Hydrogen bonding

Journal of Chromatography, 587 (1991) 213-228 Elsevier Science Publishers B.V., Amsterdam

CHROM.

23 484

Hydrogen bonding XVI. A new solute solvation parameter, T$, from gas chromatographic data Michael H. Abraham* and Gary S. Whiting Department

of Chemistry,

University

College London, 20 Gordon Street, London

WCIH

OAJ (UK)

Ruth M. Doherty Naval Surface

Warfare

Center, White Oak Laboratory,

Silver Spring, MD 20910 (USA)

Wendel J. Shuely US Army Chemical Research,

(First received

February

Development

and Engineering

19th, 1991; revised manuscript

Center, Aberdeen Proving Ground, IUD 21010 (USA)

received May 23rd, 1991)

ABSTRACT The general

solvation

equation,

log v”, (or log L) = c + rR,

+ szt

+ aay + b#

+ I log L16

has been used to set up a new ny parameter of solute dipolarity-polarisability, mainly through the extensive data of McReynolds and Patte et al. Values of xy are tabulated for several hundred solutes, and two simple rules have been formulated to enable rrt to be estimated for many types of aliphatic functionally substituted compounds. A coherent set of effective solvation parameters, ,?Y<, Zay, .@, and also R, and log L16, allows the application of the general solvation equation to the characterisation of any gas-liquid chromatographic stationary phase.

INTRODUCTION

Previously, we have shown [l-3] that processes in which a solute is distributed between the gas phase and some condensed phase can usefully be described through the general solvation equation log SP = c + rR2 + SIG + aa: + bfi? + 1 log L16 (1)

Such processes include the solubility of a series of gaseous solutes in a given solvent [2], and chromato0021-9673/91/$03.50

0

1991 Elsevier Science Publishers

graphic processes in which retention data are obtained for a series of compounds on a given stationary phase, at some constant temperature [3]. As regards gas-liquid chromatography (GLC), the dependent variable in eqn. 1 can be log L (or log K), where L (or K) is the Ostwald solubility coefficient or gas-liquid partition coeffkient, log Vo, where Vo is either the specific retention volume referred to 273 K or the specific retention volume at the column temperature, or even log z, where r is the adjusted relative retention time [3]. All these dependent variables will give rise to the same values of

B.V. All rights reserved

M. H. ABRAHAM

214

r, s, a, h and I in eqn. 1, but will yield different values of the constant term. The explanatory variables in eqn. 1 are R2, an excess molar refraction that can be determined experimentally [l], x5, the solute dipolarity-polarisability, to which we shall refer later, a?, an experimentally determined solute hydrogenbond acidity [4], 07, an experimentally determined solute hydrogen-bond basicity [5], and log L16, where L” is the solute Ostwald solubility coefficient on hexadecane at 298 K [6]. Of course, values of R2, cc:, /3y and log L16 can be obtained through various approximations and estimations, all based on the original experimentally determined values. There are, however, difficulties with the solute parameter n;. Originally [7,8] 71; was taken as identical with the Kamlet-Taft solvatochromic solvent parameter rc; for non-associated liquids only. As rc; is experimentally accessible only for compounds that are liquid at 298 K, values of n; had then to be estimated not only for all associated compounds (including acids, alcohols, phenols and amides), but also for all compounds that are solid (or gaseous) at 298 K. In addition, there is present the inherent assumption that n; is identical with 7~; for non-associated liquids. We know that the KamletTaft solvatochromic solvent basicity parameter PI is not exactly equivalent to the solute parameter fly even for non-associated liquids [9], and it is possible that although n; can be taken as equal to 7~: for non-associated liquids as a generality, there may be a number of exceptions to this rule. Tt seems necessary to set up a scale of solute dipolarity-polarisability based on some experimental procedure that will include, at least in principle, all types of solute molecule. The main purpose of this paper is to use the extensive sets of GLC data of McReynolds [lo] and Patte et al. [ 1 I] to construct a new solute dipolarity-polarisability scale r$ for use in eqn. 1. At the same time, we shall set out an updated list of solute parameters that can be used in eqn. 1 to characterise GLC stationary phases and to interpret GLC retention data. Since this work was started, Li et al. [12] have also concluded that the n: scale derived from 71; is not very suitable for use in solvation equations such as eqn. 1, and have constructed an alternative rc; scale of solute dipolarity. We shall refer to this scale later.

er (II.

RESULTS

McReynolds [lo] determined Vg values for up to 376 solutes on up to 77 stationary phases. Nearly all the phases were examined at a common temperature of 120°C. Of these 77 phases, 75 were found [3] to have no hydrogen-bond acidity at all, hence the h$j term in eqn. 1 drops out, and the log po values can be correlated by the equation log JJ$~= c + rR2 + sn; + acxy + llogLr6

(2)

We thus have a series of equations (n = l-75). one for each stationary phase, where the constants c, r, s, a and I have been determined by multiple linear regression analysis (MLRA), using known values of the solute parameters Rz, n$. cc’:and log L’” for as many solutes as possible. Typically, around 150 solutes were included in each regression eqn. 2, generalised as log V&

= c, + rnRz + s&

+ a,&’ -t I,, log L” (3)

It is convenient to subsume the constant dependent variable to give 75 equations: V,,-,

= r,_1R2 + s,-~x;

+ a,-lay

c, into the

-I- I,,_rlogL1” (4)

where v, = log V&) - c,

(5)

We can now use the matrix defined by eqn. 4 in a vertical format, by regarding V,, for a given solute as the dependent variable and the constants r,, sn, a, and 1, as four explanatory variables. In this new (vertical) MLR equation, R2, TC;,c&!and log Lr6 for the particular solute now become the unknown coefficients to be evaluated by MLRA. As all the input data are now related purely to properties of the solute, we can replace zn*,with an experimentally determined parameter, n’.j: V(solute) = V, = Rzrn + T$S, + c$a,, + log L16 1, (6) We carried out an analysis using eqn. 6, where the regression equation was forced through the origin, and obtained reasonable values of RZ. ET, a! and log Lt6 for the various solutes studied. However, as R2

HYDROGEN TABLE

BONDING.

XVI.

215

I

SOME CALCULATED

PARAMETERS

USING

EQN. 7

Solute

H =2

a!

Log L’6

Pent- 1-ene

0.09 * 0.004 0.08”

0.00 & 0.007 0.00”

2.040 ) 2.013”

Toluene

0.47 ) 0.004 0.55’

+ 0.007 -0.01 0.00”

0.27 _+ 0.004 ti.27”

-0.02 f 0.00”

0.004

Diethyl

ether

Butanone

n-Propyl

S.D.

0.007

36

0.014

3.327 f 3.344”

0.008

73

0.017

0.007

1.975 f 2.061”

0.008

71

0.017

0.00 i 0.00”

0.007

2.282 f 2.287”

0.007

71

0.016

0.61 + 0.004 0.55”

0.00 f 0.00”

0.007

2.847 + 0.007 2.878”

73

0.016

0.41 + 0.009 0.40”

0.37 + 0.006 0.33”

2.060 & 0.006 2.097”

72

0.016

0.69 f 0.67” acetate

Propan-l-01

’ Previous

n

values,

see ref. 1.

is either known or can easily be calculated for any solutd, we can reduce the number of explanatory variables by incorporating R2 into the dependent variable: log VOCC”, - C” - rnRz = V’ = djs, + crya, + log L161,, (7) Again, the regression eqn. 7 is constrained to pass through the origin; we found that the results were much more self-consistent than when a constant -term was allowed to float. We can check results using our preferred eqn. 7 by comparison of calculated solute parameters with known values, where available. Some typical results are given in Table I together with the standard deviation (S.D.) of the parameter, the number of stationary phases in the set (always less than 75, because not all solutes were examined on all phases by McReynolds), and the overall S.D. of the dependent variable V’. We do not give correlation coefficients because these have little meaning for a regression equation forced through the origin. There are a number of deficiencies in McReynolds’ data, especially those connected with inter’ Like the molar refraction is almost

an additive

itself, R2, an excess molar refraction, quantity.

facial adsorption, and it is clear that for certain combinations of solute and stationary phase, the retention data are inexact owing to sorption at the liquid interface. Hydrocarbons in very polar phases are a particularly well known example. We point out, however, that our vertical or “inverse” MLRA procedure yields solvation parameters that are effectively averages for a given solute over 30-70 stationary phases (see Table I). In the event, hydrocarbons such as alkanes and alkenes behave normally in our inverse MLRA (see Table II). We list in Table II the rc: values that we obtained through eqn. 7. We note that the n’: values in Table II are effective r&j’values for a situation in which a solute molecule is surrounded by an excess of solvent molecules, and so may be more correctly denoted as Crcy. Before discussing these 7~‘: values, we first analyse the extensive GLC data of Patte et al. [I I]. Patte et al. [ll] obtained retention data for 240 solutes on live stationary phases. All these phases are non-acidic, and so we obtained [l] five regression equations of the following type, one for each phase: logL’=~+rR~+m~+acc~+1logL’~

(8)

In eqn. 8, log L’ = log L - log L(decane), but this affects only the constant in the regression equations. We cannot apply the “reverse” MLRA we used for the McReynolds data set, because we would have

II

VALUES

Ethene Propene But-I-ene Pent- 1-ene Hex- 1-ene Hept- 1-ene Ott-I-ene cis-Ott-2-ene 2-Ethylhex-1-ene a-Pinene

Alkenes

Ethane Propane Butane 2-Methylpropane Pentane Hexane 2$Dimethylbutane Heptane 2,4_Dimethylpentane Octane 2-Methylheptane 3-Methylheptane Nonane 2,2,5_Trimethylhexane Decane Undecane Dodecane Tridecane Tetradecane Hexadecane Octadecane Cyclohexane Hydrindane Decalin

Alkunes

Compound

CALCULATED

TABLE

0.09

0.05 0.07 0.05

0.03

0.03

0.01

0.02 -0.01

Eqn. I

H “2

0.14 0.22 0.27

0.08 0.19 0.23

0.32 0.25 0.21 0.19 0.11 0.11 0.09 0.12 0.13 0.18

-0.01 -0.02 0.03 -0.04 -0.03

-0.13 -0.09 ~ 0.05 - 0.05 0.00 0.06 0.08 0.11 0.16 0.30

0.01 -0.02 0.00 0.01 0.03 0.00

0.03 -- 0.04 0.03 0.08 0.07 0.03 0.16 0.03 0.03 0.03 0.03 0.03

Eqn. 8

0.11 0.08 0.05 0.07 0.03 0.02

16

0.03 0.03 0.03 0.07 0.03 0.03

Eqn.

OF n; AND LOG L16 VALUES

0.289 0.946 1.491 2.047 2.572 3.063 3.568 3.683 3.510 4.200

0.492 I.050 1.615 1.409 2.162 2.688 2.495 3.173 2.809 3.671 3.480 3.510 4.182 3.530 4.686 5.191 5.696 6.200 6.705 1.714 8.722 3.007 4.530 5.077

Log L’b

Dibutyl ether Dipentyl ether Di-3-methylbutyl ether Dihexyl ether Di-2-ethyl- 1-butyl ether Methyl propyl ether Methyl butyl ether Methyl 2-methylpropyl ether Methyl tert.-butyl ether Ethyl butyl ether Ethyl [err.-butyl ether Propyl isopropyl ether Isopropyl lert.-butyl ether Bis(2-ethoxyethyl)ether Ethyl vinyl ether Butyl vinyl ether 2-Methylpropyl vinyl ether 2-Ethyl-1-hexyl vinyl ether 2-Methoxyethyl vinyl ether Diallyl ether Ethylene oxide 1,2-Propylene oxide 1,2-Butylene oxide a-Methyl- 1,2-propylene oxide Iruns-2,3-Butylene oxide ck-2,3-Butylene oxide 1.3-Propylene oxide 1,3-Butylene oxide Furan 2-Methylfuran 2-Acetyl-3-methylfuran 2-Acetyl-5-methylfuran 2-Propanoyl-3-methytfuran Tetrahydrofuran 2-Methyltetrahydrofuran 2,5_Dimethyltetrahydrofuran 1 ,&Dioxane

Ethers (contined)

Compound

0.55 0.47 0.38 0.75

0.24 0.27 0.21 0.27 0.17 0.30 0.30 0.25 0.29 0.26 0.20 0.19 0.16 0.79 0.37 0.34 0.29 0.32 0.68 0.38 0.59 0.57 0.55 0.52 0.52 0.55 0.61 0.52 0.54 0.50

Eqn. 7

n:

0.69

1.17 1.19 0.91

0.39

0.16

Eqn. 16

0.74

0.51

0.18

Eqn. 8

2.636 2.820 2.980 2.892

3.924 4.875 4.538 5.938 5.421 2.090 2.630 2.442 2.378 2.989 2.611 2.771 2.896 4.592 1.910 2.970 2.746 4.682 2.932 2.430 1.371 1.775 2.350 2.050 2.140 2.290 2.086 2.360 2.140 2.430

Log L’b

K

k rh

k

k

s:

g

Ethers Dimethyl ether Diethyl ether Dipropyl ether Diisopropyl ether 0.36 0.27 0.23 0.16 0.19

0.65 0.69

Haloaromatics 1,ZDichlorobenzene Benzylchloride

0.53 0.57 0.56 0.63 0.60 0.61 0.64

0.25 0.28 0.35 0.32 0.27 0.34 0.62 0.30 0.30 0.33 0.35 0.38 0.40 0.41 0.41

0.70 0.55

0.50 0.48 0.47

0.48 0.47 0.47 0.50 0.47 0.46

0.66 0.65 0.35 0.74

0.30

0.17 0.19 0.16

Aromatic hydrocarbons Benzene Toluene Ethylbenzene o-Xylene m-Xylene p-Xylene 1,3,5-Trimethylbenzene 1,2-Diethylbenzene 1,3-Diethylbenzene 1,CDiethylbenzene Styrene Phenylethyne

Haloaliphatics 1-Fluorooctane Dichloromethane Trichloromethane Tetrachloromethane 1,2-Dichloroethane 1,1,2,2-Tetrachloroethane 1-Chlorohexane Trichloroethene Hexachlorobutadiene Bromoethane 1-Bromopentane 2-Bromooctane Iodomethane 1-Iodobutane 2-Iodobutane l,l-Difluorotetrachloroethane 1,2-Difluorotetrachloroethane

Alkynes But-Zyne Ott- 1-yne Ott-2-yne

0.27

0.70 0.78

0.55 0.68

0.47 0.46 0.46 0.43 0.46 0.46 0.46

0.33

0.42 0.39 0.28 0.44 0.39 0.39

0.36 0.35 0.55 0.65 0.36 0.33

0.37 0.23 0.31

1.285 2.015 2.954 2.482

4.489 4.320

2.803 3.344 3.789 3.942 3.864 3.836 4.316 4.690 4.680 4.680 3.863 3.715

2.120 3.611 5.110 2.106 3.628 3.390 2.970 3.000

3.850 2.019 2.480 2.823 2.573 3.803 3.710 2.997

1.856 3.480 3.850

Aldehydes Formaldehyde Acetaldehyde Propanal Butanal 2-Methylpropanal Pentanal 2-Methylbutanal 3-Methylbutanal 2,2_Dimethylpropanal Hexanal Heptanal Octanal

Tetrahydropyran 3,CDihydropyran Trioxane Trimethyltrioxane (paraldehyde) 2-Methyl-2-ethyl1,3-dioxolane Anethole Dimethoxymethane Methoxyethoxymethane Methoxyisopropoxymethane Diethoxymethane Ethoxypropoxymethane Ethoxyisopropoxyrnethane Ethoxy-sec.-butyloxymethane Dipropyloxymethane Propoxy-sec.-butyloxymethane Diisopropoxymethane Dibutyloxymethane Diisobutyloxymethane Di-sec.-butyloxymethane l,l-Dimethoxyethane l,l-Diethoxyethane 1,l -Dipropoxyethane 1,l -Diisobutyloxyethane 1, I-Dimethoxypropane 1,l -Diethoxypropane 1, 1-Dimethoxybutane 1,l -Dimethoxy-2-methylpropane 2,ZDimethoxypropane 2,ZDiethoxypropane 1,1,3_Trimethoxybutane Methyl phenyl ether 1,8-Cineole

0.73 0.70 0.65 0.63 0.58 0.63 0.58 0.60 0.49 0.64 0.65

0.52 0.49 0.45 0.45 0.44 0.41 0.41 0.42 0.40 0.37 0.43 0.37 0.37 0.49 0.41 0.37 0.26 0.46 0.38 0.47 0.42 0.43 0.32 0.69

0.49 0.51 1.02 0.68 0.58

0.59 0.58 0.57

0.62

0.63 0.59 0.61 0.59

0.73 0.47

1.02

0.730 1.230 1.815 2.270 2.120 2.851 2.733 2.620 2.406 3.370 3.860 4.380 (Continued on p. 218)

0.59 0.59 0.57

0.58

0.65 0.62 0.61 0.59

0.70

1.894 2.371 2.691 2.789 3.280 3.093 3.609 3.762 4.037 3.376 4.726 4.331 4.380 2.334 3.066 3.964 4.491 2.841 3.498 3.313 3.148 2.699 3.304 3.962 3.859 4.290

c! .,

r ”

3

$

2

5

3.169 2.650 3.337

is

X

2.910

3.057

II (contimed)

Ketones Propanone Butanone Pentan-2-one Pentan-3-one 3-Methylbutan-2-one Hexan-2-one Hexan-3-one 3-Methylpentan-2-one 4-Methylpentan-2-one 3,3-Dimethylbutan-2-one Heptan-2-one Heptan-3-one Heptan-$-one 4,4-Dimethylpentan-2-one 2,4-Dimethylpentan-3-one Octan-2-one Nonan-2-one Nonan-S-one Decan-Zone Undecan-2-one Dodecan-2-one Cyclopentanone Cyclohexanone Cycloheptanone

Aldehydes (continued) 2-Ethylhexanal Prop-2-ene- 1-al (acrolein) tram-But-2-ene-l-al 2-Methylprop-2-ene-l-al (methacrolein) trans-Hex-2-ene-l-al 2-Ethylbut-2-ene-l-al trans-Hept-2-ene-l-al truns-Ott-2-ene-l-al 2-Ethylhex-2-ene1-al Hexa-2,Cdienal Furfural Benzaldehyde 3-Methoxybutanal

Compound

TABLE

0.84 0.84

0.73 0.69 0.66 0.64 0.63 0.67 0.62 0.62 0.62 0.58 0.67 0.62 0.61 0.57 0.52 0.68 0.68 0.61

0.85

0.62 0.90

0.68

0.56 0.74 0.81 0.62

Eqn. 7

3

H

0.66 0.66 0.66

0.65 0.58

0.64

0.65 0.64 0.65 0.64 0.64 0.86 0.87 0.86

0.71 0.65

0.69

0.68 0.69 0.67 0.67 0.67 0.83 0.87 0.84

1.05 0.94

0.77 0.72 0.70

0.97 0.99

0.84

0.85

0.88 0.85 0.55

0.58 0.75

Eqn. 8

0.68 0.85

Eqn. 16

1.696 2.287 2.755 3.271 2692 3.262 3.271 3.163 3.089 2.928 3.760 3.176 3.705 3.344 3.403 4.251 4.135 4.698 5.245 5.732 6.167 3.221 3.792 4.376

4.371 3.800 3.262 3.985

3.436

4.179 1.656 2.570 2.180

Log L’6

-_ 2-Ethyl-1-hexyl acetate Cyclohexyl acetate Methyl propanoate Ethyl propanoate Propyl propanoate Isopropyl propanoate Butyl propanoate Isobutyl propanoate Pentyl propanoate 3-Methylbutyl propanoate 2-Pentyl propanoate 2-Ethyl-1-hexylpropanoate Methyl butanoate Ethyl butanoate Propyl butanoate Isopropyl butanoate Butyl butanoate Isobutyl butanoate Pentyl butanoate 3-Methylbutyl butanoate 2-Pentyl butanoate 2-Ethyl-1-hexyl butanoate Methyl isobutanoate Butyl isobutanoate Isobutyl isobutanoate 3-Methylbutyl isopentanoate Ally! formate Ally! acetate Ally! propanoate Vinyl acetate Vinyl butanoate I-Propenyl acetate Isopropenyl acetate Methyl acrylate Ethyl acrylate 2-Ethyl-I-hexyl acrylate Propyl acrylate Butyl acrylate Methyl methacrylate

Esters (continued)

Compound

0.76 0.72 0.67 0.66 0.56 0.67 0.68 0.68 0.64 0.61 0.62 0.62 0.62

0.60 0.69 0.62 0.58 0.57 0.52 0.57 0.54 0.58 0.56 0.52 0.55 0.61 0.56 0.56 0.51 0.56 0.54 0.57 0.55 0.51 0.57 0.56 0.51 0.49

Eqn. I

=2

”

0.56 0.55

0.54

0.56

Eqn. 16

0.46 0.55

0.51

0.58

Eqn. 8

5.025 4.454 2.431 2.807 3.338 3.028 3.883 3.635 4.331 4.153 4.024 5.486 2.893 3.271 3.783 3.482 4.275 4.097 4.764 4.597 4.472 5.856 2.636 4.068 3.885 4.371 2.256 2.723 3.241 2.152 3.191 2.741 2.611 2.360 2.758 5.445 3.260 3.790 2.880

Log Lth

-

e

k n

$

$

T:

S

m

E

Esiers Methyl formate Ethyl formate Propyl formate Isopropyl formate Butyl formate Isobutyl formate sec.-Butyl formate Pentyl formate 2-Pentyl formate 3-Pentyl formate Hexyl formate Methyl acetate Ethyl acetate Propyl acetate Isopropyl acetate Butyl acetate Isobutyl acetate sec.-Butyl acetate tert.-Butyl acetate Pentyl acetate 3-Methylbutyl acetate 2-Pentyl acetate 3-Pentyl acetate 2-Methyl-Zbutyl acetate Hexyl acetate 4-Methyl-2-pentyl acetate 2-Ethyl-1-butyl acetate Heptyl acetate

Cycle-octanone Cyclononanone Cyclodecanone Cycloundecanone Cyclododecanone Cyclotridecanone Cyclotetradecanone Carvone But-3-ene-2-one 3-Methylbut-3-ene-2-one Hex-5-ene-2-one 4-Methylpent-3-ene-2-one Butane-2,3-dione Pentane-2,3-dione Pentane-2,4-dione Acetophenone 0.72 0.67 0.65 0.62 0.66 0.62 0.61 0.66 0.60 0.60 0.67 0.67 0.62 0.61 0.57 0.61 0.58 0.56 0.50 0.62 0.60 0.56 0.56 0.51 0.63 0.55 0.60 0.63

0.76 0.68 0.75 0.70 0.52 0.47 0.56

0.60

0.61 0.59 0.57 0.58

0.59 0.53

0.63 0.60 0.60 0.59

0.58 0.59

0.99

1.09

0.56

0.74

0.85 0.84 0.84 0.83 0.83 0.82 0.82 0.98

0.71

0.83 0.83 0.83 0.83 0.83 0.82 0.82 0.86

1.285 1.845 2.443 2.230 2.958 2.789 2.730 3.448 3.250 3.226 3.970 1.911 2.314 2.819 2.546 3.353 3.161 3.054 2.802 3.844 3.740 3.568 3.679 3.340 4.351 3.822 4.178 4.865

4.981 5.537 6.063 6.621 7.222 7.783 8.334 5.330 2.330 2.691 3.181 3.300 1.639 2.209 2.772 4.483

Acetic acid Propanoic acid Butanoic acid 2-Methylpropanoic acid Pentanoic acid 2-Methylbutanoic acid 3-Methylbutanoic acid

Carboxylic acids

Pyridine 2,3,6_Trimethylpyridine Pyrrole Trimethylpyrazine 2-Methyl-3-ethylpyrazine 2-Methoxy-3-isobutylpyrazine 2,4,5-Trimethyloxazole

Heterocyclics

sec.-Butylamine Allylamine Trimethylamine

Amines

Acetonitrile 1-Cyanopropane I-Cyanobutane Benzonitrile

Nitriles

Nitromethane Nitroethane I-Nitropropane 2-Methyl-2-nitropropane 3-Nitrotoluene

Nitro compounds

Ally1 acrylate 2-Methoxyethyl acetate 2-Ethoxyethyl acetate 3-Methoxy-1-butyl acetate 3-Methoxy-I-butyl acrylate Methylene diacetate Ethylene diacetate Ethylene dipropanoate Propylene diacrylate Benzyl acetate Methyl benzoate Methyl salicylate 0.72 0.93 0.87 0.83 0.83 1.16 1.20 1.05 1.10

0.68 0.60 0.56 0.58 0.58 0.55 0.56

0.80 0.71 0.61 0.77 0.73 0.56 0.68

0.21 0.29 0.47

0.80 0.78 0.80 1.05

0.73 0.74 0.71 0.82 1.08

1.19 0.77 0.82

0.68

1.750 2.290 2.830 2.670 3.380 3.260 3.140

3.003 4.200 2.865

2.410 2.268 1.620

1.739 2.604 3.108 4.004

1.892 2.414 2.894 2.710 5.062

4.914 4.979 4.991 4.634

:

3 2 9

8

S 8 L?

4.048 4.048 3.419 3.937

S

3.747

(Continued on p. 220)

0.65

0.80

0.47

0.85 0.84 0.83 1.04

0.86 0.87 0.86 0.82 1.05

0.95 1.11

0.79

3.160 3.290

Hydroxylic compounds Water Methanol Ethanol Pr opan- 1-01 Butan-l-01 2-Methylpropan-l-01 Pentan-1-01 2-Methylbutan-l-01 3-Methylbutan-l-01 2,2-Dimethylpropan-l-01 Hexan-l-01 2-Methylpentan-l-01 3-Methylpentanl-01 4-Methylpentan-l-01 2-Ethylbutan-l-01 2.2-Dimethylbutan-l-01 Heptan- l-01 2,2-Dimethylpentan-l-01 Octan-l-01 2-Ethylhexan-l-01 2-Ethyl-4-methylpentanNonan- l-01 Decan-l-01 Undecan-l-01 Dodecan-l-01 Propan-2-01

l-01

0.39

0.39 0.39 0.33 0.42 0.40 0.44 0.43 0.40 0.37 0.43 0.37 0.43 0.41 0.39 0.39

0.40 0.39 0.40 0.41 0.42 0.38

0.39 0.39 0.39 0.38 0.42

0.39

0.39

0.40

0.46 0.41 0.42 0.41 0.42 0.41 0.41 0.42

0.66 0.98

Eqn. 16

Phenyls 2-Chlorophenol Salicylaldehyde

Eqn. I

G

0.62 0.68 0.58 0.56 0.53 0.50 0.46 0.43 0.62

II (continued)

Carboxylic acids (continued) Hexanoic acid 2-Methylpentanoic acid Heptanoic acid Octanoic acid Nonanoic acid Decanoic acid Undecanoic acid Dodecanoic acid 3-Butenoic acid

Compound

TABLE

Eqn. 8

0.260 0.970 1.485 2.031 2.601 2.413 3.106 3.011 3.011 2.650 3.610 3.530 3.500 3.500 3.523 3.320 4.115 3.780 4.619 4.433 4.266 5.124 5.628 6.130 6.640 1.764

4.937 4.750

3.920 3.680 4.460 5.000 5.550 6.090 6.640 7.180

Log Llh

Think Ethanethiol I-Propanethiol 2-Propanethiol I-Butanethiol 2-Methyl-1-propanethiol 2-Methyl-2-propanethiol

Hydroxylic cornponds (contined) Prop-2-en-l-01 (ally1 alcohol) But-2-en-l-01 But-3-en-l-01 But-3-en-2-01 2-Methylprop-2-en-l-01 Pent-3-en-l-01 Pent-4-en- 1-01 Pent-1-en-3-01 2-Methylbut-3-en-2-01 trans-Hex-2-en-l-01 truns-Hept-2-en-l-01 vans-Ott-2-en-l-01 Prop-2-yn-l-01 2-Methylbut-3-yn-2-01 2-Chloroethanol 2-Methoxyethanol 2-Ethoxyethanol 2-Butoxyethanol 2-Allyloxyethanol 2-Methoxypropan-l-01 2-Ethoxypropan-l-01 3-Ethoxypropan-l-01 1-Methoxypropan-2-01 I-Propoxypropan-2-01 3-Methoxybutan-l-01 I-Ethoxypentan-3-01 4-Methyl-4-methoxypentan-2-01 3-Hydroxybutan-a-one 4-Hydroxybutan-2-one 3-Methyl-4-hydroxybutan-2-one 3-Methyl-3-hydroxybutan-2-one 4-Methyl-4-hydroxypentan-2-one

Compound

0.46 0.47 0.54 0.59 0.56 0.57 0.64 0.58 0.56 0.57 0.61 0.57 0.66 0.60 0.65 0.78 0.85 0.81 0.75 0.83

0.44 0.49 0.47 0.43 0.45 0.50 0.46 0.43 0.41

Eqn. 7

r:

0.26 0.25 0.30 0.28 0.30 0.28

0.43 0.40 0.41

0.46

Eqn. 16

0.34 0.34 0.32 0.33 0.37 0.29

Eqn. 8

2.173 2.685 2.406 3.243 3.091 2.558

1.951 2.618 2.442 2.206 2.509 3.064 2.715 2.752 2.376 3.510 4.010 4.520 2.050 2.209 2.630 2.490 2.815 3.806 3.283 2.793 3.115 3.426 2.655 3.495 3.398 4.102 3.963 3.573 3.160 3.573 2.951 3.475

Log L’6

A

? 3 2 k

F

2

3

Butan-2-01 Pentan-2-01 Pentan-3-01 3-Methylbutan-2-01 Hexan-2-01 Hexan-3-01 3-Methylpentan-2-01 4-Methylpentan-2-01 2-Methylpentan-3-01 2,3-Dimethylbutan-2-01 3,3-Dimethylbutan-2-01 Heptan-2-01 Heptan-3-01 Heptan-Co1 2,4-Dimethylpentan-3-01 Octan-2-01 2-Methylpropan-2-01 2-Methylbutan-2-01 2-Methylpentan-2-01 3-Methylpentan-3-01 2-Methylheptan-2-01 3-Methylheptan-3-01 3-Ethylpentan-3-01 Cyclopropylcarbinol Cyclopentanol Cyclohexanol 2-Methylcyclohexanol cis,cis-2,6-Dimethylcyclohexanol cis,trans-2,6-Dimethylcyclohexanol trans,trans-2,6-Dimethylcyclohexanol &a-Terpineol exo-Ethylfenchol 1,2-Ethanediol 1,2-Propanediol 1,2-Butanediol 2-Methyl-1,Zpropanediol &2,3-Butanediol meso-2,3-Butanediol 1,3-Propanediol 1,3-Butanediol 1,4kButanediol 0.50 0.49 0.63 0.60 0.62 0.65 0.46 0.68 0.46

0.47 0.51 0.55 0.57 0.52

0.41 0.40 0.40 0.39 0.40 0.39 0.40 0.38 0.39 0.41 0.31 0.40 0.40 0.39 0.40 0.41 0.38 0.41 0.40 0.45

0.43 0.45 0.51 0.57 0.52

0.47

0.50 0.47 0.48 0.47 0.47 0.46

0.44 0.41

0.44

2.661 2.918 3.525 3.190 3.250 3.291 3.263 3.642 3.795

2.338 2.840 2.860 2.793 3.340 3.343 3.371 3.179 3.240 3.167 3.090 3.842 3.860 3.850 3.603 4.343 1.963 2.630 3.081 3.271 3.990 4.000 3.785 2.675 3.241 3.758 4.110

0.21 0.21 0.26 0.21 0.26 0.26 0.25 0.70 0.43 0.71 0.35

0.68 0.40 0.37 0.36 0.28 0.38 0.44 0.38 0.49 0.39 0.47 0.50 0.55 0.60 0.47 0.49 0.53 0.65 0.61 0.59 0.61

1.oo 0.60 0.61 0.76

I-Pentanethiol 3-Methyl-1-butanethiol I-Hexanethiol I-Heptanethiol I-Octanethiol I-Nonanethiol I-Decanethiol Thiophenol 1,ZEthanedithiol Benzylthiol Allylthiol Sulphides Dithiapentane Dimethyl sulphide Diethyl sulphide Dipropyl sulphide Methyl ethyl sulphide Methyl propyl sulphide Diisopentyl sulphide Dibutyl sulphide Diallyl sulphide Propylene sulphide Tetrahydrothiophene Thiophene 2-Methylthiophene 2,5_Dimethylthiophene Dimethyl disulphide Diethyl disulphide Dimethyl trisulphide Methyl thioacetate Methyl thiopropanoate Methyl thiobutanoate Methyl thiopcntanoate Thiocyanates and isothiocyanates Phenyl isothiocyanate Ally1 isothiocyanate Ethyl isothiocyanate Methyl thiocyanate

0.50 0.50 0.53 0.49 0.41 0.44

0.34 0.28 0.33

0.37 0.34 0.31

2.654

0.44

2.238 3.104 4.120 2.730 3.240 5.540 4.950 3.750 2.870 3.660 2.943 3.302 3.806 3.550 4.210

4.720 4.220 5.270 5.790 6.318 4.118

3.720 3.360

0.34 0.18 0.35 0.33 0.33 0.33 0.33 0.84

r r

3

$

Q

B

M. H. ABRAHAM

222

only five data points in each regression, and no less than four explanatory variables. In principle, since we have five equations and (for each solute) four unknowns, viz., RZ, rc;, /?I: and log Lt6, we could determine these unknowns through a set of simultaneous equations. This procedure proved to be useless, probably because there is not a wide enough range of constants in the five equations of the type of eqn. 8. However, Patte et al. [Ill did manage to analyse the 240 x 5 data matrix to yield five characteristic solute parameters, denoted a, u’, 8, n and fl. In order to avoid confusion with our own parameters, we refer to Patte et al’s set as rL, wL, EL, nL and PL. Each of these parameters for the 240 solute set can be examined via eqn. 1, where log SP = CCL,wL, etc. We found that aL was mainly a size factor and that /3Lwas a general combination of factors. For the other three solute parameters of Patte et al. we obtained the following regressions: 7cL = -0.040 EL

+ 0.342R2 - 0.265~;

0.165 + 2.796R2 - 0.602n;

=

WL = -0.081

Eqns.

= 0.0218 -t 0.0335n.L

a:

- 1.4267

- 1.700R2 + 2.490~;

9-11 can be rearranged

+ 2.540~7

+ 0.561~;

(9) (10) (11)

to yield

- 0.0251~L + 0.37221rL (12)

T;(z~) = -0.0060

+ 0.4755wL

+ 0.2826&L + 0.05367rL (13)

=

R2

0.0492 + 0.1195wL

+ 0.4057&L + 0.2014nL (14)

If R2 is known, as it usually is, then any two equations out of eqns. 9-11 will yield c$ and n;. However, the best pair of equations to use is clearly eqns. 9 and 11, which yield NY

= 0.0187 - 0.0620R2

+ 0.0409wL

+ 0.3847~L (15)

rc;(n;)

4 0.0287 + 0.6954R2

+ 0.3932wL

- 0.0789nL (16)

Values of 7~‘:calculated via eqn. 16 are listed in Table II. We can also simply take the set of live equations, eqn. 8, and, knowing RZ, log L” and where necessary c(~, H back-calculate values of r&j. For each solute the five back-calculated $ values can be averaged, and this average is also given in Table II.

et al.

The error in ny between the five equations is ca. 0.03 unit. There are a few omissions in this set of ~llf values; these arise through the lack of one or another of the remaining solute parameters. Although the combination of solutes in the McReynolds and Patte et al. sets numbers several hundred, there are some notable omissions. First, most of the solutes are aliphatic, so that some of the simplest functionally substituted aromatic solutes are missing. Second, many of the polyhalogenated aliphatic solutes are either missing, or have rcy values that are discordant when calculated from the McReynolds or Patte et al. set. Finally, a number of important solutes such as nitroalkanes and nitriles need to be studied further. Fellous et al. [13] listed GLC data for seventeen aromatic solutes on a number of stationary phases. In order to back-calculate rc: using the general solvation equation (eqn. l), it is essential that the s coefficient be as large as possible, i.e., that the stationary phase be polar. Results from the seven most polar phases used by Fellous et al. are given in Table III. There is generally good agreement with values listed in Table II. Several workers have examined sets of halogenated or polyhalogenated solutes on various stationary phases [14-181. In Table IV we give n’;: values back-calculated from the general solvation regression equation (eqn. 1) and also from our own results on a variety of polar stationary phases. McReynolds [lo] did not examine any aliphatic nitro compounds or nitriles, but in Table II we give values of rcy for a few such compounds, obtained from Patte et al.‘s data set. We examined both series of solutes on a number of stationary phases, and conclude that $ is even larger than the values given in Table II. Our results suggest that for l-nitroalkanes rr’jjis 0.95 and that for n-alkyl cyanides 7~; is ca. 0.90 unit (see Table IV). We have not detailed the $ values calculated from eqn. 7 or 15 because these follow closely the original hydrogen-bond a: values described before [4]. Only with the carboxylic acids do the new effective or C$ values (0.60 unit) differ markedly from I$ (0.54 unit). In Table IV we collect all the Cc$ values that correspond to the 7~; values we have set out. Although it was not our intention to construct a new C$j’ scale, we thought it prudent to check that

HYDROGEN TABLE

BONDING.

XVI.

223

III

VALUES OF i$ FOR SOME AROMATIC COMPOUNDS CALCULATED FROM RESULTS OF FELLOUS ETAL. [13]

XinPhX

H CFs CHs OCHJ F Cl Br I CHO SH C02CH3 CN COCH3 NH2 NO2 CHzOH OH

H R2

0.53 0.45 0.52 0.73 0.57 0.67 0.73 0.79 0.99 0.78 0.85 1.07 0.98 0.96 1.10 0.85 0.88

’ Average deviation b For 3-nitrotoluene.

S.D.”

0.02 0.02 0.01 0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.02 0.01 0.01 0.01

$

(Table II)

Eqn. 7

Eqn. 16 Eqn. 8

0.48

0.53

0.47

0.47

0.57 0.73

0.46 0.70

0.99 0.70 0.77 1.05 1.09

0.94 0.84 1.11 1.04 0.99

1.08b

1.05b

from 7 results.

the combined solvation parameters do yield reasonable results in systems where solute basicity is important. We therefore give in Table IV preliminary C/I? values, again based on our original /?‘;’values [5]. We hope in the near future to report on a much more comprehensive list of effective or Cg’: values. Finally, we include in Table II the log L16 values that we have used. Where these differ from previous values, the new set is to be preferred. DISCUSSION

The “inverse matrix” method we have used to analyse the data of McReynolds is a novel approach to the extraction of solvation parameters from data on a large number of stationary phases. The method works very well, but is limited in scope to results for a given set of solutes on at least fifteen phases. Our back-calculation of parameters from regression equations based on Patte et al’s data set, eqn. 8, is likely to be the most common procedure. In principle, as pointed out above, if three solvation parameters are unknown (e.g., ~7, a’: and log L16 in eqn. 8),

it is possible to calculate all three using three simultaneous equations derived from retention data on three phases. In practice, this method can hardly ever be used unless the three phases are specifically chosen to give rise to solvation equations with very different coefficients. In the event, all of our new rc! values have been obtained by either the inverse matrix method or simple back-calculation and averaging. Overall we think that the rcy values listed in Table IV are accurate to ca 0.02 unit, but not more. As can be seen from the data collected in Table II, there is a compelling need to correlate and interpret rcy values in order to codify existing data and to help in the estimation of further values. An analysis of all of our results has led us to two very simple rules governing 7~‘:values for aliphatic solutes: Rule I. In any homologous series of functionally substituted aliphatic compounds, rc’: is constant except for the first one or two members of the series. Rule 2. In any given series of functionally substituted aliphatic compounds, I$ decreases by 0.03 unit for each branch in a carbon chain. We now examine these rules in turn. Rule 1 would be extremely valuable in the estimation of r&j values, because if I$ was known for a few members of a homologous series, then the same value could be applied to all other members. Unfortunately, Li et aE. [ 121 apparently find that their own rc; parameter varies markedly along homologous series. Thus along the homologous series of n-alkylcarboxylic acids, rc; increases from 0.50 (acetic acid) to 0.72 (nonanoic acid) (see Table V), whereas our r&j value is constant at 0.60 unit after the first few members of the series. We note that n; and I$ are “scaled” differently, so that for the present discussion only trends in these parameters are important. How the two sets of rc2 values in Table V both result in good fits to experimental data can be seen by inspection of the corresponding Cay values, also given in Table V. Our constant rcy value is accompanied by a constant Cay value, whereas Li et al.‘s increase in rr; is counteracted by a decrease in ZaQ, so that both combinations of rc2/Cc&’ fit the experimental data with respect to the solvation eqn. 1. We suggest, however, that other experimental evidence suppor4s the constancy of rc: and Cay. Thus, the dipole moment of the n-alkylcarboxylic acids (except for formic acid) remains constant [19], the gas-phase proton transfer acidities of acetic acid, propanoic

224 TABLE

M. H. ABRAHAM

et a[.

IV

RECOMMENDED Values in parentheses

SOLVATION

PARAMETERS

are approximate

FOR USE IN EQN.

la

values.

Solute Rare gas Hydrogen Oxygen Nitrogen Nitrous oxide Carbon monoxide Carbon dioxide Alkane Cycloalkane Decalin Hydrindane Ethene Other alkene Cycloalkene c+Pinene Diene Ethyne Propyne But- 1-yne Other alk-1-yne Alk-2-yne Benzene Toluene o-Xylene m-Xylene g-Xylene Ethylbenzene n-Propylbenzene Isopropylbenzene 1,2,3_Trimethylbenzene 1,2,4_Trimethylbenzene 1,3,5Trimethylbenzene n-Alkylbenzene Styrene Phenylethyne Naphthalene Fluoroalkane Chloromethane Chloroalkane Bromomethane Bromoalkane Iodomethane Iodoalkane sec.-Chloroalkane sec.-Bromoalkane sec.-Iodoalkane terl.-Chloroalkane tert.-Bromoalkane tert.-Iodoalkane Dichloromethane

0.00 0.00 0.00 0.00 0.35 0.00 0.42 0.00 0.10 0.25 0.20 0.10 0.08 0.20 0.24 0.23 0.25 0.25 0.25 0.23 0.30 0.52 0.52 0.54 0.52 0.52 0.52 0.52 (0.51) 0.54 0.52 0.52 0.52 0.63 0.58 0.90 0.35 0.436 0.40 o.43b 0.40 0.43b 0.40 0.35b 0.35b 0.356 0.25b 0.25’ 0.25b 0.576

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.15 0.13 0.13 0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.10

0.00 0.00 0.00 0.00 0.10 0.04 0.10 0.00 0.00 0.00 0.00 0.07 0.07 0.10 0.10 0.10 0.15 0.15 0.15 0.10 0.10 0.14 0.14 0.17 0.17 0.17 0.15 0.15 0.15 0.20 0.20 0.20 0.15 0.18 0.21 0.21 0.10 0.08 0.10 0.10 0.12 0.13 0.15 0.12 0.14 0.17 0.12 0.12 0.10 0.05

Trichloromethane Tetrachloromethane I,1 -Dichloroethane 1,2-Dichloroethane l,l,l-Trichloroethane 1,1,2-Trichloroethane 1, 1,1,2-Tetrachloroethane 1,1,2,2-Tetrachloroethane Dibromomethane Tribromomethane Fluorobenzene Chlorobenzene 1,2-Dichlorobenzene 1,3-Dichlorobenzene 1,4-Dichlorobenzene 2Chlorotoluene 3-Chlorotoluene 4-Chlorotoluene 2,4-Dichlorotoluene 2,6-Dichlorotoluene 3,4-Dichlorotoluene Bromobenzene 1,2-Dibromobenzene 1,3-Dibromobenzene 1,4-Dibromobenzene Iodobenzene

0.49 0.38 0.49 0.64 0.41 0.68 0.63 0.76 0.67 0.68 0.57 0.67 0.79 0.74 0.69 0.66 0.67 0.67 0.73 0.73 0.79 0.73 0.89 0.84 0.79 0.79

0.15 0.00 0.10 0.10 0.00 0.13 0.10 0.16 0.10 0.15 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.02 0.00 0.10 0.11 0.09 0.08 0.08 0.12 0.10 0.09 0.10 0.09 0.03 0.03 0.03 0.09 0.09 0.09 0.03 0.03 0.03 0.09 0.03 0.03 0.03 0.09

Dimethyl ether Di-n-alkyl ether Furan 2-Methylfuran Tetrahydrofuran 2-Methyltetrahydrofuran 3,5_Dimethyltetrahydrofuran Tetrahydropyran 1,cDioxane Paraldehyde Methyl phenyl ether Ethyl phenyl ether Benzodioxane Formaldehyde Acetaldehyde n-Alkanal Prop-2-en-l-al truns-Alk-2-en- 1-al Benzaldehyde 2-, 3- or 4-methylbenzaldehyde

0.27 0.25b 0.53 0.50 0.52 0.48 0.38 0.47 0.75 0.68 0.73 0.72 1.01 0.70 0.67 0.65b 0.74 0.80 0.99 0.95

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.41 0.45 0.15 (0.15) 0.48 0.55 0.55 0.55 0.64

Propanone Butanone Alkan-2-one

0.70 0.70 0.6gb

0.04 0.00 0.00

(0.33) (0.33) (0.33) 0.45 0.45 0.45 0.45 (0.42) (0.44) 0.51 0.51 0.51

HYDROGEN TABLE

BONDING.

XVI.

IV (continued)

Solute 0.00

Alkan-(3,4,5)-one Cycloalkanone Acetophenone

0.666 0.86’ 0.98

Methyl formate Ethyl formate n-Alkyl formate Methyl acetate Ethyl acetate n-Alkyl acetate Methyl propanoate Ethyl propanoate n-Alkyl propanoate Vinyl acetate Methyl acrylate Ethyl acrylate n-Alkyl acrylate Methyl benzoate n-Alkyl benzoates

0.68 0.66 0.63* 0.64 0.62 0.60b 0.60 0.58 0.56* 0.64 0.66 0.64 0.62* 0.85 0.80

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.38 0.38 0.38 0.45 0.45 0.45 0.45 0.45 0.45 0.42 0.42 0.42 0.42 0.50 0.50

Nitromethane Nitroethane I-Nitropropane I-Nitroalkane Nitrobenzene 2-, 3- or 4-nitrotoluene

0.95 0.95 0.95 0.95b 1.10 1.10

0.12 0.05 0.02 0.00 0.00 0.00

0.27 0.27 0.27 0.27 0.27 0.27

Acetonitrile Propionitrile n-Alkyl cyanide Benzonitrile

0.90 0.90 0.90 1.07*

0.09 0.02 0.00 0.00

0.30 0.35 0.36 (0.30)

Ammonia Primary n-alkylamines Dimethylamine sec.-dialkylamines Triethylamine Aniline o-Toluidine m-Toluidine p-Toluidine 2,6_Dimethylaniline N-Methylaniline N,N-Dimethylaniline

0.35’ 0.35’ 0.30’ 0.30’ 0.15’ 0.96’ 0.94 0.94 0.94 0.93 0.94 0.82

0.10 0.10 0.08 0.08 0.00 0.26 0.23 0.23 0.23 0.20 0.17 0.00

0.62 0.64 0.67 0.70 0.81 (0.53) (0.57) (0.55) (0.57) (0.60) (0.47) (0.48)

0.00 0.00 0.00

0.51 0.52 (0.51)

D Values of ny (this work) derived from those in Tables II and III plus other values we have calculated. Values of Cay and Z&’ are based on those given in refs. 4 and 5. b Subtract 0.03 from nf for each additional branch. ’ Provisional values. d See text.

acid and butanoic acid are almost the same (if anything, there is a slight increase in acidity along this series) [20] and the gas-phase hydrogen-bond

Pyridine 2-Methylpyridine 3-Methylpyridine 4-Methylpyridine 2,4,6_Trimethylpyridine

0.82 0.80 0.80 0.80 0.72

0.00 0.00

Acetic acid Propanoic acid Butanoic acid n-Alkanoic acids

0.65 0.65 0.62 0.60*

0.61 0.60 0.60 0.60

0.41 0.43 0.43 0.43

Water Methanol Ethanol Primary alcohols Secondary alcohols Tertiary alcohols Trifluoroethanol Hexafluoropropan-2-01 Decafluoroheptan-l-01

0.45 0.44 0.42 0.42b 0.36b 0.30* 0.60 0.55 0.55

0.82 0.43 0.37 0.37 0.33 0.31 0.57 0.77 0.60

0.35 0.47 0.48 0.48 0.56 0.60 (0.15) (0.03) 0.22

Phenol o-Cresol m-Cresol p-Cresol 2,3-Dimethylphenol 2,CDimethylphenol 2,5-Dimethylphenol 2,6_Dimethylphenol 3,4-Dimethylphenol 3,5_Dimethylphenol 2,4,6-Trimethylphenol Benzyl alcohol

0.88 0.86 0.87 0.87 0.82 0.82 0.82 0.82 0.87 0.87 0.83 0.85

0.60 0.52 0.57 0.57 0.53 0.53 0.54 0.39 0.56 0.57 0.37 0.39

Carbon disulphide Methanethiol I-Alkanethiol 3-Methyl-1-butanethiol Thiophenol Di-n-alkyl sulphide Tetraalkyltin

0.21 (0.35) 0.35* 0.18* 0.78 0.38b 0.00

0.00 0.00 0.00 0.00 0.12 0.00 0.00

0.00 0.00 0.00

0.07 0.24 (0.15) 0.32 0.00

acidity of propanoic acid is slightly less than that of acetic acid [21], not larger. As retention data can be accommodated as well by our constant r$ and Z$ values as by the variable paramete;s of Li et al., we feel that Rule 1 is operative here. There are other homologous series for which Li et al. found 71%to be a variable quantity, but for which Ca! = 0, e.g., the alkan-Zones or the cycloalkanones where rc; increases sharply along the series. In

M. H. ABRAHAM

226 TABLE

V

COMPARISON

R in ROCIH

Methyl Ethyl n-Propyl n-Butyl n-Pentyl n-Hexyl n-Heptyl n-Octyl

OF 7~; WITH x; FOR CARBOXYLIC

ACIDS

Li et al. [12]

This work n!

c?:’

=“z

H %

0.65 0.65 0.62 0.60 0.60 0.60 0.60 0.60

0.61 0.60 0.60 0.60 0.60 0.60 0.60 0.60

0.50 0.61 0.57 0.56 0.60 0.64 0.68 0.72

0.72 0.67 0.62 0.62 0.52 0.47 0.41 0.35

some other series, however, rci decreases slightly (the alk- 1-ene series), or remains approximately constant (the alkanal or the alkylbenzene series). For the cycloalkanone series, as an example, we feel that the difference between Li et d’s result and our findings is not fundamental at all, but is probably due to small but systematic differences in the log L16 values. As the sign of the s7r2 and 1 log L16 coefficients is always positive, a systematic trend in rci increasing, together with a trend in log L’” becoming slightly smaller than expected, would tend to cancel out. This can be seen by comparison of the figures in Table VI. Just as for the carboxylic acid results, the combination of n% with Li et d’s calculated log L1” values will lead to very nearly the same goodness-of-tit as our combination of rc? and log L16. As it is always found that solute dipolarity,

TABLE

VI

COMPARISON

n in (CH,).CO

4 5 6 7 8 ‘) 10 11

OF z; WITH “‘2 FOR CYCLOALKANONES

This work

Li et al. [12]

H %

Log L’6

“‘z

Log L’6

0.86 0.86 0.86 0.86 0.86 0.86 0.86 0.86

3.221 3.792 4.376 4.98 1 5.537 6.063 6.621 7.226

0.58 0.59 0.66 0.69 0.72 0.75 0.78 0.8 1

3.120 3.616 4.110 4.610 5.110 5.610 6.110 6.600

et al.

as the dipole moment, is constant along any homologous series, we again feel that Rule 1 applies to the various homologous series we have considered. Rule 2 is not so well founded, and we think it possible that there will be exceptions or amendments to the rule. However, at the moment, we feel that application of Rule 2 does allow a very large number of 7~; values to be estimated for aliphatic compounds. We note that the starting point for application of the rule is not always the simplest member of any series. According to our results in Table II, the alkanols are a significant exception to Rule 2, as n: seems roughly constant over non-branched and branched members. However, because the coefficients of rc: and CX’;’ are both positive, and indeed follow each other for most stationary phases, there will be various combinations of ~7 and LX’:that give rise to the same (or very similar) goodness-of-fit in any given solvation equation. We have checked that I$ values for alkanols calculated using Rules 1 and 2, together with the c&’values listed in Table IV, yield regression eqations that are just as good as if r&’and af: are allowed to “float”. We give in Table IV our suggested 7~‘:and a$ values for alkanols, noting that we have deliberately amended the first-calculated values in Table II. We also find a few minor anomalies, with respect to Rule 2. Thus, 7~: for isopentanethiol is 0.18 (using Patte et al.,‘s set) rather than 0.32 as calculated by Rule 2. Whether or not this is the result of a systematic experimental error, or even of an incorrectly named compound, we cannot say. Interestingly, Li et al. [12] also found an anomalously low nS value for isopentylthiol. Finally, we can compare our ret scale, as summarised in Table IV, with the 7~; scale of Li et al.. We agree completely with Li et al. in that a new rc2 scale is needed in place of 7-c;.Apart from the difference in treatment of homologous series, the two scales are in approximate agreement. For 198 of the 203 compounds listed by Li et ul. [12], we have I$ values, and find that 7c; = -0.103

+ 0.8457$

(17)

with Y = 0.944 and S.D. = 0.083 units. The intercept of -0.103 arises because Li et al. took cyclohexane as the zero (7-t; = 0.00) but we take alkanes as zero. On the 7~‘:scale, cyclohexane has rcy = 0.10 units.

HYDROGEN

BONDING.

XVI.

221

As mentioned above, we include in Table IV a provisional set of Cgrj values to use with our new r$ and our Zc$ scale. In our view, it is most important that these three scales are constructed more or less simultaneously in order that they all be compatible. How well the scales listed in Table IV deal with various processes remains to be seen, but at the moment we can compare regressions of Patte et aZ.‘s data using the Table IV values with our original regression equations. Details are given in Table VII and show that the new equations are much better than the old ones in terms of the correlation constant and standard deviation. However, the characteristic constants, r, s, a and I, are almost unchanged. Similarly, regression equations using McReynolds’ data are much better than the original ones, whilst still giving very similar characteristic constants. Hence our analysis of the McReynolds’ phases into

TABLE

clusters or groups remains unchanged, and it is not necessary to repeat the 75 regressions. We give in Table VII a few comparisons to show exactly the connection between the old and the new equations. In conclusion, we have constructed a comprehensive rc’:scale, based only on solute properties, for use in solvation equations. As the dependent variable, log L’ or log Vo, in the equations used to calculate x’: is a free energy-related term, then rc? also will be related to Gibbs energy. We are now in a position where the main terms in eqn. 1, viz., dj, ,Yay, C/3! and log L16, are all related to Gibbs energy and hence form a thermodynamically consistent set of explanatory variables. The new $ scale has an advantage in that the characteristic constants in all our previous equations remain the same, within any reasonable experimental error, so that our previous analyses and conclusions are unchanged.

VII

COMPARISON

Phase Patte et al.‘s set Carbowax DEGS* PPE (6 rings)* TCEP ZE7*

The McReynolds’ Apiezon J

OF NEW AND OLD

c

r

-2.01 -2.07 - 1.71 -1.83 -2.51 -2.55 -1.69 -1.75 -1.99 -2.07

set at 120°C -0.48 -0.48 PPE (5 rings) -0.69 -0.70 Pluronic L72 -0.54 -0.54 Carbowax 1540 -0.75 -0.75 DEGS* -0.97 -0.99 ZE7* -0.76 -0.82

REGRESSIONS”

s

a

I

S.D.

R

No.

0.25 0.26 0.35 0.35 0.14 0.19 0.26 0.23 -0.41 -0.38

1.26 1.37 1.58 1.70 0.89 0.98 1.93 2.12 1.46 1.61

2.07 2.11 1.84 1.92 0.67 0.59 1.88 1.94 0.77 0.70

0.429 0.442 0.383 0.396 0.547 0.552 0.365 0.379 0.432 0.442

0.07 0.13 0.07 0.15 0.06 0.11 0.06 0.16 0.07 0.13

0.997 0.986 0.997 0.981 0.997 0.991 0.998 0.982 0.995 0.983

199 168 199 168 199 168 199 168 199 168

0.24 0.21 0.14 0.21 0.09 0.17 0.22 0.31 0.26 0.43 -0.42 -0.28

0.15 0.13 0.92 0.88 0.93 0.89 1.37 1.34 1.76 1.74 1.55 1.63

0.13 0.13 0.61 0.54 1.42 1.41 1.92 1.87 1.80 1.68 0.78 0.69

0.596 0.594 0.560 0.564 0.529 0.531 0.456 0.457 0.375 0.379 0.448 0.449

0.02 0.03 0.02 0.06 0.03 0.08 0.04 0.09 0.05 0.11 0.07 0.07

0.999 0.998 0.999 0.994 0.998 0.992 0.998 0.987 0.995 0.975 0.991 0.990

165 148 I68 155 163 153 169 151 158 145 170 150

a The new constants in eqn. 1 are on the top lines and the old constants * Abbreviations: DEGS = diethylene glycol succinate; PPE = polyphenyl

on the bottom lines; in all instances b = 0. ether; TCEP = tricyanoethoxypropane; ZE7

= zonyl E-7.

M. H. ABRAHAM

228 ACKNOWLEDGEMENTS

We thank the US Army Research, Development and Standardisation Group for support under Contract DAJA 45-87-C-0004, and we are very grateful to Professor Peter W. Carr for a preprint of ref. 12. REFERENCES M. H. Abraham, G. S. Whiting, R. M. Doherty and W. J. Shuely, J. Chem. Sot., Perkin Trans. 2, (1990) 1451. M. H. Abraham, G. S. Whiting, R. M. Doherty and W. J. Shuely, J. Chem. Six., Perkin Trans. 2, (1990) 1851. M. H. Abraham, G. S. Whiting, R. M. Doherty and W. J. Shuely, J. Chromatogr.. 518 (1990) 329. M. H. Abraham, P. L. Grellier, D. V. Prior, P. P. Duce, J. J. Morris and P. J. Taylor, J. Chem. Sm., Perkin Trans. 2, (1989) 699. M. H. Abraham, P. L. Grellier, D. V. Prior, J. J. Morris and P. J. Taylor, J. Chem. SW., Perkin Truns. 2, (1990) 521. M. H. Abraham, P. L. Grellier and R. A. McGill, J. Chem. Sot.. Perkin Trans. 2, (1987) 797. M. J. Kamlet, M. H. Abraham, R. M. Doherty and R. W. Taft, Nature (London), 106 (1984) 464. R. W. Taft, M. H. Abraham, G. R. Famini, R. M. Doherty, J.-L. M. Abboud and M. J. Kamlet. J. Pharm. Sci., 74 (1985) 807.

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