Abraham model correlations for ionic liquid solvents computational methodology for updating existing ion specific equation coefficients

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Physics and Chemistry of Liquids
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Abraham model correlations for ionic liquid
solvents: computational methodology for updating
existing ion-specific equation coefficients
William E. Acree Jr. & Bihan Jiang
To cite this article: William E. Acree Jr. & Bihan Jiang (2016): Abraham model correlations for
ionic liquid solvents: computational methodology for updating existing ion-specific equation
coefficients, Physics and Chemistry of Liquids, DOI: 10.1080/00319104.2016.1218878
To link to this article: http://dx.doi.org/10.1080/00319104.2016.1218878
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LETTER
Abraham model correlations for ionic liquid solvents:
computational methodology for updating existing ion-specific
equation coefficients
William E. Acree Jr. and Bihan Jiang
Department of Chemistry, University of North Texas, Denton, TX, USA
ABSTRACT
The computational methodology for updating existing values of
Abraham model ion-specific equation coefficients is illustrated using
published experimental solubility and partition coefficient for solutes
dissolved in 1-ethyl-3-methylimidazolium trifluoroacetate, 1-butyl-3-
methylimidazolium trifluoroacetate and 1-hexyl-3-methylimidazolium tri-
fluoroacetate. The updated Abraham model ion-specific equation coeffi-
cients that are reported for the trifluoroacetate anion are based on 51
experimental values.
ARTICLE HISTORY
Received 31 May 2016
Accepted 27 July 2016
KEYWORDS
Ionic liquids; Abraham
model; ion-specific equation
coefficients; trifluoroacetate
anion
The last set of updated Abraham model ion-specific equation coefficients for ionic liquid (IL)
solvents were reported in this journal [1] for 40 different cations and 16 different anions. The
equation coefficients, when combined as a cation plus anion sum, yield mathematical correlations:
log P ¼ cp;cation þ cp;anion þ ep;cation þ ep;anion
À Á
E þ sp;cation þ sp;anion
À Á
S þ ap;cation þ ap;anion
À Á
A
þ bp;cation þ bp;anion
À Á
B þ vp;cation þ vp;anion
À Á
V
(1)
log K ¼ ck;cation þ ck;anion þ ek;cation þ ek;anion
À Á
E þ sk;cation þ sk;anion
À Á
S þ ak;cation þ ak;anion
À Á
A
þ bk;cation þ bk;anion
À Á
B þ lk;cation þ lk;anion
À Á
L
(2)
for predicting the logarithms of the water-to-liquid and gas-to-liquid partition coefficients, log P
and log K, of solutes dissolved in 640 (40 × 16) anhydrous ionic liquid solvents. In Equations (1)
and (2) the lowercase alphabetic characters on the right-hand side represent the cation-specific
and anion-specific equation coefficients. The uppercase alphabetic characters represent the solute
descriptors, which are designated as follows: the solute excess molar refractivity in units of
(cm3
mol–1
)/10 (E), the solute dipolarity/polarisability (S), the overall or summation hydrogen-
bond acidity and basicity (A and B, respectively), the McGowan volume in units of (cm3
mol–1
)/
100 (V), and the logarithm of the gas-to-hexadecane partition coefficient at 298 K (L).
Since the publication of the updated ion-specific equation coefficients, we have added values for
several new cations (namely 1-butyl-2,3-dimethylimidazolium,[2] 4-cyano-1-butylpyridinium,[2] 1-
hexylquinuclidinium,[3] 1-octyalquinuclidinium,[3] 2-methoxyethyl(dimethyl)ethylammonium [4])
and new anions (4,5-dicyano-2-(trifluoromethyl)imidazolide,[5] L-lactate,[6] (1S)-(+)-10-camphorsul-
fonate [6]). The added values were based on experimental partition coefficient data for solutes dissolved
CONTACT William E. Acree Jr. acree@unt.edu
© 2016 Informa UK Limited, trading as Taylor & Francis Group.
PHYSICS AND CHEMISTRY OF LIQUIDS, 2016
http://dx.doi.org/10.1080/00319104.2016.1218878

in a single IL solvent containing the new cation and/or anion. The added ion-specific equation
coefficients were calculated as the ionic liquid-specific equation coefficient minus the corresponding
equation coefficient for the counter-ion. For example, let’s suppose that one wished to calculate the ion-
specific equation coefficients for the 4-cyano-1-butylpyridinium cation from experimental partition
coefficient data of solutes dissolved 4-cyano-1-butylpyridinum tetrafluoroborate. One would first
determine the IL-specific equation coefficients for the IL solvent by regressing the partition coefficient
in accordance with the Abraham model. Such analysis would give the six equation coefficients as their
respective cation plus anion sum. The ion-specific equation coefficients of 4-cyano-1-butylpyridinum
could be obtained as the difference in the calculated IL-specific equation coefficient minus the
respective ion-specific equation coefficient for the tetrafluoroborate anion (e.g. ck;cation ¼ ck;il À
ck;anion; ek;cation ¼ ek;il À ek;anion; sk;cation ¼ sk;il À sk;anion; ak;cation ¼ ak;il À ak;anion; bk;cation ¼ bk;il À
bk;anion; lk;cation ¼ lk;il À lk;anion), provided of course that the ion-specific equation coefficients for the
tetrafluoroborate anion are known.
At the time the ion-specific equation coefficient version of the Abraham model was first
proposed provisions were made for adding coefficients for new cations/anions and for revising
existing coefficient values as new experimental data became available. A methodology was
proposed that did not require regression analysis of the entire set of log P and log K values,
which now numbers over 4000 experimental data points in each data set, every time new
values were added or existing values were updated. Thus far we have been primarily concerned
with adding new values. The opportunity has arisen where we can now illustrate the computa-
tional methodology for updating existing equation coefficients. We illustrate the methodology
for the trifluoracetate anion. Our existing equation coefficients for trifluoroacetate [1] were
based on a total 32 experimental data points, namely on the partition coefficient data for 28
organic solutes dissolved in 1-ethyl-3-methylimidazolium trifluoroacetate, ([EMIm]+
[AcF3]–
),
[7] on solubility data for carbon dioxide dissolved in ([EMIm]+
[AcF3]–
),[8] and on solubility
data for three gases (hydrogen,[9] carbon monoxide [10] and carbon dioxide [11]) dissolved in
1-butyl-3-methylimidazolium trifluoroacetate, ([BMIm]+
[AcF3]–
). The existing equation coeffi-
cients for trifluoroacetate that are reported in the paper by Stephens and co-workers [1] have a
fairly large standard error associated with the individual values, for example sk,anion = 0.545
(0.368) and ak,anion = 3.113(0.735), where the standard error in the respective equation
coefficient is given in parentheses. Recently published infinite dilution activity coefficients,
γ1
solute, for solutes dissolved in 1-hexyl-3-methylimidazolium trifluoroacetate,
([HMIm]+
[AcF3]–
),[12] provide us experimental data for a third IL solvent containing the
trifluoroacetate anion.
The computations begin by first converting the published γ1
solute data for solutes dissolved in
([HMIm]+
[ACF3]−
) to log K and log P values using standard thermodynamic relationships [13]:
log K ¼ log
RT
γ1
solutePo
soluteVsolvent

(3)
log P ¼ log K À log Kw (4)
where R is the universal gas constant, T is the system temperature, Po
solute is the vapour pressure of
the solute at T, Vsolvent is the molar volume of the solvent, and log Kw is the logarithm of the
solute’s gas-to-water partition coefficient at the system temperature, which for the present
communication is 298.15 K. Defined in this way, K is dimensionless. The log K and log P values
for solutes dissolved in ([EMIm]+
[AcF3]–
) and ([BMIm]+
[AcF3]–
) were taken from Stephens et al.
[1] For convenience we have tabulated the log P and log K values for the three ionic liquids in
Table 1. To isolate the ion-specific equation coefficients for the trifluoroacetate anion one then
subtracts the cation contribution to the log P and log K values yielding:
2 W. E. ACREE AND B. JIANG

log P À cp;cation À ep;cationE À sp;cationS À ap;cationA À bp;cationB À vp;cationV ¼ cp;anion þ ep;anionE
þ sp;anionS þ ap;anionA þ bp;anionB þ vp;anionV
(5)
Anion contribution to log P ¼ cp;anion þ ep;anion E þ sp;anionS þ ap;anionA þ bp;anionB
þ vp;anionV (6)
log K À ck;cation À ek;cation E À sk;cationS À ak;cationA À bk;cationB À lk;cationL ¼ ck;anion þ ek;anionE
þ sk;anionS þ ak;anionA þ bk;anionB þ lk;anionL
(7)
Anion contribution to log K ¼ ck;anion þ ek;anionE þ sk;anionS þ ak;anionA þ bk;anionB
þ lk;anionL (8)
Also given in Table 1 are the anion contribution to log P and anion contribution to log K
values, which were calculated using the cation-specific equation coefficients for [EMIm]+
,
[BMIm]+
, and [HMIm]+
taken from Tables 7 and 9 of the paper by Stephens and co-workers.[1]
The anion-specific equation coefficients for [AcF3] –
are the equation coefficients of Equations
(9) and (10):
Anion contribution to log P 298Kð Þ ¼ À 0:361 0:069ð Þ þ 0:203 0:124ð ÞS þ 4:082 0:238ð ÞA À 0:427 0:212ð ÞB
þ 0:092 0:071ð ÞV
(9)
SD ¼ 0:137; N ¼ 51; R2
¼ 0:946; and F ¼ 201:0
À Á
and
Anion contribution to log K 298Kð Þ ¼ À 0:340 0:039ð Þ þ 0:144 0:129ð ÞE þ 0:069 0:166ð ÞS þ 4:208 0:194ð ÞA
À 0:479 0:203ð ÞB þ 0:022 0:015ð ÞL
(10)
SD ¼ 0:105; N ¼ 51; R2
¼ 0:968; and F ¼ 274:9
À Á
which were obtained simply by regressing the 51 anion contribution to log P and 51 anion
contribution to log K numerical values in the last two columns of Table 1 in accordance with
Abraham model Equations (6) and (8) above. Standard errors in the calculated anion-specific
equation coefficients are given in parentheses immediately following the respective coefficient.
The statistical information associated with the Equations (9) and (10) includes the number of
experimental data points (N), the standard deviation (SD), the squared correlation coefficient
(R2
) and the Fisher F-statistic (F). Also included in the regression analyses are the logarithms
of the solubility ratios, log (CS,organic/CS,water) and log (CS,organic/CS,gas), calculated from the
molar solubility of xylitol logarithm of the aqueous molar solubility = log 0.62;
log Kw = 12.13) in ([EMIm]+
[AcF3]–
) determined by Carneiro et al. [14] The subscripts
indicate the phase to which the solute molar concentrations pertain. For convenience we
have tabulated the numerical values of the solute descriptors used in the regression analyses in
Table 2. The updated ion-specific equation coefficients for the trifluoroacetate anion are based
on 51 experimental data points, and as one might expect, the standard errors in each
calculated equation coefficient have been significantly reduced. There is insufficient experi-
mental data for us to determine the predictive ability of the revised ion-specific equation
coefficients for the trifluoroacetate anion. In terms of predictive ability, we remind readers
that the predictions require knowledge of both the cation-specific and anion-specific equation
PHYSICS AND CHEMISTRY OF LIQUIDS 3

coefficients. As such, it is difficult to give a predictive ability without knowing the uncertainty
in the cation-specific equation coefficient. Several of our existing cation-specific equation
coefficients are based on several hundred experimental values, while other cation-specific
equation coefficients are based on relatively few experimental values. The computational
Table 1. Numerical values of the logarithms of the partition coefficients and anion’s contribution to log K and log P values used
in determining updated anion-specific equation coefficients for the trifluoroacetate ion.
Solute log K log P Anion Contribution to log Ka
Anion Contribution to log Pb
IL = ([HMIm]+
[AcF3]–
)
Benzene 2.562 1.932 −0.245 −0.174
Toluene 2.925 2.275 −0.288 −0.336
Ethylbenzene 3.258 2.678 −0.278 −0.391
m-Xylene 3.308 2.698 −0.299 −0.331
p-Xylene 3.298 2.798 −0.310 −0.230
o-Xylene 3.491 2.831 −0.271 −0.216
Styrene 3.709 2.759 −0.197 −0.183
Acetone 2.257 −0.533 −0.429 −0.452
Methanol 3.795 0.055 1.322 1.481
Ethanol 3.775 0.105 1.086 1.004
1-Propanol 4.183 0.623 1.083 1.018
2-Propanol 3.675 0.195 0.947 0.916
2-Methyl-1-propanol 4.382 1.082 1.056 0.984
Tetrahydrofuran 2.354 −0.196 −0.555 −0.429
1,4-Dioxane 2.990 −0.720 −0.671 −0.539
Acetonitrile 2.905 0.055 −0.201 −0.142
Ethyl acetate 2.468 0.308 −0.410 −0.521
Chlorobenzene 3.392 2.572 −0.291 −0.339
IL = ([MEIm]+
[AcF3]–
)
Pentane 0.601 2.301 −0.308 −0.222
Hexane 0.922 2.742 −0.318 −0.227
Heptane 1.248 3.208 −0.294 −0.206
Octane 1.597 3.707 −0.303 −0.153
Nonane 1.940 4.090 −0.290 −0.216
Decane 2.271 4.591 −0.289 −0.161
Cyclopentane 1.126 2.006 −0.243 −0.274
Cyclohexane 1.442 2.342 −0.249 −0.390
Cycloheptane 1.953 2.533 −0.226 −0.656
Cyclooctane 2.415 3.185 −0.178 −0.463
1-Pentene 0.848 2.078 −0.226 −0.068
1-Hexene 1.230 2.390 −0.186 −0.199
1-Heptene 1.539 2.759 −0.200 −0.279
1-Octene 1.860 3.270 −0.209 −0.214
1-Pentyne 1.806 1.816 0.083 0.090
1-Hexyne 2.121 2.331 0.143 0.139
1-Heptyne 2.624 3.064 0.340 0.326
1-Octyne 2.730 3.250 0.129 0.071
Benzene 2.614 1.984 −0.051 0.004
Toluene 2.937 2.287 −0.080 −0.137
Ethylbenzene 3.178 2.598 −0.126 −0.228
o-Xylene 3.404 2.744 −0.126 −0.072
p-Xylene 3.235 2.645 −0.133 −0.144
m-Xylene 3.232 2.622 −0.136 −0.169
Methanol 3.613 −0.127 1.100 1.234
Ethanol 3.714 0.044 1.049 0.939
1-Propanol 4.063 0.503 1.042 0.954
1-Butanol 4.482 1.022 1.089 1.030
Carbon dioxide 0.439 0.519 0.073 0.045
Xylitol 11.831 −0.299 1.921 1.986
IL = ([MBIm]+
[AcF3]–
)
Carbon monoxide −1.298 0.322 −0.306 −0.209
Hydrogen −1.620 0.100 −0.345 −0.220
Carbon dioxide 0.384 0.464 −0.008 −0.021
a
Anion contribution to log K is defined according to Equations (7) and (8).
b
Anion contribution to log P is defined according to Equations (5) and (6).

methodology that we have used in the present communication allows one to update existing
ion-specific equation coefficients as new experimental data becomes available.
Acknowledgement
Bihan Jiang thanks the University of North Texas’s Texas Academy of Math and Science (TAMS) program for a
summer research award.
Disclosure statement
No potential conflict of interest was reported by the authors.
Table 2. Numerical values of the solute descriptors for the compounds studied.
Solute E S A B L V
Hydrogen 0.000 0.000 0.000 0.000 −1.200 0.1086
Carbon monoxide 0.000 0.000 0.000 0.040 −0.836 0.2220
Carbon dioxide 0.000 0.280 0.050 0.100 0.058 0.2810
Pentane 0.000 0.000 0.000 0.000 2.162 0.8130
Hexane 0.000 0.000 0.000 0.000 2.668 0.9540
Heptane 0.000 0.000 0.000 0.000 3.130 1.0950
Octane 0.000 0.000 0.000 0.000 3.677 1.2360
Nonane 0.000 0.000 0.000 0.000 4.182 1.3770
Decane 0.000 0.000 0.000 0.000 4.686 1.5180
Cyclopentane 0.263 0.100 0.000 0.000 2.477 0.7050
Cyclohexane 0.305 0.100 0.000 0.000 2.964 0.8450
Cycloheptane 0.350 0.100 0.000 0.000 3.704 0.9863
Cyclooctane 0.413 0.100 0.000 0.000 4.329 1.1272
1-Pentene 0.093 0.080 0.000 0.070 2.047 0.7700
1-Hexene 0.078 0.080 0.000 0.070 2.572 0.9110
1-Heptene 0.092 0.080 0.000 0.070 3.063 1.0520
1-Octene 0.094 0.080 0.000 0.070 3.568 1.1930
1-Pentyne 0.172 0.230 0.120 0.120 2.010 0.7271
1-Hexyne 0.166 0.220 0.100 0.120 2.510 0.8680
1-Heptyne 0.160 0.230 0.090 0.100 3.000 1.0090
1-Octyne 0.155 0.220 0.090 0.100 3.521 1.1500
Benzene 0.610 0.520 0.000 0.140 2.786 0.7160
Toluene 0.601 0.520 0.000 0.140 3.325 0.8570
Ethylbenzene 0.613 0.510 0.000 0.150 3.788 0.9980
o-Xylene 0.663 0.560 0.000 0.160 3.939 0.9980
p-Xylene 0.613 0.520 0.000 0.160 3.839 0.9980
m-Xylene 0.623 0.520 0.000 0.160 3.839 0.9980
Styrene 0.849 0.650 0.000 0.160 3.908 0.9550
Methanol 0.278 0.440 0.430 0.470 0.970 0.3080
Ethanol 0.246 0.420 0.370 0.480 1.485 0.4490
1-Propanol 0.236 0.420 0.370 0.480 2.031 0.5900
1-Butanol 0.224 0.420 0.370 0.480 2.601 0.7309
2-Propanol 0.212 0.360 0.330 0.560 1.764 0.5900
2-Methyl-1-propanol 0.217 0.390 0.370 0.480 2.413 0.7309
Acetone 0.179 0.700 0.040 0.490 1.696 0.5470
Tetrahydrofuran 0.289 0.520 0.000 0.480 2.636 0.6223
1,4-Dioxane 0.329 0.750 0.000 0.640 2.892 0.6810
Acetonitrile 0.237 0.900 0.070 0.320 1.739 0.4042
Ethyl acetate 0.106 0.620 0.000 0.450 2.314 0.7470
Chlorobenzene 0.718 0.650 0.000 0.070 3.657 0.8388
Xylitol 1.040 1.770 0.540 1.430 6.087 1.1066
PHYSICS AND CHEMISTRY OF LIQUIDS 5

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