may be neglected and S can be written as
11 [13]
where o. and ft are the coefficients of thermal expansion
and compressibility (9).
Hildebrand's Model with Dispersion Term Only:
Hildebrand's solubility parameter concept has
been useful for regular solutions (4). Regular solutions
are nonpolar solutions, where the cohesive energy is only
due to dispersion forces. They are also solutions that
have an ideal entropy of formation even though the
enthalpy of formation is not ideal. Thus far the various
expressions have dealt only with pure liquids. What
happens when two liquids are mixed will now be discussed.
The change in enthalpy of mixing two nonpolar
liquids is (4)
AH (mix) = V.2 *, < 8,
"
*J [14]
where V2 is the molar volume of the solute, 0} is the
volume fraction of the solvent, and 6, and S2 are the
solubility parameters of the solvent and solute
11
respectively. This expression explains the like
dissolved like statement. Equation [14] always gives a
positive or unfavorable AH (mix) since the difference in2
S term is squared. Therefore, solubility is enhanced
when AH (mix) is minimized. This happens when the 8
values are similar. Thus, a small difference in S
values leads to high solubility and a large difference
leads to low solubility. The similarity of the cohesive
energy densities as expressed in the solubility
parameters is now a quantitative measure of likeness.
However, this simple one component parameter
proposed by Hildebrand becomes less accurate for more
polar substances. Significant deviations can happen with
the combination of polar solvents with polar solutes.
Polar interactions can cause nonideal entropy of
formation. Therefore, the one component S which is
directly proportional to AH does not accurately describe
the mixing or solvation processes in these systems.
Models with Dispersion and Polar Terms:
Various methods have been used to include polar
interactions. A general method has been developed which
divides the cohesive energy into polar and nonpolar
contributions (10). The solubility parameter then takes
12
the form
2 ->2
S =-E/V = (-E nonpolar/V) + (-E polar/V) = \ + * [15]
The solubility parameter then is composed of
1*
and \>
which are the polar and nonpolar components respectively.
The polar and nonpolar solubility parameters, T
and A, , may be estimated by using the homomorph
concept (11). The homomorph of a polar molecule is a
nonpolar molecule having the same size and shape. The
dispersion or nonpolar component, A,, of a polar liquid is
calculated from the experimental vaporization enthalpy of
the homomorph determined at the same reduced temperature
( the actual temperature) and molar volume. Plots of the
homomorph vaporization enthalpy against molar volume can
be used when the molar volume of the homomorph is not the
same as the polar molecule (7,10,12). The polar
solubility parameter, T , can then be calculated from
equation [ 15] .
Keller et al. (13) emphasized that polar
interactions are of two types, symmetrical dipole
orientation and unsymmetrical dipole induction. In
dipole orientation, two dipoles interact. In dipole
induction, one dipole on a molecule polarizes another
molecule. Thus in a pure polar liquid without H-bonding,
13
the total solubility parameter ( S ) takes the form:o
*o=
6d + Sor + 2 Sin 8d C16]
where the component solubility parameters are the
dispersion ( S. ) parameter, the orientation ( S ) para-d or
meter, and the induction ( S ) parameter.in
There are some problems associated with both of
these models. It is difficult to reliably obtain the
polar solubility terms. Also, H-bonding interactions
are not considered.
Hansen's Model with Dispersion. Polar, and H-Bonding:
Hansen (14) assumed that the cohesive energy
comes from the contribution of nonpolar or dispersion
interactions (-E. ), polar interactions (-E ), andH-
d p
bonding interaction (-E. ):n
-E = - ( Ed+ Ep + Eh ) [17]
This can be rewritten to give individual dispersion,
polar, and H-bonding solubility parameters , using
equation [1] :
E/V = - ( Ed+
Ep+ Eh )/V [18]
14
8o=
8d +SP
+ S" ^^
These individual S's can be evaluated by experimental
solubility observations and have been tabulated for
many compounds in Barton's book (15). Some of these
methods are discussed below.
The dispersion or London forces exist between all
adjacent pairs of molecules (16). Their origin is the
instantaneous electrical dissymmetry of electrons in one
molecule polarizing the electron cloud in adjacent
molecules, and inducing instantaneous dipoles of opposite
polarity- This temporary dipole results in
intermolecular attraction. The magnitude of the
dispersion cohesive energy, -E , can be approximated by:
3 !I jl j U-E. =
j : [20]d
2 ( 'I + 'I )
where <* is the polarizability , I is the first ionization
energy of each molecule, and r is the distance between
two molecules i and j. Using equation [20] and the
relation between polarizability and refractive index,
Koenhen and Smolders (17) found an empirical correlation
expressed as:
g (MPaV2) = 19.5nQ
- 11.4 [21]
15
between the dispersion cohesion parameter S and the
refractive index at the sodium"D"
line, n
Koenhen and Smolders (17) also developed an
expression for the polar solubility parameter, SP
S(cal/cm3
)1/2= feju
V3/i
[22]
where yu is the dipole moment in debyes , V is the molar
volume, and & is a constant with a numerical value of
50. 1.
It is sometimes more convenient to estimate the
Hansen solubility parameters S . , S S. from structural
group molar attraction contributions (12,18). It is
assumed that each functional group within a molecule
contributes to the total cohesive energy of the molecule,
2
-E = ( "2. F ) / V , and that each molar attraction
constant, F , is composed of dispersion, polar and
H-bonding components. The dispersion parameter can be
calculated by summing all the dispersion molar attraction
constants, Fd , for groups such as methyl, methylene,
phenyl, etc. ( 12) .
S^= 2 (
'F ) / V [23]
d j d
It is possible to evaluate S if only one polar group is
present by dividing the polar molar attraction constant,
16
F, by the molar volume (18):
Sp= Fp/V [24]
But if more than one polar group is present, then it is
necessary to correct for the interaction of the polar
groups (18) by using:
( ? 'Fp / V [25]
The dispersion and polar group molar attraction constants
have been tabulated by Barton (9).
This F-method, summing molar attraction
contributions, can not be used in the calculation of S .
h
Hansen and Beerbower (12) have assumed that H-bonding
cohesive energies are additive, leading to:
sh= <" ? V / v
)V2
C26]n i h
Many values of E. for various groups have been
tabulated (9,12). However, they urged extreme caution in
adding group contributions in the use of g. to describen
an interaction which really requires both donor and
acceptor components .
An expression similar to equation [14] has been
written for the change in dispersion energy on mixing
17
polar liquids (14) as:
AH2 [mix] =
V2JZf2
[(S,-
S2)2
+ (S,-
S2)2p+ (S,
-
S2 ] [27]
This expression as in equation [14] correlates the degree
of solubility of the solute and solvent with the square
of the differences of the solubility parameters in the
dispersion, polar, and H-bonding terms. Thus the
criteria for high solubility is still one of"likeness"
or small differences even though now it is athree-
dimensional vector quantity. This model has been quite
useful in qualitatively extending the concepts of
regular solution theory to a much broader range of
solvents and solutions, although quantitatively, the
model has not been very successful. This is because
there are some serious problems with this model which
can be revealed upon examination of equation [27]. The
most important of these are the inability to deal with
exothermic heats of mixing and the incorrect modeling of
H-bonding interactions. Equation [27] contains the
squares of the differences of the individual solubility
parameters. This can only lead to positive or
endothermic values of AH [mix]. Thus this model is
incapable of accounting for the few exothermic systems
such as water- triethylamine.
In the second problem, the H-bonding interaction
18
2
is incorrectly modeled. The difference term ( 8,-
S )' 2 h
implies that, like dispersion interactions, effective
solute-solvent H-bonding depends on some likeness or
similarity of the two liquids. In reality, H-bonding
depends on the complimentary matching of donor and
acceptor properties of the two liquids. The strongest
H-bonding interaction should occur between a strong
proton donor compound and a strong proton acceptor
compound. The above model would incorrectly predict a
small difference in S's and little H-bonding for these
two types of compounds .
Model Incorporating Proton Donor-Acceptor Properties:
A simple way of incoporating the inherently
complimentary nature of H-bonding into the expression
for AH [mix] is to make- A E [H-bond], the product of
a pure liquids s proton donor ability ( PD ) and its
proton acceptor ability ( PA ) :
- AE [H-bond] = ( PD ) ( PA ) [28]i i
It should be noted that the large magnitude for the
range of H-bonding energies can not be described by the
sum of PA and PD. Using similar expresions for H-
bonding between different species, the change in the
19
H-bonding energy on mixing two liquids can be
approximated by summing the various interactions:
AE mix [H-bond] = PD .PA+ PD .PA
- PD . PA -PD .PA [29]11 22 1221
Rearrangement of this expression gives the result first
suggested by Small (19):
AE mix [H-bond] = ( PD,
-
PD2 )( PA,- PA
2) [30]
This equation incorporates complimentarity and correctly
predicts that the most favorable interaction will involve
a high PA - low PD liquid and a low PA - high PD liquid.
The equation also resolves the first problem since the
product of the two differences may be either positive
(endothermic) or negative (exothermic). Most mixtures
result in a positive or endothermic AE mix, and a few
result in exothermic AE mix, such astriethylamine-
Some mixtures, even nonpolar solvents, can have very
small negative AE mix values.
Keller et al. (13) used a similar expression in
defining the H-bonding interaction in terms of a set of
Bronsted base, S. (equivalent to PA), and Bronsted acid,D
S (equivalent to PD) , solubility parametersa
A E [H-bond] = 2 V S S [31]iab
20
The corresponding expression for H [mix] was written
AH [mix] =
V202
+
(S,-S2)p+ 2(S, -S 2)a (S, -S2 >b ] [32]
Unlike Hansen's model, this approach incorporates both
complimentarity and the possibility of exothermic
interactions. But there are still two potential
problems. The use of a composition dependent H-bonding
2
term ( via the V? 0, multiplier ) is questionable.H-
bonding is a specific interaction and adducts of fixed
composition are formed. Unlike the nature of the
dispersion interactions, the composition of these adducts
does not depend on the bulk composition of the solution.
Even if the bulk composition changes the same adduct will
be formed. Thus ideally the enthalpy of this interaction
should not depend on the composition of the bulk solution
whereas the dispersion term does. A second problem is
the difficulty in obtaining a sufficiently broad range of
S and S. values for common solvents. Also values of Sa b a
obtained are not chemically self consistent. Thus at a
practical level, Keller's equation has not been
extensively used.
This research proposes to keep the correctly
modeled nonspecific dispersion term intact while
replacing the specific interaction terms ( the hydrogen
21
bonding interaction ) with a Lewis acid-base term. This
proposal along with the appropriate Lewis acid-base
concepts are explained in the next section.
22
LEWIS ACID-BASE CONCEPTS IN SOLUBILITY THEORY
Definitions:
The Lewis acid-base concepts were first formulated
by the American physical chemist G. N. Lewis (3) in 1923
and defined an acid as any species which can accept a
share in a pair of electrons during the course of a
chemical reaction. A base was defined as any species
capable of donating that pair of electrons.
Neutralization becomes, in turn, 6imple coordinate or
heterogenic bond formation between the acid and base:
A + :B > A:B [33]
Lewis Arid-Base Donor-Acceptor Term:
The H-bonding interaction is not a particular
kind of intermolecular force like the dispersion force
but is an example of a generalized electron-pair donor-
acceptor interaction (20). Thus this research proposes
to replace the Bronsted acid-base term in Keller's
expressions, equations [29] and [30], with a generalized
electron-pair donor (EPD)- electron-pair acceptor (EPA)
term. Since H-bonding interactions are specific and
23
give adducts ( however short lived ) , they should be
modeled after Small's complimentarity equation (19).
The proton acceptor ( PA ) and the proton donor ( PD )
parameters in equation [30] can be replaced with a more
generalized electron pair donor number ( DN ) and
electron pair acceptor number ( AN ) . Thus aDonor-
Acceptor H mixing term can be written as:
AH mix [DA] = k ( AN - AN )( DN,- DN
_ ) [34]1 2 1 2
where k is a scaling constant of some sort. This should
give an improvement over Keller's equation [32] since the
AN and DN values for a broad range of solvents are
readily obtainable and a composition dependency is not
included.
A Concept Combining Dispersion and Donor-Acceptor Terms:
Since most specific electrostatic or polar
interactions can also be included in conventional
measures of electron pair donor and acceptor strengths, a
separate polar term in a solubility equation is
redundant and not needed. Thus the simplest chemical
model for the cohesive energy for a pure liquid is just:
AE [vap] = AE (dispersion) + A E ( DA ) [35]
24
a two term equation with polar and H-bonding interactions
included in the Lewis acid-base donor-acceptor term:
AE; [vap] = VS. + k ( AN: )( DN. ) [36]i id '
The enthalpy of mixing would also be a two term equation:
^2 2.^H [mix] = V 0 (S -g ) + k ( AN -AN )( DN -DN ) [37]
2 21 12d 1 2 1 2
In order to be able to use these new equations for
predicting solubility, the AN and DN values have to be
known. Therefore the first part of this research has
been devoted to expanding the list of AN and DN values
currently available.
Determination of Acceptor and Donor Numbers:
The donor number ( DN ) was originally defined by
Gutman (21). The DN represents a liquids ability to
donate a pair of electrons. It is based on the heat of
reaction, -AH mix, of the the standard Lewis acid or
electron-
pair acceptor ( EPA ) probe antimony
pentachloride with a particular compound of interest in a
dilute 1 , 2-dichloroethane solution:
D: + SbCl > D:SbCl [38]5 5
J
DN = -AH [ EPD > SbCl ] (kcal/mol)
25
The acceptor number ( AN ) represents a liquid's
ability to accept an electron pair. It is based on the
31
P NMR shift induced in the standard Lewis base or
electron-pair donor ( EPD ) probe triethylphosphineoxide
by the species of interest relative to that induced by
n-hexane :
Et3P=0 + A > Et3P-0 -*A [39]
This relative shift in ppm is scaled, in turn, relative
to the shift induced by SbCl in dilute 1,2-
dichloroethane solution:
AN- 100 ( SEtapQ^-
SEt3PQ-Hexane ^
BEt3PO-SbCl5"EtgPO-Hexane/
These shifts are also extrapolated to infinite dilution
and corrected for the difference between the change in
volume on mixing of hexane and the solvents in question.
The dimensionless AN are arbitrarily fixed and vary from
0 for hexane to 100 for Et3P0->SbCl5 .
Donor number values have been experimentally
determined for 53 liquids and acceptor number values for
34 liquids. However, both values have only been reported
for 25 liquids, too few to be practical (21).
Fortunately, there are other probes which are also
26
selectively sensitive to either Lewis acidity or
basicity. One of the most comprehensive solvent scales
is the E (30) scale which was developed by Dimroth et al.
[21] . This scale is based on the transition energy for
the solvatochromic intramolecular charge transfer
absorption of 2 , 6-diphenyl-4(2 , 4 , 6-triphenyl-l-pyridinio)
phenolate :
_i
E (30) Kcal/mol = he V NA = 2.859 x 10V (cm )Avo
[41]
The structure of the dye is shown in figure 1 . The
E (30) is a solvent dependent absorption of the above
solvatochromic dye. As shown in the below structure, the
Figure 1. Structure of phenolate dye.
dye has acid and base sites. The positive charge of the
dye is delocalized over the pyridinium ring and shielded
by phenyl groups. Therefore, only the base site, the
phenolate anion, is accessable. Thus the dye only
interacts with solvents which are Lewis Acids. If the
27
phenolate is strongly solvated by the sovent , then the
dipolar ground state of the dye will be stabilized. The
greater the Lewis acid strength of the solvent, the more
the dipolar ground state is stabilized and the larger the
transition energy becomes. Thus the transition energy of
the phenolate dye, and the E (30) values depend on the
Lewis acidity of the solvent.
Reichardt (23) plotted E (30) values against AN
values for 38 solvents and obtained the correlation
equation below for AN and which is shown in figure 2.
AN = 1.598 E (30) - 50.69 [42]
Deviating solvents such as acetic acid and chloroform
were excluded. Schmid (24) also plotted ET(30) values
against AN values for only 21 solvents and obtained a
similar correlation which is shown in figure 3.
AN = 1.29 E ( 30) - 48.52 [43]
Highly structured solvents such as alcohols, acids, as
well as chlorinated hydrocarbons were not used in the
correlation. Thus AN values for additional liquids can be
calculated using these correlation equations. Schmid
(24) also found a correlation of AN and DN with the
dielectric constant for 31 solvents
28
i m
so
10
AN
30
20
10
110
M?
100 OwoX"1US MH >
20*116
30 40 50
fT(30l (kcol/mell
60
Figure 2. Reichardt's correlation of AN and ET (30)
for pure organic solvents.
Correlation equation
AN - 1.598 ET (30) - 50.69
Correlation coefficient
R - 0.956
(reproduced from reference 23)
29
AN
Figure 3. Schmid's correlation of AN and ET (30)
Solvents labelled by full circles have been
used to calculate the following correlation
AN (a) - -40.50 + 1.29 E (30)
A Highly structured solvent not used in
correlation
O Highly structured chlorinated hydrocarbons
not used in the correlation
( reproduced from reference 24)
30
log = 0.0711 AN + 0.0054 DN + 0.2581 [44]
The highly structured solvents not used in the AN-E (30)
correlation equation [43] were also excluded in this
equation. This correlation can be used to calculate
either AN or DN values if one of the other two values and
the dielectric constant are known.
Other donor scales such as AV_(25), D {11,1}
(25), ^ (26) and -AH [BF ] (27) have been correlated
with the DN scale. The correlation equations and their
correlation coefficients are given below:
DN = 0.20 (AVD) +3.03
DN = 10.11 D{II,I] - 12.17
DN = 38.4 ( ) - 0.78
DN = 0.261 (- A H__ ) - 1.15
DN = 0.19 B - 0.636
The availability of experimentally determined AN
and DN values is not a practical limitation as is the
case for limited availability of Bronsted acid and base
terms in Keller's model since AN and DN values may be
calculated from other acceptor and donor experimental
data. Thus the simple solubility concept developed in
equation [37] with AN and DN values should be more widely
applicable than Keller's equation [32]. This concept is
further developed and tested in the following sections.
31
R = 0.,984 [45]
R = 0.,995 [46]
R = 0,,98 [47]
R = 0,,9684 [48]
[49]
EXPERIMENTAL
Materials:
Solvents of high purity were used as received.
These include: acetone (EM Science), benzonitrile
(Fisher), carbon disulfide (Fisher), carbon tetrachloride
(Fisher), chloroform (Fisher), cyclohexanone (Baker),
o-dichlorobenzene (Kodak), ethyl acetate (Baker), ethyl
benzoate (Fi6her), ethyl ether (Fisher), ethyl formate
(Fisher), ethylene glycol (Fisher), Formamide (Aldrich) ,
glycerol (Aldrich), methyl ethyl ketone (Baker),
nitrobenzene (Baker), nitroethane (Kodak), nitromethane
(Kodak), pentanol (Baker), water (HPLC grade-EM Science),
m-xylene (Kodak), and o-xylene (Kodak). Other solvents
were distilled and stored over molecular sieves prior to
use include: Acetophenone (Baker), aniline (Baker),
benzene (Baker), t-butylamine (Fisher), butanol (Baker),
butyl ether (Fisher), chlorobenzene (Kodak), cyclohexanol
(Fisher), N,N-dimethyl aniline (Fisher), ethanol
(absolute, US Industries), methanol (absolute, Baker),
and triethylamine (Kodak).
32
CorrelatinriB-
A least squares linear regression analysis was
used to determine correlation equations for acceptor
number ( AN ) and E (30) values for the highly structured
solvents not used in equations [42] and [43]. The method
of least squares assumes that errors in the y values
( AN ) are greater than the errors in the x values,
ET(30). The line for the equation is:
AN (cal) = m E (30) + b [50]
where m is the slope and b is the y intercept. The
vertical deviation, d., of a point from the line is given
by y.-
y where y is the ordinate of the straight line
when x = x. .
i
d. = y.-
y = (AN exp- AN cal) [51]
Minimizing the squares of the deviations gives
d? = ( y.-
y
)2
= ( AN exp- AN cal [52]
The least squares slope and intercept are given by the
following equations
33
m =
IXj yj ?X;
n
D [53]
b =
J(Xj )
2X:
2xi y\
*y-.
7 D [54]
where n is the number of points and the value of D is
given by
D =
2(x-, )
Sx;
Ix.
n
[55]
The correlation coefficient was found by the following
expression
r =
2 2 2
lJx- ( r ys ) "
d\
[56]
Zy. - ( Iy8 ) /n
The error analysis for equations [53] and [54] results
from the variances of the slope and intercept
34
^e7
= [57]
el zu,)
V[58]
2'
where the standard deviation of the vertical deviation is
defined as
7-1
Z(d; )
v V [59]
n-2
The MINITAB statistical program on the RIT VAX
computer system was used to develop multiple regression
correlations of AN, DN and dielectric constant ( )
similar to equation [44] for each cIsee of chemical
compounds, for example, alcohols, hydrocarbons etc.
Miscibility Det.erminat.ion:
Experimentally ,mutual miscibility of binary
mixtures was determined by adding solute to solvent in 9
test tubes in proportions of 10% to 90% by volume in 10%
35
increments. The test tubes were maintained at a constant
temperature of 25 C for 20 minutes in a water bath
(Science / Electronics Inc., model SE) . In many cases
miscibility of mixtures could be determined by the
absence of a meniscus. The presence of a meniscus
indicated either immiscibility or partial miscibility.
Partial miscibility was determined by significant changes
in the refractive index of either layer versus the
refractive index of the pure liquid.
Construction of Miscibility Sorting Maps:
A LOTUS 1-2-3'
program was used to establish a
data base for 43 liquids. The AN, DN , and dispersion
solubility parameter ( S . ) values were entered in
appropriate columns. This data was expanded so that each
liquid was paired with the other liquids. This created
42 possible pairs for each liquid for a total of 43x42 or
1806 possible binary pairs. The Lotus 1-2-3v
program was
used to calculate the values of the two terms
0.01 ( AN,-
AN2 )( DN,-
DN2 ) and ( g,-
82 for
each binary liquid pair. Then literature data, if
available was entered into the data base as to whether
each binary pair was miscible or immiscible. Literature
data which was conflicting, for example, listed as both
miscible and immiscible, was entered as questionable.
36
Miscibility sorting maps for each of the 43
e
solvents were constructed using LOTUS 1-2-3 PRINT GRAPH
program with the above data base. For each map the
acceptor-donor term [ 0.01 ( AN,-
AN2 ) ( DN,-
DN2 ] was
plotted against the dispersion solubility parameter term
( fi,-
S, ) for each of the 42 possible binary pairs.
Thus each map could have 42 points. Miscible pairs were
plotted as squares, immmiscible pairs as plus signs, and
questionable pairs as diamonds. Bianary solvent mixtures
without reported miscibility data were not plotted so
each map generally had less than 42 points.
37
RESULTS AND DISCUSSION
Research Objectives:
This thesis research has been directed towards the
development and substantiation of the solubility concept
proposed in a previous section which incorporates the
dispersion solubility term [14] from equation [27] and a
Lewis acid acceptor-donor term from equation [34]
AH [mix] = V 6 (S -S ) + k (AN -AN )(DN -DN ) [37]2r
1 1 2d 12 12
These terms, [14] and [27] are defined in previous
sections .
To accomplish this, four research goals were
established. The first goal was to develop a better
correlation of AN and E (30) values in order to expand
the list of available AN values, especially for the
highly structured solvents which were not used in
Schmid's correlation equation (24). A similar goal was
established for Peter Michelsen's thesis (29) research in
extending the list of available DN values through the use
of correlation of DN with other donor scales.
The second goal was to develop a better
correlation of AN, DN and dielectric constant ( e ) using
38
the AN and DN values obtained in the first part of the
research together with available AN, DN and dielectric
constant values. The purpose of these two goals was to
obtain more new AN and DN values for use in the third
goal.
A third goal was to construct miscibility sorting
maps by plotting the values of the acceptor-donor term
against the dispersion term of the above equation [37]
for several binary liquid mixtures. Ideally, these maps
should have regions of miscible binary mixtures and
immiscible binary mixtures.
The fourth goal was to test these sorting maps by
experimentally determining the miscibility of binary
liquid mixtures. Another part of this goal was to test
the usefulness of these sorting maps in predicting the
miscibility of binary liquid mixtures before experimental
verification.
Correlation of AN and ETf30):
Error Analysis of Schmidts Equation:
A list of experimental AN values for 34 solvents
was compiled with a Lotus 1-2-3 program. Additional AN
values were determined from solvents having Ey(30) values
using Schmid's correlation equation [43]. This expanded
39
the list of solvents with AN values to 113. These values
are include in Table A-l in the appendix. Schmid 's
correlation equation was not U6ed to calculate AN values
for alcohols and chlorinated hydrocarbons, since these
highly structured solvents were not used in determining
the correlation.
Schmid did not give a correlation coefficient
value for equation [43] even though he claimed it had a
better correlation than Reichardt's correlation [42],
Since no correlation coefficient or any type of error
was given for Schmid 's equation [43], an error analysis
of Schmid 's equation was conducted. The calculations are
summarized in Table 2 and below.
I(dj ) 33.09
n- 2
1.7415
19
[59]
D -
1 (x/ ) Xx.
n
D = (35333. 22M21)- (857)(857) = 7548.62
[55]
m
6~y n
D
(1.7415H21)
7548.62
= 0.004845 [57]
40
TABLE 2
ERROR ANALYSIS FOR SCHMID'S CORRELATION EQUATION
aXi
Xi2
Yl Y d Yi-Yd,2
SOLVENTS EtOO) EtOO) AN(txp) ANCeal)1
1. acetone 42.2 1760.84 12.S 13.9 -1.4 1.96
2. aeetoni trile 46 2116 18.9 18.8.0.1 0.01
3. bvnzoni trile 42 1764 13.3 13.7 1.8 3.24
4. diglyme 36.6 1489.96 9.9 9.3 0.6 0.369. diethylether 34.6 1197.16 3.9 4.1 -0.2 0.04
6. DMA 43.7 1909.69 13.6 13.9 -2.3 5.297. OMF 43.6 1916.44 16 16 0 08. DMSO 43 2023 19.3 17.S 1.8 3.249. ethylaeetate 38.1 1431.61 9.3 8.6 0.7 0.4910. ipa 40.9 1672.61 10.6 12.2 -1.6 2.5611. hexane 30.9 954.81 0 -0.66 0.66 0.435612. metthylacetate 40 1600 10.7 11.1 -0.4 0.1613. NIP 42.2 1780.84 13.3 13.9 -0.6 0.3614. nitrobenzene 42 1764 14.8 13.7 1.1 1.2113. ni tromethane 46.3 2143.69 20.3 19.2 1.3 1.6916. pyridine 40.2 1616.04 14.2 11.3 2.9 8.4117. THF 37.4 1396.76 8 7.7 0.3 0.0918. TBP 39.6 1368.16 9.9 10.6 -0.7 0.4919. triethylamine 33.3 1108.89 1.4 2.4 -1 120. TWP 43.6 1900.96 16.3 15.7 0.6 0.3621. PC 46.6 2171.36 18.3 19.6 -1.3 1.69
SUMf) 837 35333.22 33.09
a Highly structure solvents are not Included in
Schold's correlation such as alcohols and some
chlorinated hydrocarbons.
41
, 6~v x. (1.7415)(35333.32)5"b2
= y- l-= [58]
D 7548.62
= 8.1515
6~m =0.07 and 6"b =2.86
Thus the correlation equation was rewitten with the error
included
y = ( m +CTm ) x + ( b +
CTb ) [60]
Schmid 's equation was then written as
AN = ( -40.52 + 2.86 ) + ( 1.29 0.07 ) ET(30) [61]
The total error for AN was given by
AN error = ^ 6~b +0~m2
=
J(2.86)2+(0.07)2
=2.86 [62]
The correlation coefficient was also calculated
from the data in Table A-l using equation [56] and found
to be F = 0.974. This value indicates a somewhat better
correlation than for Reichardt's correlation. However,
neither correlation included highly structured solvents
such as alcohols and chlorinated hydrocarbons.
42
Correlation of AN and ETf3Cn for Alcohols and
Chlorinated Hydrocarbons:
Several attempts were made to improve the
correlation of AN and E (30) values, especially for
highly structured solvents which were not included in
Schmid 's or Reichardt's work. Including these solvents
only resulted in a poor correlation. Another means of
correlating AN and E (30) for these solvents was used.
Examination of Schmid 's plot of AN versus E (30) in
figure 3 shows that the highly structured solvents which
were excluded from the correlation fall into a separate
group such that a different line can be drawn just
through that group as shown in figure 4.
If the AN and E (30) values for seven alcohols and
water were plotted, then the following correlation
equation was obtained
AN (b) = -39.69 + 1.503 E (30) [63]
A linear regression analysis gave a correlation
coefficient of R = 0.9622. However, an even better
correlation equation was established by linear regression
analysis for the above seven alcohols, water, and three
chlorinated hydrocarbons ( methylene chloride,
chloroform, and carbontetrachloride ) with a correlation
43
AN
Figure 4. Correlation of AN and E (30) for alcohols,
three chlorinated hydrocarbons and water.
AN (c) --38.536 + 1.4826 E (30)
1. carbontetrachloride (CC1 ) 6. n-butanol
3. chlof orm (CHClj )
2. methylenechloride (CH2C1 ) 7. 1-propanol
8. ethanol
A. t-butyl alcohol 9. methanol
5. i-propanol 10. water
11. 2-aminoe thauol
44
coefficient R = 0.9821.
AN (c) = -38.536 + 1.4826 E (30) [64]
This equation was then used to calculate AN (c) values
for 32 alcohols and deuterium oxide (DO) which did not
have experimental AN values.
These calculations expanded the list of liquids
with AN values to 153. The experimental AN values and
the calculated AN values ( AN (a) from Schmid's
correlation [43] or AN (c) from the above correlation
[64] ) are listed in Table A-2 in the appendix.
Error Analysis of Correlation Equation For
Alcohols and Chlorinated Hydrocarbons:
In order to show that equation [64] for alcohols
and chlorinated hydrocarbons is as reliable as Schmid s
correlation equation [43] for other solvents, an error
analysis for equation [64] was also conducted. The data
is summarized in Table 3. The following calculations
give the error in the correlation as
AN (c) = (-38.536 3.909) + (1.4826 0.0789) E (30) [65]
The total AN error then was calculated as
45
TABLE 3
ERROR ANLYSIS OF CORRELATION EQUATION
FOR ALCOHOLS AND CHLORINATED HYDROCARBONS
xi(Xi)2
Yj Y d. Y -Y dfSOLVENTS
ET(30) (ET(30)) AN( exp) AN( cal)
i
1. CHzCl2. 41.1 1669.21 20.4 22.4 -2 4
2. CC14 32.5 1056.25 8.6 9.6 -1 1
3. CHC13 39.1 1528.81 23.1 19.4 3.7 13.69
4. methanol 55.5 3080.25 41.3 43.7 -2.4 5.76
5. ethanol 51.9 2693.61 37.1 38.4 -1.3 1.69
6. 1-butanol 50.2 2520.04 36.8 35.9 0.9 0.81
7. 2-propanol 46.6 2361.96 35.5 33.5 2 4
8. t-butylaleohoi 43.9 1927.21 27.1 26.6 0.5 0.25
9. 1-propanol 50.7 2570.49 37.3 36.6 0.7 0.49
10. 2,2,2-tri- 59.5 3540.25 53.5 49.7 3.8 14.44
f luoroethanol
11. water 3.1 3981.61 54.8 55 -0.2 0.04
SUM (2 ) 536.1 26949.69 46.17
.2 -
m
46.17
n-2
26949.69
536.1
46.17
536.1
11
y tn
5.13
9043.36
(5.13K11)
9043.38
l(5.13)(26949.69)
0.0789931
0.07899
9043.38
3.909940
3.9099
AN -38.536 + 1.4826 x E (30)
AN -(38.536* 3.909) + (l .4826 0 .0789 ) E(30)
AN 3.91
46
AN error =
\|(3.909)2
+ = 3.91 [66]
Correlation of AN. DN and Dielectric Constant :
The second part of the research was to expand the
list of available donor number ( DN ) . Using the above
expanded AN list (Table A-2), the expanded DN list
developed in Peter Michelsen's thesis (Table A-3), and
available dielectric constants (Table A-l), correlations
similar to Schmid's correlation equation [44] were
developed by using theMINITAB'
statistical program on the
RIT VAX computer system. An equation developed for all
solvents including alcohols, chlorinated hydrcarbons and
water had poor correlation with a correlation
coefficient of R = 0.701.
log g = 0.574 + 0.0253 AN + 0.00353 DN [67]
When alcohols, water and chlorinated hydrocarbons are
excluded, a much better correlation was obtained with a
correlation coefficient of R = 0.886
log = 0.340 + 0.603 AN - 0.00115 DN [68]
Examination of this correlation reveals that two solvents
do not fit the correlation. They are formamide and
47
methyl formamide. If these two solvents were excluded,
then the correlation would be much the same as Schmid 's
equation. Thus just doubling the data points in a
correlation like Schmid's equation [44] does not really
improve the correlation.
Schmid had used just one or two of the simplest
compounds in each class of copounds . The correlation in
equation [67] includes several compounds in each class.
However, these solvents tend to cluster around the
correlation line rather than aligning with it. Thus any
improvement gained by more points is cancelled by losses
due to more scatter within classes of compounds.
As can be noted the correlations in equations [44]
and [67] are for solvents of low or moderate dielectric
constant ( t ) . The dielectric constant ( 6 ) appears to
be a measure of the amphoteric character of solvents.
Solvents with strong acceptor properties (high AN values)
do not fit these correlations . These include the
alcohols, formamide, methyl formamide, chloroform,
carbon tetrachloride, and methylene chloride. Schmid
explains that these highly structured solvents deviate
because the bonds between solvent molecules have to be
broken before they can act as donors or acceptors (24).
Another reason given is that the coordination properties
of these solvents is not constant, but depends on
complimentary solute properties.
48
Since the highly structurted solvents could not be
included in a general correlation, separate correlations
of AN, DN and for each class of compounds were
developed. The correlation equations and the
corresponding correlation coefficients are given in
Table 4. Surprisingly, the alcohols, amides and halides
show good correlation within each class while the less
polar classes such as ketones, ethers and hydrcarbons
which had a good overall correlation have very poor
correlations within each class. Perhaps this is not as
surprising as it first seems. Examination of the list of
alcohols in Table A-2 shows that there is a strong
correlation of E and AN on the chain length of the
alcohols. As the chain length increases, both the AN and
values decrease. This occurs over a large range of AN
and . For solvents having low such as ketones,
ethers, and hydrocarbons, changes in chain length causes
only small changes in already low AN and . values.
These small changes are difficult to correlate,
especially with limited data.
At least for now, Schmid's correlation, equation
[44], can be used for low or moderately polar solvents,
and the newly developed equations in Table 4 can be used
for strongly polar or protic solvents.
Before these correlations were used to calculate
additional DN values, new DN values were made available
49
TABLE 4
CORRELATION OF AN, DN, AND E
FOR DIFFERENT CLASSES OF SOLVENTS
Log 8 = C+a(AN)+b(DN)
alcohols
amides
halides
esters
amines
nitro &
nitriles
ketones
hydrocart
ethers
0 0840 0 0330 -0 00015 0 938 0 969
0 708 0 0188 0 0190 0 960 0 980
0 686 0 0375 -0 0922 0 941 0 980
0 172 0 956 -0 0179 0 845 0 919
1 32 0 0180 -0 0181 0 703 0 838
1 18 0 0225 -0.00869 0 558 0 747
0 919 0 0101 0.0135 0 454 0 674
0 307 0 00765 0.00352 0 420 0 648
0 382 0 0290 0.00390 0 258 0 508
AN Acceptor Number
DN Donor Number
Dielectric constant (25'C
C, a, b Constants
P Correlation coefficient
50
by Marcus (30). These values were used instead of the
values calculated from the above correlation equations.
However, these new DN values from Marcus were found to be
consistent with and close to the values predicted by the
correlations. Thus these correlations can at least be
used to calculate dielectric constant ( ) values.
A final list was compiled in Table A-4 (appendix)
which includes experimental AN values, and AN values
calculated from either Schmid 's correlation or the
structured solvent correlation [64]. This list includes
the average DN values from Table A-3 and the new DN
values obtained from Marcus. The dispersion solubility
parameter ( S ) is also included in the list.d
Miscibility Sorting Maps:
The third portion of the research involved
construction of sorting maps of miscibility for binary
liquid mixtures. A sorting map is a graphical procedure
that allows the display of an empirically known
dependency of a given property ( ie. solubility, phase
diagram behavior ) on parameters for which the exact
mathematical dependency is not known (31). In this
research only two parameters are used, the acceptor-donor
term and the dispersion solubility parameter term of
equation [37]. Miscibility of binary mixtures are
plotted in an XY plane as a function of these two terms.
This plane is then emperically divided to sort areas of
solubility or insolubility. These areas can not be
predicted ahead of time since the exact dependency of
miscibility is known only after a plot is drawn. Then
areas or regions of miscibility and immiscibility can be
drawn and the plot optimized. The value of such a
sorting map is the convenient graphical display of the
relation of miscibility to the dispersion and the
acceptor-donor terms. More importantly a miscibility
sorting map allows prediction of miscibility or
immiscibility of other binary liquid mixtures which were
not used to make the original plot.
Initially a list of the 106 solvents in the
previous section with their AN and DN was made using
LOTUS 1-2-3 (Table A-4). The dispersion solubility
parameter term ( S. ) obtained from Barton (9) for 87 of
d
the above liquids were also included in the list. The d
values for the remaining liquids were calculated from
Beerbower's, Hansen's (12) and Van Krevelen's group
contribution method (18) using equation [22]. These
values were also included in the list.
A literature search was conducted to find reported
miscibility data for the possible binary liquid mixtures
of solvents in that list. However, very little
miscibility data was available. For many solvents only
miscibility data with a few common solvents were listed.
Adequate data could only be obtained for 43 solvents (32)
Thus only these 43 solvents, in which miscibility data in
many solvents is given, were used to construct 43
miscibility sorting maps. A list of these 43 solvnets
is given in Table 5.
As explained in the experimental section, the
acceptor-donor term ( AN ) ( DN ) was plotted against the
2
dispersion solubility parameter term ( - S ) . fori 2 d
each binary liquid mixture. The resulting point was
drawn as a square (D ) if the binary mixture was miscible
or as a plus ( + ) if the mixture was immiscible.
Generally, for most sorting maps, areas of mutual
miscibility and immiscibility could be clearly
distinguished. On the sorting maps, points for miscible
binary liquid mixtures tended to congregate near the
origin of the X and Y axes. Points for the few
immiscible binary mixtures tend to be much further away.
In most cases the immiscible points are well separated
from the miscible points. Lines could be drawn around
both sets of points forming immiscible and miscible areas
which were quite clearly separated from each other.
As part of the fourth research goal, several
sorting maps were examined in order to evaluate them.
This generally consisted of verifying the borders of the
immiscible and miscible regions by experimentally
53
determining the miscibility of binary mixture points
which were near the borders. Another part of this
evaluation was extending or extrapolating these two
regions by including experimentally measured points.
Sorting maps evaluated by this process include benzene,
hexane, toluene, methanol, ethanol, chloroform, acetone,
diethylether, and formamide. Two sorting maps in
particular, benzene and hexane, were examined in greater
detail. A major reason for this is that the immiscible
and miscible regions were not clearly distinquishable, as
they were on all the other sorting maps. The data used
to construct these two maps is given in Table 5. These
two maps were evaluated fully in order to determine
whether the immiscible and miscible regions could be
separated. Finally these maps were tested by determining
whether these regions on the maps could predict
miscibility by interpolation within the regions. These
predictions were then verified experimentally.
Benzene-Solvent Binary Mixtures Sorting Map:
Analysis of Benzene Sorting Map:
For benzene, three sorting maps are shown in
figures 5,6,7. The first sorting map attempted is shown
in figure 5. Most of the points for the benzene-solvent
54
TABLE 5
DATA FOR SORTING MAP FOR BINARY LIQUID SYSTEM
HYDROCARBONS
LIQUID 1 LIQUID 2
S AD
M Iri
n-htxint benzaldehyde 3.24 3.58n-hexane t-butylamine
n-hexane o-xylene
n-hexane fn-xylene
nhexane tr iethylamine 0 0.6n-hexane itoamylalcohol 0.09 9.82n-hexane c-hexane
n-hexane benzene 2.69 0.01
n-hexane toluene 2.25 0.01
n-hexane ethylenechlorlde
n-hexane CC1.
CHCl,
1.96 -0.18
n-hexane 1.96 0.05
n-hexane chlo'robenzene 4 -0.08
n-hexane o-dichlorobenzene
n-hexane ni tromathane
n-hexane ni trotthane
n-hexane ni trobenzene 6.25 0.64
n-hexane propieni trile 0.04 1.78
n-hexane benzoni trile
n-hexane ethylacetate
n-hexane ethyl formate
n-hexane ethylbenzoate
n-hexane acetone 0.09 1.75
n-hexane methylethylketone
n-hexane cyclohexanone
n-hexane acatophenone 5.29 1.66
n-hexane diethylether 0.04 0.6
n-hexane di-n-butylether
n-hexane aniline 4.84 5.11
n-hexane NfN-dimethylaniline
n-hexane pyridine 4 4.57
n-hexane formamide 1.21 11.5
n-hexane CS2 7.29 0.01
n-hexane tri-n-butylpho*phateB.04
n-hexane methanol 0.01
n-hexane ethanol 0.16 7.03
n-hexane 2-propanol
n-hexane 1-butanol
n-hexane 1-pentanol
n-hexane cyclohexanol
n-hexane benzylalcohol
n-hexane ethylene glycol 1 7.18
n-hexane glycerin 1.44 7.3
n-hexane water 0.09 ie.3
TABLE 5 ( continued )
AD
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzene
benzaldehyde
t-butylamine
e-xylene
m-xylene
triethylamine
iaoamylalcohole-hexane
n-hexane
toluene
ethylenechloride
CCI4
CHCljchlorobenzene
o-dichlor0benzene
ni tromethane
ni trot thane
ni trobenzene
propioni trile
benzoni trile
ethylacetate
ethylformate
ethylbenzoate
acetone
methylethylketone
Cyclohexanone
acatophenone
diethylether
di-n-butylether
aniline
N,N-dimethylanilin
pyridine
formamide
CS2tr i-n-butylphotpha
methanol
ethanol
2-propanol
1-butanol
1-pentanol
eyelohexanol
benzylalcohol
ethylene glycol
glycerin
water
0.01 2. 52
2.2s -0.65
2.89 -1.85
1.96 7.43
2.89 0.27
0 0.01
0.04 -0.02
0.09 -0.01
0.09 -0.03
0.16 -0.01
1.69
1.44 0.11
0.64 0.27
2.25 0.85
0.25 0.68
1.69 0.13
1.96 0.56
0.01 0.05
1.96 0.6
1.44 0.6
0.09 0.39
0.36 0.59
3.61 -0.65
2.56 -0.83
0.25 2.56
0.09 1.93
0.36 9.06
1
1 0.35
2.56 6.49
1.69 5.49
1.69 8.19
1.44 7.06
1.44 5.98
0.25 4.75
0 4.32
0.49 5.83
0.25 9.94
1.96 13.8
0.36
-0.03
Solubility parameter term of equation [37]
( S)
AD Acceptor-Donor term of equation [37]
0.01 ( AN,
-
AN2 ) ( DN,
- DN2 )
where values are: (M) Miscible, (I) Immiscible,
or (?) Questionable or partially miscible
56
BENZENE
Z0
z
0
r\
CM
z<
z
<
0a
0
Figure 5 .Benzene-Solvent Sorting Map
D miscible, + immiscible
+1 benzene-water, +2 beuzene-f ormamide
+3 benzene-ethylene glycol
+4 benzene-glycerol
57
mixtures are near the origin or lie along the axes.
There are also two immiscible points for benzene-solvent
mixtures. These two points, the immiscible benzene-water
(+1) and immiscible-benzene formamide (+2) mixtures, are
well separated from any miscible points. These two
mixtures were checked experimentally and found to be
immiscible in all proportions, agreeing with the
literature. Thus these two points clearly establish an
immiscible region.
Two other immiscible mixtures, benzene-ethylene
glycol (+3) and benzene-glycerol (+4), were added and
evaluated in order to extrapolate or more clearly
establish the immiscible region in figure 5. Ethylene
glycol and glycerol were not in the list of 43 solvents
used in constructing the sorting maps. However these
solvents are listed in the literature (32) as forming
immiscible mixtures with benzene. Thus these mixtures
were added to figure 5. These two points were plotted in
or very near the miscible region. This expanded the
immiscible region as shown in figure 5 so that the
boundaries between the miscible and immiscible regions
were difficult to determine. Two possibilities exist for
these results: 1) the literature results for miscibility
of mixtures near the boundaries are incorrect or 2) the
AN or DN values are incorrect. The benzene mixtures with
ethylene glycol and glycerol were tested experimentally
58
and found to be immiscible in all proportions. The
miscible mixtures in the same area were also tested
experimentally and found to be miscible. Examination of
the AN values of ethylene glycol (AN = 44.9) and glycerol
(AN = 46.0) show that they are in the expected range
between methanol (AN = 41.3) and water (AN = 54.8).
However the DN values of ethylene glycol and glycerol
were found to be much lower than the other alcohols and
water. The AN and DN values for the miscible solvents
were found to be consistent with similar solvents. Thus
the problem seems to be the low DN values of ethylene
glycol and glycerol.
Several authors have noted that Gutman'
s DN values
appear to be low for certain solvents (25,33,34). For
amphoteric solvents which can act as weak bases, this
undervaluation appears to be due to dissociation of the
solvent->SbCl complex (33). Donor number (DN) has been
defined as the negative A H values for 1:1 adduct
formation of solvent with SbCl (antimony pentachloride) .
Dissociation or incomplete formation of the complex
results in low DN values. This could be what has
happened for the weakly basic solvents ethylene glycol,
glycerol and formamide. This is also supported by the
fact that several investigators have found that the donor
or basicity values of formamide from different donor
scales are close to similar solvents (25,33,34). Thus
59
the low experimental DN value of formamide (DN = 24)
might be expected to be closer to the other amides,
especially N-methyl formamide (DN = 49). Likewise, the
low DN values for ethylene glycol and glycerol might be
expected to be closer to the DN values of other alcohols.
The published DN values for glycerol (DN = 19.0)
and ethylene glycol (DN = 19.2) are not experimental
values, but rather are values calculated from a
correlation equation [ 47 1 from the scale (26). Maria
and Gal (27) pointed out that this correlation is not
appropriate for alcohols. This is supported by the fact
that these calculated DN values for ethylene glycol and
glycerol are much lower than DN values of similar
alcohols, 2-propanol (DN = 35.7), 2-methyl-2-propanol (DN
= 38.0) and water (DN = 33.0).
Beerbower has provided new DN values, calculated
from a quadratic empirical relationship not yet published
(35), for formamide (DN = 49.8), ethylene glycol (DN =
38.8), and glycerol (DN = 38.4). These DN values appear
to be consistent with experimental DN values of similar
compounds. Furthermore, Beerbower 's DN values for other
amides and alcohols are very close to the experimental
values. IfBeerbowers'
DN values are used to calculate
dielectric constants from the approriate correlation
equations in Table 4, then the results are close to the
experimental dielectric constant values. Thus it seems
60
likely that Beerbower "s DN values are reasonable,
especially for formamide, ethylene glycol and glycerol.
Thus a second sorting map for benzene was made by
replacing the DN values for formamide, ethylene glycol
and glycerol in the first map, figure 5, with Beerbower rs
DN values. This second map is shown in figure 6. The
immiscible benzene-mixtures of formamide (+2), ethylene
glycol (+3), and glycerol (+4) were then located in the
immiscible area and well away from the other miscible
mixtures. All other points were not affected. The
result was that the immiscible region in figure 6 was
clearly separated from the miscible region.
Benzene Sorting Map - Miscibility Experimental:
The benzene sorting map was tested by
experimentally determining the miscibility ofbenzene-
solvent mixtures which are near the border of the
miscible and immiscible regions. These were the benzene
mixtures with methanol, formamide, glycerol and ethyene
glycol. The refractive index of these mixtures was
measured for different volume fractions in order to help
determine their miscibility. The results are listed
listed in Table 6. When a solute is dissolved in a
solvent, the refractive index of the resulting mixture
will be a volume-proportional weighted average of the
61
BENZENE
ZD
Z0
\J
r\
cs
z<
z
<
0
0
-10-
-15-
Figure 6 >Benzene-Solvent Sorting Map ( Beerbower's DN values )
Q miscible, + miscible,
+1 benzene-water, +2 benzene-f ormamide*
+3 benzene-ethyleneglycol*
+4benzene-glycerol*
* Beerbower'* DN values used
62
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51
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h m in
u
BOOU VO
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en
o
IO
tn
en mm mmm is> mmcji m oils o^i <r
no m cmm -< lti i
en en en is* en
<so 0US tA
o oCO CM
o oat
s
m
mm
10
rs.
en
en mm -oh en
m cmm <~i
en rsm S
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en
en
CO
cm m
m
en rnm
>o nm mCn V
*
me v m us enm - m -* mmen en 3* rs. cn v
ci ci
H >
-
en
m
CM
m o
en enmen
O
rs
9t en
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m
m m
m cm
en m
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en om usen
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en rs
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en
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aus
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?
om cm
en en
91 o nus mm v
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^ oe e
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w .c >, >>
t u3 (9e
63
refractive indexes of the solute and solvent. For
immiscible mixtures the proportion of the solute is very
small, so the refractive index of each layer is close to
that of the pure liquids. For partially miscible
mixtures, the refractive index of the mixture varies
proportionally with the volume % of the liquids. The
benzene mixtures of formamide, glycerol, and ethylene
glycol were found to be immiscible. The refractive
index measurements for these mixtures indicated that the
solvents have very low solubilities in each other. The
benzene-methanol (Q5) mixture was found to be miscible in
all proprtions. These results helped to define the
miscible and immiscible regions as shown in figure 7.
Several miscible benzene-solvent mixtures from the map
were also evaluated and found to be miscible by simple
mixing experiments. This expanded the miscible region.
Thus the area within the boundary line was confirmed to
be the miscible region with no immiscible points.
Benzene Sorting Map - Error Analysis:
In order to determine the reliability of the
benzene sorting map, an error analysis was conducted for
all of the benzene-solvent mixtures used in the map. The
calculations and results are given in Table 7. The AN
error was calculated in a previous section from equations
64
BENZENE
Z
0
z
0
z<
z<
Figure 7 .Benzene-Solvent Sorting Map ( Final Map )
O miscible, + immiscible
+1 benzene-water, +2 benzeue-f ormamide*
* a
+3 benzene-ethylene glycol, +4 benzene-glycerol
05 benzene-methanol , 06 benzeue-ethauol
* Beerbower'
s DN values were used
65
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66
[61J and [65]. The DN error was obtained from Peter
Michelsen's thesis (29) and is given in Table A-3. The
total ( ANi-
AN2)( DNi- DN ) error is generally small
for most points. The benzene-chloroform error is high
due to the high chloroform DN error. The high benzene-
dichlorobenzene error is due to the very small AN
values. However, the total error is small for each
immiscible mixture and each miscible mixture that are
located near the boundaries of the regions. Thus the
reliability of the benzene sorting map appears to be
good, especially in the critical areas between the
miscible and immiscible regions.
Benzene Sorting Map to Predict Misnihilitv nf
Mixtures:
In order for the sorting map to be useful, it must
be able to correctly predict the miscibility of binary
liquid mixtures. This was demonstrated for several
solvents which were not used in constructing the sorting
map. Solvents representing different groups were chosen
such as acetonitrile, N-methyl formamide, ethyl acetate,
2-butanone, di-n-butyl ether and t-butanol. Since the
AN, DN and S. values for these solvents were available ind
Table A-4, the points corresponding to the benzene-
solvent mixtures were plotted on the third benzene
67
sorting map. This plot is shown in figure 8 without
points for most of the mixtures so the points for the six
mixtures could be easily seen. The benzene mixtures of
acetonitrile, ethyl acetate, 2-butanone, butyl ether and
t-butanol are located in the miscible region. These
mixtures were predicted to be miscible. Since the N-
methylformamide mixture is located outside of both
regions, it was predicted to be miscible or partially
miscible, but not immiscible because it was not close to
the immiscible region. All mixtures were found to be
miscible in all proportions and the results are
summarized in Table 8. This helped to confirm the
boundaries of the miscible region. Thus the benzene
sorting map sucessfully predicted miscibilities of
benzene in a wide variety of solvents, including some
polar, highly structured solvents.
TABLE 8
PREDICTING MISCIBILITY OF MIXTURES
WITH BENZENE SORTING MAP
System Predicted Experimental
1 benzene-N-methylformamide miscible miscible
2 benzene-acetonitrile miscible miscible
3 benzene-ethy lacetate miscible miscible
4 benzene-2-butanone miscible miscible
5 benzene-di-butyl ether miscible miscible
6 benzene- t-butanol miscible miscible
68
BENZENE
z
Q
Z0
z<
z
<
0
0
-5-
-10-
-15-
-20
2
i
4
T T T
Figure 8.
0 2 4 b 8 10
(S.-Ud*
Benzene-Solvent Sorting Map- ( Predictions )
? miscible,+ immiscible
0 1 beuzene-N-methylformamide, D 2 benzene-acetonitrile
D3 benzene-ethyl acetate, D k beuzene-2-butanone
D5 benzene-butyl ether, D 6 benzene-t-butanol
69
Hexane - Solvent Binary Mixture Sorting Hap
Evaluation of Hexane Sorting Man:
Similar to benzene, Three sorting maps were
constructed for hexane. The first map, which is shown in
figure 9, shows the points plotted with experimental AN
values. Calculated AN values are used when experimental
AN values are not available. On the map, there are five
immiscible hexane-solvent mixtures. The points for the
immiscible hexane-water (+1), hexane-formamide (+2), and
hexane-aniline (+3) mixtures are well separated from the
miscible region. The other two immiscible hexane
mixtures with glycerol (+6) and ethylene glycol (+5)
appear to be in the miscible region. Thus when the
immiscible and miscible regions are drawn in figure 9,
they overlap slightly. The hexane-methanol mixture (4)
appears in the overlapping miscible and immiscible
regions. The literature is not clear as to the status of
the miscibility of this mixture so it was plotted as
questionable until it could be evaluated experimentally.
The second map (figure 10) shows that the two
points representing the immiscible mixtureshexane-
ethylene glycol (+5) and hexane-glycerol (+6) were moved
into the immiscible region when Beerbower's (35) DN
values for ethylene glycol and glycerol were used. Once
70
n-HEXANEE
20
5 -iona
0
-15-1
-20
(*,-*.),
10
Figure 9- Hexane-Solvent Sorting Map
q miscible, + immiscible, Oques tionable
miscibility
+ 1 hexane-water , + 2 hexane- formamide
+ 3 hexane-ani 1 ine ,*4 hexane-me thanol
+5 hexane-e thylene glycol, +6 hexane-glycerol
71
n-HEXANE
(*,-*,>:2'd
Figur. 10. Hexane-Solvent Sorting Map ( Beerbower's DN values )
D miscible, + immiscible, Q questionable
misciblity
+ 1 hexane-vater , +2 hexane-formamide
+3 hexane-anlllne, 0 4 hexane-methanol
+5 hexane-ethylene glycol, +6 hexane-glycerol
0 7 hexaue-isoamylalcohol , O 8 hexane-ethanol
72
again it appears that the calculated values published for
these two solvents are too low and that Beerbower s DN
values are more apropriate. The immiscible hexane-
formamide mixture (+2) was also moved further into the
immiscible region when Beerbower's (35) DN value for
formamide was used.
This second sorting map shows that the miscible
and immiscible areas are fairly well defined with the
exception of the hexane-methanol mixture. The hexane-
methanol mixture (O 4) still falls in the miscible region
between the miscible hexane-isoamyl alcohol ( a 7) and
hexane-ethanol (0 8) mixtures as indicated in figure 10.
Again, two possible reasons for this deviation existed:
the miscibility data was incorrect or some of the AN or
DN values for these alcohols were incorrect.
Experimental miscibility results from Table 9 show that
hexane is miscible with isoamyl alcohol and ethanol, but
only partially miscible with methanol. The DN value of
isoamyl alcohol (DN = 32.0) is consistent with values
obtained from several sources. However, the experimental
DN values for methanol (DN = 19.0) and ethanol (DN =
20.0) are lower than values calculated from other
correlations. As discussed previously in the case of
ethylene glycol, glycerol and formamide, the DN values of
methanol and ethanol are probably too low and should be
higher. These DN values are also much lower than similar
73
to
CM
en
encm
mco
co
2 8
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oeoeo
to
en
? e m en m r c mCM CO m en (SI O cm en
o CO r~ f cm r^ r*. r-
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r> to r* CO r" r* cm r> r>. r OI
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ui
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74
alcohols. Beerbower s DN values (35) for methanol (DN =
36.2) and ethanol (35.2) are close to the DN values of
other alcohols and are certainly more reasonable. Thus a
third and final sorting map for hexane was plotted using
Beerbower's DN values for methanol and ethanol as well as
for ethylene glycol, glycerol and formamide. This map is
shown in figure 11. The original DN values for other
mixtures were used since they were not significantly
different from Beerbower's DN values. Thus all the other
points were not changed. In this third and final map,
all the immiscible points are separated from the miscible
points giving two distinct regions.
Hexane Sorting Map - Miscibility Experimental:
In order to test the hexane sorting map, the
mixtures which defined the immiscible region and the
border points of the miscible region were evaluated
experimentally. The refractive indexes of the mixtures
were also measured in order to help determine the degree
of miscibility. These results are given in Table 9.
Miscible mixtures have only one refractive index value,
immiscible or partially miscible mixtures have refractive
index values for upper and lower layers.
Both ethanol and isoamyl alcohol form miscible
mixtures in all proportions with hexane. This is also
75
n-HEXANE
Z
0
z
0
r\
z<
z<
0
0
0 2 4
(Si"S2>dFigure 11 Hexane-Solvent Sorting Map ( Final Map )
O miscible, + Immiscible, <> partial
miscibility
+1 hexane-water, +2 hexane-formamide
+ 3 hexane-aniline, <> 4 hexane-methanol
+5 hexane-ethylene glycol -H hexane-glycerol
Q 7 hexane-isoamylalcohol,0 8 hexane-ethanol
76
shown as a steady change in the refracitive index as the
proportions of the mixture are changed. Ethylene glycol,
glycerol, formamide and aniline form immiscible mixtures
with hexane. The very small changes in the refractive
index values indicate that hexane is soluble to the
extent of only 1% or less in these solvents for all
proportions tested. These mixtures are definately
immiscible. The hexane-methanol mixture shows partial
miscibility-
depending on the proportions of each
liquid. The 40% - 50% volume/volume hexane-methanol
range was reexamined in more detail using a series of
mixture containing between 40% - 50% hexane in methanol
in 1% increments. Maximum miscibility of hexane in
methanol at 25 C was found to be 45% hexane. The results
are shown in Table 10. Thus the experimental miscibility
data helps to establish the miscible and immiscible
regions .
The line establishing the miscible region is
defined so that only totally miscible mixtures are within
the region. Thus, miscible mixtures such as hexane-
ethanol ( D 8) andhexane- isoamyl alcohol ( Q 7) fall
within the miscible region shown in figure 11.
Immiscible mixures are outside this region and make up
their own region. Partially miscible mixtures such as
hexane-methanol (0 4) by definition are outside but very
near the miscible region. Thus the line defining the
77
TABLE 10
MISCIBILITY OF HEXANE-METHANOL MIXTURES
Hexane
X volume 90 80 70 60 50 40 30 20 10
volume(ml) 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5
Methanol
volume(ml) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Z volume 10 20 30 40 50 60 70 80 90
Miscibility IIIIIMMMM
Hexane
Z volume 50 49 48 47 46 45 44 43 42 . .
volume(ml) 2.5 2.45 2.4 2.35 2.3 2.25 2.2 2.15 2.1..
Methanol
volume(ml) 2.5 2.55 2.60 2.65 2.7 2.75 2.8 2.85 2.9..
2 volume 50 51 52 53 54 55 56 57 58
Miscibility IIIIIMMMM
Maximum miscibility of hexane in methanol is 4 5 % : 5 5%
78
miscible region can be drawn just above the hexane-
ethanol (D8) and hexane isoamyl (07) points and just
below the hexane-methanol (Q 4) point. Note that if the
definition of the miscible region includes partially
miscible mixtures, then the line establishing the region
would be drawn above the hexane-methanol (04).
Hexane Sorting Map - Error Analysis:
In order to determine if the final hexane sorting
map was reliable, an error analysis was conducted for all
the hexane-solvent mixtures used in constructing the
hexane sorting map. The calculations and results are
summarized in Table 11.
The total ( AN,- AN
2 ) ( DN,-
DN2 ) error for
each mixture is quite small. The noted exception is the
hexane-chloroform mixture which has a small DN divided
into a large DN error of chloroform. Thus the error
analysis shows that the error associated with each point
is generally small, especially for immiscible binary
mixtures or miscible binary mixtures near the boundaries.
Hexane Sorting Map to predict Miscibility
of Mixtures:
The usefulness of the hexane sorting map was
79
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80
demonstrated in the same manner as for the benzene
sorting map in correctly predicting the miscibilities of
a variety of hexane-solvent mixtures. The same six
solvents used for testing the benzene map were used to
test the hexane map. These solvents were acetonitrile ,
N-methyl formamide, ethyl acetate, 2-butanone, di-n-butyl
ether, and t-butanol. The points corresponding to the
hexane-solvent mixtures were plotted on the third hexane
sorting map (figure 11). For clarity, most of the other
hexane-solvent mixtures were not shown in this prediction
map given in figure 12. The hexane-N-methyl formamide
mixture (+1) falls within the immiscible region and
therefore was predicted to be immiscible. The other five
mixtures were predicted to be miscible since the
respective points were located in the miscible region.
These predictions were confirmed experimentally and are
summarized in Table 12. Thus the hexane as well as the
benzene sorting maps have been successfully used in
predicting the miscibilities of binary liquid mixtures.
81
n-HEXANE
Z
0
z
Q
Z
<
z
<
0
0
0 2 4 6 8 10
Figure 12. Hexane-Solvent Soritng Map- Prediction
O miscible, + immiscible, $ partial
miscibility
+ 1 hexane-N-methylf ormamide , D 2 hexane-ace toni trile
03 hexane-ethyl acetate ,04 hexane-2-butanone
05 hexane-butyl ether, D6 hexane- t-butanol
82
TABLE 12
PREDICTING MISCIBILITY OF MIXTUES
WITH HEXANE SORTING MAP
System Predicted Experiment
1 hexane-N-me thy Iformamide immiscible immiscible
O hexane-acetonitrile miscible miscible
3 hexane-ethyl acetate miscible miscible
4 hexane -2-butanone miscible miscible
5 hexane-di-butyl ether miscible miscible
6 hexane- t-butanol miscible miscible
83
CONCLUSION
A simple solubility expression has been developed
based on solubility parameter theory and Lewis acid-base
theory. This new expression as described in equation
[27] combines a dispersion solubility parameter term for
nonpolar interactions and a Lewis acid-base term for
polar and hydrogen bonding interactions. The Lewis acid-
base term was written as the product of the difference
of the acceptor numbers (AN) and the difference of the
donor numbers (DN) for two liquids.
In order to test this new expression, four
research goals were established. The first two goals
were to expand the small list of available AN and DN
values so that this expression could be used. The third
goal was to use this expression to construct miscibility
sorting maps for binary liquid mixtures. The fourth goal
was to test the sorting maps and thereby the solubility
expression. These goals have generally been successfully
accomplished.
A good correlation of experimental AN and ET(30)
values for alcohol and chlorinated hydrocarbon solvents
was developed. This expression compliments the
correlation established by Schmid which did not include
alcohols and chlorinated hydrocarbons. Many AN values
84
were then calculated from experimental ET(30) using
either Schmid 's correlation or the correlation developed.
in this work.
An attempt to improve the overall correlation of
AN, DN and dielectric constant by including amphoteric
solvents did not work. However, individual correlations
were developed for each class of the amphoteric solvents,
such as alcohols, amides and chlorinated hydrocarbons. A
problem with the highly structured amphoteric solvents is
that the dielectric constant correlates well with
experimental AN values but not with experimental DN
values .
Miscibility sorting maps for binary liquid
mixtures were constructed for 43 liquids. For 41 of these
maps areas defining miscible and immiscible mixtures
could cleary be distinguished. However, this distinction
was not clear in the special cases for the benzene and
hexane sorting maps. The problem appeared to be
associated with the low experimental DN values of a few
but not all of the amphoteric solvents. When higher DN
values for methanol, ethanol, ethylene glycol, glycerol
and formamide obtained from Beerbower were used, then the
benzene and hexane sorting maps successfully indicated
separate miscible and immiscible regions. A few
additional maps representing each class of compounds
(toluene, methanol, ethanol, chloroform, acetone, diethyl
85
ether, formamide) were also evaluated experimentally.
The binary mixtures in the immiscible regions were found
to be immiscible and the mixtures defining the boundaries
of the miscible regions were found to be miscible. Thus
these maps and the revised benzene and hexane maps
successfully indicated separate miscible and immiscible
regions .
The miscibility sorting maps were tested by using
them to predict the miscibility of several binary
mixtures. These mixtures were later evaluated
experimentally and found to agree with the predictions.
This demonstrated the usefulness of the sorting maps.
The usefulness of the sorting maps, and thereby
the solubility expression, depends upon the availability
of good, reliable AN and DN values. For most solvents,
reliable values have been compiled in this and other
work. A problem appears to exist for certain amphoteric
solvents which have low DN values. However, recently
obtained DN values for these solvents are more reasonable
and do not seem to present any problem. Additionally,
the sorting maps themselves serve as a check on the
reliability of the AN and DN values.
The solubility expression developed in this thesis
has been demonstrated to be useful in constructing
miscibility sorting maps for binary liquid mixtures or
binary liquid systems. Future work may extend this
86
expression into other areas such as in studying three or
more liquids in a mixture or in studying liquid-surface
interactions .
87
REFERENCES
1. Snyder, L. Chem Tech. 1979, 750.
2. Hildebrand, J. H., J. Am. C.h <w 1916) ^ 1452
3. Lewis, G. N., "Valence and the structure of the
Ai^ms andMolecules/'
, pp 141-142, The Chemical
Catalog Company, NY, 1923.
4. Hildebrand, J. H.; Prausnitz, M. M.; Scott, R. L.,
"Regular and Related Solution^'. Van Nostrand-
Reinhold, New York, NY., 1970.
5. Hildebrand, J. H.; Scott, R. L., "Soluhi 1 itv of Non-
ElectrolYtes"
, 3 ed., Reinhold, New York, NY., 1958.
6. Konstam, A. H.; Feairheller, W. R., Am. Inst. Chem.
Eng . J . . 1970, 16_, 837.
7. Beerbower, A. J. Colloid and Interface Soi . . 1971,
3_5_, 126.
8. Hildebrand, J. H.;Scott,-
R. L., "Regular Solutions".
Prentice-Hall, Englewood Cliffs, NJ., 1962.
9. Barton, A. F. M., "The Dynamic Liquid State".
Longman, London, 1974.
10. Blanks, R. F.; Prausnitz, J. M., Ind. Eng. Chem.
Enndam. , 1964, 3_, l.
11. Bondi, A.; Simkin, D. J., J. Chem. Phvs . . 1956, 25_,
1073.
12. Hansen, C. M . ; Beerbower, A., in Kirk Othmer Encyclo
pedia of Chemical Technology. Suppl. Vol., 2nd ed . ,
Standen, A., Ed., Interscience , New York, 1971, 889.
88
13. Keller, R. A.; Kanger, B . L . ; Snyder, L. R., Gas.
Chromatogr. . Proct . Tnt. Svmp . (Knr ) 1971, 8., 125.
14. Hansen, C. M., Chem. T^chnol, 1972, 2., 547.
15. Barton, A. F. M., "Handbook of Solubility Parameters
and Other Cohesion Para^^rff', CRC Press, Bocaraton
Fl., 1983.
16. London, F., Trans. Faradav Soc . . 1937, S_3_, 8.
17. Koehen, D. M.; Smolders, C. A., J. AppI . Polvm. Sci. .
1975, 19_, 1163.
18. Van Krevelen, D. W.; Hoftyzer, P. J., J. AppI. Polvm.
Sci. . 1967, II, 2189.
19. Small, P. A., J. AppI. Chem.,1953. 3_, 71.
20. Jensen, W. B., Rubber Chem. Techno! . . 1982, 5_5_, 881.
21. Gutman, V., "The Donor-Acceptor Approach to Molecular
Interactions"
. Pelenium, NY., 1978.
22. Dimroth, K.; Reichardt, C, Z. Anal. Chem. . 1966,
215., 344.
23. Reichardt, C, "Molecular Interactions'. Vol 3,
240, Edited by Ratajezak, H. and Orville-Thomas W.
J., John Wiley and Sons, Ltd., New York, 1982.
24. Schmid, R., J Solution Chem. . 1983, iZ, Vol. 2, 135.
25. Griffiths, T. R.; Pugh, D. C, Coordination Chemistry
Reviews. 1979. 29_, 129.
26. Kamlet, M. J.; Abboud, J. I.; Taft , R. W., Frofir.
Phvs. Chftm 1981, H, 618.
89
27. Maria, P. C; Gal, J. F., J. Am. Chem. Soc . . 1985,
8_3_, 1296.
28. Harris, D. C, "Quantitative Chemical Analysis'-.
W. K. Freeman and Company, New York, 1982.
29. Michelsen, P. J., Thesis, Rochester Institute of
Technology, in progress.
30. Marcus, Y., J. Solution Chem. . 1986, 15_, 291.
31. Beerbower, A.; Jensen, W. B., Inorganic Chemica Acta.
1983. 75_, 193.
32. Francis, A. W., Advances in Chemistry Series No. 3_1,
American Chemical Society, Washington D. C, 1961.
33. Rolling , 0. W., Anal. Chem. 1982, 5A, 260.
34. Olofsson, G., J. Am. Chem. Soc. . 1973, 9_5_, 7231.
35. Beerbower, A., Private Communication with Jensen, W.
90
APPENDIX
91
TABLE A-l
LIST OF ET(30), AN ( experimental and calculated ),
ANP DIELECTRIC CONSTANT ( 6 )
AROMATICS
bftnzftna
toluene
o-xyln
p-xylnft
m-xyl*n
chlor obenzne
bromcb*n:ini
c-di chlorobnz*ne
m-di chlorobftnzftn
i odobenzftn*
f iuorobftnzcn*
methoxybftnzftnft
t t hoxybftnz int
rresi tylftn*
thylbenzftnft
styrftn*
o-mftthyl*tyTftn
p-iTiethylstyrnft
ALIPHATICS
AN
(ftxpt)
8.2
AN"
(E_(30)
E (30)
NITRO COMPOUNDS
6 (25CC>
3.983 34.5 2.283.211 33.9 2.383.727 34.3 2.568 (20)2.695 33.5 2.27 (20)2.437 33.3 2.374 (20)7.855 37.5 5.627.e55 37.5 5.4
8.629 38.1 9.93
7.21 37 5.04
8.371 37.9 4.63 (20)
8.629 3S.1 5.42
7.468 37.2 4.33
6.436 36.4 4.22 (20)
2.179 33.1 2.2s (20)
2.4 (20)
2.426 (20)
n-hexan 0 -0.639 30.9 i.ee
1 , 2-di chloroftthanft 16..7 13.531 41.9 10.36
1 , 1-di chloroftthanft 10.306 39.4 10 (18)
dibromomftthan* 10.306 39.4
di chloromftthan* 20,.4 12.499 41.1 8.93
1 ,1 ,2,2-tetrachloroftthan* 9.403 38.7 8.2 (20)1 ,2-dimthoxyftthanft 10,.2 8.758 36.2 7.2
1 ,2-dibromoftthanft 7.468 37.2
bromofthan* 7.984 37.6 9.39
1-chloropropan* 7.726 37.4 7.7 (20)
1 ,1 ,1-tri chloroftthanft 6.178 36.2 7.53 (20)
tr ichloroftthylftn* 5.791 35.9 3.42 (16)
tttrachloroftthylftnft 0.631 31.9 2.3
carbontfttrachlorid* 8 .6 1.405 32.5 2.24 (20)
chloroform 23 .1 9.919 39.1 4.61 (20)
cyclohftxan* -0.272 31.2 2.02 (20)
cyclohftxftn* 1.147 32.3 2.2 (20)
n-hftptanft 19.2
2-ni tropropan* 14.692 42.8 25.32 (30)
ni tromftthan* 20.5 19.207 46.3 33.67 (30)
ni troftthane 15.724 43.6 26. Of (30)n l trobftnzftn* 14.8 13.66 42 34 . 62
92
TABLE A-l (continued)
18.82 46 37.5 (20)
15.853 43.7 27.2 (20)
19.723 46.7 33 (20)
15.079 43.1 20.3 (21)
13.66 42 25.2
14.821 42.9 18.7 (27)
20.4 (24)
26.689 32.1
22.561 46.9
NITRILES
acstonitril* 18.9
prop l oni tr ilft
acryloni trile
n-bu tyroni trile
benzoni trile 15.5
phenyl ace t oni trile
i so -bu tyroni trile
tert-butyl nitrile
cyclohexylni trile
3-chloropropioni trile
4-chlor obu tyroni trile
NITRATE
isopropylni trate 15.079 43.1
ESTERS
methylaeetate
etnylacetate
v inylacetate
methylacrylate
et:->vi aery late
propylacetate
etnylf ormate
rrethylf ormate
ethylbenzoate
methylbenzoate
dimethylphthalate
methyl chloroacetate
methyl di chloroacetate
methyl propionate
ethyl propionate 5.63 (19)
ethyl chloroacetate
methyl isobutyrate
methyl methacrylate 2.9
LACTONES
B-prop ion lac tone
4-butyrolactone 16.627 44.3 39 (20)
E-caprolactone
KETONES
0.7 11.08 40 6.63
9.3 6.629 3.l 6.02
8.5 36
16.855 44.5
7.635 37.5 6 (20)
12.241 40.9 7.16
8.5 (2C)
8.629 38.1 6.02 (20)
6.59 (20)
11.933 40.7
13.66 42
acetone 12.5 13.918 42.2 20.7
3,3-aimethylbutanone 9.79 39
93
TABLE A-l (continued)
12.757 41.3 18.51 (20)
10.177 39.3 17 (20)
12.499 41.1 15.4 (20)
9.403 38.7
6.5 38
9.661 38.9
11.209 40.1
12.241 40.9
10.306 39.4
10.822 39.6 16.3 (20)
12.757 41.3 17.39
10.306 39.4 13.11 (20)
methylethylketone
diethyl ketone
methylpropylketone
di i sopropylketone
diisobutylketone
4-hep tanone
2-hexanone
isopropylme thy Ike tone
cyclopen tanone
cyclohexanone
acatophenone
4-methyl-2-p en tanonecyclobutanone
cyciohep tanone
methylvinyl ketone
i sophorone
camphor 11.35 (20)
tr t chloroacetone
dimethyl-G-py rone
benzcphenone
bi acetyl
di-ter t-bu tyl ketone
ETHERS
diethylether
di i sop ropy lether
di-n-bu tylether
1 ,2-dirr.ethoxyethar.e
ant sole
propvleneoxide
di glyme
furan
tetrahydrofuran
1 ,4-dioxane
1 ,3-di oxolane
phenatole
di-n-propyl ether
ethyl butyl ether
ethyl uinyl ether
n-butyl vinyl ether
isobutyl vinyl ether
diallyl ether
epichlorohydr in
styrene oxide
3,3-bischloromethyloxetane
2-methyl-l ,3-dioxalane
4-methyl-l,3-d:oxalane
2-phenyl-l,3-dioxalane
4-chl or ome thy 1-1 ,3-dioxalane
dibenzyl ether
3,,9 4.114 34.6 4.34 (20)
3.34 34 3.66
2.566 33.4 3.08 (20)
10,.2 8.758 38.2 7.2
7.468 37.2 4.33
10.822 39.8
9 .9 9.274 38.6
3,,3 2.942
8 7.726 37.4 7.56
10,.8 5.92
15.079
36
43.1
2.21
6.436 36.4 4.22
3.39
(20)
(26)
22.6 (22)
94
TABLE A-l (continued)
diphenyl ether 3.656oxepane
2-methyltetrahydrof uran 6.565 36.5tetrahydropyran 3.61tr igiyme 9.661 38.9 7.3
4 3.146 35.4 3.58 (21)
4 2.437
2.437
6.932
33.3
33 . 3
ScT.S
2.42
16.627 44.3 6.89 (20)
9 13.66
14.303
6.3
42
42.5
38
12.9
2 11.338 40.2 12.4 (21)
8.887 38.3 5.S (20)
ALDEHYDES
acetaldehyde 21.1 (21)prcpi onaldehyde 16.5 (17)
butyraidehyde 13.4 (26)
acrolein
cro tcnaidehvde
benzaldehyde 17.6 (20)
AMINES AND DERINATIVES
di ethvlami re 9,
tr iethyia.Tiine 1.
diisoprcpylan :ne
ter t-bu tyl a.Ti;ne
aniline
ethvieneoi amine 20.
n-ir.ethylai-i il : nen
n-dimethylaniiine
pyridine 14,
a-pi col i ne
b-pt coli ne
o-pi coline
4-ethvlpyridine
2,4,6-trimethylpvridine
2-chloropyridine 13.531 41.9
3 ,5-di chloropyr lcine3bromopvr 1 dine
4-winylpyridine
4-dimethyl ami nopyr i dine
2 ,6-luti dine
1-formvlpiper i dine
piper idine
quinoline
n-methyl-2-pyrrolido 13.3
dimethylethyleneurea
tetramethylurea
ammonia
ethylamine
n -propylamine
di -propylamine
o-toluidine
N-me t hy1 -E-cap r o 1 ac t am
N-fliethylpyrrolidin**2
N-isopropyl-2-pyrrol idine
6.823 36.7
3.273
3.275
35.5
35.3 5.8 (20)
10.306 39.4 9
13.918 42.2 32
14.305
12.37
42.5
41 23.45
16.9
3.58 (21)
5.31 (20)
3.066 (20)
6.34 (18)
95
TABLE A-l (continued)
39.6 32.494 56.6 111 (20)
32.1 29.269 54.1 182.4
26.56 52 191.3 (32)
16 13.962 43.8 36.7
13.6 15.853 43.7 37.78
10.6 12.241 40.9 29.6
dimethylpropvleneureatr i-bu tylamine
N,N-dimethyl benzyl amine
IMINES
ethylenimine 16.3
N-phenylethylenimi ne
AMIDES
formamide
n-methvlformamide
n -me t hy 1 ace t am i de
n,n -dime thy If ormami d
n , n-di me thy lace tarn id
hexamethylphosphoami
N,N'-di ethy If ormami de
N,N-di ethyl ace t ami de
N-methylpyrroli done
dimethyl tr if luor oacetamide 32
dimethylchloroacetamide
SULFIDES
carbondisulf ide 1.534 32.6 2.64 (20)
S'JLPHOXIDES, SULPHONES AND SULFITES
dimethvlsuifoxides 19.3
dimethyl sulfone
dibutyl sulphone
sulfolane 19.2
di-butyl sulphoxide
diphenyl sulphoxide
dimethyl sulfite
diethyl sulfite
ethylene sulfite
SULFONIC ACIDS
methanesulfonicacid 126.3
ACID AND DERIVATIVES
formic acid 83.6 38.5 (16)
acetic acid 52.9 26.173 51.7 6.15 (20)
trifluoroaceticacid 105.3 8.35 (20)
acetic anhydride 20.7 (19)
acetyl chloride15-a <22)
benzoyl chloride 23 <20>
benzoyl fluoride
17.53 45 46.68
21.4 46
14.692 42.8
16.24 44 43.3 (30)
9.016 38.4
96
TABLE A-l (continued)
CARBONATES
ethylenecarbonate
propvlenecarbonate 18.3dimethyl carbonate
diethylcarbonatedichloroethylene carbonate
tetrachloroethylene carbonate
propanediol-l,2-carbonate
PHOSPHOROUS COMPOUNDS
22.174 48.6 69.6 (40)
19.594 46.6 65.1
12.499 41.1
6.178 36.2 2.62 (20)
tr imethylphosphate 16.3tr ie thy lphosphatetr i-n-propylphosphatetr i-n-bu tylphosphate 9.9
tripiperidinophosphine oxide
tripyrrolidinophosphine oxide
tr iphenylphosphine oxide
trimethyiphosphine oxide
ALCOHOLS
15.724 43.6 20.6 (20)
13.273 41.7
11.723 40.5
10.564 39.6 7.939 (30)
methanol 41,.3 31.075 55.3 32.7ethanol 37,,1 26.431 51.9 24.55n-bu tanol 36,,6 24.238 50.2 17.311-pen tanol 22.619 49.1 13.91-hexanol 22.432 48.8 13.31 -hep tanol 22.045 48.5
1-octanol 21.787 46.3 10.34 (20)
1-decanol 20.884 47.6 6.1 (20)
1-aodecanol 19.723 46.7
2-propanol 35,,5 22.174 48.6 19.92
2-butanol 20.239 47.1 16.56
2-pentanol 19.465 46.5 13.62 (22)
3-pentanol 18.433 43.7 13.02 (2)
i sobutylalcohol 22.69 49 17.93
isoamyl alcohol 22.69 49 14.7
cyclopentanol 21.013 47.7
cyclohexanol 19.207 46.3 15
t-butyl alcohol 27.,1 16.111 43.9 12.5
t-pentyl alcohol 13.531 41.9 5.62
1-propanol 37,.3 24.883 50.7 20.33
2,2,2-tr if luoroethan 53,,5 36.235 59.52,2,3,3-tetrafluoro-l-propano 36.106 59.4
2 , 2 ,2- 1 r l chloroethanol 32.494 56.6
2-propen-l-ol 26.689 52.1 21.6 (15)
2-propyn-l-ol 53
2-ftminoethanol 33.,7 26.302 51.8 37.72
97
TABLE A-l (continues)
3-amino-l-propanol 43.12-chloroethanol 25.8
l-bromo-2-propanol 31.42-ethoxyethanol 23.27 31 29.6 (24)
2-methoxy ethanol 26.947 32.3 16.93
2-n-butoxy ethanol 24.238 30.2 9.3benzyl alcohol 25.012 50.8 13.1 (20)furfuryl alcohol 50.3tet r ahy dr of ur fury 1 alcohol 24.367 50.3 13.611-phenyl ethanol 19.723 46.7
2-phenyl ethanol 23.335 49.5
3-phenyl-l-propanol 22.045 48.5glycerol 33.01 57 42.51 ,2-ethanediol 32.107 56.3 37.7
1 ,2-propanediol 29.269 54.1 32 (20)
1 ,3-propanediol 30.301 34.9 35 (20)
1 ,3-butanediol 27.592 52.8
pentanediol 31.3
diethylene glycol 28.882 53.8 31.69 (20)
triethyler.e glycol 28.495 53.3 23.69 (20)
water 54.8 40.879 63.1 78.54
deuterium oxide 40.492 62.8 78.25
INORGANIC HAL IDES
sulphuryl chloride
thionyl chloride
selenium oxychloride
phosphorous oxychlor
phenylphos'c difluoride
11
a Experimental AN from Gutman (21)
b AN (a) values are calculated from E (30) values using
equation [43] from Schmid (24)
c E (30) values from Reichardt (23)
d Dielectric Constanta from Schmid (24)
98
TABLE A-2
LIST OF AN VALUES CALCULATED FROM EITHER
SCHMID'S OR ALCOHOL'S CORRELATIONS
SOLVENT
a
AN
(expt)
AN AN
(E (30) (alcohol)
AROMATICS
benzene
toluene
o-xylene
m-xylene
p-xylene
chlorobenzene
bromobenzene
o-di chlorobenzene
m-di chlorobenzene
i odobenzene
f luorobenzene
methoxybenzene
ethoxybenzen
mesi tylene
ni trobenzene
e thy lbenzene
styrene
o-methylstyrene
p-methylstyrene
ALIPHATICS
8.2
14.2
4
3.211
3.727
2.437
2.695
7.855
7.855
6.629
7.21
8.371
8.629
7.466
6.436
2.179
13.7
n-hexane 0 -0.6
1 ,2-dichloroethane 16.7 13.5
1 , 1-dichloroe thane 10.306
dichlorome thane 20.4 12.5 22.,4
1,1 ,2,2-tetrachloroethane 9.403
1 ,2-dimethoxyethane 10.2 8.8
bromoethane 7.984
1-chloropropane 7.726
1 ,1 ,1-trichloroethane 6.178
tr ichlor o ethylene 5.791
tetr achloro ethylene 5.791
carbon tetrachloride 8.6 1.4 9.,6
chloroform 23.1 9.9 19 .4
cyclohexan* -0.272
eyclohexene 1.147
n-heptane
NITRO COMPOUNDS
2-ni tropropane
ni tromethane
ni troethane
ni trobenzene
14.692
20.5 19.3
15.724
14.8 13.7
99
10.7 11.1
9.3 8.6
8.5
16.885
7.855
12.241
6.629
11.933
TABLE A-2 (continued)
NITRILES
acetonitrile 18.9 18.8
propioni trile 15.853
acryloni trile 19.723
n-butyroni trile 15.079
benzonitrile 13.5 13.7
phenylacetoni trile 14.821
i so-bu tyroni trile
tert-butyl nitrile
cyclohexyl nitrile
NITRATE
isopropylni trate 15.079
ESTERS
methy lacetate
ethylacetate
uinylacetate
methylacrylate
propylacetate
ethylf ormate
ethylbenzoate
dimethylphthalate
methyl chloroacetate
methyl dichloroacetate
methyl propionate
ethyl propionate
ethyl chloroacetate
methyl isobutyrate
ethyl acrylate
methyl methacrylate
methyl formate
methyl benzoate
LACTONES
B-propionlactone
4-butyrolactone 16.627
E-caprolactone
KETONES
acetone 12.5 13.9
methylethylketone 12.737
3,3-dimethylbutanone 9.79
difttylkfttonft 10.177
mftthylpropylkfttone 12.499
di isopropylketone 9.403
di isobutylketone 6.5
4-heptanon* 9.661
isopropylmethylketone 12.241
cyclopen tanone 10.306
cyclohexanone 10.822
100
TABLE A-2 (continued)
azetophenone 12.737
2-hexanone 11.209
4-methyl-2-pentanone 10.3C6
cyclobutanone
cyclohep tanone
methyluinyl ketone
i sophorone
camphor
isopropyl methyl ketone
tr i chloro acetone
dime thyl-G-py rone
benzophenone
biacetyl
di-ter t-bu tyl ketone
ETHERS
diethylether
di isopropylether
di-n-butylether
1 . 2-dime tho xyethane
am sole
propyleneoxide
di glyme
f uran
tetrahvdrofur an
1 ,4-dioxane
1 , 3-dioxolane
phenatole
di-n-propyl ether
ethyl butyl ether
ethyl uinyl ether
n-butyl uinyl ether
isobutyl vinyl ether
diallyl ether
epichlorohydrin
styrene oxide
3,3-bi schloromethyloxetane
2-me thy1-1 ,3-dioxalane
4-me thy1-1 ,3-dioxalane
2-phenyl-l ,3-dioxalane
4-chloromethyl-l ,3-dioxalane
dibenzyl ether
diphenyl ether
oxepane
2-methyltetrahydrofuran b.o*>3
ALDEHYDES
acetaldehyde
prop ion aldehyde
butyraldehydft
acrolein
crotonaldehyde
benzaldehyde
3.9 4.1
3.34
2.566
10.2 8.8
7.468
10.822
9.9 9.3
3.3
6 7.7
10.8 5.9
15.079
6.436
101
TABLE A-2 (continued)
AMINES AND DERIVATIVES
oietnyiamine 9.4 5.1
tr i ethylami ne 1.4 2.4
di l sopropylamine 2.437
ter t-butylamine 6.952
aniline 16.627
ethylenediamine 20.9 13.7
n-methylaniline 14.305
n-n-dimethylanil ine 8.5
pyridine 14.2 11.3
2-methylpyridine 8.887
2,6-lutidine 6.823
1-formylpiperidine 5.275
piperidine 5.017
cuinoline 10.306
n-methyl-2-pyrrolidone 13.3 13.9
2-chloropyr idine 13.531
dimethylethvleneurea 14.305
tetramethylurea 12.37
ammonia
ethyl am ine
n -propyl amine
di -propylamine
a-picoline
-pi coline
4-ethylpyr i dine
o-tolui dine
4-wi nylpyr idine
N-methyl-E-capro lac tarn
2-methylpyr idi ne4nethylpyr idine
N-methylpyrrol idine
2,6-dimethylpvridine
2,4,6-trimethylpyridine
N-i sopropyl-2-pyrrol idine
dimethylpropyleneurea
3,5-dichloropyr idine
3-bromopyr idine
4-dimethylaminopyr idine
tr i-butylamine
N,N-dimethylbenzyl amine
IMINES
ethylenimine
N-phenylethylenimine
AMIDES
f ormami de
n-me thy If ormami de
n-me thyl ace t amide
n ,n-dime thyIf ormami de
n rn -d i me thyl ace t amide
hex ame thylp ho spho amide
39.8 32.5
32.1 29.3
26.56
16 16
13.6 15.6
10.6 12.2
102
TABLE A-2~(coutiuued)
N,N-di ethyl formamide
N,N-aiethv lace t amide
N-methylpy rroli done
dimethyltri f luoroacet ami de
dimethylchloroacetamide
SULFIDES
carbondisulf ide 1.534
SULPHOXIDES, 3ULPHONES AND SULFITES
dimethylsulfoxides 19.3 12.5
sulfolane 19.2 16.2
tetramethyl sulphone
di-butyl sulphoxide
diphenyl sulphoxide
dimethyl sulfite
diethyl sulfite
ethylene sulf i :e
SULFONIC ACIDS
methanesulf onicacid 126.3
ACID AND DERIVATIVES
formic acid 83.6
acetic acid 52.9
trif luoroacet icacid 105.3
acetic anhyande
acetyl chloride
benzoyl chloride
benzoyl fluoride
CAR9CNATES
ethylenecarbonate 22.174
propylenecarbonate 18.3 19.6
dimethylcarbonate 12.499
diethylcarbonate 6.178
di chloroethylene carbonate
tetrachloroethylene carbonate
propanediol-1 ,2-carbonate
PHOSPHOROUS COMPOUNDS
tr imethylphosphate 16.3 15.7
triethylphosphate 13.273
tri-n-propylphosphate 11.725
tri-n-butylphosphate 9.9 10.6
tr ipiper idinophosphine oxide
tr ipyrrol idmophosphine oxide
tr iphenylphosphine oxide
tr imethylphosphine oxide
103
TABLE A-2 (continued)
ALCOHOLS
methanol
ethanol
n-bu tanol
n-amyl alcohol
1-hexanol
1-hep tanol
1-octanol
1-decanol
1-dodecanol
2-propanol
2-butanol
2-pen tanol
3-pen tanol
i sobutylalcohol
isoamyl alcohol
cyclopen tanol
cyclohexanol
t-butyl alcohol
t-pentyl alcohol
1-propanol
2,2,2-trifluoroethanol
2,2.3,3-tetrafluoro-l-propanol2,2,2-trichloroethanol
2-propen-l-ol
2-ami noethanol
2-chloroethanol
2-ethoxyethanol
2-methoxy ethanol
2-n-butoxy ethanol
benzyl alcohol
2-hydroxymethyl tetrahydrofuran
1-phenyl ethanol
2-phenyl ethanol
3-phenyl-l-propanol
1,2,3-propantriol
1 ,2-ethanediol
1 ,2-propanediol
1 ,3-propan*diol
1 ,3-butanediol
diethylene glycol
triethylene glycol
water
deuterium oxide
41,,3 31.1 43.7
37,.1 26.4 38.4
36.,8 24.2 35.9
22.619 34.3
22.432 33.8
22.045 33.4
21.787 33.1
20.884 32
19.723 30.7
33,.5 22.2 33.5
20.239 31.3
19.465 30.4
18.433 29.2
22.69 34.1
22.69 34.1
21.013 32.2
19.207 30.1
27,,1 16.1 26.6
13.531 23.6
37,,3 24.9 36.6
33,,5 36.2 49.7
36.106 49.5
32.494 43.5
26.689 38.7
33,,7 26.3 38.3
25.27 37.1
26.947 39
24.236 35.9
25.012 36.8
24.367 36
19.723 30.7
23.335 34.9
22.045 33.7
33.01 46
32.107 44.9
29.269 41.7
30.301 42.9
27.592 39.7
28.882 41.2
28.495 40.8
54,,6 40.9 55
40.492 54.6
104
TABLE A-2 (continued)
INORGANIC HALIDES
sulphuryl chloride
thionyl chloride
felenium oxychloride
phosphorous oxychloride nphenylphos'c difluoride
phenylphos'c dichloride
di phenylphos'c chloride
a Experimental AN values from Gutman (21)
b AN (a) values are calculated from E_(30) using
equation [34] from Schmid (24)
c AN (c) values are calculated from E (30) using
alcohol and chlorinated hydrocarbon correlation
equation.
105
TABLE A-3
LIST OF DN VALUES AND DN ERROR
Compound
AROMATICS
a Nb c d e f gexp 4^ D[1I,I B -*H.r Beta Ave DN Error
n-hex an*
benzene
toluene
HAL IDES
chlorobenzene
bromobenzene
1 ,2-dichlorobenzene
chloroform
carbon tetrachloride
di chlor omethane
1 ,2-dichloroethane
1 ,1-di chloroe thane
NITRO COMPOUNDS
ni tr omethane
ni troethane
ni trobenzene
NITRILES
acetonitrile
propioni trile
acryloni trile
n-butyroni trile
benzoni trile
phenyl ace toni trile
ESTERS
3.2
3
3.4
3.8
3.5
3.5
3.9
3.2
3.06 3.3 0.3fl
3.444 3.6 0.23
2.6 2.2 1.908 2.2 0.35
2.6 2.2 1.524 2.2 0.64
0.8 0.8
0.4 7.4 3.5 5.52
1.2 -1.4 -1.3 0.76
0.6 1.2 1.450 1.1 0.44
3.4 2.9 3.2 0.35
0.6 0.6
2.7 4.2 10.7 4.6 6.648 6.2 3.33
4.6 5 4.8 0.28
4.4 7.2 7.5 3.7 8.169 14.19 7.5 3.73
14.1 12.8 14.1 13.2 14.57 11.12 13.3 1.26
16.1 13.4
10.4
13.4 14.72 14.4
10.4
1.29
16.6 14.76 15.7 1.11
11.9 10.6 12 13.28 14.96 12.6 1.65
15.1 13.59 14.3 1.07
methyl acetate 16.3
ethyl acetate 17.1
methyl chloroacetate
vinyl acetate
methyl acrylate
thyl formate
thyl benzoate
4-butyrolactone
KETONES
10.2
10.8
8.4
7.Z
9
16.3
10,
10,
17.80
18.52
15.34
16.5
17.38
14.78 14.96
14
14.8
6.4
7.2
9
17.4
14.9
16.3
3.56
3.65
0.12
acetone 17 15.9 17 18.65 17,,65 17.2 1.01
methyl ethyl ketone 14.5 14.3 18.66 17,.65 16.3 2.21
diethyl ketone 14.3 12.6 17.67 14.9 2.56
cvclopentanone 19.01 19,,16 19.1 0.12
cyclohexanone 16.3 18.7 18.73 19,,57 18.3 1.41
acetophenone 14.3 14.1 18.25 18,,03 16.2 2.28
di-isopropyl ketone 16.37 16.6
isopropyl methyl ketone 18.34 16.3
106
TABLE A-3 (continued)
Compound exp ^ D[II,1] B -*HgfBeta Ave DN Error
ETHERS
diethyl ether 19.2 16.7 18,,1 19,,36 17.26 18.5 0.86
di-n-propyl ether 17.7 19.,53 16.68 16 1.36
di-isopropyl ether 18.1 18,,80 18.03 18.3 0.43
1 ,2-dimethoxyethane 17.3 17.3
anisole 8.2 7,.9 7.668 7.9 0.27
phenetole 6 6.9 7.5 0.78
propylene oxide 14.9 14.9
furan 3.8 4,,3 4.1 0.35
tetrahydrofuran 20 21.1 19.56 20,,6 22 ,39 20.34 20.7 1
1 , 3-di oxalane 14.7 14.7
1,4-dioxane 16.5 28.5 18 18.14 13.42 19.3 5.54
AMINES
tr i ethyl ami ne 61 50.7 53.5 34.24 26,.46 45.2 14.31
aniline 34.7 33.3 34 0.99
N-rnethylaniline 33.3 33.3
N,N-dimethylaniline 32.7 27.28 30 3.83
pyridine 33.1 36.7 32,.2 43 32.21 35.4 4.61
2-picoline 39.7 32.95 36.3 4.77
piper idine 51 51.1 28,,5 48.7 44.8 10.94
quinoline 30,,4 30.4
2,6-lutidine 24.30 24.3
39.9 32 11.24
24.5 27.7 25.1 27.63 25.71 26.2 1.33
25.7 27.4 28.05 28.40 27.5 1.06
35.19 28.78 30.4 4.19
24.61 24.6
27.14 29.17 28.2 1.44
AMIDES
formamide 24
N,N-dimethylformamid 26.6
N,N-dimethylacetamid 27.6
N-methyl-2-pyrrolido 27.3
dimethylethyleneurea
tetramethylurea
SULFOXIDES
dimethyl sulphoxide 29.8 31.3 30.1 26.28 28.40 29.2 1.92
tetramethyl sulphone 14.6 12.21 13.5 1.83
di-n-butyl sulphoxide 26.87 31.09 29 2.98
ALCOHOLS
methanol
ethanol
n-butanol
tert-butanol
2-propanol
2-phenyl ethanol
ethylene glycol
benzyl alcohol 1S-42 18.42
19 32.5 12 23.02 21.6 8.56
20 30.9 6.5 28.78 21.5 11.09
29.3 24 33.01
38.00
33.7
22.64
19.18
26.8
38
35.7
22.6
19.2
4.53
107
TABLE A-3 (continued)
Compound
CARBONATES
ethylene carbonate
propylene carbonate
dimethyl carbonate
diethyl carbonate
PHOPHATES
<P t\ DC II, I] 6-&Hfif
Beta Ave DN Error
16.4
23trimethyl phosphate
triethyl phosphate
tri-n-butyl phosphat 23.7
hex ame thyl phosphor amide
16.4
15.56 15.6
16.46 16.5
17.35 17.4
20.92 27.25 23.7 3.23
28.76 26.6
23.7
38.1 39.54 38.8 1.02
a DN experimental values
b DN values are calculated from equation [45]
c DN values are calculated from equation [46]
d DN values are calculated from equation [49]
e DN values are calculated from equation [48]
f DN values are calculated from equation [47]
g Average DN values
h DN error
* All of these DN values are obtained from Peter
Michelsen
108
TABLE A-4
LIST OF AN, DN, AND Sd
a bedSOLVENT AN ON S
d
HYDROCARBONS
1. n-hexane 0* 3.2 7.3
2. c-hexane o 0 7.3
3. benzene 8.2*3.3 9
4. toluene 3.2 3.6 8.8
S. 1,2-dimethylbenzene 3.7 3.6 8,7a6. 1,3-dtmethylbenzene 2.4 3 8.7
7. 1 .3,3-trimethylbenzene 2.2IO*
8.8
HALIDES
8. 1,2-dichloroethane 16. 7* 3.2 9.3
9. 1 ,1-dichloroethane 10.3 0.6 8.1
10. dichloromethane 22.4 1.1 8.9
11. carbontetrachlor ide 9.6 1.3 8.7
12. chloroform 19.4 3.S 8.7
13. bromobenzene 7.9 2.2 10
14. chlorobenzene 7.9 2.2 9.3
15. f luorobenzene 8.63+
(8.6)16. iodobenzene 8.4
4"*"
(9.1)17. 1 ,2-dichlorobenzene 8.6 0.8 9.4
NITRO COMPOUNDS
18. nitromethane 20.5 6.2 7.7
19. nitroethane 15.7 4.8 7.8
20. nitrobenzene14.8*
7.5 9.8
NITRILES
21. acetonitrile18.9*
13.3 7.5
22. propionitrile 15.9 14.4 7.5
23. acrylonitrile 19.7 10.4 8
24. n-butyroni trile 15.1 15.7 7.5
25. benzonitrile 13.3*
12.6 8.5
26. phenylacetonitrile 14.8 14.39.2*
ESTERS*
27. methylecetate 10.7*
14 7.6
28. ethylacetate9.3X
14.8 7.7
29. vinylacetate 8.5 7*2* (7.5)30. propylacetate 7.9 16* (7.5)
31. ethylbutryate 9.1 16.8 (7.5)32. methylacrylate 16.9 9 (7.7)
33. ethviformate 12.2 17.4 7.6
34. ethylbenzoate 8.6 14.9 8.9 *
109
TABLE A-4 (continued)
35. methylchloroacetate
36. 4-butyrolactone
KETONES
37. 2-propanone
38. 2-butanone
39. 3-pentanone
40. di isopropylketone
41. 3-methyl-2-butanone
42. cyclopentanone
43. cyclohexanone
44. acetophenone
ETHERS
45. diethyl ether
46. diisopropyl ether
47. dipropyl ether
48. dl-n-butyl ether
49. dimethoxyethane*
50. phenylmethyl ether
51. propylene oxide
52. furan
53. tetrahydrofuran
54. 1,4 dioxalane*
55. 1,3 dioxalane*
56. phenylethyl ether
AMINES
57. t-butylamine
58. diethylamine
59. trierhylamine
60. ethylenedi amine*
61. aniline
62. N-methylaniline
63. N,N-dimethylaniline
64. 2-chloroaniline
65. pyridine
66. 2-picollne
67. 2,6-lutidine
68. piperidine
69. qulnoline
AMIDES*
70. formamide
71. N-me thyl formamide
72. N,N-dimethylformami de
73. N,N-dimethylacetamide
74. N-methyl-2-pyrrolidone
75. 1-formylpiper idine
76. dimethylethylurea
77. tetramethylurea
SULFIDES
78. carbondisulfide 1*5 3.8 10
13.7 8.4 (8.5)16.6 16.3 9.3
12.5*
17.2 7.6
12.8 16.3 7.8
10.2 14.9 7.7
9.4 16.6 (7.4)
12.2 18.3 (7.4)(8.6)10.3 19.1
10.8 18.3 8.7
12.8 16.2 9.6
3.9* 18.5 7,1a
3.3 18.3.6.7*
3.318+ (7.2)
2-6^ 18.1 7.4
10.2*
17.3 7.7
7.5 7.9 8.7
10.8 14.9 (7.4)3.3* 4.1 8.78*
20.7 8.2
8.4 19.3 9.3
15.1
6.4
14.7
7.5 is! 6)
7rf+
57.5 (7.5)
9-< 50 + 7.3*
1.4*
45.2 (7.3)20.9* 55+ ( 8)16.6 34 9.5
14.3 33.3 9.3*
8.5 30 8.9*
18.2 31+ (9.3)14.
2X35.4 9.3
6.9 36.3 (9.7}6.8 24.3 (10. 1)5 44.8
B.6A
10.3 30.4 9.5
39.8*
32+
49+8.4
32.1* 8.4*
16*-26.2 8.5
13.6* 27.5 8.2
13. 3* 30.4 8.85.3 28.6 (8.8)14.3 24.6
12.4 28.2 8.2
110
TABLE A-4 (continued)
SULFOXIDES
79. dimethyl sulfoxide
80. tetramethylene sulfone*
81. dibutyl sulfoxide
CARBONATES*
82. ethylene carbonate
83. propylene carbonate
84. dimethyl carbonate
85. diethyl carbonate
PHOSPHATES*
86. trimethyl phosphate
87. triethyl phosphate
88. tri-n-butyl phosphate
89. hexamethyl phosphoramid
ALCOHOLS
90. methanol
91. ethanol
92. 2-propanol93. 1-butanol
94. 2-methyl-2-propanol95. 1-pentanoi
96. 3-methyl-l-butanol97. 2-methyl-l-butanol98. 1-octanol
99. cyclohexanol
100. benzyl alcohol
101. 2-phenyl ethanol
102. ethylene glycol*
103. glycerin
104. water
MISCELLANEOUS
105. benzaldehyde
106. acetic anhydride
a * indicates multiple interaction sites.
b AN values calculated from Table A-2, those with X
indicate experimental values.
c DN values from Michelsen (29) in Table A-3, those with
+ from Marcus (30).
d 8j values from Barton (15), values in parenthesis
were approximated using van Krevelen's additivity
values (18), values with A from Beerbower (35).
19.3*
29.2 9
19.2X
13.5
9 29 (7.3)
22. 2V 16.4 9.5
18.3X
15.6 9.8
12.5 16.5 (8.5)6.2 17.4 8.1
16.3X
23.7 8.2
13.3 28.8 8.29.9* 23.7 8
11.4 38.8 9
41.3*21.6 7.4
37.1*21.5 7.7
35.5* 35.7 7.736.8*
28.8 7.827.1* 38 (7.3)34.3 26.2 7.8
34.1 32 (7.6)
(7.5)31.1 32
33.1 32 7.7
30.1 25 8.5
36.8 18.4 9
34.9 22.6 (8.9)44.9 19.2, 8.3
46 19+8.5
54.8*
33 7.6
28 16+ ^lV16.1 10.5 7.8*
111