Temperature effect on the characteristic solute±solvent retentioninteractions, calculated with Abraham's solvation model,
for 16 GLC stationary phases
Jose MarõÂa Santiuste*
Department of Structure and Molecular Dynamics, Instituto de QuõÂmica FõÂsica `̀ Rocasolano'' CSIC, C. Serrano 119, 28006-Madrid, Spain
Received 12 March 1998; received in revised form 10 August 1998; accepted 15 August 1998
Abstract
Speci®c stationary phase constants used in Abraham's solvation model were determined by multiple linear regression analysis
(MLRA) for 16 stationary phases (SP) at various temperatures. Hydrogen-bond acidity complexes were negligible for all SPs.
The in¯uence of temperature on the solute±SP interactions and on its different terms, both nonpolar (or cavity-dispersion), and
polar, has been determined for a series of solutes. Good negative-slope straight lines both for the cavity-dispersion vs. T and
for the polar contribution vs. T plots were obtained, the former having a much greater slope than the latter.
Also, the dependence of the cavity-dispersion and of the polar retention terms for various chemical functions in three SPs at
different temperatures was studied. The cavity-dispersion term increased with decreasing temperature, while the polar term
was almost temperature independent. At each temperature, the cavity-dispersion term increased with the Z chain length,
excellent linear correlations being obtained for every chemical function tested. # 1998 Elsevier Science B.V. All rights
reserved.
Keywords: Gas±liquid chromatography; Stationary phases; Solutes and chemical functions; Abraham's solvation model; Temperature
dependence
1. Introduction
The mechanism by which an analyte is retained in a
chromatographic column at a given temperature has
been successfully treated by several solvation models:
the models of Abraham et al. [1±3], Carr et al. [4,5]
and by the Gibbs energy of solvation model of Poole
et al. [6±10]. Although with some differences, the
essence of all these models is that when a substrate is
injected into a column coated with an organic solvent
called stationary phase (SP) and pushed through by a
carrier gas called mobile phase, three phenomena
occur: ®rst, a cavity of a similar size to that of a
solute molecule is created into the solvent; second,
solvent molecules rearrange around the cavity; and
third, a solute molecule gets into the cavity and solute±
solvent interactions take place. In the gas±liquid
chromatography (GLC) solvation process a solute
molecule is transferred from the mobile phase to
the SP, so that the ratio of solute concentrations on
the SP and on the mobile phase is ruled by a dynamic
equilibrium. The total change in the Gibbs energy of
Analytica Chimica Acta 377 (1998) 71±83
*Fax: 34-1-564-2431; e-mail: [emailprotected]
0003-2670/98/$ ± see front matter # 1998 Elsevier Science B.V. All rights reserved.
P I I : S 0 0 0 3 - 2 6 7 0 ( 9 8 ) 0 0 5 9 3 - 5
solution is the sum of the Gibbs energy of solution
released in each of the three above processes, as
Golovnya et al. [11,12] stated.
In the present work the solvation model according
of Abraham et al. was used. Its master equation allows
the calculation of the speci®c retention volume, Vgi:
log Vgi � c� rR2 � s�H2 � a�H
2 � b�H2 � l log L16;
(1)
where r, s, a, b and l are the characteristic constants of
each SP and R2, �H2 ; �
H2 ; �
H2 and log L16 are the
explanatory variables [13] or descriptors of each
solute. The different binary products determine each
characteristic intermolecular solute±SP interaction, in
this order: n/� electron pairs (rR2), dipoles (s�H2 ),
hydrogen-bond basicity complexes (a�H2 ) and hydro-
gen-bond acidity complexes (b�H2 ). l log L16 is mainly
associated with the dispersion forces. The constant c is
always negative; it is obtained by multiple linear
regression analysis (MLRA), and its value depends
on the quality of the ®tting.
As is well known [14]
�GSPi �SOLTN� � ÿ2:303RT log KLi; (2)
where �GSPi �SOLTN� is the partial molar Gibbs
energy of solution of solute i on the stationary phase
SP, R the gas constant�1.987 cal molÿ1 Kÿ1, T the
column temperature (in K) and KLi is the gas±liquid
partition coef®cient (moles of solute per unit volume
of liquid/moles of solute per unit volume of gas phase)
of solute i in the stationary phase SP. It is assumed that
adsorption is unimportant at these temperatures, and
therefore the retention mechanism is mainly based on
partition.
The relation between Vgi and KLi can be described
by [15]
Vgi � 273:2KLi
T�; (3)
where � is the stationary phase density in g mlÿ1.
Rearranging leads to
log KLi � logVgiT�
273:2
� �: (4)
Substitution of log KLi of Eq. (4) in Eq. (2) yields
�GSPi �SOLTN�ÿ2:303RT
� logVgiT�
273:2
� �: (5)
Rearranging gives
log Vgi � �GSPi �SOLTN�ÿ2:303RT
� const: (6)
This expression is used here to evaluate the two more
important solute±solvent interaction retention contri-
butions (as a function of the dimensionless log Vgi):
the cavity-dispersion or nonpolar contribution, which
will be denoted as ÿ�G(C/D)/2.303RT [14] and the
polar contribution, which will be denoted asÿ�G(P)/
2.303RT, [14]:
ÿ�G�C=D�2:303RT
�X
c� l log L16ÿ �
; (7)
ÿ�G�P�2:303RT
�X
rR2 � s�H2 � a�H
2 � b�H2
ÿ �; (8)
both dimensionless, and
�G�C=D� � ÿ2:303RTX�c� l log L16� (9)
or
�G�P� � ÿ2:303RTX
rR2 � s�H2 � a�H
2 � b�H2
ÿ �(10)
in cal molÿ1 or J molÿ1, depending on the units cho-
sen. The treatment of Carr et al. [4,5] is almost equal to
that of Abraham et al., the differences being restricted
to some of the explanatory variables.
The Gibbs energy solvation model of Poole and
coworkers [6±10] can be formulated as
�GSPi �SOLTN� � �GSP
i �CAV� ��GSPi �NP�
��GSPi �P�; (11)
where the left member is the same as in Eq. (2), but the
Gibbs energy is given as partial molal energy instead
of partial molar energy, �GSPi �CAV� is the partial
molal Gibbs energy of cavity formation of solute i on
the stationary phase SP, and �GSPi �NP� and �GSP
i �P�are the nonpolar and polar contributions to the partial
molar Gibbs energy of solution of solute i on the
stationary phase SP, respectively. Good correlations
between the two models, Poole et al. and Abraham et
al., have been obtained [16,17].
Temperature is one of the most important variables
in gas±liquid chromatography, its control being cru-
cial in the optimization of separations. Since speci®c
retention volumes depend on temperature, their dis-
tinct contributions as given by Eq. (1), must be
affected by it.
72 J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83
Poole et al. [6] reported increasing polar and non-
polar retention contributions with increasing tempera-
ture at two temperatures for compounds retained by a
mixed retention mechanism. Besides, they studied the
effect of temperature on the retention mechanism for
10 SPs spanning a wide range of solvents properties
and 46 solutes of different sizes and polarities over the
temperature range 60±1408C [17], and the solution
properties of 48 solutes in two SPs: n-octyl phthalate
and n-octyl tetrachlorophthalate over the temperature
range 60±1208C [18].
In the ®rst case it appeared that the contributions
from polar interactions were only weakly tempera-
ture-dependent, while the cavity-dispersion interac-
tion term showed a much more signi®cant variation,
becoming less favourable for solute transfer at higher
temperatures. For all systems, the contribution of the
cavity-dispersion interaction was favourable for solute
transfer from the gas phase to the liquid phase.
In the second case, for di-n-octyl phthalate the
constants s, a and l decreased with increasing tem-
perature, while the constant c became more negative.
For di-n-octyl tetrachlorophthalate the constants c and
a diminished with increasing temperature, while the
constants r, l and s were virtually unchanged. The
study of the contributions from individual intermole-
cular interactions to the gas±liquid partition coef®-
cient of benzyl alcohol in di-n-octylphthalate as a
function of temperature revealed an important
decrease in the cavity-dispersion term with increasing
temperature, and a slight decrease in the dipole and
solute hydrogen-bond acid/solvent hydrogen-bond
base interactions. Almost the same was found for
di-n-octyl tetrachlorophthalate, the difference being
that the n/� electron donor/acceptor interaction con-
tribution was not zero.
In this work studies about the effect of temperature
on the different intermolecular solute±solvent inter-
actions of about 100 solutes and 16 SPs over the 60±
1808C temperature range were carried out, in order to
elucidate the effect of temperature on the different
interactions taking part in the retention process.
2. Experimental
Stationary phases. (a) Group I consisted of seven
poly(methyl-3,3,3-tri¯uoropropyl) siloxanes: TFPS00,
TFPS09, TFPS15, TFPS25, TFPS26 [19,20], TFPS50
(OV-215 and QF-1) [21], with, respectively, 0, 9, 15,
25, 26 and 50% of TFP (tri¯uoropropyl) group sub-
stitution, and XF-1150 [22±24]; (b) group II consisted
of eight SPs according to Tian and Munk [25]: PEE,
poly(ethylethylene); PP1, polypropylene; PDMS,
poly(dimethylsiloxane); PCL, polycaprolactone;
PECH, poly(epichlorohydrin); PMA, poly(methyl
acrylate) and PBMA, poly(n-butyl methyl acrylate).
Solutes. (a) n-alkanes (from n-hexane to n-hexade-
cane, standards); (b) the 10McReynolds' tests: benzene,
n-butanol, pentan-2-one, 1-nitropropane, pyridine,
2-methyl-pentan-2-ol, 1-iodobutane, oct-2-yne, 1,4-
dioxane and cis-hydrindane [26]; (c) solutes with
unifunctional groups: alkyl benzenes (from benzene
to n-pentyl benzene); alkanols (from propanol-1 to
octanol-1) and cyclohexanol; alkan-2-ones (from pro-
panone to undecan-2-one) and cyclohexanone; esters:
formates (methyl, ethyl, n-propyl and n-butyl) and
acetates (methyl, etyhyl, n-propyl and n-butyl);
nitriles (propionitrile, butyronitrile, valeronitrile, hex-
anenitrile and benzonitrile); aniline and N,N-dimethyl
aniline, nitrobenzene, chlorobenzene, 1-chlorobutane
and 1,1,1-trichloroethane; (d) other solutes used by
Tian and Munk different from those above: cycloalk-
anes (cyclopentane, cyclohexane, cycloheptane and
cyclooctane); cyclohexene, chloromethanes (methyl
chloride, methylene chloride, chloroform and carbon
tetrachloride); n-alkyl chlorides (n-butyl, n-pentyl, n-
hexyl and n-octyl); 1,1-dichloroethane, 1,2-dichloro-
ethane, methylchloroform and tetrahydrofuran [25].
Temperature ranges. 60±1408C for TFPS00,
TFPS09 and TFPS15 (®ve spaced temperatures,
208C apart); 80±1408C for TFPS25 and TFPS26 (four
spaced temperatures, 208C apart); 90±1808C for OV-
215 and QF-1 (four spaced temperatures, 308C apart);
90±1508C for XF-1150 (®ve spaced temperatures,
158C apart); 60±1208C for PEE, PDMS, PECH and
PMA (seven spaced temperatures, 108C apart), and
70±1208C for PCL, PEA, PP1 and PBMA (six spaced
temperatures, 108C apart) [22].
Chromatographs and other apparatus have been
described elsewhere [19±21,23,24,27]. SPs were
applied as packed and wall-coated open tubular
(WCOT) capillary columns. The carrier gas was nitro-
gen. Vgi values were taken as the mean of six chro-
matograms per each compound of the SPs of group I.
As for the SPs of group II, Vgi were obtained with an
J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83 73
accuracy of 1%, and `̀ in most cases, the retention of
the support was within 2% of the corrected retention
volume of the probe'' [25]. Vgi values at 1208C were
estimated by extrapolation for the SPs of group II.
3. Results and discussion
3.1. Dependence of specific phase constants on
column temperature
Table 1 lists the values of the characteristic con-
stants obtained by applying MLRA to the two above
groups of SPs taken from [19±24]: group I, with
phases 1±8 (60±1508C temperature range) and group
II, with phases 9±16 (60±1208C temperature range).
Statistical factors R (multiple correlation coef®cient),
F (Fisher constant) and s.d. (standard deviation of the
estimate), respectively, are also included. Thirty to
fourty-®ve solutes were used for the ®ttings but for
OV-215 and QF-1, which were characterized with only
23 and 18 solutes, respectively. Two plots are given to
improve the comprehension of Table 1.
Fig. 1 is the plot of the constant s vs. T (8C)
for SPs 1±8, where eight straight lines (average
r2�0.985) were obtained. The negative slopes of
these straight lines decreased with decreasing SP
polarity.
Fig. 2 is the constant l vs. T (8C) plot of SPs 9±16
(group II), for which the constant l diminishes as T
increases. The dependence of the constant l on tem-
perature is also clear in group I (SPs 1±8). The least
mean square regression (lmsr) parameters of the con-
stant s vs. T, averaged over all SPs, were: av. slope�ÿ2.6135�10ÿ3, av. intercept�0.7741 and av. r2�0.995 for the SPs of group I, and av. slope�ÿ3.0709�10ÿ3, av. intercept�0.8719 and av. r2�0.991 for
constant l vs. T for the SPs of group II. Good lmsr
straight lines were also obtained for the constant c vs.
T plots for all SPs of group I, with av. slope�2.1247�10ÿ3, av. intercept�ÿ0.1299 and av. r2�0.966; as for
group II, good correlations were also obtained for all
SPs but PMA. Disregarding this SP, the lmsr para-
meter values were: av. slope�2.6309�10ÿ3, av. inter-
cept�ÿ0.0773 and av. r2�0.8943. With respect to the
dependence of the constant s on T, somewhat worse
decreasing lmsr straight lines were found for the SPs
11, 15 and 16, and increasing straight lines for the
remaining SPs in group II, the averaged regression
parameter values being: av. slope�ÿ2.0366�10ÿ3,
av. intercept�0.7403 and av. r2�0.931. For group I
all the lmsr straight lines obtained were decreasing,
Fig. 1. Plot of the phase constant s vs. temperature for the
stationary phases of group I. SPs: 1, TFPS00; 2, FTFPS09; 3,
TFPS15; 4, TFPS25; 5, TFPS26; 6, TFPS50 (OV-215); 7, TFPS50
(QF-1); and 8, XF-1150.
Fig. 2. Plot of the phase constant l vs. temperature for the
stationary phases of group II. SPs: 9, PEE; 10, PDMS; 11, PCL; 12,
PEA; 13, PECH; 14, PP1; 15, PMA; and 16, PBMA.
74 J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83
Table 1
Characteristic specific phase constants and corresponding fitting parameters at several temperatures
SP no. T (8C) c r s a l R F�103 s.d.
Group I
1 TFPS00 60 ÿ0.0318 ÿ0.0657 0.2489 0.2679 0.6891 0.9978 1.866 0.0233
80 ÿ0.0971 ÿ0.0298 0.2218 0.2128 0.6144 0.9983 2.385 0.0184
100 ÿ0.1488 ÿ0.0010 0.2004 0.1870 0.5491 0.9986 2.886 0.0153
120 ÿ0.1935 0.0229 0.1810 0.1401 0.4920 0.9990 3.980 0.0113
140 ÿ0.2311 0.0357 0.1695 0.1355 0.4417 0.9990 3.960 0.0099
2 TFPS09 60 ÿ0.0899 ÿ0.2320 0.5691 0.2493 0.6820 0.9983 2.353 0.0216
80 ÿ0.1529 ÿ0.1866 0.5253 0.2287 0.6085 0.9986 2.850 0.0183
100 ÿ0.2069 ÿ0.1442 0.4770 0.1936 0.5450 0.9987 3.214 0.0157
120 ÿ0.2498 ÿ0.1012 0.4227 0.1624 0.4888 0.9988 3.570 0.0137
140 ÿ0.2869 ÿ0.0770 0.3970 0.1630 0.4394 0.9989 3.579 0.0125
3 TFPS15 60 ÿ0.1540 ÿ0.3185 0.7752 0.2687 0.6723 0.9980 2.066 0.0238
80 ÿ0.2102 ÿ0.2612 0.7039 0.2289 0.5988 0.9982 2.283 0.0207
100 ÿ0.2604 ÿ0.2156 0.6433 0.2043 0.5354 0.9984 2.489 0.0178
120 ÿ0.3002 ÿ0.1757 0.5900 0.1854 0.4796 0.9983 2.472 0.0164
140 ÿ0.3065 ÿ0.1231 0.5525 0.2476 0.4228 0.9918 4.946 0.0238
4 TFPS25 80 ÿ0.280 ÿ0.263 0.803 0.074 0.5733 0.9969 1.379 0.0259
100 ÿ0.336 ÿ0.242 0.777 0.098 0.5137 0.9973 1.566 0.0226
120 ÿ0.382 ÿ0.213 0.731 0.105 0.4615 0.9969 1.385 0.0219
140 ÿ0.421 ÿ0.188 0.689 0.111 0.4152 0.9966 1.260 0.0207
5 TFPS26 80 ÿ0.2929 ÿ0.3370 0.9392 0.2267 0.5761 0.9974 1.557 0.0243
100 ÿ0.3383 ÿ0.2958 0.8769 0.2165 0.5147 0.9971 1.405 0.0228
120 ÿ0.3819 ÿ0.2553 0.8106 0.2010 0.4620 0.9968 1.271 0.0217
140 ÿ0.4192 ÿ0.2211 0.7559 0.1916 0.4153 0.9964 1.144 0.0213
6 OV-215 90 ÿ0.3689 ÿ0.4898 1.3975 0.2719 0.4883 0.9977 0.780 0.0187
120 ÿ0.4024 ÿ0.4180 1.2416 0.3263 0.4056 0.9978 0.832 0.0204
150 ÿ0.4938 ÿ0.3302 1.1908 0.3773 0.3392 0.9920 0.210 0.0331
180 ÿ0.5086 ÿ0.3178 1.0463 0.3437 0.2921 0.9970 0.526 0.0190
7 QF-1 90 ÿ0.4556 ÿ0.4466 1.3509 0.3099 0.4990 0.9992 1.532 0.0138
120 ÿ0.5232 ÿ0.3832 1.2203 0.3171 0.4180 0.9986 0.960 0.0162
150 ÿ0.5391 ÿ0.3225 1.0859 0.2757 0.3493 0.9977 0.514 0.0179
180 ÿ0.579 ÿ0.3140 1.0157 0.3297 0.3009 0.9969 0.386 0.0188
8 XF-1150 90 ÿ0.5797 ÿ0.0173 1.6898 1.5568 0.4731 0.9882 0.391 0.0622
105 ÿ0.6494 0.0091 1.5838 1.3938 0.4352 0.9888 0.412 0.0556
120 ÿ0.6920 0.0273 1.529 1.298 0.3965 0.9873 0.363 0.0582
135 ÿ0.719 0.0457 1.476 1.223 0.3598 0.9867 0.346 0.0559
150 ÿ0.7434 0.0488 1.4167 1.1228 0.3303 0.9859 0.328 0.0538
Group II
9 PEE 60 ÿ0.1147 0.1722 0.0805 ÿ0.0404 0.7710 0.9994 5.184 0.0186
70 ÿ0.1387 0.1667 0.1036 ÿ0.0482 0.7331 0.9992 4.186 0.0190
80 ÿ0.1182 0.1654 0.0956 ÿ0.0950 0.6870 0.9970 1.054 0.0249
90 ÿ0.1519 0.1292 0.1475 ÿ0.0339 0.6577 0.9994 5.855 0.0156
100 ÿ0.1701 0.1325 0.1612 ÿ0.0781 0.6259 0.9990 3.275 0.0179
110 ÿ0.1684 0.1097 0.2051 ÿ0.0351 0.5916 0.9993 4.593 0.0159
120 ÿ0.1827 0.1036 0.2051 ÿ0.0472 0.5616 0.9992 3.805 0.0159
10 PDMS 60 ÿ0.0028 0.3358 ÿ0.1435 0.3031 0.7003 0.9989 3.049 0.0208
70 ÿ0.0066 0.2958 ÿ0.1164 0.2656 0.6571 0.9991 3.505 0.0183
80 ÿ0.0250 0.2805 ÿ0.0811 0.2230 0.6234 0.9993 4.529 0.0145
90 ÿ0.0419 0.2634 ÿ0.0594 0.2127 0.5909 0.9993 4.850 0.0131
J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83 75
with av. slope�ÿ2.8609�10ÿ3, av. intercept�1.1932
and av. r2�0.985.
The dependence of the constant r on T was as
follows: increasing straight lines were obtained for
all SPs of group I, with av. slope�2.9555�10ÿ3, av.
intercept�ÿ0.3926, and av. r2�0.969. For group II,
SPs 11, 15 and 16 yielded increasing straight lines,
while the others yielded decreasing straight lines, with
av. slope�ÿ1.3096�10ÿ4, av. intercept�ÿ9.908�10ÿ4 and av. r2�0.939.
The dependence of the constant a on T was more
complex. Considering group I, for the SP 7 a straight
Table 1 (Continued )
SP no. T (8C) c r s a l R F�103 s.d.
100 ÿ0.0333 0.2353 ÿ0.0364 0.1940 0.5556 0.9994 5.477 0.0379
110 ÿ0.0713 0.2201 ÿ0.0230 0.1420 0.5328 0.9994 5.136 0.0116
120 ÿ0.0691 0.1970 0.0034 0.1278 0.4998 0.9995 6.348 0.0096
11 PCL 70 ÿ0.4331 0.1236 1.3914 1.967 0.6451 0.9998 2.742 0.0179
80 ÿ0.4395 0.1506 1.3183 1.828 0.6116 0.9988 2.467 0.0171
90 ÿ0.4444 0.1736 1.2505 1.708 0.5796 0.9988 2.698 0.0170
100 ÿ0.4716 0.2071 1.1767 1.589 0.5539 0.9987 2.412 0.0217
110 ÿ0.4861 0.2160 1.1291 1.481 0.5284 0.9986 2.325 0.0162
120 ÿ0.4934 0.2439 1.0622 1.373 0.5100 0.9984 1.999 0.0169
12 PEA 70 ÿ0.4131 1.4420 0.0789 1.945 0.6089 0.9982 1.663 0.0220
80 ÿ0.4159 1.3670 0.1046 1.809 0.5754 0.9985 2.029 0.0188
90 ÿ0.4203 1.2940 0.1259 1.693 0.5456 0.9985 1.722 0.0202
100 ÿ0.4232 1.2382 0.1316 1.575 0.5158 0.9980 1.486 0.0207
110 ÿ0.4404 1.2101 0.1212 1.489 0.4943 0.9967 0.908 0.0230
120 ÿ0.4439 1.1287 0.1521 1.364 0.4678 0.9974 1.168 0.0200
13 PECH 60 ÿ0.7001 1.5100 0.2508 1.242 0.6459 0.9971 1.097 0.0315
70 ÿ0.6879 1.4050 0.2869 1.137 0.6102 0.9970 1.079 0.0303
80 ÿ0.6738 1.3230 0.2985 1.053 0.5759 0.9970 1.067 0.0292
90 ÿ0.6884 1.2660 0.3147 0.931 0.5493 0.9960 0.846 0.0322
100 ÿ0.6880 1.2000 0.3195 0.890 0.5233 0.9960 0.866 0.0298
110 ÿ0.6866 1.1520 0.3212 0.859 0.4983 0.9954 0.697 0.0310
120 ÿ0.6790 1.0630 0.3540 0.743 0.4710 0.9957 0.738 0.0286
14 PP1 70 ÿ0.1850 0.1765 0.0726 0.0185 0.7436 0.9991 3.652 0.0208
80 ÿ0.1677 0.1456 0.0826 ÿ0.0003 0.6999 0.9996 9.264 0.0120
90 ÿ0.2120 0.1436 0.1291 ÿ0.0435 0.6715 0.9992 4.071 0.0175
100 ÿ0.2427 0.1813 0.1371 ÿ0.0362 0.6418 0.9990 3.115 0.0172
110 ÿ0.2850 0.0931 0.1974 ÿ0.0192 0.6232 0.9986 2.172 0.0220
120 ÿ0.3024 0.1293 0.2077 ÿ0.0348 0.5863 0.9979 1.519 0.0243
15 PMA 60 ÿ0.9110 0.0791 2.1340 2.4050 0.6353 0.9914 1.047 0.0367
70 ÿ0.7454 0.1667 1.8638 2.1282 0.5751 0.9974 1.225 0.0297
80 ÿ0.6634 0.2046 1.6796 1.9201 0.5340 0.9976 1.308 0.0272
90 ÿ0.6291 0.2367 1.5617 1.7802 0.5025 0.9972 1.124 0.0274
100 ÿ0.6175 0.2571 1.4717 1.6558 0.4747 0.9969 1.042 0.0274
110 ÿ0.6219 0.2691 1.3886 1.5396 0.4524 0.9966 0.947 0.0264
120 ÿ0.5520 0.2837 1.2617 1.3872 0.4221 0.9941 0.541 0.0311
16 PBMA 70 ÿ0.3615 ÿ0.0118 1.0610 1.6800 0.6935 0.9992 3.976 0.0152
80 ÿ0.3845 0.0311 1.0052 1.5469 0.6612 0.9990 3.075 0.0167
90 ÿ0.3899 ÿ0.0102 1.0317 1.4651 0.6344 0.9948 0.613 0.0266
100 ÿ0.3965 0.0602 0.9243 1.3512 0.6000 0.9986 2.198 0.0190
110 ÿ0.4254 0.1613 0.7912 1.2307 0.5715 0.9970 1.054 0.0231
120 ÿ0.4129 0.1790 0.7606 1.1127 0.5385 0.9974 1.246 0.0228
76 J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83
line parallel to the T axis was obtained; for SPs 1±3, 5
and 8 decreasing straight lines were obtained, while
SPs 4 and 6 gave increasing straight lines; SPs 3 and 6
yielded bad correlations. After elimination of these
two lines the averaged parameter values were: av.
slope�ÿ1.2923�10ÿ3, av. slope�0.6270 and av.
r2�0.946. Considering group II, a vs. T plots gave
quasi-zero slope straight lines parallel to the T axis for
SPs 9 and 14. Decreasing straight lines with averaged
slope�9.7316�10ÿ3, av. intercept�2.2327 and av.
r2�0.985 for the the remaining SP plots were
obtained. In short, most speci®c SP constants showed
a good linear temperature dependence within the
temperature ranges studied.
3.2. Dependence on temperature of the interaction
retention
Retention, estimated as log Vgi, as calculated from
Eq. (1), is composed of two contributions: nonpolar
(or cavity-dispersion), equal toP�c� l log L16� �
ÿ�G�C=D�=2:303RT, and polar, equal toP�rR2�
s�H2 � a�H
2 � � ÿ�G�P�=2:303RT , because b�0 in all
the SPs tested. Both interactions were studied in detail
for a series of solutes on two chosen SPs.
Table 2 listsP�c� l log L16� and
P�rR2 � s�H2
�a�H2 � for n-hexane and other 11 solutes: cyclohex-
ane, cyclohexene, benzene, n-butyl acetate, amyl
alcohol, methylethyl ketone, trichloromethane, 1,2-
dichloroethane, chlorobenzene, tetrahydrofuran and
chlorohexane on PEA, poly(ethyl acrylate), at 708C,
808C, 908C, 1008C, 1108C and 1208C, Vgi values at the
last temperature were obtained by extrapolation. In
Table 3 values for n-hexane and other 10 solutes
pertaining to various chemical functions on TFPS26
at 808C, 1008C, 1208C and 1408C are presented. Both
retention terms decreased with increasing tempera-
ture, the gradient for the nonpolar term being much
larger.
Table 4 shows the lmsr straight lines obtained for
the two ®ttings: ÿ�G�C=D�=2:303RT vs. T and
ÿ�G�P�=2:303RT vs. T. The averaged values for
the above 12 solutes were: av. slope�ÿ8.869�10ÿ3,
av. intercept�1.9905 and av. r2�0.998 for the former
®tting, and av. slope�ÿ3.414�10ÿ3, av. inter-
cept�1.1025 and av. r2�0.971 (for 11 solutes since
n-hexane was disregarded) for the latter ®tting. The
averaged slope ratio was 8.869�10ÿ3:3.414�10ÿ3
�2.6, which quanti®es that the straight lines for the
cavity-dispersion vs. T plots decrease more strongly.
Table 5 lists the lmsr parameter values of the cavity-
dispersion vs. T and of the polar retention contribution
vs. T for n-hexane and the solutes: benzene, hexan-2-
one, cyclohexanol, n-butyl acetate, hexanenitrile,
nitrobenzene, aniline, chlorobenzene, pyridine and
1-nitropropane on TFPS26 (80±1408C temperature
range). The average values were: av. slope�ÿ0.0112,
av. intercept�2.5545 and av. r2�0.997 for the former
®tting, and av. slope�ÿ1.457�10ÿ3, av. intercept�0.687 and av. r2�0.993 (n-hexane disregarded in this
case) for the latter ®tting. The averaged slope ratio was
Table 2
Cavity-dispersion and polar interaction±retention values of
n-hexane and 11 other solutes on PEA (temperature range:
70±1208C)
T (8C)
70 80 90 100 110 120P�c� l log L16�n-C6 1.211 1.119 1.035 0.953 0.879 0.804
CC6 1.392 1.289 1.197 1.106 1.025 0.943
CHX 1.426 1.322 1.228 1.135 1.053 0.969
BNZ 1.283 1.187 1.100 1.014 0.937 0.859
NBA 1.629 1.513 1.409 1.306 1.217 1.125
AOH 1.478 1.371 1.275 1.179 1.095 1.009
MEK 0.979 0.900 0.827 0.757 0.690 0.626
CL3 1.097 1.011 0.933 0.856 0.786 0.716
D12 1.153 1.064 0.984 0.904 0.832 0.760
CLB 1.814 1.688 1.575 1.463 1.368 1.267
THF 1.192 1.101 1.018 0.937 0.863 0.789
CLH 1.887 1.757 1.641 1.525 1.427 1.323
P�rR2 � s�H2 � a�H
2 � �b � 0�n-C6 0.000 0.000 0.000 0.000 0.000 0.000
CC6 0.168 0.169 0.168 0.164 0.158 0.159
CHX 0.514 0.496 0.478 0.457 0.439 0.422
BNZ 1.072 1.028 0.987 0.945 0.912 0.861
NBA 0.871 0.828 0.758 0.752 0.735 0.688
AOH 1.342 1.266 1.197 1.132 1.086 1.012
MEK 1.022 0.974 0.927 0.888 0.867 0.815
CL3 1.032 0.986 0.942 0.899 0.868 0.822
D12 1.150 1.099 1.050 1.005 0.974 0.857
CLB 0.994 0.964 0.931 0.899 0.874 0.843
THF 0.773 0.741 0.709 0.682 0.664 0.631
CLH 0.593 0.568 0.543 0.522 0.508 0.482
Solutes: CC6, cyclohexane; CHX, cyclohexene; BNZ, benzene;
NBA, n-butyl acetate; AOH, amyl alcohol; MEK, methyl ethyl
ketone; CL3, chloroform; D12, 1,2-dichloroethane; CLB, chloro-
benzene; THF, tetrahydrofuran and CLH, chlorohexane.
J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83 77
now 7.7, con®rming, therefore, that the variation of the
polar contribution with T is much smaller than that of
the cavity-dispersion.
Fig. 3 is the cavity-dispersion term vs. T plot, for
the solutes n-hexane, benzene, pyridine, hexan-2-one,
chlorobenzene, aniline and nitrobenzene in XF-1150
(90±1508C T range), ®ve temperatures at 158C inter-
vals. Good negative slope straight lines were obtained
Table 3
Cavity-dispersion and polar interaction retention of n-hexane and 10 polar solutes on TFPS26 (temperature range: 80±1408C)
Solute T (8C) T (8C)
80 100 120 140 80 100 120 140P�c� l log L16� P�rR2 � s�H2 � a�H
2 �n-Hexane 1.244 1.035 0.851 0.689 0.000 0.000 0.000 0.000
Benzene 1.312 1.096 0.905 0.738 0.282 0.276 0.265 0.256
Hexan-2-one 1.586 1.341 1.125 0.936 0.593 0.556 0.516 0.484
Cyclohexanol 1.872 1.596 1.354 1.141 0.424 0.406 0.385 0.367
n-Butyl acetate 1.639 1.387 1.167 0.973 0.539 0.505 0.468 0.437
Hexanenitrile 1.786 1.519 1.285 1.079 0.789 0.740 0.687 0.643
Nitrobenzene 2.332 2.007 1.723 1.473 0.749 0.715 0.678 0.646
Aniline 1.973 1.686 1.436 1.215 0.580 0.546 0.534 0.515
Chlorobenzene 1.814 1.544 1.308 1.100 0.368 0.358 0.344 0.332
Pyridine 1.448 1.217 1.014 0.836 0.576 0.549 0.520 0.496
1-Nitropropane 1.374 1.151 0.955 0.783 0.810 0.761 0.708 0.665
Table 4
Least mean square regression of cavity-dispersion �ÿ�G�C=D�=2:303RT� interaction vs. T and of polar interaction �ÿ�G�P�=2:303RT� vs. T. SP: PEA (temperature range: 70±1208C)
Solute Slope (8Cÿ1) Intercept r2 Covariancexy
ÿ�G�C=D�=2:303RT vs. T
n-C6 ÿ8.106Eÿ03 1.7702 0.9983 ÿ2.837
CC6 ÿ8.937Eÿ03 2.0077 0.9980 ÿ3.128
CHX ÿ9.100Eÿ03 2.0533 0.9981 ÿ3.185
BNZ ÿ8.446Eÿ03 1.8657 0.9983 ÿ2.956
NBA ÿ10.030Eÿ03 2.3195 0.9977 ÿ3.511
AOH ÿ9.340Eÿ03 2.1218 0.9981 ÿ3.269
MEK ÿ7.043Eÿ03 1.4656 0.9986 ÿ2.465
CL3 ÿ7.591Eÿ03 1.6210 0.9985 ÿ2.657
D12 ÿ7.831Eÿ03 1.6935 0.9984 ÿ2.741
CLB ÿ10.880Eÿ03 2.5625 0.9976 ÿ3.807
THF ÿ8.029Eÿ03 1.7460 0.9984 ÿ2.810
CLH ÿ11.200Eÿ03 2.6590 0.9976 ÿ3.926
Average ÿ8.869Eÿ03 1.9905 0.9980 ÿ2.664
ÿ�G�P�=2:303RT vs. T
CC6 ÿ2.343Eÿ04 0.1866 0.8187 ÿ0.082
CHX ÿ1.863Eÿ03 0.6446 0.9993 ÿ0.652
BNZ ÿ4.129Eÿ03 1.3597 0.9980 ÿ1.806
NBA ÿ3.429Eÿ03 1.0977 0.9368 ÿ1.200
AOH ÿ6.443Eÿ03 1.7846 0.9957 ÿ2.255
MEK ÿ3.986Eÿ03 1.2941 0.9891 ÿ1.395
CL3 ÿ4.134Eÿ03 1.3176 0.9973 ÿ1.447
D12 ÿ5.386Eÿ03 1.5341 0.9593 ÿ1.885
CLB ÿ3.020Eÿ03 1.2044 0.9987 ÿ1.057
THF ÿ2.766Eÿ03 0.9627 0.9936 ÿ0.968
CLH ÿ2.160Eÿ03 0.7412 0.9935 ÿ0.756
Average ÿ3.414Eÿ03 1.1025 0.9709 ÿ1.227
Solute legend (see Table 2).
Fig. 3. Plot of the interaction cavity-dispersion term,P�c�
l log L16�, as a function of temperature for seven solutes on XF-
1150 (90±1058C). Solutes: 1, n-hexane; 2, benzene; 3, pyridine; 4,
hexan-2-one; 5, chlorobenzene; 6, aniline; and 7, nitrobenzene.
78 J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83
in all cases, showing decreasing ÿ�G�C=D�=2:303RT values with increasing temperature. The
averaged lmsr parameters were: av. slope�ÿ0.0108,
av. intercept�1.9883 and av. r2�0.990.
Fig. 4(a) and (b) show the plots of the retention
interaction contributions of benzene on TFPS09 (60±
1408C T range) and on XF-1150 (90±1508C T range),
respectively. A smooth variation of the n/� electronic
polarizability interaction (1) with temperature was
found for the two plots, with slopes of 0.001207
and 0.000685, respectively. The dipole interactions
term s�H2 (2) was somewhat larger for the more polar
XF-1150 (Fig. 4(b)). Their respective variations with
temperature yielded decreasing straight lines with
increasing temperature, the ratio of the slope of the
dipole interaction vs. T for XF-1150 to that for
TFPSO9 was nearly 2. The dashed curve (overall
polar term) for XF-1150 was rather more signi®cant
(0.8<interaction<1.0) than that for the much less polar
TFPS09 (0.0<interaction<0.3). Cavity-dispersion
interactions also gave decreasing straight lines as T
increased. The temperature dependence of the non-
polar interaction was somewhat more important in
TFPS09 (slope�ÿ0.010879) than in XF-1150
(slope�ÿ0.009347), the ratio being 1.2.
Fig. 5(a) and (b) show the temperature dependence
plots of the interaction retention (log Vg) of cyclohex-
anol on TFPS09 (60±1408C T range) and on XF-1150
(90±1508C), respectively. Fig. 5(a) shows the domi-
nance of the cavity-dispersion term for cyclohexanol
on the less polar TFPS09, while rR2 and a�H2 inter-
actions were similar for both SPs. On the contrary, s�H2
interaction and polar interaction (dashed line) were
much larger for the polar XF-1150 (Fig. 5(b)). The rR2
interaction contributions to retention and their respec-
tive variations with temperature were very small,
yielding quasi-horizontal straight lines, slopes being
0.0009105 and 0.0005171, respectively. The s�H2 inter-
Table 5
Least mean square regression of cavity-dispersion interaction ��G�C=D�=2:30RT� vs. T and of polar interaction ��G�P�=2:303RT� vs. T. SP:
TFPS26 (temperature range: 80±1408C)
Solute Slope (8Cÿ1) Intercept r2 Covariancexy
ÿ�G�C=D�=2:303RT vs. T
Benzene ÿ9.565Eÿ03 2.0649 0.9967 ÿ6.377
Hexan-2-one ÿ10.800Eÿ03 2.4383 0.9967 ÿ10.830
Cyclohexanol ÿ12.200Eÿ03 2.8300 0.9967 ÿ8.117
n-Butyl acetate ÿ11.100Eÿ03 2.5110 0.9966 ÿ7.393
Hexanenitrile ÿ11.780Eÿ03 2.7125 0.9966 ÿ7.850
Nitrobenzene ÿ14.300Eÿ03 3.4573 0.9966 ÿ9.537
Aniline ÿ12.600Eÿ03 2.9567 0.9966 ÿ8.413
Chlorobenzene ÿ11.900Eÿ03 2.7494 0.9966 ÿ7.927
Pyridine ÿ10.200Eÿ03 2.2502 0.9966 ÿ6.797
n-Hexane ÿ9.245Eÿ03 1.9717 0.9968 ÿ6.163
1-Nitropropane ÿ9.845Eÿ03 2.1487 0.9966 ÿ6.563
Average ÿ11.200Eÿ03 2.5545 0.9966 ÿ7.815
ÿ�G�P�=2:303RT vs. T
Benzene ÿ0.445Eÿ03 0.3187 0.9883 ÿ0.297
Hexan-2-one ÿ1.835Eÿ03 0.7391 0.9982 ÿ1.223
Cyclohexanol ÿ0.960Eÿ03 0.5011 0.9990 ÿ0.640
n-Butyl acetate ÿ1.715Eÿ03 0.6759 0.9989 ÿ1.143
Hexanenitrile ÿ2.455Eÿ03 0.9848 0.9988 ÿ1.637
Nitrobenzene ÿ1.730Eÿ03 0.8873 0.9993 ÿ1.153
Aniline ÿ1.035Eÿ03 0.6576 0.9561 ÿ0.690
Chlorobenzene ÿ0.610Eÿ03 0.4176 0.9962 ÿ0.407
Pyridine ÿ1.345Eÿ03 0.3832 0.9987 ÿ0.897
1-Nitropropane ÿ2.440Eÿ03 1.0044 0.9984 ÿ1.627
Average ÿ1.457Eÿ03 0.6870 0.9930 ÿ0.809
J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83 79
action contribution showed decreasing straight lines
with increasing temperature, the slopes being
ÿ0.0012045 for TFPS09 and ÿ0.002353 for XF-
1150, respectively. The variation of a�H2 with tem-
perature yielded decreasing straight lines with increas-
ing temperature. Their slopes,ÿ0.000382 for TFPS09
and ÿ0.00222 for XF-1150, respectively, suggest that
the T-dependence was stronger for the more polar SP.
The cavity-dispersion interaction was of similar
importance in the two SPs. The effect of temperature
on the cavity-dispersion interaction for cyclohexanol
on TFPS09 and on XF-1150 showed decreasing
straight lines as T increased, with excellent correlation
coef®cients, r2�0.99 or even better (both slopes equal
to ÿ0.01382).
In short, the temperature dependence of the cavity-
dispersion term was much more important than that of
any other retention interaction contribution. It is clear
that at larger temperatures the cavity-dispersion con-
tributions are smaller, which means that it may be
Fig. 4. Plot of the interaction±retention contributions vs. tempera-
ture for benzene on two stationary phases: TFPS09 (a) and XF-
1150 (b). Identifications of lines and symbols: 1, rR2; 2, s�H2 .
Dashed curve, polar interaction: 1�2. 4, cavity-dispersion.
Fig. 5. Plots of the interaction±retention contributions vs. tempera-
ture of cyclohexanol on two stationary phases: TFPS09 (a) and XF-
1150 (b). Identification of lines and symbols: 1, rR2; 2, s�H2 ; and 3,
a�H2 . Dashed line, polar interaction�1�2�3. 4, cavity-dispersion.
80 J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83
more dif®cult to create the cavity at higher tempera-
tures, thus worsening the retention.
The individual polar interaction retentions exhibit a
similar temperature dependence trend, but their gra-
dients were much smaller in both cases.
TFPS15 is an SP of little polarity, while XF-1150 is
a quite polar SP, which causes differences in the
retention behaviour of the common chemical func-
tions studied. In fact, the cavity-dispersion term is
smaller in the more polar SP for all functions. In
contrast, the polar contribution increases for the more
polar SP. For example, on comparing the behaviour of
octan-1-ol, octan-2-one, hexane nitrile and n-butyl
benzene (Table 6) at 1208C, ÿ�G�C=D�=2:303RT ,
for hexanenitrile on TFPS15 duplicates the correspond-
ing value on XF-1150, while ÿ�G�P�=2:303RT on
TFPS15 is one third of the value for XF-1150. Abra-
ham's solvation model permits to predict the retention
behaviour of a solute i on a given SP simply by
calculating these two interactions.
3.3. Dependence on temperature of the interaction±
retention for several chemical functions
Cycloalkanes, alkyl chlorides, alkyl acetates, alkyl
benzenes, n-alkanols, alkan-2-ones and nitriles on
PCL (70±1208C), TFPS15 (60±1408C) and XF-1150
(90±1508C) were studied. Good linear correlations for
the ÿ�G�C=D�=2:303RT vs. chain length, Z, at each
temperature on PCL were obtained for cycloalkanes
(av. r2�0.994) (Fig. 6(a)) and alkyl acetates (av.
r2�0.996), and somewhat worse correlations for alkyl
chlorides (av. r2�0.970) (correlation coef®cients were
the average of the six temperatures).
Excellent linear relationships betweenP�c� l log L16� and Z for alkyl benzenes (av.
r2�0.9991), nitriles (av. r2�0.9989) (Fig. 6(b)), alkyl
benzenes (av. r2�0.9995) and alkan-2-ones (av.
r2�0.9992) on TFPS15 were obtained (correlation
coef®cients were the average for ®ve temperatures).
For instance, at 1208C, an lms regression straight line
of parameters: slope�0.2465, intercept�ÿ0.0505 and
r2�0.9996 was obtained.
Furthermore, very good lms regression straight
lines were obtained for ÿ�G�C=D�=2:303RT vs. Z
on XF-1150: alkyl benzenes (av. r2�0.9990), nitriles
(av. r2�0.9989), n-alkanols (av. r2�0.9996) and
alkan-2-ones (av. r2�0.9997) (Fig. 6(c)) (correlation
coef®cients were the average of ®ve temperatures).
The retention (log Vgi) polar term against tempera-
ture increases very little with increasing Z, for
instance, ÿ�G�P�=2:303RT � 0:2749, 0.2770,
0.2779, 0.2795, 0.2793 and 0.2814 for n-alkanols
Z�3, 4, 5, 6 and 7, respectively, on TFPS15 within
the above temperature range. The slope of the lmsr
straight line for this case was very small, 0.00117 (as
compared with that of theÿ�G�C=D�=2:303RT vs. Z
lmsr straight line, 0.2465), showing that the polar term
for the various chain lengths for n-alkanols on TFPS15
is almost constant. The same trend was observed for
cycloalkanes (Fig. 6(a)), alkane nitriles (Fig. 6(b))
and methylketones (Fig. 6(c)), i.e. the variation with
Z of the polar part is quite small in comparison with
that of the nonpolar part.
In short, the cavity-dispersion term increases
with increasing chain length at each temperature.
On the contrary, the polar term remains virtually
unchanged.
Table 6
Comparison of interactive±retention terms of four solutes of different polarity on two unequally polar stationary phases at 1208C
Solute Stationary phase
TFPS15 XF-1150
ÿ�G�C=D�=2:303RT ÿ�G�P�=2:303RT ÿ�G�C=D�=2:303RT ÿ�G�P�=2:303RT
Octan-1-ol 1.9151 0.2814 1.1394 1.1279
Octan-2-one 1.7415 0.3940 0.9959 1.0427
Hexanenitrile 1.4302 0.5018 0.7386 1.3806
n-Butyl benzene 1.9683 0.2014 1.1834 0.7809
ÿ�G�C=D�=2:303RT �P�c� l log L16�, cavity-dispersion interaction term.
ÿ�G�P�=2:303RT �P�rR2 � s�H2 � a�H
2 �, polar interaction term.
J.M. Santiuste / Analytica Chimica Acta 377 (1998) 71±83 81
Acknowledgements
This work was developed under Project no. PB 91-
0077 of the Spanish DGICYT.
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