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A simple solubility theory combining solubilityparameter and Lewis acid-base conceptsLan Tuyet Evans

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Recommended CitationEvans, Lan Tuyet, "A simple solubility theory combining solubility parameter and Lewis acid-base concepts" (1988). Thesis. RochesterInstitute of Technology. Accessed from

A SIMPLE SOLUBILITY THEORY COMBINING SOLUBILITY

PARAMETER AND LEWIS ACID-BASE CONCEPTS

by

Lan Tuyet Evans

July, 1988

THESIS

SUBMITTED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

APPROVED:

Project Advisor

Project Co-advisor

Department Head

Library

Rochester Institute of Technology

Rochester, New york 14623

Department of Chemistry

Title of Thesis "A Simple solubility Theory Combining

Solubility Parameter and Lewis Acid-Base Concepts"

I, Lan Tuyet Evans, hereby grant permission to the

Wallace Memorial Library, of R.I.T., to reproduce my

thesis in whole or in part. Any reproduction will not be

for commercial use or profit.

Date

Dedication

To Bill, who gave me support and encouragement when I

needed it most.

ii

ACKNOWLEDGEMENTS

I would like to express my sincere thanks to my research

advisors, Dr. L. Paul Rosenberg and Dr. William B. Jensen,

without whose guidance and encouragement this thesis

would not have been possible. I wish to thank my

graduate committee, especially Dr. Laura Tubbs and Dr.

Joseph Hornak, for their suggestions. I wish to thank

Peter Michelsen for his assistance. I also wish to thank

Nancy L. Wengenack for her help with the computer. The

financial assistance from the Department of Chemistry in

the form of a teaching assistantship is gratefully

acknowledged .

iii

TABLE OF CONTENTS

ABSTACT 1

GENERAL IMPORTANCE OF SOLUBILITY PHENOMENON 3

SOLUBILITY PARAMETER THEORY 5

Introduction 5

Definition of Solubility Parameter 6

Evaluation of Molar Cohesive Energy 7

Evaluation of 8 in Terms of Heat of Vaporization . . 8

Empirical Methods for Evaluation of Solubility .... 9

Hildebrand's Model with Dispersion Term only 11

Models with Dispersion and Polar Terms 12

Hansen's Model with Dispersion, Polar and H-bonding.14

Model Incorporating Proton Donor-Acceptor

Properties 19

LEWIS ACID-BASE CONCEPTS IN SOLUBILITY THEORY 23

Definitions 23

Lewis Acid-Base Donor-Acceptor Term 23

A concept Combining Dispersion and Donor-Acceptor

Terms 24

Determination of Acceptor and Donor Numbers 25

EXPERIMENTAL 32

Materials 32

Correlations 33

Miscibility Determination 35

Construction of Miscibility Sorting Maps 36

IV

RESULTS AND DISCUSSION 38

Research Objectives 38

Correlation of AN and Ey(30) 39

Error Analysis of Schmid's Equation 39

Correlation of AN and Ej(30) for Alcohols

and Chlorinated Hydrocarbons 43

Error Analysis of Correlation Equation for

Alcohols and Chlorinated Hydrocarbons 45

Correlation of AN, DN and Dielectric Constant 47

Miscibility Sorting Maps 51

Benzene-Solvent Binary Mixtures Sorting Map 54

Analysis of Benzene Sorting Map 54

Benzene Sorting Map- Miscibility Experimental . . 61

Benzene Sorting Map- Error Analysis 64

Benzene Sorting Map to Predict Miscibility

of Mixtures 67

Hexane- Solvent Bianary Mixtures Sorting Map 70

Evaluation of Hexane Sorting Map 70

Hexane SortingMap- Miscibility Experimental ... 75

Hexane Sorting Map- Error Analysis 79

Hexane Sorting Map to Predict Miscibility

of Mixtures 79

CONCLUSION 84

REFERENCES 88

APPENDIXES 91

LIST OF TABLES

1 . SOLUBILITY OF NAPTHALENE 5

2. ERROR ANALYSIS FOR SCHMID'S CORRELATION EQUATION. 41

3. ERROR ANALYSIS OF CORRELATION EQUATION FOR

ALCOHOLS AND CHLORINATED HYDROCARBONS 46

4. CORRELATION OF AN, DN, AND e FOR DIFFERENT

CLASSES OF SOLVENTS 50

5. DATA FOR SORTING MAP FOR BINARY LIQUID SYSTEM ... 55

6. REFRACTIVE INDEX AND MISCIBILITY OF

BENZENE-SOLVENT MIXTURES 63

7. ERROR ANALYSIS OF BENZENE-SOLVENT SORTING MAP ... 66

8. PREDICTING MISCIBILITY OF MIXTURES WITH

BENZENE SORTING MAP 68

9. REFRACTIVE INDEX AND MISCIBILITY OF

HEXANE-SOLVENT MIXTURES 74

10. MISCIBILITY OF HEXANE-METHANOL MIXTURES 78

11. ERROR ANALYSIS OF HEXANE-SOLVENT SORTING MAP .... 80

12. PREDICTING MISCIBILITY OF MIXTURES WITH

HEXANE SORTING MAP 83

A-l. LIST OF E_(30), AN (experimental and calculated),

AND DIELECTRIC CONSTANT ( 6 ) 92

A-2. LIST OF AN VALUES CALCULATED FROM EITHER SCHMID

OR ALCOHOL CORRELATION 99

A-3. LIST OF DN VALUES AND DN ERROR 106

A-4. LIST OF AN, DN, AND 8 109

VI

LIST OF FIGURES

1 . Structure of phenolate dye 27

2. Reichardt's correlation of AN and ET(30)

for pure organic solvents 29

3. Schmid's correlation of AN and ET(30) 30

4. Correlation of AN and Ej(30) for alcohols,

5. Benzene-Solvent Sorting Map 57

6. Benzene-Solvent Sorting Map(Beerbower's DN Values). 62

7. Benzene-Solvent Sorting Map (Final Map) 65

8. Benzene-Solvent Sorting Map (Predictions) 69

9. Hexane-Solvent Sorting Map 71

10. Hexane-Solvent Sorting Map (Beerbower's DN Values). 72

11. Hexane-Solvent Sorting Map (Final Map) 76

12. Hexane-Solvent sorting Map (Predictions) 82

vii

ABSTRACT

A simple model of liquid / liquid solubility has

been developed. The existing solubililty parameter

theory which tries to explain solvent-

salute

interaction in terms of dispersion ,polar

, and hydrogen

bonding interactions is discussed. The current theory

has been widely used qualitatively but can not be used

quantitatively due largely to incorrect modeling of the

hydrogen bonding interactions.

This research proposes modifications to the

current solubility parameter theory that are designed to

overcome the problems encountered with hydrogen bonding

interactions in which the hydrogen bonding interactions

are described as a special case of more general Lewis

acid- base or donor acceptor interactions. The specific

electron-

pair acceptor- donor properties themselves

are quantitatively characterized using acceptor numbers

( AN ) and donor numbers ( DN ) .

This modified model predicts that the enthalpy of

mixing of two liquids can be represented using the

equation :

AH [mix] - V 02

( S. -S)2

+ k ( AN - AN > ( DN - DN )2 2 1 2 1 2 *

where V2 is the molar volume of the solute, 0] is the

volume fraction of the solvent and Sj is the dispersion

solubility parameter. AN and DN are electron-

pair

acceptor number and electron pair donor number

respectively. Research discussed in this thesis includes

development of empirical relationships to extend the

limited range of available AN and DN values for liquids,

and the experimental testing of the model using

qualitative sorting maps. These maps consist of a plot

of the acceptor- donor term against the dispersion term

of the above equation to empirically determine areas of

miscibility and immiscibi 1 i ty using liquids of known

AN,

DN and known miscibi 1 i ties . Once these regions are

established, the maps can be used to predict the

miscibility of other liquid pairs via interpolation.

GENERAL IMPORTANCE OF SOLUBILITY PHENOMENON

The importance of solvents is their ability to

dissolve different solutes. Solvents can act as an inert

carr ier for solutions, chemical reactions and seperation

processes. Solutes may also form complexes or react with

the solvent. If solubility can be predicted for a given

solute combination or for the change of one solvent for

another, then solvents can be used more effectively-

Solubility of organic compounds may be estimated

by many methods (1). One is a simple trial and error

method of attempting to dissolve a compound in a variety

of different solvents. This random process is

inefficient and can take a long time. More experience

leads to the use of the "like dissolved like"

rule of

thumb to estimate the solubility of organic compounds in

selected solvents (2). It is generally expected that a

compound with properties and structures similar to a

solvent would be soluble in that solvent. However, this

rule is very limited. A major problem is determining

when two compounds are alike when there is no

quantitative measure of"

likeness ".

A better way of predicting solubility is to use

the solubility parameter concept proposed by

Hilderbrand nearly 70 years ago. This theory provides a

means of measuring the likeness between solute and

solvent. Maximum solubility occurs when there is little

or no difference in the nonspecific dispersion forces of

the salute and solvent. Dispersion forces or London

forces, arising from the fluctuating dipoles which result

from a positive nucleus and negative electron"

cloud"

in each atom, occur in all molecules whether polar or

not .

In contrast, the Lewis acid- base concepts

predict solubility in term of highly specific electron

pair donor acceptor interactions (3). This theory

defines an acid as an electron pair acceptor and a base

as an electron pair donor. Maximum interaction of solute

and solvent occurs not with similar acid- base

properties, but with complementary properties.

This present research seeks to a develop a simple

solubility concept which combines the nonspecific

interaction of the solubility parameter concept with the

specific interactions of the Lewis acid- base theory.

SOLUBILITY PARAMETER THEORY

Introduction:

The solubility parameter, 8 , as originally

proposed, is related to nonspecific dispersion forces

present in liquids (2). Mixing of two liquids is

favorable when there is little or no differences in

theses forces. Thus Hildebrand found that a good solvent

has a solubility parameter, 6 , that is close to the 6 of

the solute. This is illustrated for the solubility of

napthalene in Table 1.

Table 1

SOLUBILITY'

OF NAPTHALENE

6 AS (cal/cm3)^

Napthalene 9.9

Hexane 7.3 9.9 - 7.3 = 2.6

Toluene 8.9 9.9 - 8.9 = 1.0

Water 23.4 23.4 - 9.9 - 13.5

Diethylether 7.5 9.9 - 7.5 = 2.4

Methyl iodide 9.9 9.9 - 9.9 = 0.0

Ethanol 12.9 12.9 - 9.9 = 3.0

The absolute difference in 6 values of 1 . 0 for napthalene

and toluene indicates that toluene is a good solvent for

napthalene. Other values in Table 1 predict that methyl

iodide is a very good solvent for napthalene, while

hexane, ether, and ethanol are not quite as good. Water

is not a solvent for napthalene, as can be seen by the

large difference in 6 values. These predictions are

experimentally verified ( 2 ) .

Definition of Solubility Parameter:

The basic assumption in the solubility parameter

concept is that there is a correlation between the

cohesive energy density ( potential energy per unit

volume ) and mutual solubility (4). The solubility

parameter, S , can be defined as the square root of the

cohesive energy density of a liquid:

( -E / V )^( cal/cm3)^ [1J

where -E is the cohesive energy and V is the molar

volume. The solubility parameter, 8 , is usually

3 ^expressed in units of ( cal/ cm ) but may also be

expressed in units of ( MPa 2) . Since the molar volume of

a liquid is easily determined at any temperature, the

evaluation of 8 is mainly dependent on the determination

of the molar cohesive energy, -E. The molar cohesive

energy is the energy associated with the net attractive

interactions in a mole of substance. These include

dispersion forces, polar interactions and hydrogen

bonding interactions. Hildebrand originally proposed the

solubility parameter concept for nonpolar, regular

solutions where dispersion forces dominate (4). Concepts

of solubility parameters which include polar and

hvdrogen-bonding interactions will be discussed later.

Evaluation of Molar Cohesive Energy:

The molar cohesive energy (-E) is the energy of a

liquid relative to its ideal vapor at the same

temperature ( assuming that the intramolecular properties

- those associated with individual molecules-

are

identical in gaseous and liquid states, which may not be

true in the case of a complex organic molecule) . It can

be seen that -E consists of two parts: the energy ( L . E )

required to vaporize the liquid to its saturated vapor

and the energy required to isothermally expand the

saturated vapor to infinite volume:

-E- A?E + \V=0(^E/'2>V) dV

[2]

At a temperature below a liquid's boiling point, the

second term is small and may be neglected to give

equation [ 3] .

- E =

A^ E [3]

If ideal gas behavior is assumed, then this expression

may be rewitten as:

E =

A^ H - RT [4]

where A H is the heat of vaporization.

Evaluation of S in Terms of Heat of Vaporization:

The solubility parameter may be witten in terms

of AH by :

( -E / V V - [(AH - RT ) / V] [5]

The heat of vaporization may be determined experimentally

by calorimetry or by the temperature dependence of the

vapor pressure through the use of the Clausius-Clapeyron

equation:

d In p AH

dTRT2

r6]

The heat of vaporization of nonpolar liquids may also be

estimated by using Hildebrand "s rule

2

AH (cal/mol) = -2950 + 23.7 Tfa + 0.020 T"b [7]

where T. is the boiling point of the liquid,D

Empirical Methods for Evaluation of Solubility Parameters:

Various empirical methods have been used to

estimate S values (5). For a series of compounds having

a common functional group, plots of S versus V are

linear. Therefore, S values of other compounds in the

same series can be determined by interpolation or

extrapolation of the plot (6).

The surface tension of nonpolar substances has

been suggested to have a close relation to the heat of

vaporization. Experimental data gives the relation of

surface tension, Y , to cohesive molar energy density (7):

Y/AE\M6

[8]

v "3 Vv I

Beerbower combined equations [1] and [8] and obtained a

relationship where S may be determined from the surface

tension, t , by the empirical equation (7):

u, 0. 4 s, ,

5 = k ( Y / V/2) [9]

where V is in cm /mole, Y is in dyne/cm 5 is in

(cal/cm3/2and k is a proportionality constant with a

numerical value of 4.1 at25

C.

Equations of state for gases do not fit liquids

well. However, for many liquids the following expression

has been used as a workable approximation

-E/V = ( "&E / *V ) = [10]

where a is the Van der Waal constant for the gas and

( "& E / *&V) is the internal pressure of a liquid (8).

Thus S can be expressed as:

S = ( -E /v'/2

) = a'/2/ V [11]

The internal pressure can also be related to the thermal

pressure by:

l E \ U'

= T

& V ) \W ,

E12J

T V

For nonpolar liquids at low pressure, the pressure P is

10

small and may be neglected and S can be written as

11 [13]

where o. and ft are the coefficients of thermal expansion

and compressibility (9).

Hildebrand's Model with Dispersion Term Only:

Hildebrand's solubility parameter concept has

been useful for regular solutions (4). Regular solutions

are nonpolar solutions, where the cohesive energy is only

due to dispersion forces. They are also solutions that

have an ideal entropy of formation even though the

enthalpy of formation is not ideal. Thus far the various

expressions have dealt only with pure liquids. What

happens when two liquids are mixed will now be discussed.

The change in enthalpy of mixing two nonpolar

liquids is (4)

AH (mix) = V.2 *, < 8,

"

*J [14]

where V2 is the molar volume of the solute, 0} is the

volume fraction of the solvent, and 6, and S2 are the

solubility parameters of the solvent and solute

11

respectively. This expression explains the like

dissolved like statement. Equation [14] always gives a

positive or unfavorable AH (mix) since the difference in2

S term is squared. Therefore, solubility is enhanced

when AH (mix) is minimized. This happens when the 8

values are similar. Thus, a small difference in S

values leads to high solubility and a large difference

leads to low solubility. The similarity of the cohesive

energy densities as expressed in the solubility

parameters is now a quantitative measure of likeness.

However, this simple one component parameter

proposed by Hildebrand becomes less accurate for more

polar substances. Significant deviations can happen with

the combination of polar solvents with polar solutes.

Polar interactions can cause nonideal entropy of

formation. Therefore, the one component S which is

directly proportional to AH does not accurately describe

the mixing or solvation processes in these systems.

Models with Dispersion and Polar Terms:

Various methods have been used to include polar

interactions. A general method has been developed which

divides the cohesive energy into polar and nonpolar

contributions (10). The solubility parameter then takes

12

the form

2 ->2

S =-E/V = (-E nonpolar/V) + (-E polar/V) = \ + * [15]

The solubility parameter then is composed of

1*

and \>

which are the polar and nonpolar components respectively.

The polar and nonpolar solubility parameters, T

and A, , may be estimated by using the homomorph

concept (11). The homomorph of a polar molecule is a

nonpolar molecule having the same size and shape. The

dispersion or nonpolar component, A,, of a polar liquid is

calculated from the experimental vaporization enthalpy of

the homomorph determined at the same reduced temperature

( the actual temperature) and molar volume. Plots of the

homomorph vaporization enthalpy against molar volume can

be used when the molar volume of the homomorph is not the

same as the polar molecule (7,10,12). The polar

solubility parameter, T , can then be calculated from

equation [ 15] .

Keller et al. (13) emphasized that polar

interactions are of two types, symmetrical dipole

orientation and unsymmetrical dipole induction. In

dipole orientation, two dipoles interact. In dipole

induction, one dipole on a molecule polarizes another

molecule. Thus in a pure polar liquid without H-bonding,

13

the total solubility parameter ( S ) takes the form:o

*o=

6d + Sor + 2 Sin 8d C16]

where the component solubility parameters are the

dispersion ( S. ) parameter, the orientation ( S ) para-d or

meter, and the induction ( S ) parameter.in

There are some problems associated with both of

these models. It is difficult to reliably obtain the

polar solubility terms. Also, H-bonding interactions

are not considered.

Hansen's Model with Dispersion. Polar, and H-Bonding:

Hansen (14) assumed that the cohesive energy

comes from the contribution of nonpolar or dispersion

interactions (-E. ), polar interactions (-E ), andH-

d p

bonding interaction (-E. ):n

-E = - ( Ed+ Ep + Eh ) [17]

This can be rewritten to give individual dispersion,

polar, and H-bonding solubility parameters , using

equation [1] :

E/V = - ( Ed+

Ep+ Eh )/V [18]

14

8o=

8d +SP

+ S" ^^

These individual S's can be evaluated by experimental

solubility observations and have been tabulated for

many compounds in Barton's book (15). Some of these

methods are discussed below.

The dispersion or London forces exist between all

adjacent pairs of molecules (16). Their origin is the

instantaneous electrical dissymmetry of electrons in one

molecule polarizing the electron cloud in adjacent

molecules, and inducing instantaneous dipoles of opposite

polarity- This temporary dipole results in

intermolecular attraction. The magnitude of the

dispersion cohesive energy, -E , can be approximated by:

3 !I jl j U-E. =

j : [20]d

2 ( 'I + 'I )

where <* is the polarizability , I is the first ionization

energy of each molecule, and r is the distance between

two molecules i and j. Using equation [20] and the

relation between polarizability and refractive index,

Koenhen and Smolders (17) found an empirical correlation

expressed as:

g (MPaV2) = 19.5nQ

- 11.4 [21]

15

between the dispersion cohesion parameter S and the

refractive index at the sodium"D"

line, n

Koenhen and Smolders (17) also developed an

expression for the polar solubility parameter, SP

S(cal/cm3

)1/2= feju

V3/i

[22]

where yu is the dipole moment in debyes , V is the molar

volume, and & is a constant with a numerical value of

50. 1.

It is sometimes more convenient to estimate the

Hansen solubility parameters S . , S S. from structural

group molar attraction contributions (12,18). It is

assumed that each functional group within a molecule

contributes to the total cohesive energy of the molecule,

2

-E = ( "2. F ) / V , and that each molar attraction

constant, F , is composed of dispersion, polar and

H-bonding components. The dispersion parameter can be

calculated by summing all the dispersion molar attraction

constants, Fd , for groups such as methyl, methylene,

phenyl, etc. ( 12) .

S^= 2 (

'F ) / V [23]

d j d

It is possible to evaluate S if only one polar group is

present by dividing the polar molar attraction constant,

16

F, by the molar volume (18):

Sp= Fp/V [24]

But if more than one polar group is present, then it is

necessary to correct for the interaction of the polar

groups (18) by using:

( ? 'Fp / V [25]

The dispersion and polar group molar attraction constants

have been tabulated by Barton (9).

This F-method, summing molar attraction

contributions, can not be used in the calculation of S .

h

Hansen and Beerbower (12) have assumed that H-bonding

cohesive energies are additive, leading to:

sh= <" ? V / v

)V2

C26]n i h

Many values of E. for various groups have been

tabulated (9,12). However, they urged extreme caution in

adding group contributions in the use of g. to describen

an interaction which really requires both donor and

acceptor components .

An expression similar to equation [14] has been

written for the change in dispersion energy on mixing

17

polar liquids (14) as:

AH2 [mix] =

V2JZf2

[(S,-

S2)2

+ (S,-

S2)2p+ (S,

-

S2 ] [27]

This expression as in equation [14] correlates the degree

of solubility of the solute and solvent with the square

of the differences of the solubility parameters in the

dispersion, polar, and H-bonding terms. Thus the

criteria for high solubility is still one of"likeness"

or small differences even though now it is athree-

dimensional vector quantity. This model has been quite

useful in qualitatively extending the concepts of

regular solution theory to a much broader range of

solvents and solutions, although quantitatively, the

model has not been very successful. This is because

there are some serious problems with this model which

can be revealed upon examination of equation [27]. The

most important of these are the inability to deal with

exothermic heats of mixing and the incorrect modeling of

H-bonding interactions. Equation [27] contains the

squares of the differences of the individual solubility

parameters. This can only lead to positive or

endothermic values of AH [mix]. Thus this model is

incapable of accounting for the few exothermic systems

such as water- triethylamine.

In the second problem, the H-bonding interaction

18

2

is incorrectly modeled. The difference term ( 8,-

S )' 2 h

implies that, like dispersion interactions, effective

solute-solvent H-bonding depends on some likeness or

similarity of the two liquids. In reality, H-bonding

depends on the complimentary matching of donor and

acceptor properties of the two liquids. The strongest

H-bonding interaction should occur between a strong

proton donor compound and a strong proton acceptor

compound. The above model would incorrectly predict a

small difference in S's and little H-bonding for these

two types of compounds .

Model Incorporating Proton Donor-Acceptor Properties:

A simple way of incoporating the inherently

complimentary nature of H-bonding into the expression

for AH [mix] is to make- A E [H-bond], the product of

a pure liquids s proton donor ability ( PD ) and its

proton acceptor ability ( PA ) :

- AE [H-bond] = ( PD ) ( PA ) [28]i i

It should be noted that the large magnitude for the

range of H-bonding energies can not be described by the

sum of PA and PD. Using similar expresions for H-

bonding between different species, the change in the

19

H-bonding energy on mixing two liquids can be

approximated by summing the various interactions:

AE mix [H-bond] = PD .PA+ PD .PA

- PD . PA -PD .PA [29]11 22 1221

Rearrangement of this expression gives the result first

suggested by Small (19):

AE mix [H-bond] = ( PD,

-

PD2 )( PA,- PA

2) [30]

This equation incorporates complimentarity and correctly

predicts that the most favorable interaction will involve

a high PA - low PD liquid and a low PA - high PD liquid.

The equation also resolves the first problem since the

product of the two differences may be either positive

(endothermic) or negative (exothermic). Most mixtures

result in a positive or endothermic AE mix, and a few

result in exothermic AE mix, such astriethylamine-

Some mixtures, even nonpolar solvents, can have very

small negative AE mix values.

Keller et al. (13) used a similar expression in

defining the H-bonding interaction in terms of a set of

Bronsted base, S. (equivalent to PA), and Bronsted acid,D

S (equivalent to PD) , solubility parametersa

A E [H-bond] = 2 V S S [31]iab

20

The corresponding expression for H [mix] was written

AH [mix] =

V202

+

(S,-S2)p+ 2(S, -S 2)a (S, -S2 >b ] [32]

Unlike Hansen's model, this approach incorporates both

complimentarity and the possibility of exothermic

interactions. But there are still two potential

problems. The use of a composition dependent H-bonding

2

term ( via the V? 0, multiplier ) is questionable.H-

bonding is a specific interaction and adducts of fixed

composition are formed. Unlike the nature of the

dispersion interactions, the composition of these adducts

does not depend on the bulk composition of the solution.

Even if the bulk composition changes the same adduct will

be formed. Thus ideally the enthalpy of this interaction

should not depend on the composition of the bulk solution

whereas the dispersion term does. A second problem is

the difficulty in obtaining a sufficiently broad range of

S and S. values for common solvents. Also values of Sa b a

obtained are not chemically self consistent. Thus at a

practical level, Keller's equation has not been

extensively used.

This research proposes to keep the correctly

modeled nonspecific dispersion term intact while

replacing the specific interaction terms ( the hydrogen

21

bonding interaction ) with a Lewis acid-base term. This

proposal along with the appropriate Lewis acid-base

concepts are explained in the next section.

22

LEWIS ACID-BASE CONCEPTS IN SOLUBILITY THEORY

Definitions:

The Lewis acid-base concepts were first formulated

by the American physical chemist G. N. Lewis (3) in 1923

and defined an acid as any species which can accept a

share in a pair of electrons during the course of a

chemical reaction. A base was defined as any species

capable of donating that pair of electrons.

Neutralization becomes, in turn, 6imple coordinate or

heterogenic bond formation between the acid and base:

A + :B > A:B [33]

Lewis Arid-Base Donor-Acceptor Term:

The H-bonding interaction is not a particular

kind of intermolecular force like the dispersion force

but is an example of a generalized electron-pair donor-

acceptor interaction (20). Thus this research proposes

to replace the Bronsted acid-base term in Keller's

expressions, equations [29] and [30], with a generalized

electron-pair donor (EPD)- electron-pair acceptor (EPA)

term. Since H-bonding interactions are specific and

23

give adducts ( however short lived ) , they should be

modeled after Small's complimentarity equation (19).

The proton acceptor ( PA ) and the proton donor ( PD )

parameters in equation [30] can be replaced with a more

generalized electron pair donor number ( DN ) and

electron pair acceptor number ( AN ) . Thus aDonor-

Acceptor H mixing term can be written as:

AH mix [DA] = k ( AN - AN )( DN,- DN

_ ) [34]1 2 1 2

where k is a scaling constant of some sort. This should

give an improvement over Keller's equation [32] since the

AN and DN values for a broad range of solvents are

readily obtainable and a composition dependency is not

included.

A Concept Combining Dispersion and Donor-Acceptor Terms:

Since most specific electrostatic or polar

interactions can also be included in conventional

measures of electron pair donor and acceptor strengths, a

separate polar term in a solubility equation is

redundant and not needed. Thus the simplest chemical

model for the cohesive energy for a pure liquid is just:

AE [vap] = AE (dispersion) + A E ( DA ) [35]

24

a two term equation with polar and H-bonding interactions

included in the Lewis acid-base donor-acceptor term:

AE; [vap] = VS. + k ( AN: )( DN. ) [36]i id '

The enthalpy of mixing would also be a two term equation:

^2 2.^H [mix] = V 0 (S -g ) + k ( AN -AN )( DN -DN ) [37]

2 21 12d 1 2 1 2

In order to be able to use these new equations for

predicting solubility, the AN and DN values have to be

known. Therefore the first part of this research has

been devoted to expanding the list of AN and DN values

currently available.

Determination of Acceptor and Donor Numbers:

The donor number ( DN ) was originally defined by

Gutman (21). The DN represents a liquids ability to

donate a pair of electrons. It is based on the heat of

reaction, -AH mix, of the the standard Lewis acid or

electron-

pair acceptor ( EPA ) probe antimony

pentachloride with a particular compound of interest in a

dilute 1 , 2-dichloroethane solution:

D: + SbCl > D:SbCl [38]5 5

J

DN = -AH [ EPD > SbCl ] (kcal/mol)

25

The acceptor number ( AN ) represents a liquid's

ability to accept an electron pair. It is based on the

31

P NMR shift induced in the standard Lewis base or

electron-pair donor ( EPD ) probe triethylphosphineoxide

by the species of interest relative to that induced by

n-hexane :

Et3P=0 + A > Et3P-0 -*A [39]

This relative shift in ppm is scaled, in turn, relative

to the shift induced by SbCl in dilute 1,2-

dichloroethane solution:

AN- 100 ( SEtapQ^-

SEt3PQ-Hexane ^

BEt3PO-SbCl5"EtgPO-Hexane/

These shifts are also extrapolated to infinite dilution

and corrected for the difference between the change in

volume on mixing of hexane and the solvents in question.

The dimensionless AN are arbitrarily fixed and vary from

0 for hexane to 100 for Et3P0->SbCl5 .

Donor number values have been experimentally

determined for 53 liquids and acceptor number values for

34 liquids. However, both values have only been reported

for 25 liquids, too few to be practical (21).

Fortunately, there are other probes which are also

26

selectively sensitive to either Lewis acidity or

basicity. One of the most comprehensive solvent scales

is the E (30) scale which was developed by Dimroth et al.

[21] . This scale is based on the transition energy for

the solvatochromic intramolecular charge transfer

absorption of 2 , 6-diphenyl-4(2 , 4 , 6-triphenyl-l-pyridinio)

phenolate :

_i

E (30) Kcal/mol = he V NA = 2.859 x 10V (cm )Avo

[41]

The structure of the dye is shown in figure 1 . The

E (30) is a solvent dependent absorption of the above

solvatochromic dye. As shown in the below structure, the

Figure 1. Structure of phenolate dye.

dye has acid and base sites. The positive charge of the

dye is delocalized over the pyridinium ring and shielded

by phenyl groups. Therefore, only the base site, the

phenolate anion, is accessable. Thus the dye only

interacts with solvents which are Lewis Acids. If the

27

phenolate is strongly solvated by the sovent , then the

dipolar ground state of the dye will be stabilized. The

greater the Lewis acid strength of the solvent, the more

the dipolar ground state is stabilized and the larger the

transition energy becomes. Thus the transition energy of

the phenolate dye, and the E (30) values depend on the

Lewis acidity of the solvent.

Reichardt (23) plotted E (30) values against AN

values for 38 solvents and obtained the correlation

equation below for AN and which is shown in figure 2.

AN = 1.598 E (30) - 50.69 [42]

Deviating solvents such as acetic acid and chloroform

were excluded. Schmid (24) also plotted ET(30) values

against AN values for only 21 solvents and obtained a

similar correlation which is shown in figure 3.

AN = 1.29 E ( 30) - 48.52 [43]

Highly structured solvents such as alcohols, acids, as

well as chlorinated hydrocarbons were not used in the

correlation. Thus AN values for additional liquids can be

calculated using these correlation equations. Schmid

(24) also found a correlation of AN and DN with the

dielectric constant for 31 solvents

28

i m

so

10

AN

30

20

10

110

M?

100 OwoX"1US MH >

20*116

30 40 50

fT(30l (kcol/mell

60

Figure 2. Reichardt's correlation of AN and ET (30)

for pure organic solvents.

Correlation equation

AN - 1.598 ET (30) - 50.69

Correlation coefficient

R - 0.956

(reproduced from reference 23)

29

AN

Figure 3. Schmid's correlation of AN and ET (30)

Solvents labelled by full circles have been

used to calculate the following correlation

AN (a) - -40.50 + 1.29 E (30)

A Highly structured solvent not used in

correlation

O Highly structured chlorinated hydrocarbons

not used in the correlation

( reproduced from reference 24)

30

log = 0.0711 AN + 0.0054 DN + 0.2581 [44]

The highly structured solvents not used in the AN-E (30)

correlation equation [43] were also excluded in this

equation. This correlation can be used to calculate

either AN or DN values if one of the other two values and

the dielectric constant are known.

Other donor scales such as AV_(25), D {11,1}

(25), ^ (26) and -AH [BF ] (27) have been correlated

with the DN scale. The correlation equations and their

correlation coefficients are given below:

DN = 0.20 (AVD) +3.03

DN = 10.11 D{II,I] - 12.17

DN = 38.4 ( ) - 0.78

DN = 0.261 (- A H__ ) - 1.15

DN = 0.19 B - 0.636

The availability of experimentally determined AN

and DN values is not a practical limitation as is the

case for limited availability of Bronsted acid and base

terms in Keller's model since AN and DN values may be

calculated from other acceptor and donor experimental

data. Thus the simple solubility concept developed in

equation [37] with AN and DN values should be more widely

applicable than Keller's equation [32]. This concept is

further developed and tested in the following sections.

31

R = 0.,984 [45]

R = 0.,995 [46]

R = 0,,98 [47]

R = 0,,9684 [48]

[49]

EXPERIMENTAL

Materials:

Solvents of high purity were used as received.

These include: acetone (EM Science), benzonitrile

(Fisher), carbon disulfide (Fisher), carbon tetrachloride

(Fisher), chloroform (Fisher), cyclohexanone (Baker),

o-dichlorobenzene (Kodak), ethyl acetate (Baker), ethyl

benzoate (Fi6her), ethyl ether (Fisher), ethyl formate

(Fisher), ethylene glycol (Fisher), Formamide (Aldrich) ,

glycerol (Aldrich), methyl ethyl ketone (Baker),

nitrobenzene (Baker), nitroethane (Kodak), nitromethane

(Kodak), pentanol (Baker), water (HPLC grade-EM Science),

m-xylene (Kodak), and o-xylene (Kodak). Other solvents

were distilled and stored over molecular sieves prior to

use include: Acetophenone (Baker), aniline (Baker),

benzene (Baker), t-butylamine (Fisher), butanol (Baker),

butyl ether (Fisher), chlorobenzene (Kodak), cyclohexanol

(Fisher), N,N-dimethyl aniline (Fisher), ethanol

(absolute, US Industries), methanol (absolute, Baker),

and triethylamine (Kodak).

32

CorrelatinriB-

A least squares linear regression analysis was

used to determine correlation equations for acceptor

number ( AN ) and E (30) values for the highly structured

solvents not used in equations [42] and [43]. The method

of least squares assumes that errors in the y values

( AN ) are greater than the errors in the x values,

ET(30). The line for the equation is:

AN (cal) = m E (30) + b [50]

where m is the slope and b is the y intercept. The

vertical deviation, d., of a point from the line is given

by y.-

y where y is the ordinate of the straight line

when x = x. .

i

d. = y.-

y = (AN exp- AN cal) [51]

Minimizing the squares of the deviations gives

d? = ( y.-

y

)2

= ( AN exp- AN cal [52]

The least squares slope and intercept are given by the

following equations

33

m =

IXj yj ?X;

n

D [53]

b =

J(Xj )

2X:

2xi y\

*y-.

7 D [54]

where n is the number of points and the value of D is

given by

D =

2(x-, )

Sx;

Ix.

n

[55]

The correlation coefficient was found by the following

expression

r =

2 2 2

lJx- ( r ys ) "

d\

[56]

Zy. - ( Iy8 ) /n

The error analysis for equations [53] and [54] results

from the variances of the slope and intercept

34

^e7

= [57]

el zu,)

V[58]

2'

where the standard deviation of the vertical deviation is

defined as

7-1

Z(d; )

v V [59]

n-2

The MINITAB statistical program on the RIT VAX

computer system was used to develop multiple regression

correlations of AN, DN and dielectric constant ( )

similar to equation [44] for each cIsee of chemical

compounds, for example, alcohols, hydrocarbons etc.

Miscibility Det.erminat.ion:

Experimentally ,mutual miscibility of binary

mixtures was determined by adding solute to solvent in 9

test tubes in proportions of 10% to 90% by volume in 10%

35

increments. The test tubes were maintained at a constant

temperature of 25 C for 20 minutes in a water bath

(Science / Electronics Inc., model SE) . In many cases

miscibility of mixtures could be determined by the

absence of a meniscus. The presence of a meniscus

indicated either immiscibility or partial miscibility.

Partial miscibility was determined by significant changes

in the refractive index of either layer versus the

refractive index of the pure liquid.

Construction of Miscibility Sorting Maps:

A LOTUS 1-2-3'

program was used to establish a

data base for 43 liquids. The AN, DN , and dispersion

solubility parameter ( S . ) values were entered in

appropriate columns. This data was expanded so that each

liquid was paired with the other liquids. This created

42 possible pairs for each liquid for a total of 43x42 or

1806 possible binary pairs. The Lotus 1-2-3v

program was

used to calculate the values of the two terms

0.01 ( AN,-

AN2 )( DN,-

DN2 ) and ( g,-

82 for

each binary liquid pair. Then literature data, if

available was entered into the data base as to whether

each binary pair was miscible or immiscible. Literature

data which was conflicting, for example, listed as both

miscible and immiscible, was entered as questionable.

36

Miscibility sorting maps for each of the 43

e

solvents were constructed using LOTUS 1-2-3 PRINT GRAPH

program with the above data base. For each map the

acceptor-donor term [ 0.01 ( AN,-

AN2 ) ( DN,-

DN2 ] was

plotted against the dispersion solubility parameter term

( fi,-

S, ) for each of the 42 possible binary pairs.

Thus each map could have 42 points. Miscible pairs were

plotted as squares, immmiscible pairs as plus signs, and

questionable pairs as diamonds. Bianary solvent mixtures

without reported miscibility data were not plotted so

each map generally had less than 42 points.

37

RESULTS AND DISCUSSION

Research Objectives:

This thesis research has been directed towards the

development and substantiation of the solubility concept

proposed in a previous section which incorporates the

dispersion solubility term [14] from equation [27] and a

Lewis acid acceptor-donor term from equation [34]

AH [mix] = V 6 (S -S ) + k (AN -AN )(DN -DN ) [37]2r

1 1 2d 12 12

These terms, [14] and [27] are defined in previous

sections .

To accomplish this, four research goals were

established. The first goal was to develop a better

correlation of AN and E (30) values in order to expand

the list of available AN values, especially for the

highly structured solvents which were not used in

Schmid's correlation equation (24). A similar goal was

established for Peter Michelsen's thesis (29) research in

extending the list of available DN values through the use

of correlation of DN with other donor scales.

The second goal was to develop a better

correlation of AN, DN and dielectric constant ( e ) using

38

the AN and DN values obtained in the first part of the

research together with available AN, DN and dielectric

constant values. The purpose of these two goals was to

obtain more new AN and DN values for use in the third

goal.

A third goal was to construct miscibility sorting

maps by plotting the values of the acceptor-donor term

against the dispersion term of the above equation [37]

for several binary liquid mixtures. Ideally, these maps

should have regions of miscible binary mixtures and

immiscible binary mixtures.

The fourth goal was to test these sorting maps by

experimentally determining the miscibility of binary

liquid mixtures. Another part of this goal was to test

the usefulness of these sorting maps in predicting the

miscibility of binary liquid mixtures before experimental

verification.

Correlation of AN and ETf30):

Error Analysis of Schmidts Equation:

A list of experimental AN values for 34 solvents

was compiled with a Lotus 1-2-3 program. Additional AN

values were determined from solvents having Ey(30) values

using Schmid's correlation equation [43]. This expanded

39

the list of solvents with AN values to 113. These values

are include in Table A-l in the appendix. Schmid 's

correlation equation was not U6ed to calculate AN values

for alcohols and chlorinated hydrocarbons, since these

highly structured solvents were not used in determining

the correlation.

Schmid did not give a correlation coefficient

value for equation [43] even though he claimed it had a

better correlation than Reichardt's correlation [42],

Since no correlation coefficient or any type of error

was given for Schmid 's equation [43], an error analysis

of Schmid 's equation was conducted. The calculations are

summarized in Table 2 and below.

I(dj ) 33.09

n- 2

1.7415

19

[59]

D -

1 (x/ ) Xx.

n

D = (35333. 22M21)- (857)(857) = 7548.62

[55]

m

6~y n

D

(1.7415H21)

7548.62

= 0.004845 [57]

40

TABLE 2

ERROR ANALYSIS FOR SCHMID'S CORRELATION EQUATION

aXi

Xi2

Yl Y d Yi-Yd,2

SOLVENTS EtOO) EtOO) AN(txp) ANCeal)1

1. acetone 42.2 1760.84 12.S 13.9 -1.4 1.96

2. aeetoni trile 46 2116 18.9 18.8.0.1 0.01

3. bvnzoni trile 42 1764 13.3 13.7 1.8 3.24

4. diglyme 36.6 1489.96 9.9 9.3 0.6 0.369. diethylether 34.6 1197.16 3.9 4.1 -0.2 0.04

6. DMA 43.7 1909.69 13.6 13.9 -2.3 5.297. OMF 43.6 1916.44 16 16 0 08. DMSO 43 2023 19.3 17.S 1.8 3.249. ethylaeetate 38.1 1431.61 9.3 8.6 0.7 0.4910. ipa 40.9 1672.61 10.6 12.2 -1.6 2.5611. hexane 30.9 954.81 0 -0.66 0.66 0.435612. metthylacetate 40 1600 10.7 11.1 -0.4 0.1613. NIP 42.2 1780.84 13.3 13.9 -0.6 0.3614. nitrobenzene 42 1764 14.8 13.7 1.1 1.2113. ni tromethane 46.3 2143.69 20.3 19.2 1.3 1.6916. pyridine 40.2 1616.04 14.2 11.3 2.9 8.4117. THF 37.4 1396.76 8 7.7 0.3 0.0918. TBP 39.6 1368.16 9.9 10.6 -0.7 0.4919. triethylamine 33.3 1108.89 1.4 2.4 -1 120. TWP 43.6 1900.96 16.3 15.7 0.6 0.3621. PC 46.6 2171.36 18.3 19.6 -1.3 1.69

SUMf) 837 35333.22 33.09

a Highly structure solvents are not Included in

Schold's correlation such as alcohols and some

chlorinated hydrocarbons.

41

, 6~v x. (1.7415)(35333.32)5"b2

= y- l-= [58]

D 7548.62

= 8.1515

6~m =0.07 and 6"b =2.86

Thus the correlation equation was rewitten with the error

included

y = ( m +CTm ) x + ( b +

CTb ) [60]

Schmid 's equation was then written as

AN = ( -40.52 + 2.86 ) + ( 1.29 0.07 ) ET(30) [61]

The total error for AN was given by

AN error = ^ 6~b +0~m2

=

J(2.86)2+(0.07)2

=2.86 [62]

The correlation coefficient was also calculated

from the data in Table A-l using equation [56] and found

to be F = 0.974. This value indicates a somewhat better

correlation than for Reichardt's correlation. However,

neither correlation included highly structured solvents

such as alcohols and chlorinated hydrocarbons.

42

Correlation of AN and ETf3Cn for Alcohols and

Chlorinated Hydrocarbons:

Several attempts were made to improve the

correlation of AN and E (30) values, especially for

highly structured solvents which were not included in

Schmid 's or Reichardt's work. Including these solvents

only resulted in a poor correlation. Another means of

correlating AN and E (30) for these solvents was used.

Examination of Schmid 's plot of AN versus E (30) in

figure 3 shows that the highly structured solvents which

were excluded from the correlation fall into a separate

group such that a different line can be drawn just

through that group as shown in figure 4.

If the AN and E (30) values for seven alcohols and

water were plotted, then the following correlation

equation was obtained

AN (b) = -39.69 + 1.503 E (30) [63]

A linear regression analysis gave a correlation

coefficient of R = 0.9622. However, an even better

correlation equation was established by linear regression

analysis for the above seven alcohols, water, and three

chlorinated hydrocarbons ( methylene chloride,

chloroform, and carbontetrachloride ) with a correlation

43

AN

Figure 4. Correlation of AN and E (30) for alcohols,

three chlorinated hydrocarbons and water.

AN (c) --38.536 + 1.4826 E (30)

1. carbontetrachloride (CC1 ) 6. n-butanol

3. chlof orm (CHClj )

2. methylenechloride (CH2C1 ) 7. 1-propanol

8. ethanol

A. t-butyl alcohol 9. methanol

5. i-propanol 10. water

11. 2-aminoe thauol

44

coefficient R = 0.9821.

AN (c) = -38.536 + 1.4826 E (30) [64]

This equation was then used to calculate AN (c) values

for 32 alcohols and deuterium oxide (DO) which did not

have experimental AN values.

These calculations expanded the list of liquids

with AN values to 153. The experimental AN values and

the calculated AN values ( AN (a) from Schmid's

correlation [43] or AN (c) from the above correlation

[64] ) are listed in Table A-2 in the appendix.

Error Analysis of Correlation Equation For

Alcohols and Chlorinated Hydrocarbons:

In order to show that equation [64] for alcohols

and chlorinated hydrocarbons is as reliable as Schmid s

correlation equation [43] for other solvents, an error

analysis for equation [64] was also conducted. The data

is summarized in Table 3. The following calculations

give the error in the correlation as

AN (c) = (-38.536 3.909) + (1.4826 0.0789) E (30) [65]

The total AN error then was calculated as

45

TABLE 3

ERROR ANLYSIS OF CORRELATION EQUATION

FOR ALCOHOLS AND CHLORINATED HYDROCARBONS

xi(Xi)2

Yj Y d. Y -Y dfSOLVENTS

ET(30) (ET(30)) AN( exp) AN( cal)

i

1. CHzCl2. 41.1 1669.21 20.4 22.4 -2 4

2. CC14 32.5 1056.25 8.6 9.6 -1 1

3. CHC13 39.1 1528.81 23.1 19.4 3.7 13.69

4. methanol 55.5 3080.25 41.3 43.7 -2.4 5.76

5. ethanol 51.9 2693.61 37.1 38.4 -1.3 1.69

6. 1-butanol 50.2 2520.04 36.8 35.9 0.9 0.81

7. 2-propanol 46.6 2361.96 35.5 33.5 2 4

8. t-butylaleohoi 43.9 1927.21 27.1 26.6 0.5 0.25

9. 1-propanol 50.7 2570.49 37.3 36.6 0.7 0.49

10. 2,2,2-tri- 59.5 3540.25 53.5 49.7 3.8 14.44

f luoroethanol

11. water 3.1 3981.61 54.8 55 -0.2 0.04

SUM (2 ) 536.1 26949.69 46.17

.2 -

m

46.17

n-2

26949.69

536.1

46.17

536.1

11

y tn

5.13

9043.36

(5.13K11)

9043.38

l(5.13)(26949.69)

0.0789931

0.07899

9043.38

3.909940

3.9099

AN -38.536 + 1.4826 x E (30)

AN -(38.536* 3.909) + (l .4826 0 .0789 ) E(30)

AN 3.91

46

AN error =

\|(3.909)2

+ = 3.91 [66]

Correlation of AN. DN and Dielectric Constant :

The second part of the research was to expand the

list of available donor number ( DN ) . Using the above

expanded AN list (Table A-2), the expanded DN list

developed in Peter Michelsen's thesis (Table A-3), and

available dielectric constants (Table A-l), correlations

similar to Schmid's correlation equation [44] were

developed by using theMINITAB'

statistical program on the

RIT VAX computer system. An equation developed for all

solvents including alcohols, chlorinated hydrcarbons and

water had poor correlation with a correlation

coefficient of R = 0.701.

log g = 0.574 + 0.0253 AN + 0.00353 DN [67]

When alcohols, water and chlorinated hydrocarbons are

excluded, a much better correlation was obtained with a

correlation coefficient of R = 0.886

log = 0.340 + 0.603 AN - 0.00115 DN [68]

Examination of this correlation reveals that two solvents

do not fit the correlation. They are formamide and

47

methyl formamide. If these two solvents were excluded,

then the correlation would be much the same as Schmid 's

equation. Thus just doubling the data points in a

correlation like Schmid's equation [44] does not really

improve the correlation.

Schmid had used just one or two of the simplest

compounds in each class of copounds . The correlation in

equation [67] includes several compounds in each class.

However, these solvents tend to cluster around the

correlation line rather than aligning with it. Thus any

improvement gained by more points is cancelled by losses

due to more scatter within classes of compounds.

As can be noted the correlations in equations [44]

and [67] are for solvents of low or moderate dielectric

constant ( t ) . The dielectric constant ( 6 ) appears to

be a measure of the amphoteric character of solvents.

Solvents with strong acceptor properties (high AN values)

do not fit these correlations . These include the

alcohols, formamide, methyl formamide, chloroform,

carbon tetrachloride, and methylene chloride. Schmid

explains that these highly structured solvents deviate

because the bonds between solvent molecules have to be

broken before they can act as donors or acceptors (24).

Another reason given is that the coordination properties

of these solvents is not constant, but depends on

complimentary solute properties.

48

Since the highly structurted solvents could not be

included in a general correlation, separate correlations

of AN, DN and for each class of compounds were

developed. The correlation equations and the

corresponding correlation coefficients are given in

Table 4. Surprisingly, the alcohols, amides and halides

show good correlation within each class while the less

polar classes such as ketones, ethers and hydrcarbons

which had a good overall correlation have very poor

correlations within each class. Perhaps this is not as

surprising as it first seems. Examination of the list of

alcohols in Table A-2 shows that there is a strong

correlation of E and AN on the chain length of the

alcohols. As the chain length increases, both the AN and

values decrease. This occurs over a large range of AN

and . For solvents having low such as ketones,

ethers, and hydrocarbons, changes in chain length causes

only small changes in already low AN and . values.

These small changes are difficult to correlate,

especially with limited data.

At least for now, Schmid's correlation, equation

[44], can be used for low or moderately polar solvents,

and the newly developed equations in Table 4 can be used

for strongly polar or protic solvents.

Before these correlations were used to calculate

additional DN values, new DN values were made available

49

TABLE 4

CORRELATION OF AN, DN, AND E

FOR DIFFERENT CLASSES OF SOLVENTS

Log 8 = C+a(AN)+b(DN)

alcohols

amides

halides

esters

amines

nitro &

nitriles

ketones

hydrocart

ethers

0 0840 0 0330 -0 00015 0 938 0 969

0 708 0 0188 0 0190 0 960 0 980

0 686 0 0375 -0 0922 0 941 0 980

0 172 0 956 -0 0179 0 845 0 919

1 32 0 0180 -0 0181 0 703 0 838

1 18 0 0225 -0.00869 0 558 0 747

0 919 0 0101 0.0135 0 454 0 674

0 307 0 00765 0.00352 0 420 0 648

0 382 0 0290 0.00390 0 258 0 508

AN Acceptor Number

DN Donor Number

Dielectric constant (25'C

C, a, b Constants

P Correlation coefficient

50

by Marcus (30). These values were used instead of the

values calculated from the above correlation equations.

However, these new DN values from Marcus were found to be

consistent with and close to the values predicted by the

correlations. Thus these correlations can at least be

used to calculate dielectric constant ( ) values.

A final list was compiled in Table A-4 (appendix)

which includes experimental AN values, and AN values

calculated from either Schmid 's correlation or the

structured solvent correlation [64]. This list includes

the average DN values from Table A-3 and the new DN

values obtained from Marcus. The dispersion solubility

parameter ( S ) is also included in the list.d

Miscibility Sorting Maps:

The third portion of the research involved

construction of sorting maps of miscibility for binary

liquid mixtures. A sorting map is a graphical procedure

that allows the display of an empirically known

dependency of a given property ( ie. solubility, phase

diagram behavior ) on parameters for which the exact

mathematical dependency is not known (31). In this

research only two parameters are used, the acceptor-donor

term and the dispersion solubility parameter term of

equation [37]. Miscibility of binary mixtures are

plotted in an XY plane as a function of these two terms.

This plane is then emperically divided to sort areas of

solubility or insolubility. These areas can not be

predicted ahead of time since the exact dependency of

miscibility is known only after a plot is drawn. Then

areas or regions of miscibility and immiscibility can be

drawn and the plot optimized. The value of such a

sorting map is the convenient graphical display of the

relation of miscibility to the dispersion and the

acceptor-donor terms. More importantly a miscibility

sorting map allows prediction of miscibility or

immiscibility of other binary liquid mixtures which were

not used to make the original plot.

Initially a list of the 106 solvents in the

previous section with their AN and DN was made using

LOTUS 1-2-3 (Table A-4). The dispersion solubility

parameter term ( S. ) obtained from Barton (9) for 87 of

d

the above liquids were also included in the list. The d

values for the remaining liquids were calculated from

Beerbower's, Hansen's (12) and Van Krevelen's group

contribution method (18) using equation [22]. These

values were also included in the list.

A literature search was conducted to find reported

miscibility data for the possible binary liquid mixtures

of solvents in that list. However, very little

miscibility data was available. For many solvents only

miscibility data with a few common solvents were listed.

Adequate data could only be obtained for 43 solvents (32)

Thus only these 43 solvents, in which miscibility data in

many solvents is given, were used to construct 43

miscibility sorting maps. A list of these 43 solvnets

is given in Table 5.

As explained in the experimental section, the

acceptor-donor term ( AN ) ( DN ) was plotted against the

2

dispersion solubility parameter term ( - S ) . fori 2 d

each binary liquid mixture. The resulting point was

drawn as a square (D ) if the binary mixture was miscible

or as a plus ( + ) if the mixture was immiscible.

Generally, for most sorting maps, areas of mutual

miscibility and immiscibility could be clearly

distinguished. On the sorting maps, points for miscible

binary liquid mixtures tended to congregate near the

origin of the X and Y axes. Points for the few

immiscible binary mixtures tend to be much further away.

In most cases the immiscible points are well separated

from the miscible points. Lines could be drawn around

both sets of points forming immiscible and miscible areas

which were quite clearly separated from each other.

As part of the fourth research goal, several

sorting maps were examined in order to evaluate them.

This generally consisted of verifying the borders of the

immiscible and miscible regions by experimentally

53

determining the miscibility of binary mixture points

which were near the borders. Another part of this

evaluation was extending or extrapolating these two

regions by including experimentally measured points.

Sorting maps evaluated by this process include benzene,

hexane, toluene, methanol, ethanol, chloroform, acetone,

diethylether, and formamide. Two sorting maps in

particular, benzene and hexane, were examined in greater

detail. A major reason for this is that the immiscible

and miscible regions were not clearly distinquishable, as

they were on all the other sorting maps. The data used

to construct these two maps is given in Table 5. These

two maps were evaluated fully in order to determine

whether the immiscible and miscible regions could be

separated. Finally these maps were tested by determining

whether these regions on the maps could predict

miscibility by interpolation within the regions. These

predictions were then verified experimentally.

Benzene-Solvent Binary Mixtures Sorting Map:

Analysis of Benzene Sorting Map:

For benzene, three sorting maps are shown in

figures 5,6,7. The first sorting map attempted is shown

in figure 5. Most of the points for the benzene-solvent

54

TABLE 5

DATA FOR SORTING MAP FOR BINARY LIQUID SYSTEM

HYDROCARBONS

LIQUID 1 LIQUID 2

S AD

M Iri

n-htxint benzaldehyde 3.24 3.58n-hexane t-butylamine

n-hexane o-xylene

n-hexane fn-xylene

nhexane tr iethylamine 0 0.6n-hexane itoamylalcohol 0.09 9.82n-hexane c-hexane

n-hexane benzene 2.69 0.01

n-hexane toluene 2.25 0.01

n-hexane ethylenechlorlde

n-hexane CC1.

CHCl,

1.96 -0.18

n-hexane 1.96 0.05

n-hexane chlo'robenzene 4 -0.08

n-hexane o-dichlorobenzene

n-hexane ni tromathane

n-hexane ni trotthane

n-hexane ni trobenzene 6.25 0.64

n-hexane propieni trile 0.04 1.78

n-hexane benzoni trile

n-hexane ethylacetate

n-hexane ethyl formate

n-hexane ethylbenzoate

n-hexane acetone 0.09 1.75

n-hexane methylethylketone

n-hexane cyclohexanone

n-hexane acatophenone 5.29 1.66

n-hexane diethylether 0.04 0.6

n-hexane di-n-butylether

n-hexane aniline 4.84 5.11

n-hexane NfN-dimethylaniline

n-hexane pyridine 4 4.57

n-hexane formamide 1.21 11.5

n-hexane CS2 7.29 0.01

n-hexane tri-n-butylpho*phateB.04

n-hexane methanol 0.01

n-hexane ethanol 0.16 7.03

n-hexane 2-propanol

n-hexane 1-butanol

n-hexane 1-pentanol

n-hexane cyclohexanol

n-hexane benzylalcohol

n-hexane ethylene glycol 1 7.18

n-hexane glycerin 1.44 7.3

n-hexane water 0.09 ie.3

TABLE 5 ( continued )

AD

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzene

benzaldehyde

t-butylamine

e-xylene

m-xylene

triethylamine

iaoamylalcohole-hexane

n-hexane

toluene

ethylenechloride

CCI4

CHCljchlorobenzene

o-dichlor0benzene

ni tromethane

ni trot thane

ni trobenzene

propioni trile

benzoni trile

ethylacetate

ethylformate

ethylbenzoate

acetone

methylethylketone

Cyclohexanone

acatophenone

diethylether

di-n-butylether

aniline

N,N-dimethylanilin

pyridine

formamide

CS2tr i-n-butylphotpha

methanol

ethanol

2-propanol

1-butanol

1-pentanol

eyelohexanol

benzylalcohol

ethylene glycol

glycerin

water

0.01 2. 52

2.2s -0.65

2.89 -1.85

1.96 7.43

2.89 0.27

0 0.01

0.04 -0.02

0.09 -0.01

0.09 -0.03

0.16 -0.01

1.69

1.44 0.11

0.64 0.27

2.25 0.85

0.25 0.68

1.69 0.13

1.96 0.56

0.01 0.05

1.96 0.6

1.44 0.6

0.09 0.39

0.36 0.59

3.61 -0.65

2.56 -0.83

0.25 2.56

0.09 1.93

0.36 9.06

1

1 0.35

2.56 6.49

1.69 5.49

1.69 8.19

1.44 7.06

1.44 5.98

0.25 4.75

0 4.32

0.49 5.83

0.25 9.94

1.96 13.8

0.36

-0.03

Solubility parameter term of equation [37]

( S)

AD Acceptor-Donor term of equation [37]

0.01 ( AN,

-

AN2 ) ( DN,

- DN2 )

where values are: (M) Miscible, (I) Immiscible,

or (?) Questionable or partially miscible

56

BENZENE

Z0

z

0

r\

CM

z<

z

<

0a

0

Figure 5 .Benzene-Solvent Sorting Map

D miscible, + immiscible

+1 benzene-water, +2 beuzene-f ormamide

+3 benzene-ethylene glycol

+4 benzene-glycerol

57

mixtures are near the origin or lie along the axes.

There are also two immiscible points for benzene-solvent

mixtures. These two points, the immiscible benzene-water

(+1) and immiscible-benzene formamide (+2) mixtures, are

well separated from any miscible points. These two

mixtures were checked experimentally and found to be

immiscible in all proportions, agreeing with the

literature. Thus these two points clearly establish an

immiscible region.

Two other immiscible mixtures, benzene-ethylene

glycol (+3) and benzene-glycerol (+4), were added and

evaluated in order to extrapolate or more clearly

establish the immiscible region in figure 5. Ethylene

glycol and glycerol were not in the list of 43 solvents

used in constructing the sorting maps. However these

solvents are listed in the literature (32) as forming

immiscible mixtures with benzene. Thus these mixtures

were added to figure 5. These two points were plotted in

or very near the miscible region. This expanded the

immiscible region as shown in figure 5 so that the

boundaries between the miscible and immiscible regions

were difficult to determine. Two possibilities exist for

these results: 1) the literature results for miscibility

of mixtures near the boundaries are incorrect or 2) the

AN or DN values are incorrect. The benzene mixtures with

ethylene glycol and glycerol were tested experimentally

58

and found to be immiscible in all proportions. The

miscible mixtures in the same area were also tested

experimentally and found to be miscible. Examination of

the AN values of ethylene glycol (AN = 44.9) and glycerol

(AN = 46.0) show that they are in the expected range

between methanol (AN = 41.3) and water (AN = 54.8).

However the DN values of ethylene glycol and glycerol

were found to be much lower than the other alcohols and

water. The AN and DN values for the miscible solvents

were found to be consistent with similar solvents. Thus

the problem seems to be the low DN values of ethylene

glycol and glycerol.

Several authors have noted that Gutman'

s DN values

appear to be low for certain solvents (25,33,34). For

amphoteric solvents which can act as weak bases, this

undervaluation appears to be due to dissociation of the

solvent->SbCl complex (33). Donor number (DN) has been

defined as the negative A H values for 1:1 adduct

formation of solvent with SbCl (antimony pentachloride) .

Dissociation or incomplete formation of the complex

results in low DN values. This could be what has

happened for the weakly basic solvents ethylene glycol,

glycerol and formamide. This is also supported by the

fact that several investigators have found that the donor

or basicity values of formamide from different donor

scales are close to similar solvents (25,33,34). Thus

59

the low experimental DN value of formamide (DN = 24)

might be expected to be closer to the other amides,

especially N-methyl formamide (DN = 49). Likewise, the

low DN values for ethylene glycol and glycerol might be

expected to be closer to the DN values of other alcohols.

The published DN values for glycerol (DN = 19.0)

and ethylene glycol (DN = 19.2) are not experimental

values, but rather are values calculated from a

correlation equation [ 47 1 from the scale (26). Maria

and Gal (27) pointed out that this correlation is not

appropriate for alcohols. This is supported by the fact

that these calculated DN values for ethylene glycol and

glycerol are much lower than DN values of similar

alcohols, 2-propanol (DN = 35.7), 2-methyl-2-propanol (DN

= 38.0) and water (DN = 33.0).

Beerbower has provided new DN values, calculated

from a quadratic empirical relationship not yet published

(35), for formamide (DN = 49.8), ethylene glycol (DN =

38.8), and glycerol (DN = 38.4). These DN values appear

to be consistent with experimental DN values of similar

compounds. Furthermore, Beerbower 's DN values for other

amides and alcohols are very close to the experimental

values. IfBeerbowers'

DN values are used to calculate

dielectric constants from the approriate correlation

equations in Table 4, then the results are close to the

experimental dielectric constant values. Thus it seems

60

likely that Beerbower "s DN values are reasonable,

especially for formamide, ethylene glycol and glycerol.

Thus a second sorting map for benzene was made by

replacing the DN values for formamide, ethylene glycol

and glycerol in the first map, figure 5, with Beerbower rs

DN values. This second map is shown in figure 6. The

immiscible benzene-mixtures of formamide (+2), ethylene

glycol (+3), and glycerol (+4) were then located in the

immiscible area and well away from the other miscible

mixtures. All other points were not affected. The

result was that the immiscible region in figure 6 was

clearly separated from the miscible region.

Benzene Sorting Map - Miscibility Experimental:

The benzene sorting map was tested by

experimentally determining the miscibility ofbenzene-

solvent mixtures which are near the border of the

miscible and immiscible regions. These were the benzene

mixtures with methanol, formamide, glycerol and ethyene

glycol. The refractive index of these mixtures was

measured for different volume fractions in order to help

determine their miscibility. The results are listed

listed in Table 6. When a solute is dissolved in a

solvent, the refractive index of the resulting mixture

will be a volume-proportional weighted average of the

61

BENZENE

ZD

Z0

\J

r\

cs

z<

z

<

0

0

-10-

-15-

Figure 6 >Benzene-Solvent Sorting Map ( Beerbower's DN values )

Q miscible, + miscible,

+1 benzene-water, +2 benzene-f ormamide*

+3 benzene-ethyleneglycol*

+4benzene-glycerol*

* Beerbower'* DN values used

62

o o~ en

51

o>

h m in

u

BOOU VO

CI

om enCM CM

en

o

IO

tn

en mm mmm is> mmcji m oils o^i <r

no m cmm -< lti i

en en en is* en

<so 0US tA

o oCO CM

o oat

s

m

mm

10

rs.

en

en mm -oh en

m cmm <~i

en rsm S

~"

en

en

CO

cm m

m

en rnm

>o nm mCn V

*

me v m us enm - m -* mmen en 3* rs. cn v

ci ci

H >

-

en

m

CM

m o

en enmen

O

rs

9t en

m i/>

m

m m

m cm

en m

v omen rs

en om usen

"-1

rs

Oto

U"> CMm cm0"> <n

m

en rs

en oID -O

en

**

aus

enrs.

?

om cm

en en

91 o nus mm v

v4

u

Ci

o o

L.01 (V

O X

41 E

>ci -^

> ->

! v. L.

CI 3i. -i

x E

E Ci

i j

CDmOH

^ oe e

- -Sou

w .c >, >>

t u3 (9e

63

refractive indexes of the solute and solvent. For

immiscible mixtures the proportion of the solute is very

small, so the refractive index of each layer is close to

that of the pure liquids. For partially miscible

mixtures, the refractive index of the mixture varies

proportionally with the volume % of the liquids. The

benzene mixtures of formamide, glycerol, and ethylene

glycol were found to be immiscible. The refractive

index measurements for these mixtures indicated that the

solvents have very low solubilities in each other. The

benzene-methanol (Q5) mixture was found to be miscible in

all proprtions. These results helped to define the

miscible and immiscible regions as shown in figure 7.

Several miscible benzene-solvent mixtures from the map

were also evaluated and found to be miscible by simple

mixing experiments. This expanded the miscible region.

Thus the area within the boundary line was confirmed to

be the miscible region with no immiscible points.

Benzene Sorting Map - Error Analysis:

In order to determine the reliability of the

benzene sorting map, an error analysis was conducted for

all of the benzene-solvent mixtures used in the map. The

calculations and results are given in Table 7. The AN

error was calculated in a previous section from equations

64

BENZENE

Z

0

z

0

z<

z<

Figure 7 .Benzene-Solvent Sorting Map ( Final Map )

O miscible, + immiscible

+1 benzene-water, +2 benzeue-f ormamide*

* a

+3 benzene-ethylene glycol, +4 benzene-glycerol

05 benzene-methanol , 06 benzeue-ethauol

* Beerbower'

s DN values were used

65

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PQ

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Ed

>

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N

Z

w

co

u.

o

to

M

CO

S-

<

z

<

Oi

o

OS

w

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1

1<d k-

~ o'S fc.

5.3

co to >m m to <-i- to o in m to o m en v io ?

co in v rj <o it, m

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k-

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66

[61J and [65]. The DN error was obtained from Peter

Michelsen's thesis (29) and is given in Table A-3. The

total ( ANi-

AN2)( DNi- DN ) error is generally small

for most points. The benzene-chloroform error is high

due to the high chloroform DN error. The high benzene-

dichlorobenzene error is due to the very small AN

values. However, the total error is small for each

immiscible mixture and each miscible mixture that are

located near the boundaries of the regions. Thus the

reliability of the benzene sorting map appears to be

good, especially in the critical areas between the

miscible and immiscible regions.

Benzene Sorting Map to Predict Misnihilitv nf

Mixtures:

In order for the sorting map to be useful, it must

be able to correctly predict the miscibility of binary

liquid mixtures. This was demonstrated for several

solvents which were not used in constructing the sorting

map. Solvents representing different groups were chosen

such as acetonitrile, N-methyl formamide, ethyl acetate,

2-butanone, di-n-butyl ether and t-butanol. Since the

AN, DN and S. values for these solvents were available ind

Table A-4, the points corresponding to the benzene-

solvent mixtures were plotted on the third benzene

67

sorting map. This plot is shown in figure 8 without

points for most of the mixtures so the points for the six

mixtures could be easily seen. The benzene mixtures of

acetonitrile, ethyl acetate, 2-butanone, butyl ether and

t-butanol are located in the miscible region. These

mixtures were predicted to be miscible. Since the N-

methylformamide mixture is located outside of both

regions, it was predicted to be miscible or partially

miscible, but not immiscible because it was not close to

the immiscible region. All mixtures were found to be

miscible in all proportions and the results are

summarized in Table 8. This helped to confirm the

boundaries of the miscible region. Thus the benzene

sorting map sucessfully predicted miscibilities of

benzene in a wide variety of solvents, including some

polar, highly structured solvents.

TABLE 8

PREDICTING MISCIBILITY OF MIXTURES

WITH BENZENE SORTING MAP

System Predicted Experimental

1 benzene-N-methylformamide miscible miscible

2 benzene-acetonitrile miscible miscible

3 benzene-ethy lacetate miscible miscible

4 benzene-2-butanone miscible miscible

5 benzene-di-butyl ether miscible miscible

6 benzene- t-butanol miscible miscible

68

BENZENE

z

Q

Z0

z<

z

<

0

0

-5-

-10-

-15-

-20

2

i

4

T T T

Figure 8.

0 2 4 b 8 10

(S.-Ud*

Benzene-Solvent Sorting Map- ( Predictions )

? miscible,+ immiscible

0 1 beuzene-N-methylformamide, D 2 benzene-acetonitrile

D3 benzene-ethyl acetate, D k beuzene-2-butanone

D5 benzene-butyl ether, D 6 benzene-t-butanol

69

Hexane - Solvent Binary Mixture Sorting Hap

Evaluation of Hexane Sorting Man:

Similar to benzene, Three sorting maps were

constructed for hexane. The first map, which is shown in

figure 9, shows the points plotted with experimental AN

values. Calculated AN values are used when experimental

AN values are not available. On the map, there are five

immiscible hexane-solvent mixtures. The points for the

immiscible hexane-water (+1), hexane-formamide (+2), and

hexane-aniline (+3) mixtures are well separated from the

miscible region. The other two immiscible hexane

mixtures with glycerol (+6) and ethylene glycol (+5)

appear to be in the miscible region. Thus when the

immiscible and miscible regions are drawn in figure 9,

they overlap slightly. The hexane-methanol mixture (4)

appears in the overlapping miscible and immiscible

regions. The literature is not clear as to the status of

the miscibility of this mixture so it was plotted as

questionable until it could be evaluated experimentally.

The second map (figure 10) shows that the two

points representing the immiscible mixtureshexane-

ethylene glycol (+5) and hexane-glycerol (+6) were moved

into the immiscible region when Beerbower's (35) DN

values for ethylene glycol and glycerol were used. Once

70

n-HEXANEE

20

5 -iona

0

-15-1

-20

(*,-*.),

10

Figure 9- Hexane-Solvent Sorting Map

q miscible, + immiscible, Oques tionable

miscibility

+ 1 hexane-water , + 2 hexane- formamide

+ 3 hexane-ani 1 ine ,*4 hexane-me thanol

+5 hexane-e thylene glycol, +6 hexane-glycerol

71

n-HEXANE

(*,-*,>:2'd

Figur. 10. Hexane-Solvent Sorting Map ( Beerbower's DN values )

D miscible, + immiscible, Q questionable

misciblity

+ 1 hexane-vater , +2 hexane-formamide

+3 hexane-anlllne, 0 4 hexane-methanol

+5 hexane-ethylene glycol, +6 hexane-glycerol

0 7 hexaue-isoamylalcohol , O 8 hexane-ethanol

72

again it appears that the calculated values published for

these two solvents are too low and that Beerbower s DN

values are more apropriate. The immiscible hexane-

formamide mixture (+2) was also moved further into the

immiscible region when Beerbower's (35) DN value for

formamide was used.

This second sorting map shows that the miscible

and immiscible areas are fairly well defined with the

exception of the hexane-methanol mixture. The hexane-

methanol mixture (O 4) still falls in the miscible region

between the miscible hexane-isoamyl alcohol ( a 7) and

hexane-ethanol (0 8) mixtures as indicated in figure 10.

Again, two possible reasons for this deviation existed:

the miscibility data was incorrect or some of the AN or

DN values for these alcohols were incorrect.

Experimental miscibility results from Table 9 show that

hexane is miscible with isoamyl alcohol and ethanol, but

only partially miscible with methanol. The DN value of

isoamyl alcohol (DN = 32.0) is consistent with values

obtained from several sources. However, the experimental

DN values for methanol (DN = 19.0) and ethanol (DN =

20.0) are lower than values calculated from other

correlations. As discussed previously in the case of

ethylene glycol, glycerol and formamide, the DN values of

methanol and ethanol are probably too low and should be

higher. These DN values are also much lower than similar

73

to

CM

en

encm

mco

co

2 8

3

oeoeo

to

en

? e m en m r c mCM CO m en (SI O cm en

o CO r~ f cm r^ r*. r-

w en to en w en

to

en

en

encm eoCO ren m

en en

r> cm

enr

m

m

en(SI

iO

en

in

en

en

r. en in 10 to IO 60 tOCM CO en en cm a cm en

co r* f CM r r r wen m en ? en ? en

in

o>

e

e em m

v >o

r in in us IO io en mrsi en en en cm e cm en

CO r l cm r^ r^ r*. w

cw

in

CM

X

it

o

a

k.

CM

8 2

01

X =

e o

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01 J

an

xi

r. o r toen W r* IO r O VO v.

en cm in ~* cm en m en CM O en en X oto ^ en 00 r* pn (s, r*. r^ f OIen en en en en m en en en

c^

01>

X

01

ac

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.

k.

.c

o

OI

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

OI

3*

X

X

01w

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

uM

i

E

01

.n

ui

? en eo m r*. O m CO r* f" r ^-

e o ^* to cm en en sn CM M cm en zr> r- r. CO r*. r>. cm rv r* r*.

en en en en en in en en en

o

8** 01 s "5

e e e e "T L. Ee 01 r- O 01 a

c a a. ^m ><U u

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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>dFigure 11 Hexane-Solvent Sorting Map ( Final Map )

O miscible, + Immiscible, <> partial

miscibility

+1 hexane-water, +2 hexane-formamide

+ 3 hexane-aniline, <> 4 hexane-methanol

+5 hexane-ethylene glycol -H hexane-glycerol

Q 7 hexane-isoamylalcohol,0 8 hexane-ethanol

76

shown as a steady change in the refracitive index as the

proportions of the mixture are changed. Ethylene glycol,

glycerol, formamide and aniline form immiscible mixtures

with hexane. The very small changes in the refractive

index values indicate that hexane is soluble to the

extent of only 1% or less in these solvents for all

proportions tested. These mixtures are definately

immiscible. The hexane-methanol mixture shows partial

miscibility-

depending on the proportions of each

liquid. The 40% - 50% volume/volume hexane-methanol

range was reexamined in more detail using a series of

mixture containing between 40% - 50% hexane in methanol

in 1% increments. Maximum miscibility of hexane in

methanol at 25 C was found to be 45% hexane. The results

are shown in Table 10. Thus the experimental miscibility

data helps to establish the miscible and immiscible

regions .

The line establishing the miscible region is

defined so that only totally miscible mixtures are within

the region. Thus, miscible mixtures such as hexane-

ethanol ( D 8) andhexane- isoamyl alcohol ( Q 7) fall

within the miscible region shown in figure 11.

Immiscible mixures are outside this region and make up

their own region. Partially miscible mixtures such as

hexane-methanol (0 4) by definition are outside but very

near the miscible region. Thus the line defining the

77

TABLE 10

MISCIBILITY OF HEXANE-METHANOL MIXTURES

Hexane

X volume 90 80 70 60 50 40 30 20 10

volume(ml) 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5

Methanol

volume(ml) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Z volume 10 20 30 40 50 60 70 80 90

Miscibility IIIIIMMMM

Hexane

Z volume 50 49 48 47 46 45 44 43 42 . .

volume(ml) 2.5 2.45 2.4 2.35 2.3 2.25 2.2 2.15 2.1..

Methanol

volume(ml) 2.5 2.55 2.60 2.65 2.7 2.75 2.8 2.85 2.9..

2 volume 50 51 52 53 54 55 56 57 58

Miscibility IIIIIMMMM

Maximum miscibility of hexane in methanol is 4 5 % : 5 5%

78

miscible region can be drawn just above the hexane-

ethanol (D8) and hexane isoamyl (07) points and just

below the hexane-methanol (Q 4) point. Note that if the

definition of the miscible region includes partially

miscible mixtures, then the line establishing the region

would be drawn above the hexane-methanol (04).

Hexane Sorting Map - Error Analysis:

In order to determine if the final hexane sorting

map was reliable, an error analysis was conducted for all

the hexane-solvent mixtures used in constructing the

hexane sorting map. The calculations and results are

summarized in Table 11.

The total ( AN,- AN

2 ) ( DN,-

DN2 ) error for

each mixture is quite small. The noted exception is the

hexane-chloroform mixture which has a small DN divided

into a large DN error of chloroform. Thus the error

analysis shows that the error associated with each point

is generally small, especially for immiscible binary

mixtures or miscible binary mixtures near the boundaries.

Hexane Sorting Map to predict Miscibility

of Mixtures:

The usefulness of the hexane sorting map was

79

M

-3

ea

<

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X

uzM

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O(A

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CA

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to>

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06

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2<3

a i

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etVOtrtrsq'CVIrHOOrntiJq'inrMv

CM O . O CD0

hHOOOOOrlOO

ir)cpintotoif)int09cricnrc)tet

5 JO to .

CMTC\iCMrs,Ho<TCONdooOrtiMOinonnoNco ^ m n io rn o co o o cviino ^ ro rooNoooooort

CO MM

rs 8*i oCM V

CM

tO N

rt toCM CO

to in

to

in in

CM CO i

O O

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C3 OOOOOOO

jOTtjOVrsVCOoVION

in o co Nin ni in u m () ohoKhNN|/1(i)t(i

O I CBHOHOOrtP)

o o

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cj o

in toto o

to

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nciryfsmfOfsryocMcccfitocj

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l4nNrtHMTIi|ilJiHO N CM in

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OX

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ft*

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e oi oc cl> c 6 c o

ft ro k. o o ox - -o ft ft c

3 "J -* 0 k- a<"

w-*-Xft

-IHUH " o ll tlli-k.k.k-'-'X

O U I X - k. U (J - C 3. O O ft *

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e o

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80

demonstrated in the same manner as for the benzene

sorting map in correctly predicting the miscibilities of

a variety of hexane-solvent mixtures. The same six

solvents used for testing the benzene map were used to

test the hexane map. These solvents were acetonitrile ,

N-methyl formamide, ethyl acetate, 2-butanone, di-n-butyl

ether, and t-butanol. The points corresponding to the

hexane-solvent mixtures were plotted on the third hexane

sorting map (figure 11). For clarity, most of the other

hexane-solvent mixtures were not shown in this prediction

map given in figure 12. The hexane-N-methyl formamide

mixture (+1) falls within the immiscible region and

therefore was predicted to be immiscible. The other five

mixtures were predicted to be miscible since the

respective points were located in the miscible region.

These predictions were confirmed experimentally and are

summarized in Table 12. Thus the hexane as well as the

benzene sorting maps have been successfully used in

predicting the miscibilities of binary liquid mixtures.

81

n-HEXANE

Z

0

z

Q

Z

<

z

<

0

0

0 2 4 6 8 10

Figure 12. Hexane-Solvent Soritng Map- Prediction

O miscible, + immiscible, $ partial

miscibility

+ 1 hexane-N-methylf ormamide , D 2 hexane-ace toni trile

03 hexane-ethyl acetate ,04 hexane-2-butanone

05 hexane-butyl ether, D6 hexane- t-butanol

82

TABLE 12

PREDICTING MISCIBILITY OF MIXTUES

WITH HEXANE SORTING MAP

System Predicted Experiment

1 hexane-N-me thy Iformamide immiscible immiscible

O hexane-acetonitrile miscible miscible

3 hexane-ethyl acetate miscible miscible

4 hexane -2-butanone miscible miscible

5 hexane-di-butyl ether miscible miscible

6 hexane- t-butanol miscible miscible

83

CONCLUSION

A simple solubility expression has been developed

based on solubility parameter theory and Lewis acid-base

theory. This new expression as described in equation

[27] combines a dispersion solubility parameter term for

nonpolar interactions and a Lewis acid-base term for

polar and hydrogen bonding interactions. The Lewis acid-

base term was written as the product of the difference

of the acceptor numbers (AN) and the difference of the

donor numbers (DN) for two liquids.

In order to test this new expression, four

research goals were established. The first two goals

were to expand the small list of available AN and DN

values so that this expression could be used. The third

goal was to use this expression to construct miscibility

sorting maps for binary liquid mixtures. The fourth goal

was to test the sorting maps and thereby the solubility

expression. These goals have generally been successfully

accomplished.

A good correlation of experimental AN and ET(30)

values for alcohol and chlorinated hydrocarbon solvents

was developed. This expression compliments the

correlation established by Schmid which did not include

alcohols and chlorinated hydrocarbons. Many AN values

84

were then calculated from experimental ET(30) using

either Schmid 's correlation or the correlation developed.

in this work.

An attempt to improve the overall correlation of

AN, DN and dielectric constant by including amphoteric

solvents did not work. However, individual correlations

were developed for each class of the amphoteric solvents,

such as alcohols, amides and chlorinated hydrocarbons. A

problem with the highly structured amphoteric solvents is

that the dielectric constant correlates well with

experimental AN values but not with experimental DN

values .

Miscibility sorting maps for binary liquid

mixtures were constructed for 43 liquids. For 41 of these

maps areas defining miscible and immiscible mixtures

could cleary be distinguished. However, this distinction

was not clear in the special cases for the benzene and

hexane sorting maps. The problem appeared to be

associated with the low experimental DN values of a few

but not all of the amphoteric solvents. When higher DN

values for methanol, ethanol, ethylene glycol, glycerol

and formamide obtained from Beerbower were used, then the

benzene and hexane sorting maps successfully indicated

separate miscible and immiscible regions. A few

additional maps representing each class of compounds

(toluene, methanol, ethanol, chloroform, acetone, diethyl

85

ether, formamide) were also evaluated experimentally.

The binary mixtures in the immiscible regions were found

to be immiscible and the mixtures defining the boundaries

of the miscible regions were found to be miscible. Thus

these maps and the revised benzene and hexane maps

successfully indicated separate miscible and immiscible

regions .

The miscibility sorting maps were tested by using

them to predict the miscibility of several binary

mixtures. These mixtures were later evaluated

experimentally and found to agree with the predictions.

This demonstrated the usefulness of the sorting maps.

The usefulness of the sorting maps, and thereby

the solubility expression, depends upon the availability

of good, reliable AN and DN values. For most solvents,

reliable values have been compiled in this and other

work. A problem appears to exist for certain amphoteric

solvents which have low DN values. However, recently

obtained DN values for these solvents are more reasonable

and do not seem to present any problem. Additionally,

the sorting maps themselves serve as a check on the

reliability of the AN and DN values.

The solubility expression developed in this thesis

has been demonstrated to be useful in constructing

miscibility sorting maps for binary liquid mixtures or

binary liquid systems. Future work may extend this

86

expression into other areas such as in studying three or

more liquids in a mixture or in studying liquid-surface

interactions .

87

REFERENCES

1. Snyder, L. Chem Tech. 1979, 750.

2. Hildebrand, J. H., J. Am. C.h <w 1916) ^ 1452

3. Lewis, G. N., "Valence and the structure of the

Ai^ms andMolecules/'

, pp 141-142, The Chemical

Catalog Company, NY, 1923.

4. Hildebrand, J. H.; Prausnitz, M. M.; Scott, R. L.,

"Regular and Related Solution^'. Van Nostrand-

Reinhold, New York, NY., 1970.

5. Hildebrand, J. H.; Scott, R. L., "Soluhi 1 itv of Non-

ElectrolYtes"

, 3 ed., Reinhold, New York, NY., 1958.

6. Konstam, A. H.; Feairheller, W. R., Am. Inst. Chem.

Eng . J . . 1970, 16_, 837.

7. Beerbower, A. J. Colloid and Interface Soi . . 1971,

3_5_, 126.

8. Hildebrand, J. H.;Scott,-

R. L., "Regular Solutions".

Prentice-Hall, Englewood Cliffs, NJ., 1962.

9. Barton, A. F. M., "The Dynamic Liquid State".

Longman, London, 1974.

10. Blanks, R. F.; Prausnitz, J. M., Ind. Eng. Chem.

Enndam. , 1964, 3_, l.

11. Bondi, A.; Simkin, D. J., J. Chem. Phvs . . 1956, 25_,

1073.

12. Hansen, C. M . ; Beerbower, A., in Kirk Othmer Encyclo

pedia of Chemical Technology. Suppl. Vol., 2nd ed . ,

Standen, A., Ed., Interscience , New York, 1971, 889.

88

13. Keller, R. A.; Kanger, B . L . ; Snyder, L. R., Gas.

Chromatogr. . Proct . Tnt. Svmp . (Knr ) 1971, 8., 125.

14. Hansen, C. M., Chem. T^chnol, 1972, 2., 547.

15. Barton, A. F. M., "Handbook of Solubility Parameters

and Other Cohesion Para^^rff', CRC Press, Bocaraton

Fl., 1983.

16. London, F., Trans. Faradav Soc . . 1937, S_3_, 8.

17. Koehen, D. M.; Smolders, C. A., J. AppI . Polvm. Sci. .

1975, 19_, 1163.

18. Van Krevelen, D. W.; Hoftyzer, P. J., J. AppI. Polvm.

Sci. . 1967, II, 2189.

19. Small, P. A., J. AppI. Chem.,1953. 3_, 71.

20. Jensen, W. B., Rubber Chem. Techno! . . 1982, 5_5_, 881.

21. Gutman, V., "The Donor-Acceptor Approach to Molecular

Interactions"

. Pelenium, NY., 1978.

22. Dimroth, K.; Reichardt, C, Z. Anal. Chem. . 1966,

215., 344.

23. Reichardt, C, "Molecular Interactions'. Vol 3,

240, Edited by Ratajezak, H. and Orville-Thomas W.

J., John Wiley and Sons, Ltd., New York, 1982.

24. Schmid, R., J Solution Chem. . 1983, iZ, Vol. 2, 135.

25. Griffiths, T. R.; Pugh, D. C, Coordination Chemistry

Reviews. 1979. 29_, 129.

26. Kamlet, M. J.; Abboud, J. I.; Taft , R. W., Frofir.

Phvs. Chftm 1981, H, 618.

89

27. Maria, P. C; Gal, J. F., J. Am. Chem. Soc . . 1985,

8_3_, 1296.

28. Harris, D. C, "Quantitative Chemical Analysis'-.

W. K. Freeman and Company, New York, 1982.

29. Michelsen, P. J., Thesis, Rochester Institute of

Technology, in progress.

30. Marcus, Y., J. Solution Chem. . 1986, 15_, 291.

31. Beerbower, A.; Jensen, W. B., Inorganic Chemica Acta.

1983. 75_, 193.

32. Francis, A. W., Advances in Chemistry Series No. 3_1,

American Chemical Society, Washington D. C, 1961.

33. Rolling , 0. W., Anal. Chem. 1982, 5A, 260.

34. Olofsson, G., J. Am. Chem. Soc. . 1973, 9_5_, 7231.

35. Beerbower, A., Private Communication with Jensen, W.

90

APPENDIX

91

TABLE A-l

LIST OF ET(30), AN ( experimental and calculated ),

ANP DIELECTRIC CONSTANT ( 6 )

AROMATICS

bftnzftna

toluene

o-xyln

p-xylnft

m-xyl*n

chlor obenzne

bromcb*n:ini

c-di chlorobnz*ne

m-di chlorobftnzftn

i odobenzftn*

f iuorobftnzcn*

methoxybftnzftnft

t t hoxybftnz int

rresi tylftn*

thylbenzftnft

styrftn*

o-mftthyl*tyTftn

p-iTiethylstyrnft

ALIPHATICS

AN

(ftxpt)

8.2

AN"

(E_(30)

E (30)

NITRO COMPOUNDS

6 (25CC>

3.983 34.5 2.283.211 33.9 2.383.727 34.3 2.568 (20)2.695 33.5 2.27 (20)2.437 33.3 2.374 (20)7.855 37.5 5.627.e55 37.5 5.4

8.629 38.1 9.93

7.21 37 5.04

8.371 37.9 4.63 (20)

8.629 3S.1 5.42

7.468 37.2 4.33

6.436 36.4 4.22 (20)

2.179 33.1 2.2s (20)

2.4 (20)

2.426 (20)

n-hexan 0 -0.639 30.9 i.ee

1 , 2-di chloroftthanft 16..7 13.531 41.9 10.36

1 , 1-di chloroftthanft 10.306 39.4 10 (18)

dibromomftthan* 10.306 39.4

di chloromftthan* 20,.4 12.499 41.1 8.93

1 ,1 ,2,2-tetrachloroftthan* 9.403 38.7 8.2 (20)1 ,2-dimthoxyftthanft 10,.2 8.758 36.2 7.2

1 ,2-dibromoftthanft 7.468 37.2

bromofthan* 7.984 37.6 9.39

1-chloropropan* 7.726 37.4 7.7 (20)

1 ,1 ,1-tri chloroftthanft 6.178 36.2 7.53 (20)

tr ichloroftthylftn* 5.791 35.9 3.42 (16)

tttrachloroftthylftnft 0.631 31.9 2.3

carbontfttrachlorid* 8 .6 1.405 32.5 2.24 (20)

chloroform 23 .1 9.919 39.1 4.61 (20)

cyclohftxan* -0.272 31.2 2.02 (20)

cyclohftxftn* 1.147 32.3 2.2 (20)

n-hftptanft 19.2

2-ni tropropan* 14.692 42.8 25.32 (30)

ni tromftthan* 20.5 19.207 46.3 33.67 (30)

ni troftthane 15.724 43.6 26. Of (30)n l trobftnzftn* 14.8 13.66 42 34 . 62

92

TABLE A-l (continued)

18.82 46 37.5 (20)

15.853 43.7 27.2 (20)

19.723 46.7 33 (20)

15.079 43.1 20.3 (21)

13.66 42 25.2

14.821 42.9 18.7 (27)

20.4 (24)

26.689 32.1

22.561 46.9

NITRILES

acstonitril* 18.9

prop l oni tr ilft

acryloni trile

n-bu tyroni trile

benzoni trile 15.5

phenyl ace t oni trile

i so -bu tyroni trile

tert-butyl nitrile

cyclohexylni trile

3-chloropropioni trile

4-chlor obu tyroni trile

NITRATE

isopropylni trate 15.079 43.1

ESTERS

methylaeetate

etnylacetate

v inylacetate

methylacrylate

et:->vi aery late

propylacetate

etnylf ormate

rrethylf ormate

ethylbenzoate

methylbenzoate

dimethylphthalate

methyl chloroacetate

methyl di chloroacetate

methyl propionate

ethyl propionate 5.63 (19)

ethyl chloroacetate

methyl isobutyrate

methyl methacrylate 2.9

LACTONES

B-prop ion lac tone

4-butyrolactone 16.627 44.3 39 (20)

E-caprolactone

KETONES

0.7 11.08 40 6.63

9.3 6.629 3.l 6.02

8.5 36

16.855 44.5

7.635 37.5 6 (20)

12.241 40.9 7.16

8.5 (2C)

8.629 38.1 6.02 (20)

6.59 (20)

11.933 40.7

13.66 42

acetone 12.5 13.918 42.2 20.7

3,3-aimethylbutanone 9.79 39

93

TABLE A-l (continued)

12.757 41.3 18.51 (20)

10.177 39.3 17 (20)

12.499 41.1 15.4 (20)

9.403 38.7

6.5 38

9.661 38.9

11.209 40.1

12.241 40.9

10.306 39.4

10.822 39.6 16.3 (20)

12.757 41.3 17.39

10.306 39.4 13.11 (20)

methylethylketone

diethyl ketone

methylpropylketone

di i sopropylketone

diisobutylketone

4-hep tanone

2-hexanone

isopropylme thy Ike tone

cyclopen tanone

cyclohexanone

acatophenone

4-methyl-2-p en tanonecyclobutanone

cyciohep tanone

methylvinyl ketone

i sophorone

camphor 11.35 (20)

tr t chloroacetone

dimethyl-G-py rone

benzcphenone

bi acetyl

di-ter t-bu tyl ketone

ETHERS

diethylether

di i sop ropy lether

di-n-bu tylether

1 ,2-dirr.ethoxyethar.e

ant sole

propvleneoxide

di glyme

furan

tetrahydrofuran

1 ,4-dioxane

1 ,3-di oxolane

phenatole

di-n-propyl ether

ethyl butyl ether

ethyl uinyl ether

n-butyl vinyl ether

isobutyl vinyl ether

diallyl ether

epichlorohydr in

styrene oxide

3,3-bischloromethyloxetane

2-methyl-l ,3-dioxalane

4-methyl-l,3-d:oxalane

2-phenyl-l,3-dioxalane

4-chl or ome thy 1-1 ,3-dioxalane

dibenzyl ether

3,,9 4.114 34.6 4.34 (20)

3.34 34 3.66

2.566 33.4 3.08 (20)

10,.2 8.758 38.2 7.2

7.468 37.2 4.33

10.822 39.8

9 .9 9.274 38.6

3,,3 2.942

8 7.726 37.4 7.56

10,.8 5.92

15.079

36

43.1

2.21

6.436 36.4 4.22

3.39

(20)

(26)

22.6 (22)

94

TABLE A-l (continued)

diphenyl ether 3.656oxepane

2-methyltetrahydrof uran 6.565 36.5tetrahydropyran 3.61tr igiyme 9.661 38.9 7.3

4 3.146 35.4 3.58 (21)

4 2.437

2.437

6.932

33.3

33 . 3

ScT.S

2.42

16.627 44.3 6.89 (20)

9 13.66

14.303

6.3

42

42.5

38

12.9

2 11.338 40.2 12.4 (21)

8.887 38.3 5.S (20)

ALDEHYDES

acetaldehyde 21.1 (21)prcpi onaldehyde 16.5 (17)

butyraidehyde 13.4 (26)

acrolein

cro tcnaidehvde

benzaldehyde 17.6 (20)

AMINES AND DERINATIVES

di ethvlami re 9,

tr iethyia.Tiine 1.

diisoprcpylan :ne

ter t-bu tyl a.Ti;ne

aniline

ethvieneoi amine 20.

n-ir.ethylai-i il : nen

n-dimethylaniiine

pyridine 14,

a-pi col i ne

b-pt coli ne

o-pi coline

4-ethvlpyridine

2,4,6-trimethylpvridine

2-chloropyridine 13.531 41.9

3 ,5-di chloropyr lcine3bromopvr 1 dine

4-winylpyridine

4-dimethyl ami nopyr i dine

2 ,6-luti dine

1-formvlpiper i dine

piper idine

quinoline

n-methyl-2-pyrrolido 13.3

dimethylethyleneurea

tetramethylurea

ammonia

ethylamine

n -propylamine

di -propylamine

o-toluidine

N-me t hy1 -E-cap r o 1 ac t am

N-fliethylpyrrolidin**2

N-isopropyl-2-pyrrol idine

6.823 36.7

3.273

3.275

35.5

35.3 5.8 (20)

10.306 39.4 9

13.918 42.2 32

14.305

12.37

42.5

41 23.45

16.9

3.58 (21)

5.31 (20)

3.066 (20)

6.34 (18)

95

TABLE A-l (continued)

39.6 32.494 56.6 111 (20)

32.1 29.269 54.1 182.4

26.56 52 191.3 (32)

16 13.962 43.8 36.7

13.6 15.853 43.7 37.78

10.6 12.241 40.9 29.6

dimethylpropvleneureatr i-bu tylamine

N,N-dimethyl benzyl amine

IMINES

ethylenimine 16.3

N-phenylethylenimi ne

AMIDES

formamide

n-methvlformamide

n -me t hy 1 ace t am i de

n,n -dime thy If ormami d

n , n-di me thy lace tarn id

hexamethylphosphoami

N,N'-di ethy If ormami de

N,N-di ethyl ace t ami de

N-methylpyrroli done

dimethyl tr if luor oacetamide 32

dimethylchloroacetamide

SULFIDES

carbondisulf ide 1.534 32.6 2.64 (20)

S'JLPHOXIDES, SULPHONES AND SULFITES

dimethvlsuifoxides 19.3

dimethyl sulfone

dibutyl sulphone

sulfolane 19.2

di-butyl sulphoxide

diphenyl sulphoxide

dimethyl sulfite

diethyl sulfite

ethylene sulfite

SULFONIC ACIDS

methanesulfonicacid 126.3

ACID AND DERIVATIVES

formic acid 83.6 38.5 (16)

acetic acid 52.9 26.173 51.7 6.15 (20)

trifluoroaceticacid 105.3 8.35 (20)

acetic anhydride 20.7 (19)

acetyl chloride15-a <22)

benzoyl chloride 23 <20>

benzoyl fluoride

17.53 45 46.68

21.4 46

14.692 42.8

16.24 44 43.3 (30)

9.016 38.4

96

TABLE A-l (continued)

CARBONATES

ethylenecarbonate

propvlenecarbonate 18.3dimethyl carbonate

diethylcarbonatedichloroethylene carbonate

tetrachloroethylene carbonate

propanediol-l,2-carbonate

PHOSPHOROUS COMPOUNDS

22.174 48.6 69.6 (40)

19.594 46.6 65.1

12.499 41.1

6.178 36.2 2.62 (20)

tr imethylphosphate 16.3tr ie thy lphosphatetr i-n-propylphosphatetr i-n-bu tylphosphate 9.9

tripiperidinophosphine oxide

tripyrrolidinophosphine oxide

tr iphenylphosphine oxide

trimethyiphosphine oxide

ALCOHOLS

15.724 43.6 20.6 (20)

13.273 41.7

11.723 40.5

10.564 39.6 7.939 (30)

methanol 41,.3 31.075 55.3 32.7ethanol 37,,1 26.431 51.9 24.55n-bu tanol 36,,6 24.238 50.2 17.311-pen tanol 22.619 49.1 13.91-hexanol 22.432 48.8 13.31 -hep tanol 22.045 48.5

1-octanol 21.787 46.3 10.34 (20)

1-decanol 20.884 47.6 6.1 (20)

1-aodecanol 19.723 46.7

2-propanol 35,,5 22.174 48.6 19.92

2-butanol 20.239 47.1 16.56

2-pentanol 19.465 46.5 13.62 (22)

3-pentanol 18.433 43.7 13.02 (2)

i sobutylalcohol 22.69 49 17.93

isoamyl alcohol 22.69 49 14.7

cyclopentanol 21.013 47.7

cyclohexanol 19.207 46.3 15

t-butyl alcohol 27.,1 16.111 43.9 12.5

t-pentyl alcohol 13.531 41.9 5.62

1-propanol 37,.3 24.883 50.7 20.33

2,2,2-tr if luoroethan 53,,5 36.235 59.52,2,3,3-tetrafluoro-l-propano 36.106 59.4

2 , 2 ,2- 1 r l chloroethanol 32.494 56.6

2-propen-l-ol 26.689 52.1 21.6 (15)

2-propyn-l-ol 53

2-ftminoethanol 33.,7 26.302 51.8 37.72

97

TABLE A-l (continues)

3-amino-l-propanol 43.12-chloroethanol 25.8

l-bromo-2-propanol 31.42-ethoxyethanol 23.27 31 29.6 (24)

2-methoxy ethanol 26.947 32.3 16.93

2-n-butoxy ethanol 24.238 30.2 9.3benzyl alcohol 25.012 50.8 13.1 (20)furfuryl alcohol 50.3tet r ahy dr of ur fury 1 alcohol 24.367 50.3 13.611-phenyl ethanol 19.723 46.7

2-phenyl ethanol 23.335 49.5

3-phenyl-l-propanol 22.045 48.5glycerol 33.01 57 42.51 ,2-ethanediol 32.107 56.3 37.7

1 ,2-propanediol 29.269 54.1 32 (20)

1 ,3-propanediol 30.301 34.9 35 (20)

1 ,3-butanediol 27.592 52.8

pentanediol 31.3

diethylene glycol 28.882 53.8 31.69 (20)

triethyler.e glycol 28.495 53.3 23.69 (20)

water 54.8 40.879 63.1 78.54

deuterium oxide 40.492 62.8 78.25

INORGANIC HAL IDES

sulphuryl chloride

thionyl chloride

selenium oxychloride

phosphorous oxychlor

phenylphos'c difluoride

11

a Experimental AN from Gutman (21)

b AN (a) values are calculated from E (30) values using

equation [43] from Schmid (24)

c E (30) values from Reichardt (23)

d Dielectric Constanta from Schmid (24)

98

TABLE A-2

LIST OF AN VALUES CALCULATED FROM EITHER

SCHMID'S OR ALCOHOL'S CORRELATIONS

SOLVENT

a

AN

(expt)

AN AN

(E (30) (alcohol)

AROMATICS

benzene

toluene

o-xylene

m-xylene

p-xylene

chlorobenzene

bromobenzene

o-di chlorobenzene

m-di chlorobenzene

i odobenzene

f luorobenzene

methoxybenzene

ethoxybenzen

mesi tylene

ni trobenzene

e thy lbenzene

styrene

o-methylstyrene

p-methylstyrene

ALIPHATICS

8.2

14.2

4

3.211

3.727

2.437

2.695

7.855

7.855

6.629

7.21

8.371

8.629

7.466

6.436

2.179

13.7

n-hexane 0 -0.6

1 ,2-dichloroethane 16.7 13.5

1 , 1-dichloroe thane 10.306

dichlorome thane 20.4 12.5 22.,4

1,1 ,2,2-tetrachloroethane 9.403

1 ,2-dimethoxyethane 10.2 8.8

bromoethane 7.984

1-chloropropane 7.726

1 ,1 ,1-trichloroethane 6.178

tr ichlor o ethylene 5.791

tetr achloro ethylene 5.791

carbon tetrachloride 8.6 1.4 9.,6

chloroform 23.1 9.9 19 .4

cyclohexan* -0.272

eyclohexene 1.147

n-heptane

NITRO COMPOUNDS

2-ni tropropane

ni tromethane

ni troethane

ni trobenzene

14.692

20.5 19.3

15.724

14.8 13.7

99

10.7 11.1

9.3 8.6

8.5

16.885

7.855

12.241

6.629

11.933

TABLE A-2 (continued)

NITRILES

acetonitrile 18.9 18.8

propioni trile 15.853

acryloni trile 19.723

n-butyroni trile 15.079

benzonitrile 13.5 13.7

phenylacetoni trile 14.821

i so-bu tyroni trile

tert-butyl nitrile

cyclohexyl nitrile

NITRATE

isopropylni trate 15.079

ESTERS

methy lacetate

ethylacetate

uinylacetate

methylacrylate

propylacetate

ethylf ormate

ethylbenzoate

dimethylphthalate

methyl chloroacetate

methyl dichloroacetate

methyl propionate

ethyl propionate

ethyl chloroacetate

methyl isobutyrate

ethyl acrylate

methyl methacrylate

methyl formate

methyl benzoate

LACTONES

B-propionlactone

4-butyrolactone 16.627

E-caprolactone

KETONES

acetone 12.5 13.9

methylethylketone 12.737

3,3-dimethylbutanone 9.79

difttylkfttonft 10.177

mftthylpropylkfttone 12.499

di isopropylketone 9.403

di isobutylketone 6.5

4-heptanon* 9.661

isopropylmethylketone 12.241

cyclopen tanone 10.306

cyclohexanone 10.822

100

TABLE A-2 (continued)

azetophenone 12.737

2-hexanone 11.209

4-methyl-2-pentanone 10.3C6

cyclobutanone

cyclohep tanone

methyluinyl ketone

i sophorone

camphor

isopropyl methyl ketone

tr i chloro acetone

dime thyl-G-py rone

benzophenone

biacetyl

di-ter t-bu tyl ketone

ETHERS

diethylether

di isopropylether

di-n-butylether

1 . 2-dime tho xyethane

am sole

propyleneoxide

di glyme

f uran

tetrahvdrofur an

1 ,4-dioxane

1 , 3-dioxolane

phenatole

di-n-propyl ether

ethyl butyl ether

ethyl uinyl ether

n-butyl uinyl ether

isobutyl vinyl ether

diallyl ether

epichlorohydrin

styrene oxide

3,3-bi schloromethyloxetane

2-me thy1-1 ,3-dioxalane

4-me thy1-1 ,3-dioxalane

2-phenyl-l ,3-dioxalane

4-chloromethyl-l ,3-dioxalane

dibenzyl ether

diphenyl ether

oxepane

2-methyltetrahydrofuran b.o*>3

ALDEHYDES

acetaldehyde

prop ion aldehyde

butyraldehydft

acrolein

crotonaldehyde

benzaldehyde

3.9 4.1

3.34

2.566

10.2 8.8

7.468

10.822

9.9 9.3

3.3

6 7.7

10.8 5.9

15.079

6.436

101

TABLE A-2 (continued)

AMINES AND DERIVATIVES

oietnyiamine 9.4 5.1

tr i ethylami ne 1.4 2.4

di l sopropylamine 2.437

ter t-butylamine 6.952

aniline 16.627

ethylenediamine 20.9 13.7

n-methylaniline 14.305

n-n-dimethylanil ine 8.5

pyridine 14.2 11.3

2-methylpyridine 8.887

2,6-lutidine 6.823

1-formylpiperidine 5.275

piperidine 5.017

cuinoline 10.306

n-methyl-2-pyrrolidone 13.3 13.9

2-chloropyr idine 13.531

dimethylethvleneurea 14.305

tetramethylurea 12.37

ammonia

ethyl am ine

n -propyl amine

di -propylamine

a-picoline

-pi coline

4-ethylpyr i dine

o-tolui dine

4-wi nylpyr idine

N-methyl-E-capro lac tarn

2-methylpyr idi ne4nethylpyr idine

N-methylpyrrol idine

2,6-dimethylpvridine

2,4,6-trimethylpyridine

N-i sopropyl-2-pyrrol idine

dimethylpropyleneurea

3,5-dichloropyr idine

3-bromopyr idine

4-dimethylaminopyr idine

tr i-butylamine

N,N-dimethylbenzyl amine

IMINES

ethylenimine

N-phenylethylenimine

AMIDES

f ormami de

n-me thy If ormami de

n-me thyl ace t amide

n ,n-dime thyIf ormami de

n rn -d i me thyl ace t amide

hex ame thylp ho spho amide

39.8 32.5

32.1 29.3

26.56

16 16

13.6 15.6

10.6 12.2

102

TABLE A-2~(coutiuued)

N,N-di ethyl formamide

N,N-aiethv lace t amide

N-methylpy rroli done

dimethyltri f luoroacet ami de

dimethylchloroacetamide

SULFIDES

carbondisulf ide 1.534

SULPHOXIDES, 3ULPHONES AND SULFITES

dimethylsulfoxides 19.3 12.5

sulfolane 19.2 16.2

tetramethyl sulphone

di-butyl sulphoxide

diphenyl sulphoxide

dimethyl sulfite

diethyl sulfite

ethylene sulf i :e

SULFONIC ACIDS

methanesulf onicacid 126.3

ACID AND DERIVATIVES

formic acid 83.6

acetic acid 52.9

trif luoroacet icacid 105.3

acetic anhyande

acetyl chloride

benzoyl chloride

benzoyl fluoride

CAR9CNATES

ethylenecarbonate 22.174

propylenecarbonate 18.3 19.6

dimethylcarbonate 12.499

diethylcarbonate 6.178

di chloroethylene carbonate

tetrachloroethylene carbonate

propanediol-1 ,2-carbonate

PHOSPHOROUS COMPOUNDS

tr imethylphosphate 16.3 15.7

triethylphosphate 13.273

tri-n-propylphosphate 11.725

tri-n-butylphosphate 9.9 10.6

tr ipiper idinophosphine oxide

tr ipyrrol idmophosphine oxide

tr iphenylphosphine oxide

tr imethylphosphine oxide

103

TABLE A-2 (continued)

ALCOHOLS

methanol

ethanol

n-bu tanol

n-amyl alcohol

1-hexanol

1-hep tanol

1-octanol

1-decanol

1-dodecanol

2-propanol

2-butanol

2-pen tanol

3-pen tanol

i sobutylalcohol

isoamyl alcohol

cyclopen tanol

cyclohexanol

t-butyl alcohol

t-pentyl alcohol

1-propanol

2,2,2-trifluoroethanol

2,2.3,3-tetrafluoro-l-propanol2,2,2-trichloroethanol

2-propen-l-ol

2-ami noethanol

2-chloroethanol

2-ethoxyethanol

2-methoxy ethanol

2-n-butoxy ethanol

benzyl alcohol

2-hydroxymethyl tetrahydrofuran

1-phenyl ethanol

2-phenyl ethanol

3-phenyl-l-propanol

1,2,3-propantriol

1 ,2-ethanediol

1 ,2-propanediol

1 ,3-propan*diol

1 ,3-butanediol

diethylene glycol

triethylene glycol

water

deuterium oxide

41,,3 31.1 43.7

37,.1 26.4 38.4

36.,8 24.2 35.9

22.619 34.3

22.432 33.8

22.045 33.4

21.787 33.1

20.884 32

19.723 30.7

33,.5 22.2 33.5

20.239 31.3

19.465 30.4

18.433 29.2

22.69 34.1

22.69 34.1

21.013 32.2

19.207 30.1

27,,1 16.1 26.6

13.531 23.6

37,,3 24.9 36.6

33,,5 36.2 49.7

36.106 49.5

32.494 43.5

26.689 38.7

33,,7 26.3 38.3

25.27 37.1

26.947 39

24.236 35.9

25.012 36.8

24.367 36

19.723 30.7

23.335 34.9

22.045 33.7

33.01 46

32.107 44.9

29.269 41.7

30.301 42.9

27.592 39.7

28.882 41.2

28.495 40.8

54,,6 40.9 55

40.492 54.6

104

TABLE A-2 (continued)

INORGANIC HALIDES

sulphuryl chloride

thionyl chloride

felenium oxychloride

phosphorous oxychloride nphenylphos'c difluoride

phenylphos'c dichloride

di phenylphos'c chloride

a Experimental AN values from Gutman (21)

b AN (a) values are calculated from E_(30) using

equation [34] from Schmid (24)

c AN (c) values are calculated from E (30) using

alcohol and chlorinated hydrocarbon correlation

equation.

105

TABLE A-3

LIST OF DN VALUES AND DN ERROR

Compound

AROMATICS

a Nb c d e f gexp 4^ D[1I,I B -*H.r Beta Ave DN Error

n-hex an*

benzene

toluene

HAL IDES

chlorobenzene

bromobenzene

1 ,2-dichlorobenzene

chloroform

carbon tetrachloride

di chlor omethane

1 ,2-dichloroethane

1 ,1-di chloroe thane

NITRO COMPOUNDS

ni tr omethane

ni troethane

ni trobenzene

NITRILES

acetonitrile

propioni trile

acryloni trile

n-butyroni trile

benzoni trile

phenyl ace toni trile

ESTERS

3.2

3

3.4

3.8

3.5

3.5

3.9

3.2

3.06 3.3 0.3fl

3.444 3.6 0.23

2.6 2.2 1.908 2.2 0.35

2.6 2.2 1.524 2.2 0.64

0.8 0.8

0.4 7.4 3.5 5.52

1.2 -1.4 -1.3 0.76

0.6 1.2 1.450 1.1 0.44

3.4 2.9 3.2 0.35

0.6 0.6

2.7 4.2 10.7 4.6 6.648 6.2 3.33

4.6 5 4.8 0.28

4.4 7.2 7.5 3.7 8.169 14.19 7.5 3.73

14.1 12.8 14.1 13.2 14.57 11.12 13.3 1.26

16.1 13.4

10.4

13.4 14.72 14.4

10.4

1.29

16.6 14.76 15.7 1.11

11.9 10.6 12 13.28 14.96 12.6 1.65

15.1 13.59 14.3 1.07

methyl acetate 16.3

ethyl acetate 17.1

methyl chloroacetate

vinyl acetate

methyl acrylate

thyl formate

thyl benzoate

4-butyrolactone

KETONES

10.2

10.8

8.4

7.Z

9

16.3

10,

10,

17.80

18.52

15.34

16.5

17.38

14.78 14.96

14

14.8

6.4

7.2

9

17.4

14.9

16.3

3.56

3.65

0.12

acetone 17 15.9 17 18.65 17,,65 17.2 1.01

methyl ethyl ketone 14.5 14.3 18.66 17,.65 16.3 2.21

diethyl ketone 14.3 12.6 17.67 14.9 2.56

cvclopentanone 19.01 19,,16 19.1 0.12

cyclohexanone 16.3 18.7 18.73 19,,57 18.3 1.41

acetophenone 14.3 14.1 18.25 18,,03 16.2 2.28

di-isopropyl ketone 16.37 16.6

isopropyl methyl ketone 18.34 16.3

106

TABLE A-3 (continued)

Compound exp ^ D[II,1] B -*HgfBeta Ave DN Error

ETHERS

diethyl ether 19.2 16.7 18,,1 19,,36 17.26 18.5 0.86

di-n-propyl ether 17.7 19.,53 16.68 16 1.36

di-isopropyl ether 18.1 18,,80 18.03 18.3 0.43

1 ,2-dimethoxyethane 17.3 17.3

anisole 8.2 7,.9 7.668 7.9 0.27

phenetole 6 6.9 7.5 0.78

propylene oxide 14.9 14.9

furan 3.8 4,,3 4.1 0.35

tetrahydrofuran 20 21.1 19.56 20,,6 22 ,39 20.34 20.7 1

1 , 3-di oxalane 14.7 14.7

1,4-dioxane 16.5 28.5 18 18.14 13.42 19.3 5.54

AMINES

tr i ethyl ami ne 61 50.7 53.5 34.24 26,.46 45.2 14.31

aniline 34.7 33.3 34 0.99

N-rnethylaniline 33.3 33.3

N,N-dimethylaniline 32.7 27.28 30 3.83

pyridine 33.1 36.7 32,.2 43 32.21 35.4 4.61

2-picoline 39.7 32.95 36.3 4.77

piper idine 51 51.1 28,,5 48.7 44.8 10.94

quinoline 30,,4 30.4

2,6-lutidine 24.30 24.3

39.9 32 11.24

24.5 27.7 25.1 27.63 25.71 26.2 1.33

25.7 27.4 28.05 28.40 27.5 1.06

35.19 28.78 30.4 4.19

24.61 24.6

27.14 29.17 28.2 1.44

AMIDES

formamide 24

N,N-dimethylformamid 26.6

N,N-dimethylacetamid 27.6

N-methyl-2-pyrrolido 27.3

dimethylethyleneurea

tetramethylurea

SULFOXIDES

dimethyl sulphoxide 29.8 31.3 30.1 26.28 28.40 29.2 1.92

tetramethyl sulphone 14.6 12.21 13.5 1.83

di-n-butyl sulphoxide 26.87 31.09 29 2.98

ALCOHOLS

methanol

ethanol

n-butanol

tert-butanol

2-propanol

2-phenyl ethanol

ethylene glycol

benzyl alcohol 1S-42 18.42

19 32.5 12 23.02 21.6 8.56

20 30.9 6.5 28.78 21.5 11.09

29.3 24 33.01

38.00

33.7

22.64

19.18

26.8

38

35.7

22.6

19.2

4.53

107

TABLE A-3 (continued)

Compound

CARBONATES

ethylene carbonate

propylene carbonate

dimethyl carbonate

diethyl carbonate

PHOPHATES

<P t\ DC II, I] 6-&Hfif

Beta Ave DN Error

16.4

23trimethyl phosphate

triethyl phosphate

tri-n-butyl phosphat 23.7

hex ame thyl phosphor amide

16.4

15.56 15.6

16.46 16.5

17.35 17.4

20.92 27.25 23.7 3.23

28.76 26.6

23.7

38.1 39.54 38.8 1.02

a DN experimental values

b DN values are calculated from equation [45]

c DN values are calculated from equation [46]

d DN values are calculated from equation [49]

e DN values are calculated from equation [48]

f DN values are calculated from equation [47]

g Average DN values

h DN error

* All of these DN values are obtained from Peter

Michelsen

108

TABLE A-4

LIST OF AN, DN, AND Sd

a bedSOLVENT AN ON S

d

HYDROCARBONS

1. n-hexane 0* 3.2 7.3

2. c-hexane o 0 7.3

3. benzene 8.2*3.3 9

4. toluene 3.2 3.6 8.8

S. 1,2-dimethylbenzene 3.7 3.6 8,7a6. 1,3-dtmethylbenzene 2.4 3 8.7

7. 1 .3,3-trimethylbenzene 2.2IO*

8.8

HALIDES

8. 1,2-dichloroethane 16. 7* 3.2 9.3

9. 1 ,1-dichloroethane 10.3 0.6 8.1

10. dichloromethane 22.4 1.1 8.9

11. carbontetrachlor ide 9.6 1.3 8.7

12. chloroform 19.4 3.S 8.7

13. bromobenzene 7.9 2.2 10

14. chlorobenzene 7.9 2.2 9.3

15. f luorobenzene 8.63+

(8.6)16. iodobenzene 8.4

4"*"

(9.1)17. 1 ,2-dichlorobenzene 8.6 0.8 9.4

NITRO COMPOUNDS

18. nitromethane 20.5 6.2 7.7

19. nitroethane 15.7 4.8 7.8

20. nitrobenzene14.8*

7.5 9.8

NITRILES

21. acetonitrile18.9*

13.3 7.5

22. propionitrile 15.9 14.4 7.5

23. acrylonitrile 19.7 10.4 8

24. n-butyroni trile 15.1 15.7 7.5

25. benzonitrile 13.3*

12.6 8.5

26. phenylacetonitrile 14.8 14.39.2*

ESTERS*

27. methylecetate 10.7*

14 7.6

28. ethylacetate9.3X

14.8 7.7

29. vinylacetate 8.5 7*2* (7.5)30. propylacetate 7.9 16* (7.5)

31. ethylbutryate 9.1 16.8 (7.5)32. methylacrylate 16.9 9 (7.7)

33. ethviformate 12.2 17.4 7.6

34. ethylbenzoate 8.6 14.9 8.9 *

109

TABLE A-4 (continued)

35. methylchloroacetate

36. 4-butyrolactone

KETONES

37. 2-propanone

38. 2-butanone

39. 3-pentanone

40. di isopropylketone

41. 3-methyl-2-butanone

42. cyclopentanone

43. cyclohexanone

44. acetophenone

ETHERS

45. diethyl ether

46. diisopropyl ether

47. dipropyl ether

48. dl-n-butyl ether

49. dimethoxyethane*

50. phenylmethyl ether

51. propylene oxide

52. furan

53. tetrahydrofuran

54. 1,4 dioxalane*

55. 1,3 dioxalane*

56. phenylethyl ether

AMINES

57. t-butylamine

58. diethylamine

59. trierhylamine

60. ethylenedi amine*

61. aniline

62. N-methylaniline

63. N,N-dimethylaniline

64. 2-chloroaniline

65. pyridine

66. 2-picollne

67. 2,6-lutidine

68. piperidine

69. qulnoline

AMIDES*

70. formamide

71. N-me thyl formamide

72. N,N-dimethylformami de

73. N,N-dimethylacetamide

74. N-methyl-2-pyrrolidone

75. 1-formylpiper idine

76. dimethylethylurea

77. tetramethylurea

SULFIDES

78. carbondisulfide 1*5 3.8 10

13.7 8.4 (8.5)16.6 16.3 9.3

12.5*

17.2 7.6

12.8 16.3 7.8

10.2 14.9 7.7

9.4 16.6 (7.4)

12.2 18.3 (7.4)(8.6)10.3 19.1

10.8 18.3 8.7

12.8 16.2 9.6

3.9* 18.5 7,1a

3.3 18.3.6.7*

3.318+ (7.2)

2-6^ 18.1 7.4

10.2*

17.3 7.7

7.5 7.9 8.7

10.8 14.9 (7.4)3.3* 4.1 8.78*

20.7 8.2

8.4 19.3 9.3

15.1

6.4

14.7

7.5 is! 6)

7rf+

57.5 (7.5)

9-< 50 + 7.3*

1.4*

45.2 (7.3)20.9* 55+ ( 8)16.6 34 9.5

14.3 33.3 9.3*

8.5 30 8.9*

18.2 31+ (9.3)14.

2X35.4 9.3

6.9 36.3 (9.7}6.8 24.3 (10. 1)5 44.8

B.6A

10.3 30.4 9.5

39.8*

32+

49+8.4

32.1* 8.4*

16*-26.2 8.5

13.6* 27.5 8.2

13. 3* 30.4 8.85.3 28.6 (8.8)14.3 24.6

12.4 28.2 8.2

110

TABLE A-4 (continued)

SULFOXIDES

79. dimethyl sulfoxide

80. tetramethylene sulfone*

81. dibutyl sulfoxide

CARBONATES*

82. ethylene carbonate

83. propylene carbonate

84. dimethyl carbonate

85. diethyl carbonate

PHOSPHATES*

86. trimethyl phosphate

87. triethyl phosphate

88. tri-n-butyl phosphate

89. hexamethyl phosphoramid

ALCOHOLS

90. methanol

91. ethanol

92. 2-propanol93. 1-butanol

94. 2-methyl-2-propanol95. 1-pentanoi

96. 3-methyl-l-butanol97. 2-methyl-l-butanol98. 1-octanol

99. cyclohexanol

100. benzyl alcohol

101. 2-phenyl ethanol

102. ethylene glycol*

103. glycerin

104. water

MISCELLANEOUS

105. benzaldehyde

106. acetic anhydride

a * indicates multiple interaction sites.

b AN values calculated from Table A-2, those with X

indicate experimental values.

c DN values from Michelsen (29) in Table A-3, those with

+ from Marcus (30).

d 8j values from Barton (15), values in parenthesis

were approximated using van Krevelen's additivity

values (18), values with A from Beerbower (35).

19.3*

29.2 9

19.2X

13.5

9 29 (7.3)

22. 2V 16.4 9.5

18.3X

15.6 9.8

12.5 16.5 (8.5)6.2 17.4 8.1

16.3X

23.7 8.2

13.3 28.8 8.29.9* 23.7 8

11.4 38.8 9

41.3*21.6 7.4

37.1*21.5 7.7

35.5* 35.7 7.736.8*

28.8 7.827.1* 38 (7.3)34.3 26.2 7.8

34.1 32 (7.6)

(7.5)31.1 32

33.1 32 7.7

30.1 25 8.5

36.8 18.4 9

34.9 22.6 (8.9)44.9 19.2, 8.3

46 19+8.5

54.8*

33 7.6

28 16+ ^lV16.1 10.5 7.8*

111