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7-1-1988 A simple solubility theory combining solubility parameter and Lewis acid-base concepts Lan Tuyet Evans
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Recommended Citation Evans, Lan Tuyet, "A simple solubility theory combining solubility parameter and Lewis acid-base concepts" (1988). Thesis. Rochester Institute of Technology. Accessed from
This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contact [email protected]. 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:
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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
Map- Benzene Sorting 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
Map- Hexane Sorting 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 :
2 S)2 - AH [mix] - V 0 ( S. - + 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
carrier 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 napthalene The absolute difference in 6 values of 1 . 0 for 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 cohesive of the molar cohesive energy, -E. The molar 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
parts: be seen that -E consists of two 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:
- + dV -E A?E \V=0(^E/'2>V) [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
RT2 dT r6] The heat of vaporization of nonpolar liquids may also be estimated by using Hildebrand "s rule
2 = + + 0.020 AH (cal/mol) -2950 23.7 Tfa 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):
/AE\M6 Y [8]
v "3 Vv I
Beerbower combined equations [1] and [8] and obtained a
relationship where S may be determined from the surface empirical equation (7): tension, t , by the
0. 4 s u, , , 5 = k ( Y / V/2) [9]
where V is in cm /mole, Y is in dyne/cm 5 is in
(cal/cm3/2 and k is a proportionality constant with a
25 numerical value of 4.1 at 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:
v'/2 S = ( -E / ) = a'/2/ V [11]
The internal pressure can also be related to the thermal pressure by:
E U l \' = T E12J & V ) \ W , 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. < " [14] 2 *, 8, *J
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 in 2
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]
1* The solubility parameter then is composed of 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 ), and H- 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. = : [20] d j 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) = 19.5 nQ 11.4 [21]
15 between the dispersion cohesion parameter S and the
"D" refractive index at the sodium line, n
Koenhen and Smolders (17) also developed an
expression for the polar solubility parameter, S P
(cal/cm3 )1/2 V3/i S = feju [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
for groups such as constants, Fd , 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 (18): F , by the molar volume
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:
)V2 sh = <" ? / v C26] n i Vh
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 describe n 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:
JZf2 S2)2
- AH2 [mix] = V2 [(S, - + (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
"likeness" criteria for high solubility is still one of
three- or small differences even though now it is a
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:
= - + .PA . -PD .PA AE mix [H-bond] PD .PA PD PD PA [29] 11 22 1221
Rearrangement of this expression gives the result first
suggested by Small (19):
AE mix [H-bond] = ( PD - )( - PA ) [30] , PD2 PA, 2
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 as triethylamine-
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 parameters a
A E [H-bond] = 2 V S S [31] iab
20 The corresponding expression for H [mix] was written
V202 AH [mix] = + + -S ] [32] (S,-S2)p 2(S, 2)a (S, -S2 >b
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 H- term ( via the V? 0, multiplier ) is questionable.
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 S a 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
donor- but is an example of a generalized electron-pair
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 should ( however short lived ) , they 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 Donor- acceptor number ( AN ) . Thus a
Acceptor H mixing term can be written as:
AH mix = k AN - - [DA] ( AN )( DN _ ) [34] 1 2 DN,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:
[vap] = VS. + k ( AN: )( DN. ) [36] AE;i id '
The enthalpy of mixing would also be a two term equation:
^2 2. ^H = V -g + [mix] 0 (S ) 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
solution: dilute 1 , 2-dichloroethane
D: + SbCl > D:SbCl [38]J 5 5
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 Kcal/mol = he V = 2.859 x 10V (cm (30) NAAvo ) [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 the is strongly solvated by the sovent , then
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
110
M? 10 100 OwoX"1 US MH >
20* 116
30 40 50 60 fT(30l (kcol/mell
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 R 0.,984 [45]
= - = DN 10.11 D{II,I] 12.17 R 0.,995 [46]
= - = DN 38.4 ( ) 0.78 R 0,,98 [47]
= (- - = DN 0.261 A H__ ) 1.15 R 0,,9684 [48]
DN = 0.19 B - 0.636 [49]
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 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
)2 d? = ( y. - y = ( AN exp - AN cal [52]
The least squares slope and intercept are given by the following equations
33 IXj yj ?X;
m = D [53]
n
J(Xj ) 2xi y\
b = 7 D [54]
2X: *y-.
where n is the number of points and the value of D is
given by
2(x-, ) Ix.
D = [55]
Sx; n
The correlation coefficient was found by the following
expression
2 2 2
" lJx - ( r ys ) d\
r = [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 ) V zu, [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:
mutual Experimentally , 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
v 1806 possible binary pairs. The Lotus 1-2-3 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 43 Miscibility sorting maps for each of the
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 = V 6 -S + k -AN -DN [mix] r (S ) (AN )(DN ) [37] 2 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 1.7415 [59] n - 2 19
1 (x/ ) Xx.
D - [55] n
D = (35333. 22M21) - (857)(857) = 7548.62
6~y n (1.7415H21) = 0.004845 m [57] D 7548.62
40 TABLE 2
ERROR ANALYSIS FOR SCHMID'S CORRELATION EQUATION
Xi2 d,2 a Xi Yl Y d Yi-Y 1 SOLVENTS EtOO) EtOO) AN(txp) ANCeal)
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 0.36 9. 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 5.29 7. OMF 43.6 1916.44 16 16 0 0 8. DMSO 43 2023 19.3 17. S 1.8 3.24 9. ethylaeetate 38.1 1431.61 9.3 8.6 0.7 0.49 10. ipa 40.9 1672.61 10.6 12.2 -1.6 2.56 11. hexane 30.9 954.81 0 -0.66 0.66 0.4356 12. metthylacetate 40 1600 10.7 11.1 -0.4 0.16 13. NIP 42.2 1780.84 13.3 13.9 -0.6 0.36 14. nitrobenzene 42 1764 14.8 13.7 1.1 1.21 13. ni tromethane 46.3 2143.69 20.3 19.2 1.3 1.69 16. pyridine 40.2 1616.04 14.2 11.3 2.9 8.41 17. THF 37.4 1396.76 8 7.7 0.3 0.09 18. TBP 39.6 1368.16 9.9 10.6 -0.7 0.49 19. triethylamine 33.3 1108.89 1.4 2.4 -1 1 20. TWP 43.6 1900.96 16.3 15.7 0.6 0.36 21. 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 x. , (1.7415)(35333.32) 5"b2 6~vy- 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
J(2.86)2 (0.07)2 0~m2 AN error = ^ 6~b + = + =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
2. methylenechloride (CH2C1 ) 7. 1-propanol
3. chlof orm (CHClj ) 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)2 Yj Y d. Y -Y xi i df SOLVENTS ET (30) (ET(30)) AN( exp) AN( cal)
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-butylaleo hoi 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 fluoroethanol 11. water 3.1 3981.61 54.8 55 -0.2 0.04
SUM (2 ) 536.1 26949.69 46.17
46.17 46.17
.2 - 5.13 n-2
26949.69 536.1 9043.36 536.1 11
y t n (5.13K11) 0.0789931 m 9043.38
0.07899
l(5.13)(26949.69) 3.909940 9043.38 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 \|(3.909)2 AN error = + = 3.91 [66]
Correlation of AN. DN and Dielectric Constant :
The second part of the research was to expand the
of list 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
MINITAB' developed by using the 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 0 0840 0 0330 -0 00015 0 938 0 969 amides 0 708 0 0188 0 0190 0 960 0 980
halides 0 686 0 0375 -0 0922 0 941 0 980
esters 0 172 0 956 -0 0179 0 845 0 919
amines 1 32 0 0180 -0 0181 0 703 0 838 nitro &
nitriles 1 18 0 0225 -0.00869 0 558 0 747 ketones 0 919 0 0101 0.0135 0 454 0 674 hydrocart 0 307 0 00765 0.00352 0 420 0 648 ethers 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
obtained 87 of parameter term ( S . ) from Barton (9) for 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 ) . for i 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
S AD ri LIQUID 1 LIQUID 2 M I n-htxint benzaldehyde 3.24 3.58 n-hexane t-butylamine n-hexane o-xylene n-hexane fn-xylene nhexane tr iethylamine 0 0.6 n-hexane itoamylalcohol 0.09 9.82 n-hexane c-hexane n-hexane benzene 2.69 0.01 n-hexane toluene 2.25 0.01 n-hexane ethylenechlorlde n-hexane CC1. 1.96 -0.18 n-hexane CHCl, 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*phate B.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 benzaldehyde 0.01 2. 52 benzene t-butylamine 2.2s -0.65 benzene e-xylene benzene m-xylene benzene triethylamine 2.89 -1.85 benzene iaoamylalcohol 1.96 7.43 benzene e-hexane 2.89 0.27 benzene n-hexane 0 0.01 benzene toluene 0.04 -0.02 benzene ethylenechloride 0.09 -0.01 benzene CCI4 0.09 -0.03 benzene CHClj benzene chlorobenzene benzene o-dichl or 0 benzene 0.16 -0.01 benzene ni tromethane 1.69 0.36 benzene ni trot thane 1.44 0.11 benzene ni trobenzene 0.64 0.27 benzene propioni trile 2.25 0.85 benzene benzoni trile 0.25 0.68 benzene ethylacetate 1.69 0.13 benzene ethylf ormate 1.96 0.56 benzene ethylbenzoate 0.01 0.05 benzene acetone 1.96 0.6 benzene methylethylketone 1.44 0.6 benzene Cyclohexanone 0.09 0.39 benzene acatophenone 0.36 0.59 benzene diethylether 3.61 -0.65 benzene di-n-butylether 2.56 -0.83 benzene aniline 0.25 2.56 benzene N,N-dimethylanilin benzene pyridine 0.09 1.93 benzene formamide 0.36 9.06 benzene CS2 1 -0.03 benzene tr i-n-butylphotpha 1 0.35 benzene methanol 2.56 6.49 benzene ethanol 1.69 5.49 benzene 2-propanol 1.69 8.19 benzene 1-butanol 1.44 7.06 benzene 1-pentanol 1.44 5.98 benzene eyelohexanol 0.25 4.75 benzene benzylalcohol 0 4.32 benzene ethylene glycol 0.49 5.83 benzene glycerin 0.25 9.94 benzene water 1.96 13.8
Solubility parameter term of equation [37] ( S )
AD Acceptor-Donor term of equation [37]
AN - DN - DN 0.01 ( , AN2 ) ( , 2 ) where values are: (M) Miscible, (I) Immiscible, or (?) Questionable or partially miscible
56 BENZENE
Z 0
z 0
r\ CM z <
z <
0 a 0
Benzene-Solvent Figure 5 . 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
Beerbowers' values. If 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
benzene- experimentally determining the miscibility of
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
Z D
Z 0
\J
r\
cs z <
z <
-10- 0 0
-15-
Benzene-Solvent Figure 6 > Sorting Map ( Beerbower's DN values )
Q miscible, + miscible,
ormamide* +1 benzene-water, +2 benzene-f
glycol* +3 benzene-ethylene
+4 benzene-glycerol*
* Beerbower'* DN values used
62 o m en CM CM
en en mm mm o m is> mm o o cji m oils o^i ~ en no m cm mm u Ci 10 en m m cm m - m <~i m S rs. oh en en rs en ~" o o en cm m >o n m m m m en en rn Cn V CO L. * 01 (V 51 o me v m us en > m - m -* mm en en 3* rs. cn v h m in O X - 41 E en m o O 9t en > ci -^ u m m m i/> > -> BOO CM en en en rs m U VO CI m m v o en o m cm m m us en m en rs en "-1 ! v. L. CI 3 i. -i rs U"> CM en o O m cm m ID -O x o o to 0"> ** a us o 91 o n en m cm us m o o rs. en en m v at ? i j v4 CD m s OH ^ o - -S e e o u ci ci H > w .c >, >> e t u3 (9 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 < Benzene-Solvent Final Figure 7 . Sorting Map ( Map ) O miscible, + immiscible ormamide* +1 benzene-water, +2 benzeue-f * a +3 benzene-ethylene glycol, +4 benzene-glycerol benzeue-ethauol 05 benzene-methanol , 06 Beerbower' * s DN values were used 65 i 1 1 e* , o 4iMninN o ooo<) co 0 co h .-( co HfjdNoo^rf CO -H 1 CO -i 4 I bJ Z >- C0COQC"CO0DQjCDCOCOCO03a>CrjQDaiCO0iCOCOCDCOCD00COGDa)0DCOCDCO w -H W O nmnnnrinnmnnnpinnnnnnnnnnnnnnnmn Z i. N k. PQ O 0000000000000000000000 OOOOOOOO Z II < w co HraHiMOjinijiinMHramrtjinnianMNHr. inTniMirinHffiri u. A o z 000 oNNrtTdtiritni 1 cm iti 0 ng co 'xi 0 co co fj in in in m 1 1 1 1 1 H 1 r4 *4 r4 HrinniMVlMHrinNriHtl) 1 III 1 1 1 1 1 1 1 1 1 to < 1 1 1 1 1 M CO rJ^ S- o cn.nmroTCO(\j'*.H'jowvNCi I < OOC0O.-IOOOOO CO >HOO,HO 1 10 C4 OOOOOOO < 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 k. lOtOtOtOlOiOtOtOlOiOtOtototOtotOlOtotototOtOtOtOtOtotOlDtOiJ) CM M vCf>mcrivv ,mmin-vc,T'v,v,r"vininioioir)nn (0 NinrivNvniriitMnHvnuisumviDifiiiNHnmwisNN z z i 09 OOrH^OCMrslArsNiH V V CM V W CD rtrHriroffirsOOODWIA Q iir-iiniiiii 1111 1 roco 1 CO CM CM (V (M co m < 11 11 1 1 1 1 1 1 1 a a TJ C a. z Z a m -* -1 < a k- N 0 00 oca a -100 -1 a* a -. a a a c a 0. O 3. X > C l C - -1 ~ * oc -^ -1 -1 k- 3- Cfl 0"! u oftcak. < c 0 -4 O ~ i.rN*-k.e * c oi aa O -4 O a a o"ic-k x a fo n 3-1 c 0 -1 a a *- - - t_ cac -iHt-Oic Oo* ) 01 c o-4*cacc 2 c a ce 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 in d Table A-4, the points corresponding to the benzene- solvent mixtures were plotted on the third benzene 67 map. sorting 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 it regions, 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-ethylacetate miscible miscible 4 benzene- 2-butanone miscible miscible 5 benzene-di-butyl ether miscible miscible benzene- 6 t-butanol miscible miscible 68 BENZENE z Q Z 0 z < -5- z < -10- 0 0 -15- -20 i T T T 0 2 4 b 8 10 (S.-Ud* - Predictions Figure 8. Benzene-Solvent Sorting Map ( ) immiscible ? miscible, + 2 benzene-acetonitrile 0 1 beuzene-N-methylformamide, D beuzene-2-butanone D3 benzene-ethyl acetate, D k benzene-t-butanol D5 benzene-butyl ether, D 6 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 hexane- points representing the immiscible mixtures 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 -ion a 0 -15-1 -20 10 (*,-*.), Figure 9- Hexane-Solvent Sorting Map q miscible, + immiscible, Oques tionable miscibility + + hexane- 1 hexane-water , 2 formamide + 3 hexane-ani 1 ine , *4 hexane-me thanol +5 hexane-e thylene glycol, +6 hexane-glycerol 71 n-HEXANE (*,-*,>:2'd Beerbower's DN values ) Figur. 10. Hexane-Solvent Sorting Map ( questionable D miscible, + immiscible, Q misciblity hexane-formamide + 1 hexane-vater , +2 +3 hexane-anlllne, 0 4 hexane-methanol +5 hexane-ethylene glycol, +6 hexane-glycerol hexane-ethanol 0 7 hexaue-isoamylalcohol , O 8 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 cm co to en m CM co en ? e m en m r c m o CM CO m en (SI O cm en eo to o CO r~ f cm r^ r*. r- 2 8 eo en w en to en w en en cm eo en en to en CO r r> cm 3 en en m enr en r. en in 10 to IO 60 tO (SI in CM CO en en cm a cm en m iO en co r* f CM rr r w m en en en m en ? en ? en 01 X = e o r in in us IO io en m rsi en en en cm e cm en in e v >o CO r l cm r^ r^ r*. w i. 01 J in o CM r. o r toen W r* IO r O VO v. > en cm in ~* cm en m en CM O en en X o e e to ^ en 00 r* pn (s, r*. r^ f OI m m en en en en en m en en en X c 01 X ^ a it c 01 > OI in io en to in e 9 to r- eo o to *> > O CM to en CM o m en CM O en en u # r> w to co 33 CO r- cm r r r- w a w en en en en en m en r en en v I. o o cw a k. k. OI .c k. cm in e in cm cm in eo o co to ^ .c CM CO en cm en en en CM cm en X ** r V to co CO r f CM r i i" ^ en m en en en m en en en w M X OI 3 01 * w X 3 f*. in en in co en m r- CO Bin X ~ CM en en cm r. cm en CM O cm en ^ r> to r* CO r" r* cm r> r>. r OI E CM 01 u .n M u i ? en eo m r*. O m CO r* f" r i ^- e o ^* to cm en en sn CM M cm en z r> r- r. CO r*. r>. cm rv r* r*. 8 2 en en en en en in en en en 8 o ** 01 s "5 e e e e "T L. E e 01 r- O 01 a ^m u c a a. > > t a i e w e n Ul M < Ui O (9 Ik ; 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>d Figure 11 Hexane-Solvent Sorting Map ( Final Map ) O miscible, + Immiscible, <> partial miscibility +1 hexane-water, +2 hexane-f ormamide + 3 hexane-aniline, <> 4 hexane-methanol hexane-glycerol +5 hexane-ethylene glycol -H 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) and hexane- 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 volume Z 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 hexane- miscible region can be drawn just above the 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 etVOtrtrsq'CVIrHOOrntiJq'inrMv CO MM CM O . O CD 0 h HOOOOOrlOO ir)cpintotoif)int09cricnrc)tet rs 8*i o CM V JO to . 5 CMTC\iCMrs,Ho Dd > -J TrtTffiOHnrMvnr)eo(\ioDi*ntDK O CA ffl hOho W -I I i in o cm co to oo co i in ff I I I I rH hoonvhh en I I i i i i i i i i U M 2 -3 < ea X CO cfifl-cotocoNOOrsiiicor-incncM oo m co cm oi rs oi co cji M o cm m o to ro to COOrt co co ro in in h co t o in n ci ^ rt CO CTi CO to oi to CD^ts.mrjrHiri^-ooo CO Mi)IOlOV0'tOtOtOtO>J*>tOtOIOtOtO to to to dS ffi cfi vvvcvicMvvvvvctrwv CM CM CM 2 ooommooooooooo in in in z a a ,jinif)'c--fj'j in in in 06 M -e?-rtiNtovcncocriinoDcnvDCMCDOOco<-icriffi ^OBCooie^rs.,rincMCMcoto,cTiorirtrs-(j'-a> z z i I I I IrtlHrtHHIrtHCinVfl** < a i i i i i i i i i i i i i <3 z z e o < a ft ft u u C ft -H Ilk > 3k c e oi oc cl> c 6 c o ft ft ft ft ro k. o o ox - -o ftft*ft c -4 -t *" <" 3. N 3 "J -* 0 k- a w-*- Xft 3. ft c -IHUH " o ll tlli-k.k.k-'-'X X * I ft O U I X - k. U (J - C 3. O O ft <" XI ~ u u u c a "> "O ft an. . ft ft ft 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 hexane-ace toni trile + 1 hexane-N-methylf ormamide , D 2 hexane-2-butanone 03 hexane-ethyl acetate , 04 hexane- 05 hexane-butyl ether, D6 t-butanol 82 TABLE 12 PREDICTING MISCIBILITY OF MIXTUES WITH HEXANE SORTING MAP System Predicted Experiment 1 hexane- N-methyIformamide 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, a check on the the sorting maps themselves serve as reliability of the AN and DN values. this thesis The solubility expression developed in has been demonstrated to be useful in constructing liquid mixtures or miscibility sorting maps for binary 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 3. G. Lewis, N., "Valence and the structure of the Molecules/' Ai^ms and , 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. Non- Hildebrand, J. H.; Scott, R. L., "Soluhi 1 itv of 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. 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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. R. 26. Kamlet, M. J.; Abboud, J. I.; Taft , 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 AN ET(30), ( experimental and calculated ), ANP DIELECTRIC CONSTANT ( 6 ) AN AN" E (30) 6 (25CC> (ftxpt) (E_(30) AROMATICS bftnzftna 8.2 3.983 34.5 2.28 toluene 3.211 33.9 2.38 o-xyln 3.727 34.3 2.568 (20) p-xylnft 2.695 33.5 2.27 (20) m-xyl*n 2.437 33.3 2.374 (20) chlor obenzne 7.855 37.5 5.62 bromcb*n:ini 7.e55 37.5 5.4 c-di chlorobnz*ne 8.629 38.1 9.93 m-di chlorobftnzftn 7.21 37 5.04 i odobenzftn* 8.371 37.9 4.63 (20) f iuorobftnzcn* 8.629 3S.1 5.42 methoxybftnzftnft 7.468 37.2 4.33 t t hoxybftnz int 6.436 36.4 4.22 (20) rresi tylftn* 2.179 33.1 2.2s (20) thylbenzftnft 2.4 (20) styrftn* 2.426 (20) o-mftthyl*tyTftn p-iTiethylstyrnft ALIPHATICS n-hexan 0 -0.639 30.9 i.ee 16. 1 , 2-di chloroftthanft .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 NITRO COMPOUNDS 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) NITRILES acstonitril* 18.9 18.82 46 37.5 (20) prop l oni tr ilft 15.853 43.7 27.2 (20) acryloni trile 19.723 46.7 33 (20) n-bu tyroni trile 15.079 43.1 20.3 (21) benzoni trile 15.5 13.66 42 25.2 phenyl ace t oni trile 14.821 42.9 18.7 (27) i so -bu tyroni trile 20.4 (24) tert-butyl nitrile cyclohexylni trile 3-chloropropioni trile 26.689 32.1 4-chl or obu tyroni trile 22.561 46.9 NITRATE isopropylni trate 15.079 43.1 ESTERS methylaeetate 0.7 11.08 40 6.63 etnylacetate 9.3 6.629 3.l 6.02 v inylacetate 8.5 36 methylacrylate 16.855 44.5 et:->vi aery late propylacetate 7.635 37.5 6 (20) etnylf ormate 12.241 40.9 7.16 rrethylf ormate 8.5 (2C) ethylbenzoate 8.629 38.1 6.02 (20) methylbenzoate 6.59 (20) dimethylphthalate 11.933 40.7 methyl chloroacetate 13.66 42 methyl di chloroacetate methyl propionate ethyl propionate 5.63 (19) ethyl chloroacetate methyl isobutyrate methyl methacrylate 2.9 LACTONES B-prop ionlactone 4-butyrolactone 16.627 44.3 39 (20) E-caprolactone KETONES 42.2 20.7 acetone 12.5 13.918 3,3-aimethylbutanone 9.79 39 93 TABLE A-l (continued) methylethylketone 12.757 41.3 18.51 (20) diethyl ketone 10.177 39.3 17 (20) methylpropylketone 12.499 41.1 15.4 (20) di i so propyl ketone 9.403 38.7 diisobutylketone 6.5 38 4-hep tanone 9.661 38.9 2-hexanone 11.209 40.1 isopropylme thy Ike tone 12.241 40.9 cyclopen tanone 10.306 39.4 cyclohexanone 10.822 39.6 16.3 (20) acatophenone 12.757 41.3 17.39 4-methyl-2-p en tanone 10.306 39.4 13.11 (20) cyclobutanone cyciohep tanone methylvinyl ketone i sophorone camphor 11.35 (20) tr t chloroacetone di met hyl-G-py rone benzcphenone bi acetyl di-ter t-bu tyl ketone ETHERS diethylether 3,,9 4.114 34.6 4.34 (20) di i sop ropy lether 3.34 34 3.66 di-n-bu tylether 2.566 33.4 3.08 (20) 1 ,2-dirr.ethoxyethar.e 10,.2 8.758 38.2 7.2 ant sole 7.468 37.2 4.33 propvleneoxide 10.822 39.8 di glyme 9 .9 9.274 38.6 furan 3,,3 2.942 tetrahydrof uran 8 7.726 37.4 7.56 2.21 1 ,4-dioxane 10,.8 5.92 36 1 ,3-di oxolane 15.079 43.1 phenatole 6.436 36.4 4.22 (20) di-n-propyl ether 3.39 (26) ethyl butyl ether ethyl uinyl ether n-butyl vinyl ether isobutyl vinyl ether diallyl ether 22.6 (22) 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 94 TABLE A-l (continued) diphenyl ether 3.656 oxepane 2-methyltetrahydrof uran 6.565 36.5 tetrahydropyran 3.61 tr igiyme 9.661 38.9 7.3 ALDEHYDES acetaldehyde 21.1 (21) prcpi onaldehyde 16.5 (17) butyraidehyde 13.4 (26) acrolein cro tcnaidehvde benzaldehyde 17.6 (20) AMINES AND DERI NATIVES di ethvlami re 9, 4 3.146 35.4 3.58 (21) tr iethyia.Tiine 1. 4 2.437 33.3 2.42 diisoprcpylan :ne 2.437 33 . 3 ter t-bu tyl a.Ti;ne 6.932 ScT.S aniline 16.627 44.3 6.89 (20) ethvieneoi amine 20. 9 13.66 42 12.9 n-ir.ethylai-i il : ne 14.303 42.5 nn-dimethylaniiine 6.3 38 pyridine 14, 2 11.338 40.2 12.4 (21) a-pi col i ne 8.887 38.3 5.S (20) b-pt coli ne o-pi coline 4-ethvlpyridine 2,4,6-trimethylpvridine 2-chloropyridine 13.531 41.9 3 ,5-di chloropyr lcine 3bromopvr 1 dine 4-winyl pyridine 4-dimethyl ami nopyr i dine 2 ,6-luti dine 6.823 36.7 1-formvlpi per i dine 3.273 35.5 piper idine 3.275 35.3 5.8 (20) quinoline 10.306 39.4 9 n-methyl-2-pyrrolido 13.3 13.918 42.2 32 dimethylethyleneurea 14.305 42.5 tetramethylurea 12.37 41 23.45 ammonia 16.9 ethylamine 3.58 (21) 5.31 n -propylamine (20) 3.066 (20) di -propylamine 6.34 o-toluidine (18) N-me t hy1 -E-capr o 1 ac t am N-fliethylpyrrolidin* *2 N-isopropyl-2-pyrrol idine 95 TABLE A-l (continued) dimethylpropvleneurea tr i-bu tylamine N,N-di methyl benzyl amine IMINES ethylenimine 16.3 N-phenylethylenimi ne AMIDES formamide 39.6 32.494 56.6 111 (20) n-methvlformamide 32.1 29.269 54.1 182.4 n -me t hy 1 a ce t am i de 26.56 52 191.3 (32) n n , -dime thy If ormami d 16 13.962 43.8 36.7 n , n-di me thy lace tarn id 13.6 15.853 43.7 37.78 hexamethylphosphoami 10.6 12.241 40.9 29.6 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 dimethvlsuif oxides 19.3 17.53 45 46.68 dimethyl sulfone 21.4 46 dibutyl sulphone 14.692 42.8 sulfolane 19.2 16.24 44 43.3 (30) di-butyl sulphoxide 9.016 38.4 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) 15-a acetyl chloride <22) benzoyl chloride 23 <20> benzoyl fluoride 96 TABLE A-l (continued) CARBONATES ethylenecarbonate 22.174 48.6 69.6 (40) propvlenecarbonate 18.3 19.594 46.6 65.1 dimethyl carbonate 12.499 41.1 diethylcarbonate 6.178 36.2 2.62 (20) dichloroethylene carbonate tetrachloroethylene carbonate propanediol-l,2-carbonate PHOSPHOROUS COMPOUNDS tr imethylphosphate 16.3 15.724 43.6 20.6 (20) tr ie thy lphosp hate 13.273 41.7 tr i-n-propyl phosphate 11.723 40.5 tr i-n-bu tylphosphate 9.9 10.564 39.6 7.939 (30) tripiperidinophosphine oxide tripyrrolidinophosphine oxide tr iphenylphosphine oxide trimethyiphosphine oxide ALCOHOLS methanol 41,.3 31.075 55.3 32.7 ethanol 37,,1 26.431 51.9 24.55 n-bu tanol 36,,6 24.238 50.2 17.31 1-pen tanol 22.619 49.1 13.9 1-hexanol 22.432 48.8 13.3 1 -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 ifluoroethan 53,,5 36.235 59.5 2,2,3,3-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 43.1 2-chloroethanol 25.8 l-bromo-2-propanol 31.4 2-ethoxyethanol 23.27 31 29.6 (24) 2-methoxy ethanol 26.947 32.3 16.93 2-n-butoxy ethanol 24.238 30.2 9.3 benzyl alcohol 25.012 50.8 13.1 (20) furfuryl alcohol 50.3 t et r ahy dr of ur fury 1 alcohol 24.367 50.3 13.61 1-phenyl ethanol 19.723 46.7 2-phenyl ethanol 23.335 49.5 3-phenyl-l-propanol 22.045 48.5 glycerol 33.01 57 42.5 1 ,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 11 phenylphos'c difluoride 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 a AN AN AN SOLVENT (expt) (E (30) (alcohol) AROMATICS benzene 8.2 4 toluene 3.211 o-xylene 3.727 m-xylene 2.437 p-xylene 2.695 chlorobenzene 7.855 bromobenzene 7.855 o-di chlorobenzene 6.629 m-di chlorobenzene 7.21 i odobenzene 8.371 f luorobenzene 8.629 methoxybenzene 7.466 ethoxybenzen 6.436 mesi tylene 2.179 ni trobenzene 14.2 13.7 e thy lbenzene styrene o-methylstyrene p-methylstyrene ALIPHATICS n-hexane 0 -0.6 1 ,2-dichloroethane 16.7 13.5 1 , 1-dichloroe thane 10.306 dichloromethane 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 14.692 ni tromethane 20.5 19.3 ni troethane 15.724 ni trobenzene 14.8 13.7 99 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 10.7 11.1 ethylacetate 9.3 8.6 uinylacetate 8.5 methylacrylate 16.885 propylacetate 7.855 ethylf ormate 12.241 ethylbenzoate 6.629 dimethylphthalate 11.933 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-pyrone benzophenone biacetyl di-ter t-bu tyl ketone ETHERS diethylether 3.9 4.1 di isopropylether 3.34 di-n-butylether 2.566 8.8 1 . 2-di me t ho xy ethane 10.2 am sole 7.468 propyleneoxide 10.822 di glyme 9.9 9.3 f uran 3.3 tetrahvdrof ur an 6 7.7 5.9 1 ,4-dioxane 10.8 15.079 1 , 3-dioxolane phenatole 6.436 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 thy 1-1 ,3-dioxalane 4-me thy 1-1 ,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 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-f ormylpiperidine 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 ne 4nethylpyr idine N-methyl pyrrol 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 39.8 32.5 n-me thy If ormami de 32.1 29.3 n-me thyl acet amide 26.56 16 16 n ,n-di me thyIf ormami de n rn -d i me thyl ace t amide 13.6 15.6 hex ame thylp ho spho amide 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 41,,3 31.1 43.7 ethanol 37,.1 26.4 38.4 n-bu tanol 36.,8 24.2 35.9 n-amyl alcohol 22.619 34.3 1-hexanol 22.432 33.8 1-hep tanol 22.045 33.4 1-octanol 21.787 33.1 1-decanol 20.884 32 1-dodecanol 19.723 30.7 2-propanol 33,.5 22.2 33.5 2-butanol 20.239 31.3 2-pen tanol 19.465 30.4 3-pen tanol 18.433 29.2 i sobutylalcohol 22.69 34.1 isoamyl alcohol 22.69 34.1 cyclopen tanol 21.013 32.2 cyclohexanol 19.207 30.1 t-butyl alcohol 27,,1 16.1 26.6 t-pentyl alcohol 13.531 23.6 1-propanol 37,,3 24.9 36.6 2,2,2-trifluoroethanol 33,,5 36.2 49.7 2,2.3,3-tetrafluoro-l-propanol 36.106 49.5 2,2,2-trichloroethanol 32.494 43.5 2-propen-l-ol 26.689 38.7 2-ami noethanol 33,,7 26.3 38.3 2-chloroethanol 2-ethoxyethanol 25.27 37.1 2-methoxy ethanol 26.947 39 2-n-butoxy ethanol 24.236 35.9 benzyl alcohol 25.012 36.8 2-hydroxymethyl tetrahydrof uran 24.367 36 1-phenyl ethanol 19.723 30.7 2-phenyl ethanol 23.335 34.9 3-phenyl-l-propanol 22.045 33.7 1,2,3-propantriol 33.01 46 1 ,2-ethanediol 32.107 44.9 1 ,2-propanediol 29.269 41.7 1 ,3-propan*diol 30.301 42.9 1 ,3-butanediol 27.592 39.7 diethylene glycol 28.882 41.2 triethylene glycol 28.495 40.8 water 54,,6 40.9 55 deuterium oxide 40.492 54.6 104 TABLE A-2 (continued) INORGANIC HALIDES sulphuryl chloride thionyl chloride felenium oxychloride phosphorous oxychloride n phenylphos'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 a Nb c Compound d e f g exp 4^ D[1I,I B -*H.r Beta Ave DN Error AROMATICS n-hex an* 3.2 3.2 benzene 3 3.8 3.5 3.06 3.3 0.3fl toluene 3.4 3.5 3.9 3.444 3.6 0.23 HAL IDES chlorobenzene 2.6 2.2 1.908 2.2 0.35 bromobenzene 2.6 2.2 1.524 2.2 0.64 1 ,2-dichlorobenzene 0.8 0.8 chloroform 0.4 7.4 3.5 5.52 carbon tetrachloride 1.2 -1.4 -1.3 0.76 di chlor omethane 0.6 1.2 1.450 1.1 0.44 1 ,2-dichloroethane 3.4 2.9 3.2 0.35 1 ,1-di chlor oe thane 0.6 0.6 NITRO COMPOUNDS ni tr omethane 2.7 4.2 10.7 4.6 6.648 6.2 3.33 ni troethane 4.6 5 4.8 0.28 ni trobenzene 4.4 7.2 7.5 3.7 8.169 14.19 7.5 3.73 NITRILES acetonitrile 14.1 12.8 14.1 13.2 14.57 11.12 13.3 1.26 propioni trile 16.1 13.4 13.4 14.72 14.4 1.29 acryloni trile 10.4 10.4 n-butyroni trile 16.6 14.76 15.7 1.11 benzoni trile 11.9 10.6 12 13.28 14.96 12.6 1.65 phenyl acetoni trile 15.1 13.59 14.3 1.07 ESTERS methyl acetate 16.3 10.2 10, 17.80 15.34 14 3.56 ethyl acetate 17.1 10.8 10, 18.52 16.5 14.8 3.65 methyl chloroacetate 8.4 6.4 vinyl acetate 7.Z 7.2 methyl acrylate 9 9 thyl formate 17.38 17.4 thyl benzoate 14.78 14.96 14.9 0.12 4-butyrolactone 16.3 16.3 KETONES 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 16.3 isopropyl methyl ketone 18.34 106 TABLE A-3 (continued) Compound Ave DN Error exp ^ D[II,1] B -*Hgf Beta ETHERS ether 0.86 diethyl 19.2 16.7 18,,1 19,,36 17.26 18.5 1.36 di-n-propyl ether 17.7 19.,53 16.68 16 0.43 di-isopropyl ether 18.1 18,,80 18.03 18.3 1 ,2-dimethoxyethane 17.3 17.3 0.27 anisole 8.2 7,.9 7.668 7.9 phenetole 6 6.9 7.5 0.78 propylene oxide 14.9 14.9 uran f 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 AMIDES formamide 24 39.9 32 11.24 N,N-dimethylf ormamid 26.6 24.5 27.7 25.1 27.63 25.71 26.2 1.33 N,N-dimethylacetamid 27.6 25.7 27.4 28.05 28.40 27.5 1.06 N-methyl-2-pyrrolido 27.3 35.19 28.78 30.4 4.19 dimethylethyleneurea 24.61 24.6 tetramethylurea 27.14 29.17 28.2 1.44 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 19 32.5 12 23.02 21.6 8.56 ethanol 20 30.9 6.5 28.78 21.5 11.09 n-butanol 29.3 24 33.01 26.8 4.53 tert-butanol 38.00 38 2-propanol 33.7 35.7 2-phenyl ethanol 22.64 22.6 ethylene glycol 19.18 19.2 benzyl alcohol 1S-42 18.42 107 TABLE A-3 (continued) Compound DN Error CARBONATES ethylene carbonate 16.4 16.4 propylene carbonate 15.56 15.6 dimethyl carbonate 16.46 16.5 diethyl carbonate 17.35 17.4 PHOPHATES trimethyl phosphate 23 20.92 27.25 23.7 3.23 triethyl phosphate 28.76 26.6 tri-n-butyl phosphat 23.7 23.7 hex ame thyl phosphor amide 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 bed SOLVENT 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 8,7a 6. 1,3-dtmethylbenzene 2.4 3 8.7 IO* 7. 1 .3,3-trimethylbenzene 2.2 8.8 HAL IDES 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 8.6 3+ (8.6) 4"*" 16. iodobenzene 8.4 (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 14.8* 20. nitrobenzene 7.5 9.8 NITRILES 18.9* 21. acetonitrile 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 3* 25. benzonitrile 13. 12.6 8.5 9.2* 26. phenylacetonitrile 14.8 14.3 ESTERS* 7* 27. methylecetate 10. 14 7.6 9.3X 28. ethylacetate 14.8 7.7 29. vinylacetate 8.5 (7.5) 7*2*16* 30. propylacetate 7.9 (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 13.7 8.4 (8.5) 36. 4-butyrolactone 16.6 16.3 9.3 KETONES 5* 37. 2-propanone 12. 17.2 7.6 38. 2-butanone 12.8 16.3 7.8 39. 3-pentanone 10.2 14.9 7.7 40. di isopropylketone 9.4 16.6 (7.4) 41. 3-methyl-2-butanone 12.2 18.3 (7.4) 42. cyclopentanone 10.3 19.1 (8.6) 43. cyclohexanone 10.8 18.3 8.7 44. acetophenone 12.8 16.2 9.6 ETHERS 45. diethyl ether 3.9* 18.5 7,1 6.7*a 46. diisopropyl ether 3.3 18.3. 18+ 47. dipropyl ether 3.3 (7.2) 48. dl-n-butyl ether 2-6^ 18.1 7.4 49. dimethoxyethane* 10.2* 17.3 7.7 50. phenylmethyl ether 7.5 7.9 8.7 51. propylene oxide 10.8 14.9 (7.4) 52. furan 3.3* 4.1 8.7 53. tetrahydrofuran 8* 20.7 8.2 54. 1,4 dioxalane* 8.4 19.3 9.3 55. 1,3 dioxalane* 15.1 14.7 56. phenylethyl ether 6.4 7.5 is! 6) AMINES + 57. t-butylamine 7rf 57.5 (7.5) 58. diethylamine 9-< 50 + 7.3* 1.4* 59. trierhylamine 45.2 (7.3) 20.9* 60. ethylenedi amine* 55+ ( 8) 61. aniline 16.6 34 9.5 62. N-methylaniline 14.3 33.3 9.3* 63. N,N-dimethylaniline 8.5 30 8.9* 64. 2-chloroaniline 18.2 31+ (9.3) 2X 65. pyridine 14. 35.4 9.3 66. 2-picollne 6.9 36.3 (9.7} 67. 2,6-lutidine 6.8 24.3 (10. B.6A1) 68. piperidine 5 44.8 69. qulnoline 10.3 30.4 9.5 AMIDES* 8* 70. formamide 39. 32 8.4 32.1* + 8.4* 71. N-me thyl formamide 49 16*- 72. N,N-dimethylformami de 26.2 8.5 73. N,N-dimethylacetamide 13.6* 27.5 8.2 74. N-methyl-2-pyrrolidone 13. 3* 30.4 8.8 75. 1-formylpiper idine 5.3 28.6 (8.8) 76. dimethylethylurea 14.3 24.6 77. tetramethylurea 12.4 28.2 8.2 SULFIDES 78. carbondisulfide 1*5 3.8 10 110 TABLE A-4 (continued) SULFOXIDES 3* 79. dimethyl sulfoxide 19. 29.2 9 2X 80. tetramethylene sulfone* 19. 13.5 81. dibutyl sulfoxide 9 29 (7.3) CARBONATES* 82. ethylene carbonate 22. 2V 16.4 9.5 83. propylene carbonate 18. 3X 15.6 9.8 84. dimethyl carbonate 12.5 16.5 (8.5) 85. diethyl carbonate 6.2 17.4 8.1 PHOSPHATES* 3X 86. trimethyl phosphate 16. 23.7 8.2 87. triethyl phosphate 13.3 28.8 8.2 88. tri-n-butyl phosphate 9.9* 23.7 8 89. hexamethyl phosphoramid 11.4 38.8 9 ALCOHOLS 90. methanol 41.3* 21.6 7.4 91. ethanol 37.1* 21.5 7.7 92. 2-propanol 35.5* 35.7 7.7 93. 1-butanol 36.8* 28.8 7.8 94. 2-methyl-2-propanol 27.1* 38 (7.3) 95. 1-pentanoi 34.3 26.2 7.8 96. 3-methyl-l-butanol 34.1 32 (7.6) 97. 2-methyl-l-butanol 31.1 32 (7.5) 98. 1-octanol 33.1 32 7.7 99. cyclohexanol 30.1 25 8.5 100. benzyl alcohol 36.8 18.4 9 101. 2-phenyl ethanol 34.9 22.6 (8.9) 102. ethylene glycol* 44.9 19.2, 8.3 103. glycerin 46 19+ 8.5 104. water 54.8* 33 7.6 MISCELLANEOUS 105. benzaldehyde 28 16+ ^lV 106. acetic anhydride 16.1 10.5 7.8* 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). 111