This document discusses Abraham model ion-specific equation coefficients that were calculated for two ionic liquid cations, 1-butyl-2,3-dimethyimidazolium and 4-cyano-1-butylpyridinium, based on measured gas-to-liquid and water-to-liquid partition coefficient data for those cations. The document summarizes the data and correlations used to derive the new ion-specific equation coefficients, which will allow prediction of partition coefficients for solutes in additional ionic liquids containing those cations.

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Abraham model ion-specific equation coefficients
for the 1-butyl-2,3-dimethyimidazolium and 4-
cyano-1-butylpyridinium cations calculated from
measured gas-to-liquid partition coefficient data
Amber Lu, Bihan Jiang, Sarah Cheeran, William E. Acree Jr. & Michael H.
Abraham
To cite this article: Amber Lu, Bihan Jiang, Sarah Cheeran, William E. Acree Jr. & Michael
H. Abraham (2016): Abraham model ion-specific equation coefficients for the 1-
butyl-2,3-dimethyimidazolium and 4-cyano-1-butylpyridinium cations calculated from
measured gas-to-liquid partition coefficient data, Physics and Chemistry of Liquids, DOI:
10.1080/00319104.2016.1191634
To link to this article: http://dx.doi.org/10.1080/00319104.2016.1191634
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2. Abraham model ion-specific equation coefficients for the
1-butyl-2,3-dimethyimidazolium and 4-cyano-1-butylpyridinium
cations calculated from measured gas-to-liquid partition
coefficient data
Amber Lua
, Bihan Jianga
, Sarah Cheerana
, William E. Acree Jr.a
and Michael H. Abrahamb
a
Department of Chemistry, University of North Texas, Denton, TX, USA; b
Department of Chemistry, University
College London, London, UK
ABSTRACT
Partition coefficient and gas solubility data have been assembled from
the published chemical and engineering literature for solutes dissolved
in anhydrous 1-butyl-3-methylimidazolium dicyanamide, 1-butyl-2,3-
dimethylimidazolium bis(trifluoromethylsulfonyl)imide, and 4-cyano-1-
butylpyrridinium bis(trifluoromethylsulfonyl)imide. More than 60 experi-
mental data points were gathered for each IL solvent. The compiled
experimental data were used to derive Abraham model correlations for
describing the solute transfer properties into the three anhydrous IL
solvents from both the gas phase and water. The derived mathematical
correlations described the observed solute transfer properties, expressed
as the logarithm of the water-to-IL partition coefficient and logarithm of
the gas-to-IL solvent partition coefficient, to within standard deviations
of 0.125 log units (or less). Abraham model ion-specific equation coeffi-
cients are also calculated for the 1-butyl-2,3-dimethylimidazolium and 4-
cyano-1-butylpyridinium cations.
ARTICLE HISTORY
Received 24 March 2016
Accepted 16 May 2016
KEYWORDS
Ionic liquid solvents;
partition coefficients;
predictive methods; cation-
specific contributions; anion-
specific contributions
1. Introduction
Chemical sustainability and environmental safety are important considerations in the solvent
selection process. Organic solvents are omnipresent in most chemical synthetic procedures and in
chemical separation processes, such as liquid–liquid extraction and high-performance liquid
chromatography. Organic solvents represent a major manufacturing expense, and is one of the
major contributors to industrial manufacturing waste streams. Growing environmental awareness,
combined with more stringent governmental regulations regarding both worker safety and
chemical waste disposal, has prompted the manufacturing sector to search for safer and envir-
onmentally benign chemical replacements for the more toxic and more harmful organic solvents.
Of the suggested chemical replacements, ionic liquids (ILs) have shown considerable promise as
an organic solvent media for synthesising many different classes of organic compounds, as a
sorbent for greenhouse gas and acidic gas capture in natural gas and post-combustion treatments,
as a dissolving media for lignocellulosic biomass, and as a stationary phase liquid or surface-
bonded stationary phase for gas–liquid chromatography and high-performance liquid chromato-
graphy, respectively. Favourable physicochemical properties, such as high thermal and chemical
stabilities, negligible vapour pressures, low melting point temperatures, wide liquid temperature
ranges, and immiscibility with many organic solvents facilitate the use of ILs in many practical
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/10.1080/00319104.2016.1191634

3. industrial applications. The physicochemical properties and solubilising character of ILs can be
controlled by the judicious selection of cation–anion pair, and by the addition of polar and/or
hydrogen-bonding groups onto the alkyl chain of the cation. Considerable attention has been
given in recent years towards developing mathematical expressions for estimating the physical
properties and solubilising characteristics of IL solvents based on both group contribution
methods and quantitative structure–property relationships. To date group contribution methods
have been developed for predicting infinite dilution activity coefficients and gas–liquid partition
coefficients of solutes dissolved in ILs,[1–3] for predicting enthalpies of solvation of organic
solutes dissolved in ILs,[4] and for estimating viscosities,[5,6] thermal conductivities [7,8] isobaric
heat capacities,[9–11] refractive indices,[12] static dielectric constants,[13] surface tensions,[14]
densities,[15] and Daphnia magna water flea toxicities [16] of ILs at both 298 K and as a function
of temperature.
Our contributions in the area of solvent selection has been to develop solution models that
enable prediction of the solubility of crystalline non-electrolyte solutes in binary [17–21] and
ternary [22–28] solvent mixtures based on the Nearly Ideal Binary Solvent Model and Abraham
model correlations that enable estimation of the logarithm of gas-to-organic solvent partition
coefficients (log K) and logarithm of water-to-organic solvent partition coefficients (log P) in both
traditional and anhydrous IL organic solvents. Abraham model correlations have been reported
for well over 100 total different tradition organic solvents [29–46] and IL organic solvents,[47–61]
as well as for binary aqueous-ethanol [62] mixtures. Our focus in the present study is IL solvents.
For neat, anhydrous IL solvents, we have reported IL-specific Abraham model correlations
[47–61]:
log P ¼ cp;il þ ep;il Á E þ sp;il Á S þ ap;il Á A þ bp;il Á B þ vp;il Á V (1)
log K ¼ ck;il þ ek;il Á E þ sk;il Á S þ ak;il Á A þ bk;il Á B þ lk;il Á L (2)
and Abraham model correlations containing ion-specific equation coefficients [63–66]:
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
(3)
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
(4)
Abraham model correlations containing fragment-group values [1,2]:
log P ¼
X
group
ni cp;i þ
X
group
ep;i ni E þ
X
group
sp;i ni S þ
X
group
ap;i ni A þ
X
group
bp;i ni B þ
X
group
vp;i ni Vþ
ðcp;anion þ ep;anion E þ sp;anion S þ ap;anion A þ bp;anion B þ vp;anion VÞ
(5)
log K ¼
X
group
ni ck;i þ
X
group
ek;i ni E þ
X
group
sk;i ni S þ
X
group
ak;i ni A þ
X
group
bk;i ni B þ
X
group
lk;i ni L þ
ðck;anion þ ek;anion E þ sk;anion S þ ak;anion A þ bk;anion B þ lk;anion LÞ
(6)
have also been published for predicting the logarithms of solute partition coefficients into
anhydrous IL solvents from both water (log P) and gas phase (log K). In Equations (5) and (6),
2 A. LU ET AL.

4. ni denotes the number of times that the given fragment group appears in the cation, and the
summations extend over all fragment groups.
Predictive applications using Equations (1)–(6) require knowledge of the solute descriptors
(upper-case letters) and equation coefficients/fragment group values (lower-case letters) for the
solutes and ILs of interest. Solute descriptors are available for more than 5000 different organic
and inorganic compounds, and are defined as follows: the solute excess molar refractivity in units
of (cm3
mol−1
)/10 (E), the solute dipolarity/polarizability (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). To date, we
have reported IL-specific equation coefficients for more than 60 different ILs (Equations (1) and
(2)), ion-specific equation coefficients for 43 different cations and 17 different anions (Equations
(3) and (4)), and numerical group values for 12 cation fragments (CH3-, –CH2-, –O-, -O─Ncyclic,
-OH, CH2cyclic, CHcyclic, Ccyclic, Ncyclic, >N<+
, >P<+
, and >S–+
) and 9 individual anions (Tf2N−
,
PF6
−
, BF4
−
, EtSO4
−
, OcSO4
−
, SCN−
, CF3SO3
−
, AcF3
−
, and (CN)2N−
) (Equations (5) and (6)). The
43 different cation-specific and 16 different anion-specific equation coefficients can be combined
to permit the estimation of log P and log K values for solutes in a total of 731 different ILs (i.e.
43 × 17). The number of ion-specific equation coefficients and fragment group values is expected
to increase as additional experimental data become available for functionalised IL solvents.
At the time Equations (3) and (4) were published, we proposed a computational methodology
for adding new ion-specific equation coefficients to our existing database. The methodology
enables new ion-specific coefficients to be added without having to perform a regression analysis
on the entire log K (or log P) data. The methodology allows one to retain the numerical values of
the ion-specific equation coefficients that have already been calculated. For example, ion-specific
equation coefficients of a new cation could be obtained as the difference in the calculated IL-
specific equation coefficient minus the respective anion-specific equation coefficient, for example,
ck,cation = ck,il − ck,anion, ek,cation = ek,il − ek,anion, sk,cation = sk,il − sk,anion, ak,cation = ak,il − ak,anion, bk,
cation = bk,il − bk,anion, lk,cation = lk,il − lk,anion, provided of course that the anion-specific equation
coefficients are known. Our goal is to develop a similar computational methodology that allows
one to calculate values for new fragment groups from known cation-specific equation coefficients
and from known fragment group values, for example, ck;cation ¼
P
group
ni ck;i; ek;cation ¼
P
group
ek;i ni ; sk;cation ¼
P
group
sk;i ni; and so on: The advantage of such a computational method is
that the equation coefficients for the anions would be the same in both the ion-specific Abraham
model and fragment-group Abraham model, thus allowing one to add new anions in the
fragment-group model with minimal effort. Implementation and assessment of the new metho-
dology, however, does require us to add additional cation-specific equation coefficients to our
existing values as some functional groups are poorly represented in the ILs that we have studied
thus far. In the present study, we develop IL-specific Abraham model log K and log P correlations
for three additional anhydrous IL solvents, namely 1-butyl-3-methylimidazolium dicyanamide
([BMIm]+
[N(CN)2]−
), 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide
([BM2Im]+
[(Tf)2N]−
), and 4-cyano-1-butylpyrridinium bis(trifluoromethylsulfonyl)imide ([4-
CNBPy]+
[(Tf)2N]−
) from recently published log K data taken from the chemical literature [67–
69] Cation-specific equation coefficients are also calculated for both [BM2Im]+
and [4-CNBPy]+
.
As an information note, Xiang and co-workers [69] did report IL-specific Abraham model log K
correlations for ([BM2Im]+
[(Tf)2N]−
) at 313.15 K, 323.15 K, and 333.15 K. We have extended the
log K correlations for ([BM2Im]+
[(Tf)2N]−
) to include 298.15 K. Xiang and co-workers did not
report an Abraham model correlation for log P, nor did the authors consider the ion-specific
equation coefficient version of the Abraham general solvation model.
PHYSICS AND CHEMISTRY OF LIQUIDS 3

5. 2. Gas-to-IL and water-to-IL partition coefficient data sets
The published partition coefficient data for the solutes dissolved in ([BMIm]+
[N(CN)2]−
),
([BM2Im]+
[(Tf)2N]−
) and ([4-CNBPy]+
[(Tf)2N]−
) were performed at several temperatures slightly
higher than 298.15 K. The numerical log K (at 298.15 K) used in the present study were calculated
from the standard thermodynamic log K versus 1/T linear relationship based on the measured
values at either 318.15 K and 328.15 K for ([BMIm]+
[N(CN)2]−
), or 313.15 K and 323.15 K for
([BM2Im]+
[(Tf)2N]−
), or 308.15 K and 318.15 K for ([4-CNBPy]+
[(Tf)2N]−
). These were the two
lowest temperatures that were studied for each IL solvent. The linear extrapolation should be valid
as the measurements were performed at temperatures not too far removed from the desired
temperature of 298.15 K (about 30 K in the worst case).
Our search of the published literature for additional log K values did find gas solubility data for
carbon dioxide,[70] nitrogen gas,[70] nitrous oxide,[71] ethane,[72] ethylene,[72] and vinyl
acetate [73] dissolved in ([BMIm]+
[N(CN)2]−
). The published gas solubility data was reported
in terms of Henry’s law constants, KHenry. Experimental Henry’s law constants can be converted to
gas-to-IL partition coefficients through Equation (7):
log K ¼ log
RT
KHenry Vsolvent
; (7)
where R is the universal constant law constant, Vsolvent is the molar volume of the IL solvent, and
T is the system temperature. We were unable to find any solubility data for the inorganic gases or
small gaseous organic solutes dissolved in ([BM2Im]+
[(Tf)2N]−
) and ([4-CNBPy]+
[(Tf)2N]−
).
The Abraham general solvation parameter model also contains provisions for describing solute
transfer from water into anhydrous IL solvents. Here, the solute transfer represents a hypothetic
partitioning process in which the IL solvent is not in direct contact with the aqueous phase. We
still denote the transfer process as log P, and calculate the numerical via Equation (8)
log P ¼ log K À log Kw (8)
The conversion of log K data to log P requires a prior knowledge of the solute’s gas-phase
partition coefficient into water, Kw, which is available for most of the solutes being studied. Log P
values calculated in this fashion are still useful because the predicted log P values can be used to
estimate the solute’s infinite dilution activity coefficient in the IL, γsolute
∞
,
log P þ log KW ¼ log
RT
γsolute
1Psolute
o
Vsolvent
; (9)
where Psolute
o
is the vapour pressure of the organic solute at the system temperature (T). Infinite dilution
activity coefficients assist practicing analytical chemists and process chemical engineers in selecting the
‘best’ IL solvent for achieving the desired chemical separation. The solutes’ gas-phase partition coeffi-
cients into water (KW) needed for these calculations were taken from the published literature.[47,48,74]
The calculated log K and log P values at 298.15 K are assembled in Tables 1–3 for solutes dissolved
in ([BMIm]+
[N(CN)2]−
), ([BM2Im]+
[(Tf)2N]−
) and ([4-CNBPy]+
[(Tf)2N]−
), respectively. The collec-
tion of more than 60 chemically diverse organic solutes include alkanes, alkenes, alkynes, aromatic and
heterocyclic compounds, primary and secondary alcohols, dialkyl ethers and cyclic ethers, alkanones,
alkyl alkanoates, and nitroalkanes. Also, collected in Tables 1–3 are the numerical solute descriptors
for the organic compounds studied in the present investigation. Numerical values of the solute
descriptors in our database are of experimental origin and were based on observed solubility data
and Henry’s law constants,[75–78] on measured gas–liquid and high-performance liquid chromato-
graphic retention times and retention factors,[79,80] and on experimental practical partition coeffi-
cient measurements for the equilibrium solute distribution between water and an immiscible (or
partially miscible) organic solvent.[81–83] The numerical solute descriptors define a set of chemical
4 A. LU ET AL.

6. Table1.Measuredlogarithmofgas-to-ILpartitioncoefficients,logK,andlogarithmofwater-to-ILpartitioncoefficients,logP,forsolutesdissolvedinanhydrous([BMIm]+
[N(CN)2]−
)at298.15K.
SoluteESABLVLogKLogP
Carbondioxide0.0000.2800.0500.1000.0580.28090.1670.245
Nitrogen0.0000.0000.0000.000−0.9780.2222−1.5400.260
Nitrousoxide0.0680.3500.0000.1000.1640.28100.1680.398
Ethane0.0000.0000.0000.0000.4920.3900−0.3391.001
Pentane0.0000.0000.0000.0002.1620.81310.6222.322
Hexane0.0000.0000.0000.0002.6680.95400.9682.788
3-Methylpentane0.0000.0000.0000.0002.5810.95400.9382.778
2,2-Dimethylbutane0.0000.0000.0000.0002.3520.95400.7172.557
Heptane0.0000.0000.0000.0003.1731.09491.3173.277
Octane0.0000.0000.0000.0003.6771.23581.6273.737
2,2,4-Trimethylpentane0.0000.0000.0000.0003.1061.23581.1903.310
Nonane0.0000.0000.0000.0004.1821.37671.9454.095
Decane0.0000.0000.0000.0004.6861.51762.2454.565
Cyclopentane0.2630.1000.0000.0002.4770.70451.2102.090
Cyclohexane0.3050.1000.0000.0002.9640.84541.5512.451
Methylcyclohexane0.2440.0600.0000.0003.3190.98631.6602.910
Cycloheptane0.3500.1000.0000.0003.7040.98632.0812.661
Cyclooctane0.4130.1000.0000.0004.3291.12722.5423.312
Ethene0.1070.1000.0000.0700.2890.3470−0.1200.820
1-Pentene0.0930.0800.0000.0702.0470.77010.9522.182
1-Hexene0.0780.0800.0000.0702.5720.91101.2852.445
Cyclohexene0.3950.2800.0000.0902.9520.82041.9682.238
1-Heptene0.0920.0800.0000.0703.0631.05191.6202.840
1-Octene0.0940.0800.0000.0703.5681.19281.9403.350
1-Decene0.0930.0800.0000.0704.5541.47462.5414.181
1-Pentyne0.1720.2300.1200.1202.0100.72711.8381.848
1-Hexyne0.1660.2200.1000.1202.5100.86802.1782.388
1-Heptyne0.1600.2300.1200.1003.0001.00892.4782.918
1-Octyne0.1550.2200.0900.1003.5211.14982.7903.310
Benzene0.6100.5200.0000.1402.7860.71642.7732.143
Toluene0.6010.5200.0000.1403.3250.85733.1002.450
Ethylbenzene0.6130.5100.0000.1503.7780.99823.3352.755
o-Xylene0.6630.5600.0000.1603.9390.99823.6032.943
m-Xylene0.6230.5200.0000.1603.8390.99823.4182.808
p-Xylene0.6130.5200.0000.1603.8390.99823.4202.830
Propylbenzene0.6040.5000.0000.1504.2301.13903.5913.201
Isopropylbenzene0.6020.4900.0000.1604.0841.13903.4753.035
Styrene0.8490.6500.0000.1603.9080.95503.9052.955
α-Methylstyrene0.8510.6400.0000.1904.2901.09604.0953.135
Methanol0.2780.4400.4300.4700.9700.30823.297−0.443
(Continued)
PHYSICS AND CHEMISTRY OF LIQUIDS 5

7. Table1.(Continued).
SoluteESABLVLogKLogP
Ethanol0.2460.4200.3700.4801.4850.44913.403−0.267
1-Propanol0.2360.4200.3700.4802.0310.59003.7410.181
2-Propanol0.2120.3600.3300.5601.7640.59003.375−0.105
1-Butanol0.2240.4200.3700.4802.6010.73094.1010.641
2-Butanol0.2170.3600.3300.5602.3380.73093.6770.287
tert-Butanol0.1800.3000.3100.6001.9630.73093.3160.036
Thiophene0.6870.5700.0000.1502.8190.64113.0762.036
Tetrahydrofuran0.2890.5200.0000.4802.6360.62232.6270.077
1,4-Dioxane0.3290.7500.0000.6402.8920.68103.432−0.278
Methyltert-butylether0.0240.2200.0000.5502.3720.87181.7730.153
Ethyltert-butylether−0.0200.1800.0000.5902.6991.01271.6350.365
Methyltert-amylether0.0500.2100.0000.6002.9161.01272.0990.629
Diethylether0.0410.2500.0000.4502.0150.73091.4510.281
Dipropylether0.0080.2500.0000.4502.9541.01271.8720.982
Diisopropylether−0.0630.1700.0000.5702.5011.01271.5080.458
Dibutylether0.0000.2500.0000.4503.9241.29452.4791.789
Acetone0.1790.7000.0400.4901.6960.54702.670−0.120
2-Pentanone0.1430.6800.0000.5102.7550.82883.1700.590
3-Pentanone0.1540.6600.0000.5102.8110.82883.1500.650
Methylacetate0.1420.6400.0000.4501.9110.60572.5000.200
Ethylacetate0.1060.6200.0000.4502.3140.74662.6360.476
Methylpropanoate0.1280.6000.0000.4502.4310.74702.7110.561
Methylbutanoate0.1060.6000.0000.4502.9430.88802.9660.886
Butanal0.1870.6500.0000.4502.2700.68792.7610.431
Acetonitrile0.2370.9000.0700.3201.7390.40423.1770.327
Pyridine0.6310.8400.0000.5203.0220.67503.7790.339
1-Nitropropane0.2420.9500.0000.3102.8940.70553.9041.454
Vinylfluoride0.417
6 A. LU ET AL.

8. Table2.Measuredlogarithmofgas-to-ILpartitioncoefficients,logK,andlogarithmofwater-to-ILpartitioncoefficients,logP,forsolutesdissolvedinanhydrous([BM2Im]+
[(Tf)2N]−
)at298.15K.
SoluteESABLVLogKLogP
Heptane0.0000.0000.0000.0003.1731.09491.5973.557
Octane0.0000.0000.0000.0003.6771.23581.9944.104
Nonane0.0000.0000.0000.0004.1821.37672.3454.495
Decane0.0000.0000.0000.0004.6861.51762.6544.974
Methylcyclopentane0.2250.1000.0000.0002.9070.84541.5942.764
Cyclohexane0.3050.1000.0000.0002.9640.84541.7342.634
Methylcyclohexane0.2440.0600.0000.0003.3190.98631.9223.172
Cycloheptane0.3500.1000.0000.0003.7040.98632.2412.821
Cyclooctane0.4130.1000.0000.0004.3291.12722.6863.456
1-Hexene0.0780.0800.0000.0702.5720.91101.5172.677
Cyclopentene0.3350.2200.0000.0802.2730.66051.5922.002
Cyclohexene0.3950.2800.0000.0902.9520.82042.0342.304
1-Heptene0.0920.0800.0000.0703.0631.05191.8573.077
1-Octene0.0940.0800.0000.0703.5681.19282.2183.628
1-Nonene0.0900.0800.0000.0704.0731.33372.5364.046
1-Decene0.0930.0800.0000.0704.5541.47462.8684.508
1-Hexyne0.1660.2200.1000.1202.5100.86802.1852.395
1-Heptyne0.1600.2300.1200.1003.0001.00892.5032.943
1-Octyne0.1550.2200.0900.1003.5211.14982.8353.355
1-Nonyne0.1500.2200.0900.1004.0191.29073.1643.944
Benzene0.6100.5200.0000.1402.7860.71642.8282.198
Toluene0.6010.5200.0000.1403.3250.85733.1922.542
Ethylbenzene0.6130.5100.0000.1503.7780.99823.4442.864
o-Xylene0.6630.5600.0000.1603.9390.99823.6933.033
m-Xylene0.6230.5200.0000.1603.8390.99823.5272.917
p-Xylene0.6130.5200.0000.1603.8390.99823.5292.939
Methanol0.2780.4400.4300.4700.9700.30822.457−1.283
Ethanol0.2460.4200.3700.4801.4850.44912.633−1.037
1-Propanol0.2360.4200.3700.4802.0310.59002.946−0.614
2-Propanol0.2120.3600.3300.5601.7640.59002.720−0.760
1-Butanol0.2240.4200.3700.4802.6010.73093.322−0.138
2-Butanol0.2170.3600.3300.5602.3380.73092.991−0.399
2-Methyl-1-propanol0.2170.3900.3700.4802.4130.73093.121−0.179
tert-Butanol0.1800.3000.3100.6001.9630.73092.715−0.565
Thiophene0.6870.5700.0000.1502.8190.64112.9241.884
Tetrahydrofuran0.2890.5200.0000.4802.6360.62232.6670.117
1,4-Dioxane0.3290.7500.0000.6402.8920.68103.369−0.341
Methyltert-butylether0.0240.2200.0000.5502.3720.87181.9550.335
Ethyltert-butylether−0.0200.1800.0000.5902.6991.01271.9380.668
Methyltert-amylether0.0500.2100.0000.6002.9161.01272.3340.864
(Continued)
PHYSICS AND CHEMISTRY OF LIQUIDS 7

9. Table2.(Continued).
SoluteESABLVLogKLogP
Diethylether0.0410.2500.0000.4502.0150.73091.6040.434
Diisopropylether−0.0630.1700.0000.5702.5011.01271.8140.764
Acetone0.1790.7000.0400.4901.6960.54702.746−0.044
2-Pentanone0.1430.6800.0000.5102.7550.82883.3140.734
3-Pentanone0.1540.6600.0000.5102.8110.82883.2970.787
Ethylformate0.1460.6600.0000.3801.8450.60572.4960.536
Methylacetate0.1420.6400.0000.4501.9110.60572.5630.263
Ethylacetate0.1060.6200.0000.4502.3140.74662.8140.654
Vinylacetate0.2230.6400.0000.4302.1520.70402.6650.955
Propanal0.1960.6500.0000.4501.8150.54702.469−0.051
Butanal0.1870.6500.0000.4502.2700.68792.8110.481
Isobutanal0.1440.6200.0000.4502.1200.68792.6200.520
Acetonitrile0.2370.9000.0700.3201.7390.40423.1200.270
Nitromethane0.3130.9500.0600.3101.8920.42373.4000.450
Nitroethane0.2700.9500.0200.3302.4140.56463.6320.912
1-Nitropropane0.2420.9500.0000.3102.8940.70553.8541.404
2-Nitropropane0.2160.9200.0000.3302.5500.70553.6491.349
Dichloromethane0.3900.5700.1000.0502.0190.49432.2381.278
Trichloromethane0.4300.4900.1500.0202.4800.61672.5551.765
Tetrachloromethane0.4600.3800.0000.0002.8230.73912.2642.454
8 A. LU ET AL.

10. Table3.Measuredlogarithmofgas-to-ILpartitioncoefficients,logK,andlogarithmofwater-to-ILpartitioncoefficients,logP,forsolutesdissolvedinanhydrous([4-CNBPy]+
[(Tf)2N]−
)at298.15K.
SoluteESABLVLogKLogP
Pentane0.0000.0000.0000.0002.1620.81310.6222.322
Hexane0.0000.0000.0000.0002.6680.95401.0642.884
3-Methylpentane0.0000.0000.0000.0002.5810.95400.9992.839
2,2-Dimethylbutane0.0000.0000.0000.0002.3520.95400.7042.544
Heptane0.0000.0000.0000.0003.1731.09491.4403.400
Octane0.0000.0000.0000.0003.6771.23581.7923.902
2,2,4-Trimethylpentane0.0000.0000.0000.0003.1061.23581.3953.515
Nonane0.0000.0000.0000.0004.1821.37672.1464.296
Decane0.0000.0000.0000.0004.6861.51762.5264.846
Cyclopentane0.2630.1000.0000.0002.4770.70451.1522.032
Cyclohexane0.3050.1000.0000.0002.9640.84541.5162.416
Methylcyclohexane0.2440.0600.0000.0003.3190.98631.7262.976
Cycloheptane0.3500.1000.0000.0003.7040.98632.0652.645
Cyclooctane0.4130.1000.0000.0004.3291.12722.5943.364
1-Pentene0.0930.0800.0000.0702.0470.77010.9182.148
1-Hexene0.0780.0800.0000.0702.5720.91101.3842.544
Cyclohexene0.3950.2800.0000.0902.9520.82041.9602.230
1-Heptene0.0920.0800.0000.0703.0631.05191.7012.921
1-Octene0.0940.0800.0000.0703.5681.19282.0323.442
1-Decene0.0930.0800.0000.0704.5541.47462.7394.379
1-Pentyne0.1720.2300.1200.1202.0100.72711.6441.654
1-Hexyne0.1660.2200.1000.1202.5100.86802.0002.210
1-Heptyne0.1600.2300.1200.1003.0001.00892.3422.782
1-Octyne0.1550.2200.0900.1003.5211.14982.6703.190
Benzene0.6100.5200.0000.1402.7860.71642.8112.181
Toluene0.6010.5200.0000.1403.3250.85733.1992.549
Ethylbenzene0.6130.5100.0000.1503.7780.99823.4302.850
o-Xylene0.6630.5600.0000.1603.9390.99823.7413.081
m-Xylene0.6230.5200.0000.1603.8390.99823.5632.958
p-Xylene0.6130.5200.0000.1603.8390.99823.5432.953
Propylbenzene0.6040.5000.0000.1504.2301.13903.6863.296
Isopropylbenzene0.6020.4900.0000.1604.0841.13903.5343.094
Styrene0.8490.6500.0000.1603.9080.95503.9222.972
α-Methylstyrene0.8510.6400.0000.1904.2901.09604.1093.149
Methanol0.2780.4400.4300.4700.9700.30822.551−1.189
Ethanol0.2460.4200.3700.4801.4850.44912.723−0.947
1-Propanol0.2360.4200.3700.4802.0310.59003.064−0.496
2-Propanol0.2120.3600.3300.5601.7640.59002.767−0.713
1-Butanol0.2240.4200.3700.4802.6010.73093.419−0.041
2-Butanol0.2170.3600.3300.5602.3380.73093.080−0.310
(Continued)
PHYSICS AND CHEMISTRY OF LIQUIDS 9

11. Table3.(Continued).
SoluteESABLVLogKLogP
2-Methyl-1-propanol0.2170.3900.3700.4802.4130.73093.219−0.081
tert-Butanol0.1800.3000.3100.6001.9630.73092.775−0.505
1-Pentanol0.2190.4200.3700.4803.1060.87183.7740.424
Thiophene0.6870.5700.0000.1502.8190.64112.9551.915
Tetrahydrofuran0.2890.5200.0000.4802.6360.62232.8200.270
1,4-Dioxane0.3290.7500.0000.6402.8920.68103.634−0.076
Methyltert-butylether0.0240.2200.0000.5502.3720.87181.9410.321
Ethyltert-butylether−0.0200.1800.0000.5902.6991.01271.7390.469
Methyltert-amylether0.0500.2100.0000.6002.9161.01272.2960.826
Diethylether0.0410.2500.0000.4502.0150.73091.5860.416
Dipropylether0.0080.2500.0000.4502.9541.01272.0481.158
Diisopropylether−0.0630.1700.0000.5702.5011.01271.6360.586
Dibutylether0.0000.2500.0000.4503.9241.29452.6881.998
Acetone0.1790.7000.0400.4901.6960.54702.8940.104
2-Pentanone0.1430.6800.0000.5102.7550.82883.4260.846
3-Pentanone0.1540.6600.0000.5102.8110.82883.4100.910
Methylacetate0.1420.6400.0000.4501.9110.60572.7140.414
Ethylacetate0.1060.6200.0000.4502.3140.74662.9290.769
Methylpropanoate0.1280.6000.0000.4502.4310.74702.9910.841
Methylbutanoate0.1060.6000.0000.4502.9430.88803.2491.169
Butanal0.1870.6500.0000.4502.2700.68792.9270.597
Acetonitrile0.2370.9000.0700.3201.7390.40423.2310.381
Pyridine0.6310.8400.0000.5203.0220.67503.8310.391
1-Nitropropane0.2420.9500.0000.3102.8940.70553.9351.485
10 A. LU ET AL.

12. compounds having a fairly wide range of polarities and hydrogen-bonding capabilities as documented
by the values that fall within the range of: E = −0.063–0.851; S = 0.000–0.950; A = 0.000–0.430;
B = 0.000–0.640; V = 0.2222–1.5176; and L = −0.978–4.686. The above range of solute descriptors
pertain to ([BMIm]+
[N(CN)2]−
). Slightly smaller ranges are observed in the case of both
([BM2Im]+
[(Tf)2N]−
) and ([4-CNBPy]+
[(Tf)2N]−
). The smaller ranges for the latter two IL solvents,
particularly in the V and L solute descriptor ranges, results from the absence of inorganic and smaller
organic gases in the data sets. The inorganic gases and smaller organic gases have smaller V and L
descriptor values. Inorganic gases, such as nitrogen gas, nitrous oxide, and carbon dioxide have a
negative value for their L solute descriptor.
3. Results and discussion
Solute descriptors are available for 67 of the 68 organic and inorganic compounds in the
([BMIm]+
[N(CN)2]−
) database. Analysis of the experimental log P and log K values in Table 1 in
accordance with Equations (1) and (2) of the Abraham model gave the following two IL-specific
correlations:
log P ¼ À 0:272 0:065ð Þ þ 0:448 0:098ð Þ E þ 0:722 0:113ð Þ S þ 1:103 0:165ð Þ A
À 4:437 0:113ð Þ B þ 3:131 0:063ð Þ V
SD ¼ 0:118; N ¼ 67; R2
¼ 0:992; and F ¼ 1609
À Á
(10)
and
log K ¼ À0:773 0:034ð Þ þ 0:435 0:074ð Þ E þ 2:553 0:075ð Þ S þ 4:844 0:113ð Þ A
þ 0:505 0:078ð Þ B þ 0:658 0:011ð Þ L
SD ¼ 0:082; N ¼ 67; R2
¼ 0:995; and F ¼ 2561:7
À Á
;
(11)
where the standard error in each calculated equation coefficients is given in parenthesis imme-
diately after the respective coefficient. The statistical information associated with each correlation
includes the standard deviation (SD), the number of experimental data points used in the
regression analysis (N), the squared correlation coefficient (R2
), and the Fisher F-statistic (F).
The regression analyses used in deriving Equations (10) and (11) were performed using the IBM
SPSS Statistics 22 commercial software.
The Abraham model correlations given by Equations (10) and (11) are statistically very good with
SDs of less than 0.12 log units. Figure 1 compares the observed log K values against the back-calculated
values based on Equation (11). The experimental data covers a range of approximately 5.64 log units,
from log K = −1.540 for nitrogen gas to log K = 4.101 for 1-butanol. A comparison of the back-
calculated versus measured log P data is depicted in Figure 2. As expected, the SD for the log P
correlation is slightly larger than that of the log K correlations because the log P values contain the
additional experimental uncertainty in the gas-to-water partition coefficients used in the log K to log P
conversion. There is insufficient experimental data to permit a training set and test set assessment of
the predictive ability of each derived equation by randomly splitting the entire database in half.
There is solubility data for xylitol dissolved in ([BMIm]+
[N(CN)2]−
) that can be used to assess
the predictive ability of our derived correlations. Xylitol was not included in the regression
analysis, as we wanted to illustrate the predictive nature of Equations (10) and (11) with a
compound not included in the regression analysis. The solute descriptors of xylitol are known
(E = 1.040; S = 1.770; A = 0.540; B = 1.430; V = 1.1066; L = 6.087; logarithm of the aqueous molar
solubility = log 0.62; log Kw = 12.13), and when substituted into Equations (10) and (11) give
predicted values of log P = −0.812 and log K = 11.544. The predicted values are in reasonably
good agreement with the experimental values of log P = −0.631 and log K = 11.499, which were
calculated from the measured solubility of data of Carneiro and co-workers.[84] We note that
PHYSICS AND CHEMISTRY OF LIQUIDS 11

13. Paduszynski et al. [85] also measured the solubility of xylitol in ([BMIm]+
[N(CN)2]−
), and our
predicted values are in good agreement with this second set of solubility data, log P = −0.812
(predicted) versus log P = −0.666 [85] and log K = 11.544 (predicted) versus log K = 11.464.[85]
The derived Abraham model correlations for ([BMIm]+
[N(CN)2]−
) provide us with the opportu-
nity to assess the predictive applicability of the ion-specific equation coefficient form of the Abraham
model on a data set that was not used in determining the numerical values of the cation-specific and
anion-specific equation coefficients. We recently updated our existing ion-specific equation coeffi-
cients for both [BMIm]+
cation and [N(CN)2]−
anion based on 485 experimental log K and 509
experimental log P values for solutes dissolved in ILs containing the [BMIm]+
cation, and based on
150 experimental K and 136 experimental log P values for solutes dissolved in ILs containing the [N
(CN)2]−
anion.[66] The majority of the experimental partition coefficient data given in Table 1 was
measured after our updated ion-specific equation coefficients were published. The only ([BMIm]+
[N
(CN)2]−
) values from Table 1 used in determining the [BMIm]+
-specific and [N(CN)2]−
-specific
equation coefficients were the partition coefficient data for nitrogen gas, carbon dioxide, and nitrous
Figure 1. Comparison between the observed log K data and calculated log K values based on Equation (11) for the 67
inorganic and organic solutes dissolved in ([BMIm]+
[N(CN)2]−
) at 298.15 K.
Figure 2. Comparison between the observed log P data and calculated log P values based on Equation (10) for the 67 inorganic
and organic solutes dissolved in ([BMIm]+
[N(CN)2]−
) at 298.15 K.
12 A. LU ET AL.

14. oxide. The calculated [BMIm]+
-specific and [N(CN)2]−
-specific equation coefficients are combined in
accordance with Equations (3) and (4) to yield the following predictive log P and log K correlations:
log P ¼ À 0:305 0:094ð Þ þ 0:492 0:126ð Þ E þ 0:742 0:139ð Þ S þ 0:835 0:180ð Þ A
À 4:593 0:148ð Þ B þ 3:147 0:085ð Þ V
(12)
and
log K ¼ À 0:793 0:056ð Þ þ 0:378 0:108ð Þ E þ 2:610 0:108ð Þ S þ 4:551 0:142ð Þ A
þ 0:405 0:120ð Þ B þ 0:657 0:017ð Þ L
(13)
Comparison of Equations (10)–(13) shows that the equation coefficients obtained from the
individual ion-specific equation coefficients are identical to the equation coefficients of the IL-
specific Abraham model correlations to within the combined standard errors in the respective
equation coefficients. Equations (12) and (13) predict the experimental partition coefficient data
given in Table 1 to within a standard error of SE = 0.16 log units and SE = 0.11 log units,
respectively. These calculations represent outright predictions, rather than back calculations, in
that the experimental values were not used in determining the equation coefficients. The calcula-
tions are in accord with our earlier observations, in that the IL-specific Abraham model correla-
tions generally provide a slightly better mathematical description of the experimental data for the
given IL than do Abraham model correlations constructed with ion-specific equation coefficients.
Data sets for both ([BM2Im]+
[(Tf)2N]−
) and ([4-CNBPy]+
[(Tf)2N]−
) contain experimental parti-
tion coefficient data for a minimum of 60 different liquid organic compounds of varying polarity
and hydrogen-bonding character. Preliminary analysis of the experimental partition coefficient data
compiled in Table 2 revealed that the ek,il·E term in the log K equation for ([BM2Im]+
[(Tf)2N]−
)
contributed very little to the overall partition coefficient calculation. The numerical value of the
coefficient was small (ek,il = 0.031). Moreover, the standard error (standard error = 0.081) in the
calculated ek,il coefficient was more than 2.5 times greater than the coefficient itself. The ek,il·E term
was deleted from the log K correlation for ([BM2Im]+
[(Tf)2N]−
), and the data in Tables 2 and 3 were
analysed to yield the following Abraham model correlations for ([BM2Im]+
[(Tf)2N]−
):
log P ¼ À 0:347 0:128ð Þ þ 0:111 0:116ð Þ E þ 0:718 0:105ð Þ S À 1:195 0:166ð Þ A
À 4:418 0:114ð Þ B þ 3:502 0:102ð Þ V
SD ¼ 0:121; N ¼ 60; R2
¼ 0:994; and F ¼ 1896
À Á
(14)
log K ¼ À 0:641 0:078ð Þ þ 2:429 0:052ð Þ S þ 2:663 0:110ð Þ A þ 0:521 0:072ð Þ B þ 0:721 0:020ð Þ L
SD ¼ 0:085; N ¼ 60; R2
¼ 0:981; and F ¼ 692
À Á
(15)
and for ([4-CNBPy]+
[(Tf)2N]−
):
log P ¼ À 0:316 0:105ð Þ þ 0:132 0:105ð Þ E þ 1:015 0:124ð Þ S À 1:040ð0:164Þ A
À 4:399 0:122ð Þ B þ 3:272 0:093ð Þ V
SD ¼ 0:123; N ¼ 64; R2
¼ 0:992; and F ¼ 1641
À Á
(16)
log K ¼ À 0:768 0:065ð Þ þ 0:086 0:085ð Þ E þ 2:810 0:086ð Þ S þ 2:685 0:119ð Þ A
þ 0:553 0:090ð Þ B þ 0:691 0:020ð Þ L
SD ¼ 0:091; N ¼ 64; R2
¼ 0:990; and F ¼ 1127
À Á
(17)
PHYSICS AND CHEMISTRY OF LIQUIDS 13

15. No loss in descriptive ability was observed from removal of the ek,il·E term from Equation (14).
An identical SD of 0.085 was calculated for the correlation with and without the ek,il·E term. As
before, the IBM SPSS Statistics 22 software was used in performing the four regression analyses.
The low SDs and near-unity squared correlations associated with each of the derived correlations
indicate that the four IL-specific mathematical equations provide a reasonably accurate mathe-
matical description of the observed partition coefficient data. Comparisons of the observed log K
and log P data versus calculated values based on Equations (14)–(17) are depicted in Figures 3–6.
The derived Abraham model correlations for ([BM2Im]+
[(Tf)2N]−
) and ([4-CNBPy]+
[(Tf)
2N]−
) can be used to calculate ion-specific equation coefficients for both the [BM2Im]+
and [4-
CNBPy]+
cations with minimal effort. At the time we proposed the ion-specific version of the
Abraham model, we had to establish a reference point in order to calculate equation coefficients
for the individual ions. In IL solvents the ions appear as cation–anion pairs, and it is not possible
to calculate single-ion coefficients in the absence of a reference point. This is analogous to trying
Figure 3. Comparison between the observed log K data and calculated log K values based on Equation (15) for the 60 organic
solutes dissolved in ([BM2Im]+
[(Tf)2N]−
) at 298.15 K.
Figure 4. Comparison between the observed log P data and calculated log P values based on Equation (14) for the 60 organic
solutes dissolved in ([BM2Im]+
[(Tf)2N]−
) at 298.15 K.
14 A. LU ET AL.

16. to calculate the chemical potentials of single ions or ionic-limiting molar conductances of
individual ions for a dissolved ionic salt. In the latter case, one often utilises the tetrabutylammo-
nium tetraphenylborate reference electrolyte, [86] which assumes that ionic-limiting molar con-
ductance of tetrabutylammonium cation is equal to the ionic-limiting molar conductance of the
tetraphenylborate anion. The rationale for setting the ionic limiting molar conductances of these
two specific ions equal to each other was that both ions were large and were of approximately
equal size. Neither ion was expected to undergo much (if any) specific interactions with the
surrounding solvent molecules.
The reference point for calculating ion-specific Abraham model equation coefficients for IL
solvents was set more from the standpoint of mathematical convenience. At the time the ion-
specific equation version of the Abraham model was first proposed, the majority of the ILs in the
regression database contained the bis(trifluoromethylsulfonyl)imide anion, [(Tf)2N]−
. Setting all
of the [(Tf)2N]−
equation coefficients equal to zero greatly simplified the calculations. Other
Figure 5. Comparison between the observed log K data and calculated log K values based on Equation (17) for the 64 organic
solutes dissolved in ([4-CNBPy]+
[(Tf)2N]−
) at 298.15 K.
Figure 6. Comparison between the observed log P data and calculated log P values based on Equation (16) for the 64 organic
solutes dissolved in ([4-CNBPy]+
[(Tf)2N]−
) at 298.15 K.
PHYSICS AND CHEMISTRY OF LIQUIDS 15

17. reference points could have been set; however, the end result would still be the same. The sum of
the respective cation-specific plus anion-specific equation coefficients would be independent of
the reference point. Thus, the calculated coefficients in Equations (14) and (15) represent the
cation-specific Abraham model equation coefficients for [BM2Im]+
, while the calculated coeffi-
cients in Equations (16) and (17) correspond to the cation-specific equation coefficients for [4-
CNBPy]+
. The newly calculated cation-specific equation coefficients can be combined with our
existing 17 anion-specific equation coefficients [61,66] to enable one to predict log K and log P
values for solutes dissolved in an additional 34 IL solvents.
4. Conclusions
The ionic-liquid-specific Abraham model correlations that have been developed in the present
study for anhydrous 1-butyl-3-methylimidazolium dicyanamide, 1-butyl-2,3-dimethylimidazo-
lium bis(trifluoromethylsulfonyl)imide, and 4-cyano-1-butylpyrridinium bis(trifluoromethylsulfo-
nyl)imide provide very good mathematical descriptions of solute transfer into these three IL
solvents from both the gas phase and from water. The derived mathematical correlations describe
the observed solute transfer properties, log P and log K, to within SDs of 0.125 log units (or less).
The applicability of the ion-specific equation coefficient form of the Abraham model is success-
fully illustrated for 1-butyl-3-methylimidazolium dicyanamide. Previously calculated ion-specific
equation coefficients for [BMIm]+
cation and [N(CN)2]−
anion are combined to give predictive
Abraham model correlations, Equations (12) and (13), that estimate the measured log P and log K
values to within 0.16 and 0.11 log units, respectively. The measured log P and log K values for
anhydrous ([BMIm]+
[N(CN)2]−
) were not used in deriving the ion-specific equation coefficients,
so the calculations represent outright predictions. Ion-specific equation coefficients are calculated
for two additional cations, [BM2Im]+
and [4-CNBPy]+
, allowing one to estimate the partitioning
behaviour of solutes dissolved in 34 more anhydrous IL solvents.
Disclosure statement
No potential conflict of interest was reported by the authors.
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PHYSICS AND CHEMISTRY OF LIQUIDS 17

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