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New method based on the UNIFAC-VISCO model for the estimationof dynamic viscosity of (ionic liquid + molecular solvent) binarymixturesZhao, N., & Jacquemin, J. (2017). New method based on the UNIFAC-VISCO model for the estimation ofdynamic viscosity of (ionic liquid + molecular solvent) binary mixtures. Fluid Phase Equilibria, 449, 41-51.https://doi.org/10.1016/j.fluid.2017.06.006
Published in:Fluid Phase Equilibria
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Download date:25. Mar. 2021
New Method Based on the UNIFAC-VISCO Model for the
Estimation of Dynamic Viscosity of (Ionic Liquid + Molecular Solvent)
Binary Mixtures
Nan Zhao1, Johan Jacquemin1,2,*
1 School of Chemistry and Chemical Engineering, Queen’s University Belfast, Belfast,
BT9 5AG, U.K. 2 Universite Francois Rabelais, Laboratoire PCM2E, Parc de Grandmont 37200 Tours, France
Corresponding Author: *E-mail: [email protected] or [email protected]
ABSTRACT
The modified UNIFAC-VISCO model was applied to evaluate the viscosity of (ionic
liquid + molecular solvent) mixtures as the function of the composition and
temperature at atmospheric pressure. The values of interaction parameters between
ionic groups, 𝛼𝛼𝑖𝑖𝑖𝑖𝑖𝑖/𝑖𝑖𝑖𝑖𝑖𝑖 were collected from our previous paper (Zhao et al. J. Chem.
Eng. Data 61 (2016) 3908-3921), while the parameters between the common organic
groups, 𝛼𝛼𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜 were taken from Chevalier et al. (Chem. Eng. Sci. 49 (1994)
1799–1806). Another 376 unknown interaction parameters (𝛼𝛼𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜 and
𝛼𝛼𝑖𝑖𝑖𝑖𝑖𝑖/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜) were calculated by regression of 3365 experimental binary viscosity data
for 119 different binary systems as a function of temperature and component
composition. Then, this model was assessed through the evaluation of 781 viscosity
data points for 24 different binary systems not originally included in the correlation
set. The relative absolute average deviation (RAAD%) of the correlation and evaluation
for the viscosity of the investigated binary mixtures is close to 5.0% and 7.7%,
respectively, which proves that the UNIFAC-VISCO based method proposed in this
work is reliable for the estimation of the viscosity of ionic liquid-based binary mixtures.
Keywords: UNIFAC-VISCO; Ionic Liquids; Molecular Solvents; Viscosity; Group
Contribution Model
1. INTRODUCTION
In recent years, ionic liquids (ILs) have attracted the attention of scientific communities
due to their unique properties, such as chemical and thermal stability, high ionic
conductivity, low vapor pressure, and easy tuning of their physicochemical properties
by altering the cation, anion, or substituent [1]. Among the various properties,
viscosity property is of considerable importance in the design of heat transfer
equipment, liquid-liquid extractors, process piping, and other units [2]. For industrial
applications, IL-cosolvent mixtures are promising alternatives to traditional organic
liquids, since pure IL mixing with the organic liquid can confer a suitable viscosity to
the mixture [1]. Consequently, many modeling efforts have been reported in the
literature [1–13] regarding the viscosity of IL-cosolvent mixtures, used as electrolyte
solutions.
In this regard, literature models can be categorized as (i) simple correlation equations,
such as the Seddon [3], Grunberg-Nissan [9], and McAllister models [10]; (ii) Eyring’s
theory based methods, like the Eyring-UNIQUAC [11], Eyring-NRTL [12], Eyring-MTSM
[8], Eyring-Flory-Huggins [7], and Eyring-Wilson models [13]; and (iii) predictive
methods, for example, UNIFAC-VISCO [6] and ASOG-VISCO models [6].
Wang et al. [2] compared the Eyring-UNIQUAC model and the Eyring-NRTL model (𝛼𝛼
fixed at 0.25) in the case of 35 binary mixtures containing ILs with a total of 1014 data
points. The authors highlighted that a better evaluation of the viscosity could be
achieved by using the Eyring-UNIQUAC (RAAD% of 2.6%) than by using Eyring-NRTL
(RAAD% of 3.5%). Bajić et al. [6] used the Seddon, Grunberg-Nissan, McAlister, Eyring-
UNIQUAC and Eyring-NRTL models to correlate the viscosity of 11 (IL + solvent) binary
systems covering a wide temperature range. Within, McAlister and the three-
parameter Eyring-NRTL models showed the best results with average percentage
deviations (PDmax) below 1% in all cases. It should be noted that the reference in the
denominator of the percentage deviation (PDmax) calculation is the maximum of
experimental values. The Seddon model gives the highest deviation above 1% in all
cases when compared with other correlative models, except for three cases; (2-
butanone + [C4mim][BF4]), (H2O + [C3mmim][BF4]), and (methyl methacrylate +
[C4mim][PF6]). Fang et al. [7] proposed a method based on the Eyring’s absolute
reaction rate theory, which was coupled with the Flory-Huggins equation, to estimate
the viscosity of 527 binary mixtures including 63 (IL + solvent) mixtures. The RAAD%
of the proposed method assessed using 2554 data points of the 63 ionic liquid
containing systems is close to 3.73% which shows a better viscosity predictive
capability than the Grunberg-Nissan equation (7.42%), for example. Furthermore,
Ciocirlan et al. [1] tested 6 methods (i.e. G-N, McAllister, Eyring-Flory-Huggins, Eyring-
UNIQUAC, Eyring-NRTL, and Eyring-Wilson) in terms of four binary systems
([C2mim][BF4] + dimethyl sulfoxide / ethylene glycol / acetonitrile / 1,4-dioxane) at
(293.15, 298.15, 303.15, 313.15, 323.15, 333.15, 343.15, and 353.15) K. The McAllister
model gives the best viscosity evaluation below 1.34% quantified by RAAD% at each
temperature for three systems ([C2mim][BF4] + dimethyl sulfoxide / acetonitrile / 1,4-
dioxane). For the other system, [C2mim][BF4] + ethylene glycol, the best result was
reported using the Eyring-Flory-Huggins based method with a RAAD% of 1.54%, while
the McAllister method also showed a good result with RAAD% of 1.60%. The poorest
result estimated for these four systems is with the G-N model, ranging from 1.93% up
to 6.01% calculated by RAAD% at the eight temperatures. For the series of Eyring-
based models, Eyring-Wilson gives the poorest results with a RAAD% of 2.1% and 2.9%
in two systems containing dimethyl sulfoxide, and acetonitrile, respectively. Eyring-
Flory-Huggins shows the poorest estimation with a 1.5% RAAD% in the system with
ethylene glycol and also a poor result with 1.1% of RAAD% in the 1,4-dioxane
containing system. Generally, the other two Eyring-based models (i.e. UNIQUAC and
NRTL) show a better evaluation, the RAAD% are lower than 1.9% at each temperature
point for all the four investigated systems. Atashrouz et al. [8] reported an Eyring’s
theory method coupled with a modified two-suffix-margules model (Eyring-MTSM). To
validate the capability of the Eyring-MTSM model, the authors also made a clear
comparison with the Eyring-NRTL model using 5512 experimental data points for 122
IL-based mixtures. Based on this work, these authors demonstrated the higher
accuracy of the Eyring-MTSM method, with a RAAD% close to 2% compared to 2.8%
observed using the Eyring-NRTL model.
Generally, correlative models often yield lower deviations, but require enough
experimental data for the determination of parameters in the correlation equations.
However, a significant advantage of the predictive models is that a given property, such
as viscosity could be evaluated for unknown mixtures by using a set of interaction
parameters regressed using well-defined training datasets. Two predictive methods,
based on the UNIFAC-VISCO and ASOG-VISCO models, respectively were applied for
modeling the viscosity of IL-based mixtures [6]. Bajić et al. [6] calculated the
interaction parameters (𝛼𝛼𝑚𝑚𝑖𝑖 ) between the group ([C2mim][C2SO4], [-mim][BF4], [-
mim][PF6], and [C4mim][NO3]) and the organic functional groups by correlating
experimental data of 11 binary mixtures. However, the determination of the groups in
the ionic liquid components is not clear and uniform, sometimes on the basis of the
whole IL (such as [C2mim][C2SO4] and [C4mim][NO3]) and sometimes on the basis of
the core structure of the IL ([-mim][BF4] and [-mim][PF6]). In fact more work is
requested to assess properly the quality of the proposed method using novel and
original viscosity datasets.
In this work, we aim to develop the UNIFAC-VISCO model for correlation, and then
evaluation of the viscosity of (IL + molecular solvent) binary mixtures. The method
used for molecules’ cleavage is different from the division method reported by Bajić
et al. [6]. Each cation or anion, constituting the IL, is defined as an individual group,
which is coincident with the method of ionic groups determination for the viscosity
estimation of pure ILs and binary ILs mixtures reported in our previous work [14,15].
As a result, 119 binary systems with a total of 3365 experimental data points were
regressed altogether to obtain the interaction parameters between functional groups
(𝛼𝛼𝑖𝑖𝑖𝑖𝑖𝑖/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜 and 𝛼𝛼𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜). Then other 24 binary mixtures, not involved in
the training set, were compared from the pure evaluated values to test the validity of
the interaction parameters and thus the model developed in the current study.
2. DEVELOPMENT OF THE PROPOSED MODEL
2.1 Database. In this work, 4146 experimental viscosity data at 0.1 MPa for 143 binary
mixtures were collected from the NIST database, as a function of the composition over
a broad temperature range (from 273.15 K to 363.15 K). As discrepancies between the
literature datasets for a given system could be observed, the experimental viscosities
for each binary system, used to establish the UNIFAC-VISCO model, were taken only
from one reference. The UNIFAC-VISCO model calculates the binary viscosities on the
basis of the pure components’ properties. The references that also report the pure
components’ densities and viscosities were preferred, thus identical measurement
uncertainties for the properties of pure ILs and mixtures containing ILs increase the
accuracy of the optimized binary interaction parameters. If the values of the pure
component’s properties are not provided in the selected reference, the molar volume
and viscosity of pure ILs were calculated by using the methods previously proposed by
our group [14–17]. In the database, 3365 data points of 119 binary mixtures from
literature [18-86], as a function of temperature and component composition, were
used for optimization of interaction parameters and 781 data points of another 24
binary mixtures were used to validate the performance of the proposed model. Table
1 shows the list of the selected binary systems along with their corresponding
temperature range and composition.
Table 1. List of the selected (ionic liquid + molecular solvent) binary mixtures
No. Ionic Component (1) Organic Component (2) Temperature
Range (K) Range of x1 (mol%)
No. of Data
Points
Measurement
Uncertainty
RAAD
(%) Ref. (𝜇𝜇) Ref. (𝜌𝜌𝐼𝐼𝐼𝐼)
Correlation Set
1 [C2mim][C2SO4] 1-propanol 298.15 to 328.15 0.0273 to 0.8381 27 ±0.006 (mPa •s) 3.62 [18] [18]
2 [C2mim][C2SO4] methanol 298.15 to 328.15 0.0083 to 0.8654 33 ±0.006 (mPa •s) 6.35 [18] [18]
3 [C2mim][C2SO4] ethanol 298.15 to 328.15 0.0137 to 0.9377 30 ±0.006 (mPa •s) 4.34 [19] [19]
4 [C2mim][BF4] methanol 278.15 to 318.15 0.0499 to 0.9476 65 2% 2.73 [20] [20]
5 [C2mim][BF4] ethanol 288.15 to 318.15 0.5447 to 0.9054 24 0.3% 3.57 [21] [20]
6 [C2mim][C2SO4] water 298.15 to 328.15 0.0494 to 0.9285 24 ±0.006 (mPa •s) 2.54 [19] [19]
7 [C2mim][BF4] dimethyl sulfoxide 303.15 to 333.15 0.0998 to 0.8999 36 <0.6% 2.04 [22] [22]
8 [C2mim][BF4] N,N-dimethylformamide 303.15 to 333.15 0.1001 to 0.8984 36 <0.6% 0.97 [22] [22]
9 [C2mim][BF4] dimethylacetamide 303.15 to 333.15 0.1006 to 0.9004 36 <0.6% 1.47 [22] [22]
10 [C4mim][BF4] water 303.15 to 353.15 0.1001 to 0.8998 72 ±0.01 (mPa •s) 7.41 [23] [23]
11 [C4mim][BF4] methanol 303.15 to 333.15 0.0999 to 0.8997 36 ±0.35% 3.50 [24] [24]
12 [C4mim][BF4] dimethyl sulfoxide 293.15 to 353.15 0.0722 to 0.9155 63 ±0.1% 3.11 [25] [25]
13 [C4mim][BF4] 2-butanone 298.15 0.0498 to 0.8995 13 ±0.3% 2.36 [26] [26]
14 [C4mim][BF4] dimethylacetamide 303.15 to 333.15 0.1001 to 0.8994 36 ±0.35% 2.56 [24] [24]
15 [C4mim][BF4] N,N-dimethylformamide 298.15 0.053 to 0.8976 13 ±0.3% 2.46 [26] [26]
16 [C4mim][BF4] acetonitrile 298.15 0.0487 to 0.9018 13 ±0.3% 4.73 [26] [26]
17 [C4mim][BF4] ethyl formate 298.15 0.05 to 0.8996 13 ±0.3% 4.56 [27] [27]
18 [C4mim][BF4] triethanolamine 303.15 to 343.15 0.1301 to 0.7054 25 <0.1% 11.61 [28] [28]
19 [C4mim][BF4] methyl acetate 298.15 0.0501 to 0.8999 13 ±0.3% 4.58 [27] [27]
20 [C4mim][BF4] pyridine 298.15 0.193 to 0.8941 8 ±1% 0.28 [29] [29]
21 [C4mim][BF4] chloroform 298.15 0.1509 to 0.8921 9 ±1% 1.52 [29] [29]
22 [C4mim][BF4] dichloromethane 298.15 0.1605 to 0.9 9 ±1% 3.02 [29] [29]
23 [C4mim][BF4] N-methyl-2-pyrrolidone 298.15 to 318.15 0.3049 to 0.7945 15 -b 1.59 [30] [30]
24 [C2mim][NTf2] ethanol 278.15 to 338.15 0.051 to 0.907 40 0.1% 1.96 [31] [31]
25 [C2mim][NTf2] N-methyl-2-pyrrolidone 293.15 to 323.15 0.0978 to 0.9002 63 <0.1% 3.24 [32] [32]
26 [C2mim][NTf2] benzene 298.15 to 328.15 0.508 to 0.865 16 ±0.35% 1.67 [33] [33]
27 [C4mim][NTf2] thiophene 298.15 to 328.15 0.23 to 0.911 20 ±0.35% 4.17 [33] [33]
28 [C4mim][NTf2] 𝛾𝛾-butyrolactone 293.15 to 323.15 0.1005 to 0.8995 63 1% 3.06 [34] [34]
29 [C4mim][NTf2] 2,2,2-trifluoroethanol 278.15 to 333.15 0.1252 to 0.9123 72 2% 4.59 [35] [35]
30 [C4mim][NTf2] isopropyl acetate 298.15 0.1082 to 0.9486 11 ±0.5% 4.65 [36] [36]
31 [C6mim][NTf2] methyl diethanolamine 303.15 to 323.15 0.101 to 0.9011 45 -b 6.97 [37] [37]
32 [C6mim][NTf2] 1-propanol 278.15 to 338.15 0.048 to 0.8999 40 -c 3.70 [38] [38]
33 [C6mim][NTf2] chloroform 288.2 to 318.2 0.074 to 0.906 40 2~3% 4.18 [39] -a
34 [C6mim][NTf2] 1-octene 283.15 to 348.15 0.72 to 0.95 16 ±1% 3.07 [40] [41]
35 [C6mim][BF4] ethanol 288.15 to 318.15 0.098 to 0.9 36 0.3% 5.30 [21] [42]
36 [C6mim][BF4] 2-methyl-2-propanol 298.15 0.1017 to 0.9 9 ±0.01 (mPa •s) 7.98 [43] [43]
37 [C6mim][BF4] 3-amino-1-propanol 303.15 to 308.15 0.0536 to 0.9204 18 ±0.01 (mPa •s) 4.86 [43] [43]
38 [C6mim][BF4] water 288.15 to 318.15 0.28 to 0.8899 32 ±0.35% 3.79 [44] -a
39 [C6mim][BF4] propylamine 298.15 0.0988 to 0.8475 9 ±0.01 (mPa •s) 33.98 [43] [43]
40 [C6mim][BF4] 2-butanone 298.15 0.0492 to 0.8931 13 ±1% 1.83 [45] [45]
41 [C6mim][BF4] ethyl acetate 298.15 0.0498 to 0.8908 13 ±1% 0.88 [45] [45]
42 [C6mim][BF4] tetrahydrofuran 298.15 0.0498 to 0.8925 13 ±1% 1.45 [45] [45]
43 [C4py][NTf2] water 298.15 to 363.15 0.752 14 ±0.35% 2.46 [46] [46]
44 [C4py][BF4] dichloromethane 298.15 0.08071 to 0.94508 8 1% 7.72 [47] -a
45 [C4py][BF4] water 298.15 0.024 to 0.82817 9 1% 4.43 [47] -a
46 [C4py][BF4] methanol 298.15 0.05255 to 0.91576 9 1% 3.87 [47] -a
47 [C8mim][NTf2] 2-propanol 298.15 0.1034 to 0.9669 12 ±0.5% 1.76 [48] [48]
48 [C8mim][NTf2] isopropyl acetate 298.15 0.1009 to 0.9585 11 ±0.5% 1.20 [48] [48]
49 [C8mim][NTf2] methanol 298.15 0.098 to 0.9346 10 ±0.5% 3.09 [49] [49]
50 [C8mim][BF4] 1-propanol 298.15 0.0473 to 0.9118 13 -b 7.26 [50] [50]
51 [C8mim][BF4] 2-butanone 298.15 0.0482 to 0.899 13 ±0.01 (mPa •s) 1.64 [51] [51]
52 [C8mim][BF4] methanol 298.15 0.0495 to 0.9049 13 -b 1.79 [50] [50]
53 [C8mim][BF4] ethyl acetate 298.15 0.047 to 0.8908 13 ±0.01 (mPa •s) 3.88 [51] [51]
54 [C4mim][PF6] 2-butanone 298.15 0.0513 to 0.9005 13 ±0.2% 5.81 [52] [52]
55 [C4mim][PF6] acetonitrile 298.15 0.1082 to 0.901 10 ±1% 1.87 [29] [29]
56 [C4mim][PF6] dichloromethane 298.15 0.1322 to 0.9247 10 ±1% 1.99 [29] [29]
57 [C4mim][PF6] chloroform 298.15 0.2674 to 0.9143 8 ±1% 2.84 [29] [29]
58 [C4mim][PF6] cyclopentanone 298.15 0.0482 to 0.9064 13 ±0.2% 1.19 [52] [52]
59 [C4mim][PF6] N,N-dimethylethanolamine 288.15 to 323.15 0.0872 to 0.8779 72 ±0.1% 5.01 [53] [53]
60 [C4mim][PF6] N,N-dimethylformamide 303.15 to 323.15 0.0276 to 0.0988 9 0.35% 2.08 [54] [54]
61 [C4mim][PF6] dimethyl sulfoxide 298.15 0.05 to 0.893 13 ±0.5% 2.28 [55] [55]
62 [C4mim][PF6] water 298.15 0.7854 to 0.9482 5 ±1% 2.13 [29] [29]
63 [C4mim][PF6] methanol 298.15 0.0503 to 0.8889 13 ±0.5% 6.42 [55] [55]
64 [C4mim][PF6] methyl methacrylate 283.15 to 353.15 0.0993 to 0.9014 117 <2.612% 4.72 [56] [56]
65 [C4mim][PF6] monoethanolamine 288.15 to 323.15 0.0972 to 0.8815 72 ±0.1% 2.43 [53] [53]
66 [C4mim][PF6] tetrahydrofuran 298.15 0.0502 to 0.9595 13 ±0.5% 2.73 [55] [55]
67 [C4mim][PF6] 2,2,2-trifluoroethanol 278.15 to 333.15 0.0583 to 0.5368 60 2% 11.03 [35] [35]
68 [C4mim][DCA] water 278.15 to 358.15 0.5169 to 0.941 54 ±0.35% 6.88 [57] [57]
69 [C4mim][DCA] 𝛾𝛾-butyrolactone 273.15 to 323.15 0.0504 to 0.8871 56 <0.5% 2.17 [58] [58]
70 [C2mim][DCA] ethanol 298.15 to 343.15 0.0673 to 0.898 40 0.65% 4.01 [59] [59]
71 [C4mpyrro][NTf2] acetonitrile 288.15 to 308.15 0.1924 to 0.8159 12 ±0.2% 2.32 [60] [60]
72 [C4mpyrro][NTf2] N,N-dimethylformamide 295.2 0.26 to 0.87 7 ±1% 7.00 [61] -a
73 [C4mpyrro][NTf2] 𝛾𝛾-butyrolactone 298.15 to 323.15 0.1 to 0.8925 54 1% 2.07 [62] [62]
74 [C4mpyrro][NTf2] methanol 288.15 to 308.15 0.2054 to 0.7067 12 ±0.2% 1.86 [60] [60]
75 [C4mpyrro][NTf2] propylene carbonate 293.15 to 318.15 0.05 to 0.95 108 0.01 (mPa •s) 3.20 [63] [63]
76 [C4mpyrro][SCN] water 298.15 to 348.15 0.0343 to 0.9147 48 ±0.1% 7.50 [64] [64]
77 [C4mim][SCN] ethanol 298.15 to 348.15 0.0473 to 0.9174 54 <1% 8.38 [65] [65]
78 [C4mim][SCN] 1-hexanol 298.15 to 348.15 0.0898 to 0.9576 60 <0.05% 4.82 [66] [66]
79 [C4mim][SCN] 1-decanol 298.15 to 348.15 0.0747 to 0.9587 60 <1% 3.31 [67] [67]
80 [C4mim][SCN] methanol 298.15 to 328.15 0.0154 to 0.9046 44 <1% 3.42 [65] [65]
81 [C4mim][SCN] thiophene 298.15 to 328.15 0.299 to 0.897 20 ±0.35% 3.73 [33] [33]
82 [C4mim][SCN] benzene 298.15 to 328.15 0.4906 to 0.7666 16 ±0.35% 1.45 [33] [33]
83 [C1mim][C1SO4] water 298.15 to 328.15 0.0515 to 0.9503 33 <±0.2 (mPa •s) 5.72 [68] [68]
84 [C1mim][C1SO4] ethanol 298.15 to 328.15 0.055 to 0.9331 33 <±0.2 (mPa •s) 3.35 [68] [68]
85 [C4mim][OTf] benzene 298.15 to 328.15 0.427 to 0.878 20 ±0.35% 2.18 [33] [33]
86 [C2mim][OTf] water 278.15 to 348.15 0.0648 to 0.7714 40 ±2% 12.88 [69] [69]
87 [C2mim][OAc] ethanol 298.15 to 343.15 0.1334 to 0.8941 40 0.65% 6.57 [59] [59]
88 [C2mim][OAc] water 298.15 to 343.15 0.0933 to 0.9008 40 0.65% 8.96 [59] [59]
89 [C4mim][OAc] methyl diethanolamine 293.15 to 343.15 0.2 to 0.8 24 ±0.5% 9.52 [70] [70]
90 [C4mim][OAc] diethanolamine 303.15 to 343.15 0.2 to 0.8 20 ±0.5% 10.24 [70] [70]
91 [C4mim][OAc] acetonitrile 298.15 0.1244 to 0.6794 4 ±2% 7.59 [71] -a
92 [C4mim][OAc] N,N-dimethylformamide 298.15 0.1933 to 0.848 4 ±2% 6.48 [71] -a
93 [P66614][NTf2] water 298.15 to 358.15 0.912 13 ±0.35% 4.91 [72] [72]
94 [N1114][NTf2] 1,2-butanediol 323.15 to 353.15 0.0969 to 0.7709 42 ±0.1% 4.36 [73] [73]
95 [N1114][NTf2] 2,3-butanediol 323.15 to 343.15 0.1858 to 0.9121 30 ±0.1% 5.69 [73] [73]
96 [C4mmim][BF4] dimethyl sulfoxide 298.15 to 353.15 0.138 to 0.8785 56 ±0.1% 2.40 [74] [74]
97 [C4mmim][BF4] acetonitrile 298.15 to 343.15 0.1118 to 0.8423 42 ±0.1% 4.58 [74] [74]
98 [C8mim]Cl methanol 298.15 to 328.15 0.0197 to 0.9435 39 <1 (mPa •s) 9.98 [75] [75]
99 [C8mim]Cl ethanol 298.15 to 328.15 0.0206 to 0.9551 27 <1 (mPa •s) 9.11 [75] [75]
100 [C2mim][BF4] water 288.15 to 318.15 0.1009 to 0.9015 36 ±0.35% 6.65 [44] -a
101 [C4mim][BF4] ethanol 288.15 to 318.15 0.0986 to 0.9235 36 0.3% 10.65 [21] -a
102 [C4mim][BF4] methyl formate 298.15 0.05 to 0.8993 13 ±0.3% 3.81 [27] [27]
103 [C4mim][NTf2] butyl acetate 298.15 to 323.15 0.11 to 0.9056 54 3% 12.69 [76] [76]
104 [C4mim][NTf2] ethanol 298.15 0.1016 to 0.9207 12 ±0.5% 2.24 [77] [77]
105 [C6mim][BF4] butylamine 298.15 0.0492 to 0.8787 13 ±1% 8.47 [45] [45]
106 [C6mim][BF4] methyl diethanolamine 303.15 to 323.15 0.1176 to 0.903 45 ±3% 6.03 [78] [78]
107 [C8mim][NTf2] ethanol 298.15 0.1033 to 0.9041 11 ±0.5% 11.16 [79] [79]
108 [C8mim][NTf2] methyl acetate 298.15 0.1016 to 0.9301 11 ±0.5% 1.96 [49] [49]
109 [C8mim][BF4] ethanol 298.15 0.0517 to 0.9286 13 -b 1.39 [50] [50]
110 [C8mim][BF4] butyl acetate 298.15 0.05001 to 0.886 13 ±0.01 (mPa •s) 1.76 [51] [51]
111 [C8mim][BF4] methyl acetate 298.15 0.0485 to 0.8827 13 ±0.01 (mPa •s) 5.24 [51] [51]
112 [C4mim][PF6] ethanol 288.15 to 308.15 0.52 to 0.8 10 ±3% 10.08 [80] -a
113 [C2mim][DCA] water 298.15 to 343.15 0.047 to 0.8701 40 0.65% 4.92 [59] [59]
114 [C4mpyrro][DCA] 𝛾𝛾-butyrolactone 273.15 to 323.15 0.0987 to 0.9013 42 1% 1.59 [81] [81]
115 [C4mim][C1SO4] water 298.15 to 328.15 0.0534 to 0.9675 30 <±0.2 (mPa •s) 8.82 [82] [82]
116 [C4mim][C1SO4] ethanol 298.15 to 328.15 0.0555 to 0.9349 33 <±0.2 (mPa •s) 10.20 [82] [82]
117 [C4mim][OTf] water 298.15 0.0805 to 0.8907 10 ±1% 13.36 [29] [29]
118 [C4mim][OAc] water 278.15 0.03236 to 0.75268 5 ±2% 25.84 [71] -a
119 [C4mim][OAc] 1,2-ethanediol 298.15 0.12944 to 0.78032 4 ±2% 14.40 [71] -a
Test Set
1 [C2mim][C2SO4] 2-propanol 298.15 to 328.15 0.0294 to 0.8772 27 ±0.006 (mPa •s) 6.44 [18] [18]
2 [C2mim][NTf2] 1-propanol 278.15 to 338.15 0.0519 to 0.9025 35 -c 11.28 [38] [38]
3 [C4mim][BF4] acetone 298.15 0.0508 to 0.8949 13 ±0.3% 11.19 [27] [27]
4 [C4mim][NTf2] 1-butanol 298.15 0.1382 to 0.8952 7 1.5% 23.11 [83] -a
5 [C4mim][NTf2] 1-propanol 278.15 to 338.15 0.0508 to 0.9030 40 -c 8.58 [38] [38]
6 [C4mim][NTf2] ethyl acetate 298.15 0.1067 to 0.9478 11 ±0.5% 21.42 [77] [77]
7 [C6mim][NTf2] ethanol 278.15 to 338.15 0.047 to 0.903 40 0.1% 5.91 [31] [31]
8 [C6mim][BF4] 2-methyl-1-propanol 303.15 to 308.15 0.1004 to 0.8327 16 -b 7.82 [84] [84]
9 [C6mim][BF4] 1-propanol 293.15 to 333.15 0.1006 to 0.8894 35 -b 9.80 [85] [85]
10 [C6mim][BF4] 2-propanol 293.15 to 333.15 0.08354 to 0.85073 45 -b 14.55 [86] [86]
11 [C8mim][NTf2] ethyl acetate 298.15 0.0984 to 0.9507 11 ±0.5% 4.04 [79] [79]
12 [C8mim][BF4] 2-propanol 298.15 0.0459 to 0.8697 13 -b 7.11 [50] [50]
13 [C4mim][PF6] acetone 298.15 0.0519 to 0.8853 13 ±0.2% 7.55 [52] [52]
14 [C4mim][PF6] 3-pentanone 298.15 0.052 to 0.8912 13 ±0.2% 7.93 [52] [52]
15 [C4mim][PF6] ethyl acetate 298.15 0.0496 to 0.9063 13 ±0.2% 15.84 [52] [52]
16 [C4mim][SCN] 1-heptanol 298.15 to 348.15 0.0806 to 0.9793 66 <1% 4.71 [67] [67]
17 [C4mim][SCN] 1-pentanol 298.15 to 348.15 0.0865 to 0.9807 66 <0.05% 5.73 [66] [66]
18 [C4mim][SCN] 1-butanol 298.15 to 348.15 0.0262 to 0.9089 60 <0.05% 5.39 [66] [66]
19 [C4mim][SCN] 1-propanol 298.15 to 348.15 0.0267 to 0.9342 60 <1% 6.38 [65] [65]
20 [C4mim][SCN] 1-octanol 298.15 to 348.15 0.0874 to 0.9619 54 <1% 4.62 [67] [67]
21 [C4mim][SCN] 1-nonanol 298.15 to 348.15 0.1203 to 0.9651 48 <1% 3.81 [67] [67]
22 [N1114][NTf2] 1,2-propanediol 323.15 to 353.15 0.1157 to 0.868 49 ±0.1% 6.00 [73] [73]
23 [C8mim][BF4] propyl acetate 298.15 0.0471 to 0.8994 13 ±0.01 (mPa •s) 8.56 [51] [51]
24 [C8mim]Cl 1-propanol 298.15 to 328.15 0.0271 to 0.8929 33 <1 (mPa •s) 12.99 [75] [75] athe molar volume of ionic liquid is calculated using the volumetric parameters provided in Table S1 of the Supporting Information. bnot mentioned. cmeasurement uncertainties: 0.034 mPa
•s (𝜇𝜇 at 1-10 mPa •s), 0.214 mPa •s (𝜇𝜇 at 11-50 mPa •s), 0.958 mPa •s (𝜇𝜇 > 50 mPa •s).
2.2 Functional Groups. In our previous studies, the UNIFAC-VISCO model was
developed to estimate the viscosity of pure ILs where each ion was regarded as an
individual functional group [14,15]. In the present study, a similar approach was used
to define the IL-viscosity contribution for investigated mixtures. In terms of the organic
component in the mixture, the original cleavage reported by Chevalier et al. [87] was
also used in the current study. The cleavages are identical for the branched and linear
hydrocarbons with the same number of carbon atoms, which limits the number of
organic functional groups [87]. Although isomers of organic components are not
characterized by using this definition, ILs with different alkyl chain shapes (branched
and linear) could be evaluated thanks to the 3D structure of ions contributing to the
volume and surface area values (R and Q) [14].
Chevalier et al. [88] reported that methanol could not be split into the groups CH3 and
OH like other alcohols, due to a peculiarity. Several molecular solvents also show a
similar characteristic and are defined as the single groups, such as water, chloroform,
dichloromethane, pyridine, and thiophene. Table 2 shows the list of organic
components and their corresponding functional groups used during this work.
2.3 Proposed Model. The UNIFAC-VISCO model is a group contribution model
developed by Chevalier et al. [87,88] to predict the viscosity of the liquid mixtures.
Briefly, the viscosity of a given mixture is calculated as follows:
ln(𝜇𝜇) = ∑ 𝑥𝑥𝑖𝑖 ln �𝜇𝜇𝑖𝑖 ∙𝑉𝑉𝑖𝑖𝑉𝑉𝑚𝑚� + 𝑜𝑜𝑐𝑐𝐸𝐸
𝑅𝑅𝑅𝑅− 𝑜𝑜𝑟𝑟𝐸𝐸
𝑅𝑅𝑅𝑅𝐶𝐶𝑖𝑖=1 (1)
where, 𝜇𝜇 is the viscosity of the mixture; subscript 𝑖𝑖 represents the pure component
in the mixture (i.e., the IL and the solvent); 𝐶𝐶 is the total number of the pure
components existing in the mixture, and equals 2 because only binary mixtures were
investigated in this paper. 𝑥𝑥𝑖𝑖 is the mole fraction of component 𝑖𝑖; 𝜇𝜇𝑖𝑖 is the pure-
component viscosity of component 𝑖𝑖 ; 𝑉𝑉𝑖𝑖 is the pure-component molar volume of
component 𝑖𝑖; 𝑉𝑉𝑚𝑚 is the ideal molar volume of the mixture calculated by using the
following equation:
𝑉𝑉𝑚𝑚 = ∑ 𝑥𝑥𝑖𝑖𝑉𝑉𝑖𝑖𝐶𝐶𝑖𝑖=1 (2)
The UNIFAC-VISCO combinatorial term reported in the eq. 1 is defined by:
𝑜𝑜𝑐𝑐𝐸𝐸
𝑅𝑅𝑅𝑅= ∑ 𝑥𝑥𝑖𝑖𝑙𝑙𝑙𝑙
𝜙𝜙𝑖𝑖𝑥𝑥𝑖𝑖
+ 5∑ 𝑥𝑥𝑖𝑖𝑞𝑞𝑖𝑖𝑙𝑙𝑙𝑙𝜃𝜃𝑖𝑖𝜙𝜙𝑖𝑖
𝐶𝐶𝑖𝑖=1
𝐶𝐶𝑖𝑖=1 (3)
where
𝜃𝜃𝑖𝑖 = 𝑥𝑥𝑖𝑖𝑞𝑞𝑖𝑖∑ 𝑥𝑥𝑗𝑗𝑞𝑞𝑗𝑗𝑗𝑗
(4)
𝜙𝜙𝑖𝑖 = 𝑥𝑥𝑖𝑖𝑜𝑜𝑖𝑖∑ 𝑥𝑥𝑗𝑗𝑜𝑜𝑗𝑗𝑗𝑗
(5)
𝑞𝑞𝑖𝑖 = ∑ 𝑙𝑙𝑖𝑖,𝑘𝑘𝑄𝑄𝑘𝑘𝑁𝑁𝑘𝑘=1 (6)
𝑟𝑟𝑖𝑖 = ∑ 𝑙𝑙𝑖𝑖,𝑘𝑘𝑅𝑅𝑘𝑘𝑁𝑁𝑘𝑘=1 (7)
The volume 𝑅𝑅 and surface area 𝑄𝑄 of ionic groups were obtained by using the
COSMOthermX software (version C30_1601) as reported by our group previously
[14,15,89]. 𝑅𝑅 and 𝑄𝑄 values of organic groups are collected from values reported by
Fredenslund et al. [90,91]. 𝑅𝑅 and 𝑄𝑄 values of all the functional groups are presented
in the Table S2 of the Supporting Information.
The UNIFAC-VISCO residual term reported in the eq. 1 is defined by:
𝑜𝑜𝑟𝑟𝐸𝐸
𝑅𝑅𝑅𝑅= ∑ 𝑥𝑥𝑖𝑖[∑ 𝑙𝑙𝑚𝑚,𝑖𝑖(𝑙𝑙𝑙𝑙𝛾𝛾𝑚𝑚 − 𝑙𝑙𝑙𝑙𝛾𝛾𝑚𝑚,𝑖𝑖)𝑁𝑁
𝑚𝑚=1 ]𝐶𝐶𝑖𝑖=1 (8)
where 𝑁𝑁 is the total number of the functional groups existing in the binary system;
𝑙𝑙𝑚𝑚 and 𝑙𝑙𝑙𝑙𝛾𝛾𝑚𝑚 refer to the group fractions in the mixture, and 𝑙𝑙𝑚𝑚,𝑖𝑖 and 𝑙𝑙𝑙𝑙𝛾𝛾𝑚𝑚,𝑖𝑖
refer to the group fractions in pure component 𝑖𝑖. 𝑙𝑙𝑙𝑙𝛾𝛾𝑚𝑚 is defined as:
ln 𝛾𝛾𝑚𝑚 = 𝑄𝑄𝑚𝑚 �1 − ln�∑ Θ𝑖𝑖Ψ𝑖𝑖,𝑚𝑚𝑁𝑁𝑖𝑖=1 � − ∑ Θ𝑖𝑖Ψ𝑚𝑚,𝑖𝑖
∑ Θ𝑗𝑗Ψ𝑗𝑗,𝑖𝑖𝑁𝑁𝑗𝑗=1
𝑁𝑁𝑖𝑖=1 � (9)
The Θ value is obtained by using eq 10:
Θ𝑚𝑚 = 𝑥𝑥𝑚𝑚𝑄𝑄𝑚𝑚∑ 𝑋𝑋𝑖𝑖𝑄𝑄𝑖𝑖𝑁𝑁𝑖𝑖=1
,𝑚𝑚 = 1,2,3 …𝑁𝑁 (10)
The group interaction parameters Ψ𝑚𝑚𝑖𝑖 are calculated as follows:
Ψ𝑚𝑚𝑖𝑖 = exp (− 𝛼𝛼𝑚𝑚𝑚𝑚298.15
) (11)
where 𝛼𝛼𝑚𝑚𝑖𝑖 are the group interaction potential energy parameters between the
defined functional groups 𝑚𝑚 and 𝑙𝑙.
2.4 Determination of The Interaction Parameters 𝜶𝜶𝒎𝒎𝒎𝒎 . A set of interaction
parameters 𝛼𝛼𝑚𝑚𝑖𝑖 is required for the calculation of the viscosity of binary mixtures
using the UNIFAC-VISCO model. The values of interaction parameters between ionic
groups ( 𝛼𝛼𝑖𝑖𝑖𝑖𝑖𝑖/𝑖𝑖𝑖𝑖𝑖𝑖 ) were collected from our previous paper [14]. The values of
interaction parameters between some organic groups ( 𝛼𝛼𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜 ) were
collected from Chevalier et al. [88]. The other unknown interaction parameters
between organic and ionic groups (𝛼𝛼𝑖𝑖𝑖𝑖𝑖𝑖/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜 and 𝛼𝛼𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜/𝑖𝑖𝑜𝑜𝑜𝑜𝑜𝑜𝑖𝑖𝑖𝑖𝑜𝑜) were regressed
by using the experimental training datasets. To obtain the values of 𝛼𝛼𝑚𝑚𝑖𝑖 , we
performed the Marquardt [92] optimization of the following objective function:
𝑂𝑂𝑂𝑂 = 1𝑀𝑀∑ (𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒−𝜇𝜇𝑐𝑐𝑐𝑐𝑐𝑐
𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒)2𝑀𝑀
𝑖𝑖=1 → 𝑚𝑚𝑖𝑖𝑙𝑙 (12)
where 𝑀𝑀 is the number of data points; 𝜇𝜇𝑒𝑒𝑥𝑥𝑒𝑒 and 𝜇𝜇𝑜𝑜𝑜𝑜𝑐𝑐 are the experimental and
calculated viscosity data, respectively.
To carry out the regression, the ‘lsqnonlin’ function of the MATLAB Optimization
Toolbox was used. In this work, 3365 training data were regressed altogether to obtain
the global optimal values of interaction parameters.
3. RESULTS AND DISCUSSION
All the binary interaction parameters used in this work are presented in the Table S3
of the Supporting Information. The regression result was characterized by calculating
the relative absolute average deviation (RAAD%, eq. 13) between the calculated (µcal)
and experimental viscosity (µexp) data.
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅% = 100 × 1𝑀𝑀∑ �𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒−𝜇𝜇𝑐𝑐𝑐𝑐𝑐𝑐
𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒�𝑀𝑀
𝑖𝑖=0 (13)
The deviation between each experimental viscosity dataset and correlated (training
set; overall RAAD% close to 5.0%) for each investigated binary system used to
determine the missing UNIFAC-VISCO parameters is reported in Table 1. As shown in
Table 1 and in Figure 1, the quality of the developed UNIFAC-VISCO model was then
assessed by comparing experimental data with those calculated for wide ranges of
temperature, composition, and chemical structures leading to large values of viscosity
up to 14000 mPa·s. As illustrated in Figures 1 and 2, the correlated results show,
generally, a good agreement with the experimental data, except in two cases: i.e. the
([C6mim][BF4] + propylamine) viscosity dataset reported by Kermanpour et al. [43] and
the ([C4mim][OAc] + water) dataset published by Fendt et al. [71] for which a deviation
higher than 20% is observed in both cases.
To further assess the UNIFAC-VISCO model, 781 test data points for 24 binary mixtures,
not originally used during the training set, were then compared to the evaluated
viscosity data by using the interaction parameters estimated by using the training set.
An arbitrary binary mixture with unknown viscosity could also be estimated thanks to
the optimized values of the binary interaction parameters between the functional
groups, constituting the given mixture. The evaluation result for each binary system is
presented in Table 1 and is also shown in Figures 1-2. The overall RAAD% for the test
set is close to 7.7% (see Table 1 and Figure 2), which demonstrates that the interaction
parameters estimated during this work are accurate enough to evaluate then the
viscosity data for original mixtures.
Nevertheless, as shown in Figure 2, a correlated data point for the ([C4mim][OAc] +
water) binary system presents a relative deviation higher than 60%. However, only one
research group reported the experimental viscosity data for the system ([C4mim][OAc]
+ water), to date [71]. The viscosity of the pure [C4mim][OAc] measured by Fendt et al.
[71] is close to 485 mPa·s at 298.15 K; while by looking at the literature, it is obvious
to highlight a clear discrepancy between experimental viscosity values reported for
the [C4mim][OAc] at 298.15 K; e.g. 297 mPa·s [93], 440 mPa·s [94], 485.1 mPa·s [95],
and 485 mPa·s [71]. As reported in our previous paper [14], a viscosity dataset [96]
was recommended through the gnostic analysis of five viscosity datasets [71,93–96]
for [C4mim][OAc] over a temperature range from (283.15 to 393.15) K. The interaction
parameters between ions [C4mim]+ and [OAc]- were then calculated by regressing the
recommended dataset [96], leading to an estimated viscosity value close to 424.6
mPa·s at 298.15 K for the pure component [C4mim][OAc] by using the UNIFAC-VISCO
method [14]. Therefore, such a discrepancy on the pure component viscosity values
definitely contributes to increasing errors during the estimation of the viscosity for the
([C4mim][OAc] + water) binary system as shown in Figure 2.
Table 3 shows the estimation results (including correlated and evaluated data) for
several main types of molecular solvents to further analyze the effect of the molecular
solvent structure on the predictive capability of the UNIFAC-VISCO model. The
deviation between the experimental viscosity data and those determined using the
UNIFAC-VISCO model follows the order: water > amines > alcohols > esters > ketones >
amides. The binary systems with water show the poorest estimation result. This trend
could be attributed to the complexity of (IL + H2O) systems, driven by strong solvent-
ion interactions, like H-bonds, between water and IL, which may induce experimental
(hydrolysis reaction [97], trace of water originally present in the pure IL, etc.) and
computational errors. The difference between the experimental viscosity values for
pure ILs used in this work for the calculation of the viscosity data of selected mixtures
and those used in our previous paper [14] to determine the interaction parameters
𝛼𝛼𝑖𝑖𝑖𝑖𝑖𝑖/𝑖𝑖𝑖𝑖𝑖𝑖 also contribute to an increase in the observed errors of the UNIFAC-VISCO
model for some IL-based mixtures. In other words, the quality of the proposed method
is strongly affected by the overall accuracy of data reported in the literature as
expected for a such complex property like the viscosity.
Furthermore, the impact of the non-ideality of the volumetric properties of the
solution on the quality of the proposed method was also exemplified by using the
([C2mim][C2SO4] + 1-propanol) binary system. The experimental viscosities, densities,
and excess molar volumes of this selected system are collected from González et al.
[18] and provided in Table S4 of the Supporting Information, together with the
calculated binary viscosities by implementing the ideal and then the real molar
volumes into the UNIFAC-VISCO model, respectively. Figure 3 shows the excess molar
volumes of the system ([C2mim][C2SO4] + 1-propanol), along with the fitted curves by
using the Redlich-Kister [98] equation (Eq. 14) as a function of the mole fraction of
solvent.
𝑉𝑉𝐸𝐸 = 𝑥𝑥𝑠𝑠(1 − 𝑥𝑥𝑠𝑠)∑ 𝐵𝐵𝑒𝑒(2𝑥𝑥𝑠𝑠 − 1)𝑃𝑃𝑀𝑀𝑒𝑒=0 (14)
where 𝑉𝑉𝐸𝐸 is the excess molar volume; 𝑥𝑥𝑠𝑠 is the mole fraction of solvent; 𝐵𝐵𝑒𝑒 are
the Redlich-Kister fitting parameters; and 𝑀𝑀 is the degree of the polynomial
expansion. The fitting parameters reported by González et al. [18] are presented in
Table S5 of the Supporting Information.
Figure 4 shows the difference on the calculated viscosities induced by using the non-
ideality of the system ([C2mim][C2SO4] + 1-propanol). The minimum of 𝑉𝑉𝐸𝐸 presents
at approximately 𝑥𝑥𝑠𝑠=0.6, as shown in Figure 3. While the largest difference between
the calculated viscosities by two different molar volumes is present at nearly 0.8 mole
fraction of 1-propanol. The negative excess molar volume decreases as the
temperature increases. Analogous temperature dependence behavior was observed
for the calculated viscosities difference in Figure 4. However, the minimum
difference between the calculated viscosities is better than -0.6% for the system
([C2mim][C2SO4] + 1-propanol). The RAAD% between the experimental viscosities and
the calculated viscosities assuming the system to be ideal is 3.62%, and the RAAD%
between the experimental viscosities and the calculated values considering their non-
ideality is 3.55%. Hence, only a global 0.07% deviation was caused by the non-ideality
of the binary system. Therefore, it is reasonable and acceptable to assume all binary
systems investigated in this work as ideal.
4. CONCLUSIONS
In this work, the experimental viscosity values of (IL + molecular solvent) binary
mixtures were estimated by using the modified UNIFAC-VISCO model. During this work,
3365 experimental viscosity data for 119 different binary systems were regressed
altogether to determine missing interaction parameters between ions and molecular
solvent group parameters. Then, 781 experimental data of 24 binary systems, not
originally included in the training set, were used to assess the performance of the
established model. The overall estimation result is close to 5.5%, amongst 5% for the
training result and 7.7% for the test result, which proves that the UNIFAC-VISCO-based
method is able to correlate and then evaluate the viscosity of (ILs + molecular solvent)
binary mixtures as the function of temperature and composition at 0.1 MPa.
ASSOCIATED CONTENT
Supporting Information
The volumetric parameters for selected cations and anions are provided in Table S1.
𝑅𝑅 and 𝑄𝑄 values of the functional groups, and the interaction parameters 𝛼𝛼𝑚𝑚𝑖𝑖 used
in this work are presented in Tables S2-S3. Experimental density, viscosity, and excess
molar volume data, along with calculated viscosity values for the system
([C2mim][C2SO4] + 1-propanol) are given in Table S4. Parameters fitted to the Redlich-
Kister equation for the excess molar volume of ([C2mim][C2SO4] and 1-propanol) are
provided in Table S5.
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected] or [email protected]
Funding
N.Z. and J.J. acknowledge gratefully the CEA le Ripault (Grant No 4600261677/P6E31)
and the Engineering and Physical Sciences Research Council (EPSRC) for supporting
this work financially (EPSRC First Grant Scheme, Grant No EP/M021785/1).
Notes
The authors declare no competing financial interest.
ABBREVIATIONS
UNIQUAC UNIversal QUasichemical Activity Coefficient
UNIFAC-VISCO UNIversal Functional-group Activity Coefficient-VISCOsity
NRTL Non-Random Two-Liquid
MTSM Modified Two-Suffix-Margules
ASOG-VISCO Analytical Solution Of Groups-VISCOsity
Cations:
[mim]+ methylimidazolium
[C1mim]+ 1,3-dimethylimidazolium
[C2mim]+ 1-ethyl-3-methylimidazolium
[C3mmim]+ 1-propyl-2,3-dimethylimidazolium
[C4mim]+ 1-butyl-3-methylimidazolium
[C6mim]+ 1-hexyl-3-methylimidazolium
[C8mim]+ 1-octyl-3-methylimidazolium
[C4mmim]+ 1-butyl-2,3-dimethylimidazolium
[C4py]+ 1-butylpyridinium
[C4mpyrro]+ 1-butyl-1-methylpyrrolidinium
[N1114]+ butyl-trimethyl-ammonium
[P66614]+ trihexyl(tetradecyl)phosphonium
Anions:
[BF4]- tetrafluoroborate
[NO3]- nitrate
[NTf2]- bis(trifluoromethylsulfonyl)imide
[C1SO4]- methylsulfate
[C2SO4]- ethylsulfate
[PF6]- hexafluorophosphate
[DCA]- dicyanamide
[SCN]- thiocyanate
[OAc]- acetate
[OTf]- triflate
Cl- chloride
Nomenclature
Roman Letters:
𝑎𝑎 parameter in Seddon equation
𝐶𝐶 total number of pure components in UNIFAC-VISCO method
𝑔𝑔𝑜𝑜𝐸𝐸 combinatorial term in UNIFAC-VISCO method
𝑔𝑔𝑜𝑜𝐸𝐸 residual term in UNIFAC-VISCO method
𝑙𝑙𝑖𝑖,𝑘𝑘 total number of 𝑘𝑘th group present in component 𝑖𝑖
𝑀𝑀 number of data points
𝑁𝑁 total number of groups
𝑞𝑞𝑖𝑖 van der Waals’ surface area of component 𝑖𝑖
𝑄𝑄𝑘𝑘 group surface area parameter
𝑟𝑟𝑖𝑖 van der Waals’ volume of component 𝑖𝑖
𝑅𝑅𝑘𝑘 group volume parameter.
ℛ gas constant (J/mol·K)
𝑇𝑇 temperature (K)
𝑉𝑉𝑖𝑖 pure-component molar volume (m3/kmol)
𝑉𝑉𝑚𝑚 mixture molar volume (m3/kmol)
𝑥𝑥𝑖𝑖 mole fraction of the component 𝑖𝑖
𝑥𝑥𝑠𝑠 mole fraction of the molecular solvent
Greek Letters:
𝛼𝛼𝑚𝑚𝑖𝑖 group interaction parameter between groups 𝑚𝑚 and 𝑙𝑙
𝛾𝛾𝑚𝑚 residual activity coefficient
𝜌𝜌𝐼𝐼𝐼𝐼 density of pure ionic liquid (g·cm-3)
𝜃𝜃𝑖𝑖 molecular surface area fraction of component 𝑖𝑖
Θ𝑖𝑖 area fraction for group 𝑖𝑖
𝜇𝜇 viscosity of mixture (mPa·s)
𝜇𝜇𝑖𝑖 viscosity of pure component 𝑖𝑖
𝜇𝜇𝐼𝐼𝐼𝐼 viscosity of pure ionic liquid
𝜇𝜇𝑒𝑒𝑥𝑥𝑒𝑒 viscosity experimentally measured
𝜇𝜇𝑜𝑜𝑜𝑜𝑐𝑐 viscosity calculated by our method
𝜇𝜇𝑜𝑜𝑖𝑖𝑜𝑜𝑜𝑜𝑒𝑒 viscosity correlated by the Seddon equation
𝜙𝜙𝑖𝑖 molecular volume fraction of component 𝑖𝑖
Ψ𝑚𝑚,𝑖𝑖 group interaction parameter
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Table 1. List of the selected (ionic liquid + molecular solvent) binary mixtures
No. Ionic Component (1) Organic Component (2) Temperature Range (K) Range of x1 (mol%) No. of Data
Points Measurement
Uncertainty RAAD
(%) Ref. (𝜇𝜇) Ref. (𝜌𝜌𝐼𝐼𝐼𝐼)
Correlation Set 1 [C2mim][C2SO4] 1-propanol 298.15 to 328.15 0.0273 to 0.8381 27 ±0.006 (mPa •s) 3.62 [18] [18] 2 [C2mim][C2SO4] methanol 298.15 to 328.15 0.0083 to 0.8654 33 ±0.006 (mPa •s) 6.35 [18] [18] 3 [C2mim][C2SO4] ethanol 298.15 to 328.15 0.0137 to 0.9377 30 ±0.006 (mPa •s) 4.34 [19] [19] 4 [C2mim][BF4] methanol 278.15 to 318.15 0.0499 to 0.9476 65 2% 2.73 [20] [20] 5 [C2mim][BF4] ethanol 288.15 to 318.15 0.5447 to 0.9054 24 0.3% 3.57 [21] [20] 6 [C2mim][C2SO4] water 298.15 to 328.15 0.0494 to 0.9285 24 ±0.006 (mPa •s) 2.54 [19] [19] 7 [C2mim][BF4] dimethyl sulfoxide 303.15 to 333.15 0.0998 to 0.8999 36 <0.6% 2.04 [22] [22] 8 [C2mim][BF4] N,N-dimethylformamide 303.15 to 333.15 0.1001 to 0.8984 36 <0.6% 0.97 [22] [22] 9 [C2mim][BF4] dimethylacetamide 303.15 to 333.15 0.1006 to 0.9004 36 <0.6% 1.47 [22] [22]
10 [C4mim][BF4] water 303.15 to 353.15 0.1001 to 0.8998 72 ±0.01 (mPa •s) 7.41 [23] [23] 11 [C4mim][BF4] methanol 303.15 to 333.15 0.0999 to 0.8997 36 ±0.35% 3.50 [24] [24] 12 [C4mim][BF4] dimethyl sulfoxide 293.15 to 353.15 0.0722 to 0.9155 63 ±0.1% 3.11 [25] [25] 13 [C4mim][BF4] 2-butanone 298.15 0.0498 to 0.8995 13 ±0.3% 2.36 [26] [26] 14 [C4mim][BF4] dimethylacetamide 303.15 to 333.15 0.1001 to 0.8994 36 ±0.35% 2.56 [24] [24] 15 [C4mim][BF4] N,N-dimethylformamide 298.15 0.053 to 0.8976 13 ±0.3% 2.46 [26] [26] 16 [C4mim][BF4] acetonitrile 298.15 0.0487 to 0.9018 13 ±0.3% 4.73 [26] [26] 17 [C4mim][BF4] ethyl formate 298.15 0.05 to 0.8996 13 ±0.3% 4.56 [27] [27] 18 [C4mim][BF4] triethanolamine 303.15 to 343.15 0.1301 to 0.7054 25 <0.1% 11.61 [28] [28] 19 [C4mim][BF4] methyl acetate 298.15 0.0501 to 0.8999 13 ±0.3% 4.58 [27] [27] 20 [C4mim][BF4] pyridine 298.15 0.193 to 0.8941 8 ±1% 0.28 [29] [29] 21 [C4mim][BF4] chloroform 298.15 0.1509 to 0.8921 9 ±1% 1.52 [29] [29] 22 [C4mim][BF4] dichloromethane 298.15 0.1605 to 0.9 9 ±1% 3.02 [29] [29] 23 [C4mim][BF4] N-methyl-2-pyrrolidone 298.15 to 318.15 0.3049 to 0.7945 15 -b 1.59 [30] [30] 24 [C2mim][NTf2] ethanol 278.15 to 338.15 0.051 to 0.907 40 0.1% 1.96 [31] [31] 25 [C2mim][NTf2] N-methyl-2-pyrrolidone 293.15 to 323.15 0.0978 to 0.9002 63 <0.1% 3.24 [32] [32] 26 [C2mim][NTf2] benzene 298.15 to 328.15 0.508 to 0.865 16 ±0.35% 1.67 [33] [33] 27 [C4mim][NTf2] thiophene 298.15 to 328.15 0.23 to 0.911 20 ±0.35% 4.17 [33] [33]
28 [C4mim][NTf2] 𝛾𝛾-butyrolactone 293.15 to 323.15 0.1005 to 0.8995 63 1% 3.06 [34] [34] 29 [C4mim][NTf2] 2,2,2-trifluoroethanol 278.15 to 333.15 0.1252 to 0.9123 72 2% 4.59 [35] [35] 30 [C4mim][NTf2] isopropyl acetate 298.15 0.1082 to 0.9486 11 ±0.5% 4.65 [36] [36] 31 [C6mim][NTf2] methyl diethanolamine 303.15 to 323.15 0.101 to 0.9011 45 -b 6.97 [37] [37] 32 [C6mim][NTf2] 1-propanol 278.15 to 338.15 0.048 to 0.8999 40 -c 3.70 [38] [38] 33 [C6mim][NTf2] chloroform 288.2 to 318.2 0.074 to 0.906 40 2~3% 4.18 [39] -a 34 [C6mim][NTf2] 1-octene 283.15 to 348.15 0.72 to 0.95 16 ±1% 3.07 [40] [41] 35 [C6mim][BF4] ethanol 288.15 to 318.15 0.098 to 0.9 36 0.3% 5.30 [21] [42] 36 [C6mim][BF4] 2-methyl-2-propanol 298.15 0.1017 to 0.9 9 ±0.01 (mPa •s) 7.98 [43] [43] 37 [C6mim][BF4] 3-amino-1-propanol 303.15 to 308.15 0.0536 to 0.9204 18 ±0.01 (mPa •s) 4.86 [43] [43] 38 [C6mim][BF4] water 288.15 to 318.15 0.28 to 0.8899 32 ±0.35% 3.79 [44] -a 39 [C6mim][BF4] propylamine 298.15 0.0988 to 0.8475 9 ±0.01 (mPa •s) 33.98 [43] [43] 40 [C6mim][BF4] 2-butanone 298.15 0.0492 to 0.8931 13 ±1% 1.83 [45] [45] 41 [C6mim][BF4] ethyl acetate 298.15 0.0498 to 0.8908 13 ±1% 0.88 [45] [45] 42 [C6mim][BF4] tetrahydrofuran 298.15 0.0498 to 0.8925 13 ±1% 1.45 [45] [45] 43 [C4py][NTf2] water 298.15 to 363.15 0.752 14 ±0.35% 2.46 [46] [46] 44 [C4py][BF4] dichloromethane 298.15 0.08071 to 0.94508 8 1% 7.72 [47] -a 45 [C4py][BF4] water 298.15 0.024 to 0.82817 9 1% 4.43 [47] -a 46 [C4py][BF4] methanol 298.15 0.05255 to 0.91576 9 1% 3.87 [47] -a 47 [C8mim][NTf2] 2-propanol 298.15 0.1034 to 0.9669 12 ±0.5% 1.76 [48] [48] 48 [C8mim][NTf2] isopropyl acetate 298.15 0.1009 to 0.9585 11 ±0.5% 1.20 [48] [48] 49 [C8mim][NTf2] methanol 298.15 0.098 to 0.9346 10 ±0.5% 3.09 [49] [49] 50 [C8mim][BF4] 1-propanol 298.15 0.0473 to 0.9118 13 -b 7.26 [50] [50] 51 [C8mim][BF4] 2-butanone 298.15 0.0482 to 0.899 13 ±0.01 (mPa •s) 1.64 [51] [51] 52 [C8mim][BF4] methanol 298.15 0.0495 to 0.9049 13 -b 1.79 [50] [50] 53 [C8mim][BF4] ethyl acetate 298.15 0.047 to 0.8908 13 ±0.01 (mPa •s) 3.88 [51] [51] 54 [C4mim][PF6] 2-butanone 298.15 0.0513 to 0.9005 13 ±0.2% 5.81 [52] [52] 55 [C4mim][PF6] acetonitrile 298.15 0.1082 to 0.901 10 ±1% 1.87 [29] [29] 56 [C4mim][PF6] dichloromethane 298.15 0.1322 to 0.9247 10 ±1% 1.99 [29] [29] 57 [C4mim][PF6] chloroform 298.15 0.2674 to 0.9143 8 ±1% 2.84 [29] [29] 58 [C4mim][PF6] cyclopentanone 298.15 0.0482 to 0.9064 13 ±0.2% 1.19 [52] [52] 59 [C4mim][PF6] N,N-dimethylethanolamine 288.15 to 323.15 0.0872 to 0.8779 72 ±0.1% 5.01 [53] [53] 60 [C4mim][PF6] N,N-dimethylformamide 303.15 to 323.15 0.0276 to 0.0988 9 0.35% 2.08 [54] [54] 61 [C4mim][PF6] dimethyl sulfoxide 298.15 0.05 to 0.893 13 ±0.5% 2.28 [55] [55]
62 [C4mim][PF6] water 298.15 0.7854 to 0.9482 5 ±1% 2.13 [29] [29] 63 [C4mim][PF6] methanol 298.15 0.0503 to 0.8889 13 ±0.5% 6.42 [55] [55] 64 [C4mim][PF6] methyl methacrylate 283.15 to 353.15 0.0993 to 0.9014 117 <2.612% 4.72 [56] [56] 65 [C4mim][PF6] monoethanolamine 288.15 to 323.15 0.0972 to 0.8815 72 ±0.1% 2.43 [53] [53] 66 [C4mim][PF6] tetrahydrofuran 298.15 0.0502 to 0.9595 13 ±0.5% 2.73 [55] [55] 67 [C4mim][PF6] 2,2,2-trifluoroethanol 278.15 to 333.15 0.0583 to 0.5368 60 2% 11.03 [35] [35] 68 [C4mim][DCA] water 278.15 to 358.15 0.5169 to 0.941 54 ±0.35% 6.88 [57] [57] 69 [C4mim][DCA] 𝛾𝛾-butyrolactone 273.15 to 323.15 0.0504 to 0.8871 56 <0.5% 2.17 [58] [58] 70 [C2mim][DCA] ethanol 298.15 to 343.15 0.0673 to 0.898 40 0.65% 4.01 [59] [59] 71 [C4mpyrro][NTf2] acetonitrile 288.15 to 308.15 0.1924 to 0.8159 12 ±0.2% 2.32 [60] [60] 72 [C4mpyrro][NTf2] N,N-dimethylformamide 295.2 0.26 to 0.87 7 ±1% 7.00 [61] -a 73 [C4mpyrro][NTf2] 𝛾𝛾-butyrolactone 298.15 to 323.15 0.1 to 0.8925 54 1% 2.07 [62] [62] 74 [C4mpyrro][NTf2] methanol 288.15 to 308.15 0.2054 to 0.7067 12 ±0.2% 1.86 [60] [60] 75 [C4mpyrro][NTf2] propylene carbonate 293.15 to 318.15 0.05 to 0.95 108 0.01 (mPa •s) 3.20 [63] [63] 76 [C4mpyrro][SCN] water 298.15 to 348.15 0.0343 to 0.9147 48 ±0.1% 7.50 [64] [64] 77 [C4mim][SCN] ethanol 298.15 to 348.15 0.0473 to 0.9174 54 <1% 8.38 [65] [65] 78 [C4mim][SCN] 1-hexanol 298.15 to 348.15 0.0898 to 0.9576 60 <0.05% 4.82 [66] [66] 79 [C4mim][SCN] 1-decanol 298.15 to 348.15 0.0747 to 0.9587 60 <1% 3.31 [67] [67] 80 [C4mim][SCN] methanol 298.15 to 328.15 0.0154 to 0.9046 44 <1% 3.42 [65] [65] 81 [C4mim][SCN] thiophene 298.15 to 328.15 0.299 to 0.897 20 ±0.35% 3.73 [33] [33] 82 [C4mim][SCN] benzene 298.15 to 328.15 0.4906 to 0.7666 16 ±0.35% 1.45 [33] [33] 83 [C1mim][C1SO4] water 298.15 to 328.15 0.0515 to 0.9503 33 <±0.2 (mPa •s) 5.72 [68] [68] 84 [C1mim][C1SO4] ethanol 298.15 to 328.15 0.055 to 0.9331 33 <±0.2 (mPa •s) 3.35 [68] [68] 85 [C4mim][OTf] benzene 298.15 to 328.15 0.427 to 0.878 20 ±0.35% 2.18 [33] [33] 86 [C2mim][OTf] water 278.15 to 348.15 0.0648 to 0.7714 40 ±2% 12.88 [69] [69] 87 [C2mim][OAc] ethanol 298.15 to 343.15 0.1334 to 0.8941 40 0.65% 6.57 [59] [59] 88 [C2mim][OAc] water 298.15 to 343.15 0.0933 to 0.9008 40 0.65% 8.96 [59] [59] 89 [C4mim][OAc] methyl diethanolamine 293.15 to 343.15 0.2 to 0.8 24 ±0.5% 9.52 [70] [70] 90 [C4mim][OAc] diethanolamine 303.15 to 343.15 0.2 to 0.8 20 ±0.5% 10.24 [70] [70] 91 [C4mim][OAc] acetonitrile 298.15 0.1244 to 0.6794 4 ±2% 7.59 [71] -a 92 [C4mim][OAc] N,N-dimethylformamide 298.15 0.1933 to 0.848 4 ±2% 6.48 [71] -a 93 [P66614][NTf2] water 298.15 to 358.15 0.912 13 ±0.35% 4.91 [72] [72] 94 [N1114][NTf2] 1,2-butanediol 323.15 to 353.15 0.0969 to 0.7709 42 ±0.1% 4.36 [73] [73] 95 [N1114][NTf2] 2,3-butanediol 323.15 to 343.15 0.1858 to 0.9121 30 ±0.1% 5.69 [73] [73]
96 [C4mmim][BF4] dimethyl sulfoxide 298.15 to 353.15 0.138 to 0.8785 56 ±0.1% 2.40 [74] [74] 97 [C4mmim][BF4] acetonitrile 298.15 to 343.15 0.1118 to 0.8423 42 ±0.1% 4.58 [74] [74] 98 [C8mim]Cl methanol 298.15 to 328.15 0.0197 to 0.9435 39 <1 (mPa •s) 9.98 [75] [75] 99 [C8mim]Cl ethanol 298.15 to 328.15 0.0206 to 0.9551 27 <1 (mPa •s) 9.11 [75] [75]
100 [C2mim][BF4] water 288.15 to 318.15 0.1009 to 0.9015 36 ±0.35% 6.65 [44] -a 101 [C4mim][BF4] ethanol 288.15 to 318.15 0.0986 to 0.9235 36 0.3% 10.65 [21] -a 102 [C4mim][BF4] methyl formate 298.15 0.05 to 0.8993 13 ±0.3% 3.81 [27] [27]
103 [C4mim][NTf2] butyl acetate 298.15 to 323.15 0.11 to 0.9056 54 3% 12.69 [76] [76]
104 [C4mim][NTf2] ethanol 298.15 0.1016 to 0.9207 12 ±0.5% 2.24 [77] [77] 105 [C6mim][BF4] butylamine 298.15 0.0492 to 0.8787 13 ±1% 8.47 [45] [45] 106 [C6mim][BF4] methyl diethanolamine 303.15 to 323.15 0.1176 to 0.903 45 ±3% 6.03 [78] [78] 107 [C8mim][NTf2] ethanol 298.15 0.1033 to 0.9041 11 ±0.5% 11.16 [79] [79] 108 [C8mim][NTf2] methyl acetate 298.15 0.1016 to 0.9301 11 ±0.5% 1.96 [49] [49] 109 [C8mim][BF4] ethanol 298.15 0.0517 to 0.9286 13 -b 1.39 [50] [50] 110 [C8mim][BF4] butyl acetate 298.15 0.05001 to 0.886 13 ±0.01 (mPa •s) 1.76 [51] [51] 111 [C8mim][BF4] methyl acetate 298.15 0.0485 to 0.8827 13 ±0.01 (mPa •s) 5.24 [51] [51] 112 [C4mim][PF6] ethanol 288.15 to 308.15 0.52 to 0.8 10 ±3% 10.08 [80] -a 113 [C2mim][DCA] water 298.15 to 343.15 0.047 to 0.8701 40 0.65% 4.92 [59] [59] 114 [C4mpyrro][DCA] 𝛾𝛾-butyrolactone 273.15 to 323.15 0.0987 to 0.9013 42 1% 1.59 [81] [81] 115 [C4mim][C1SO4] water 298.15 to 328.15 0.0534 to 0.9675 30 <±0.2 (mPa •s) 8.82 [82] [82] 116 [C4mim][C1SO4] ethanol 298.15 to 328.15 0.0555 to 0.9349 33 <±0.2 (mPa •s) 10.20 [82] [82] 117 [C4mim][OTf] water 298.15 0.0805 to 0.8907 10 ±1% 13.36 [29] [29] 118 [C4mim][OAc] water 278.15 0.03236 to 0.75268 5 ±2% 25.84 [71] -a 119 [C4mim][OAc] 1,2-ethanediol 298.15 0.12944 to 0.78032 4 ±2% 14.40 [71] -a
Test Set 1 [C2mim][C2SO4] 2-propanol 298.15 to 328.15 0.0294 to 0.8772 27 ±0.006 (mPa •s) 6.44 [18] [18] 2 [C2mim][NTf2] 1-propanol 278.15 to 338.15 0.0519 to 0.9025 35 -c 11.28 [38] [38] 3 [C4mim][BF4] acetone 298.15 0.0508 to 0.8949 13 ±0.3% 11.19 [27] [27] 4 [C4mim][NTf2] 1-butanol 298.15 0.1382 to 0.8952 7 1.5% 23.11 [83] -a 5 [C4mim][NTf2] 1-propanol 278.15 to 338.15 0.0508 to 0.9030 40 -c 8.58 [38] [38] 6 [C4mim][NTf2] ethyl acetate 298.15 0.1067 to 0.9478 11 ±0.5% 21.42 [77] [77] 7 [C6mim][NTf2] ethanol 278.15 to 338.15 0.047 to 0.903 40 0.1% 5.91 [31] [31] 8 [C6mim][BF4] 2-methyl-1-propanol 303.15 to 308.15 0.1004 to 0.8327 16 -b 7.82 [84] [84] 9 [C6mim][BF4] 1-propanol 293.15 to 333.15 0.1006 to 0.8894 35 -b 9.80 [85] [85]
10 [C6mim][BF4] 2-propanol 293.15 to 333.15 0.08354 to 0.85073 45 -b 14.55 [86] [86] 11 [C8mim][NTf2] ethyl acetate 298.15 0.0984 to 0.9507 11 ±0.5% 4.04 [79] [79] 12 [C8mim][BF4] 2-propanol 298.15 0.0459 to 0.8697 13 -b 7.11 [50] [50] 13 [C4mim][PF6] acetone 298.15 0.0519 to 0.8853 13 ±0.2% 7.55 [52] [52] 14 [C4mim][PF6] 3-pentanone 298.15 0.052 to 0.8912 13 ±0.2% 7.93 [52] [52] 15 [C4mim][PF6] ethyl acetate 298.15 0.0496 to 0.9063 13 ±0.2% 15.84 [52] [52] 16 [C4mim][SCN] 1-heptanol 298.15 to 348.15 0.0806 to 0.9793 66 <1% 4.71 [67] [67] 17 [C4mim][SCN] 1-pentanol 298.15 to 348.15 0.0865 to 0.9807 66 <0.05% 5.73 [66] [66] 18 [C4mim][SCN] 1-butanol 298.15 to 348.15 0.0262 to 0.9089 60 <0.05% 5.39 [66] [66] 19 [C4mim][SCN] 1-propanol 298.15 to 348.15 0.0267 to 0.9342 60 <1% 6.38 [65] [65] 20 [C4mim][SCN] 1-octanol 298.15 to 348.15 0.0874 to 0.9619 54 <1% 4.62 [67] [67] 21 [C4mim][SCN] 1-nonanol 298.15 to 348.15 0.1203 to 0.9651 48 <1% 3.81 [67] [67] 22 [N1114][NTf2] 1,2-propanediol 323.15 to 353.15 0.1157 to 0.868 49 ±0.1% 6.00 [73] [73] 23 [C8mim][BF4] propyl acetate 298.15 0.0471 to 0.8994 13 ±0.01 (mPa •s) 8.56 [51] [51] 24 [C8mim]Cl 1-propanol 298.15 to 328.15 0.0271 to 0.8929 33 <1 (mPa •s) 12.99 [75] [75]
athe molar volume of ionic liquid is calculated using the volumetric parameters provided in Table S1 of the Supporting Information. bnot mentioned. cmeasurement uncertainties: 0.034 mPa •s (𝜇𝜇 at 1-10 mPa •s), 0.214 mPa •s (𝜇𝜇 at 11-50 mPa •s), 0.958 mPa •s (𝜇𝜇 > 50 mPa •s).
Table 2. List of the molecules’ cleavage
Component Cleavage Component Cleavage 1,2-butanediol 4CH2 + 2OH diethanolamine 4CH2 + 2OH + NH 1,2-ethanediol 2CH2 + 2OH dimethyl sulfoxide 2CH3 + S=O
1,2-propanediol 3CH2 + 2OH dimethylacetamide 3CH3 + CON 1-butanol CH3 + 3CH2 + OH N,N-dimethylethanolamine 2CH3 + 2CH2 + OH + N 1-decanol CH3 + 9CH2 + OH N,N-dimethylformamide 2CH3 + HCON 1-heptanol CH3 + 6CH2 + OH ethanol CH3 + CH2 + OH 1-hexanol CH3 + 5CH2 + OH ethyl acetate 2CH3 + CH2 + COO 1-nonanol CH3 + 8CH2 + OH ethyl formate HCOO + CH2 + CH3 1-octanol CH3 + 7CH2 + OH 𝛾𝛾-butyrolactone 3CH2cy + COO 1-octene CH3 + 5CH2 + CH2=CH isopropyl acetate 2CH3 + 2CH2 + COO
1-pentanol CH3 + 4CH2 + OH methanol CH3OH 1-propanol CH3 + 2CH2 + OH methyl acetate 2CH3 + COO
2,3-butanediol 4CH2 + 2OH methyl diethanolamine CH3 + 4CH2 + 2OH + N 2-butanone 2CH3 + C=O + CH2 methyl formate CH3 + HCOO
2-methyl-2-propanol CH3 + 3CH2 + OH methyl methacrylate 2CH3 + COO + CH2=C 2-propanol CH3 + 2CH2 +OH monoethanolamine 2CH2 + OH + NH2
3-amino-1-propanol 3CH2 + OH + NH2 N-methyl-2-pyrrolidone 3CH2cy + CH3 + CON 3-pentanone 2CH3 + 2CH2 + C=O propyl acetate 2CH3 + 2CH2 + COO
acetone 2CH3 + C=O propylamine CH3 + 2CH2 + NH2 acetonitrile CH3 + C≡N propylene carbonate CH2 + 2CH2cy + CO3
benzene 6CHar pyridine C5H5N butyl acetate 2CH3 + 3CH2 + COO tetrahydrofuran 3CH2cy + FCH2O butylamine CH3 + 3CH2 + NH2 thiophene C4H4S chloroform CHCl3 triethanolamine 6CH2 + 3OH + N
cyclopentanone 4CH2cy + C=O 2,2,2-trifluoroethanol CF3 + CH2 + OH dichloromethane CH2Cl2 water H2O
Table 3. Analysis of the deviation between experimental and estimated viscosity values using
the UNIFAC-VISCO model for different groups of solvents
Type of solvents RAAD No. of data points No. of systems
water 7.2% 505 17 ketones 4.9% 104 8 alcohols 6.2% 1836 54 amines 6.8% 343 10 esters 5.1% 441 19
amides 2.2% 141 7
Figure 1. Comparison of experimental (𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒) and calculated (𝜇𝜇𝑐𝑐𝑐𝑐𝑐𝑐) data for the binary mixtures
investigated in this work: (○), the training set; and (●), the test set; a), at low-viscosity range;
and b), at high-viscosity range.
Figure 2. Relative deviation of calculated viscosity values (𝜇𝜇𝑐𝑐𝑐𝑐𝑐𝑐 ) versus experimental data
(𝜇𝜇𝑒𝑒𝑒𝑒𝑒𝑒): (○), the training set; and (●), the test set.
Figure 3. Excess molar volume, 𝑉𝑉𝐸𝐸, with the fitted curves for the ([C2mim][C2SO4] + 1-propanol)
binary system as a function of the 1-propanol mole fraction, xs. Experimental points at: +,
298.15 K; ○, 313.15 K; and □, 328.15 K from González et al. [18].
Figure 4. Comparison of the calculated viscosities through the ideal volumes (𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖𝑒𝑒𝑐𝑐𝑐𝑐−𝑣𝑣𝑣𝑣𝑐𝑐𝑣𝑣𝑣𝑣𝑒𝑒)
and through the real volumes (𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑟𝑟𝑒𝑒𝑐𝑐𝑐𝑐−𝑣𝑣𝑣𝑣𝑐𝑐𝑣𝑣𝑣𝑣𝑒𝑒 ) for the ([C2mim][C2SO4] + 1-propanol) binary
system as a function of the 1-propanol mole fraction, xs, at: +, 298.15 K; ○, 313.15 K; and □,
328.15 K.
Supporting Information
New Method Based on the UNIFAC-VISCO Model for the
Estimation of Viscosity of (Ionic Liquid + Molecular Solvent) Binary
Mixtures
Nan Zhao1, Johan Jacquemin1,2,*
1 School of Chemistry and Chemical Engineering, Queen’s University Belfast, Belfast,
BT9 5AG, U.K.
2 Universite Francois Rabelais, Laboratoire PCM2E, Parc de Grandmont 37200 Tours,
France
Table S1. Parameters of effective molar volume for cations and anions
Ion D0
cm3·mol-1
D1
cm3·mol-1·K-1
D2
cm3·mol-1·K-2 RAAD
[C2mim]+ 100.25 0.0656 4.57E-05 2.40E-04 [C4mim]+ 134.11 0.0927 -2.99E-05 2.26E-03 [C6mim]+ 168.60 0.1131 4.93E-05 7.83E-04 [C4py]+ 129.98 0.0799 2.60E-05 4.17E-03
[C4mpyrro]+ 145.15 0.0929 -7.70E-06 2.75E-03 [BF4]- 53.75 0.0258 -3.40E-05 1.31E-03 [NTf2]- 157.60 0.1043 5.05E-05 0 [PF6]- 72.85 0.0363 -3.84E-05 1.93E-03 [OAc]- 54.44 0.0237 -7.98E-05 4.97E-04
Table S2. UNIFAC-VISCO volume (R) and surface area (Q) parameters for ionic groups and organic groups
Ionic Group R Q
[C1mim]+ 4.1183 3.4946
[C2mim]+ 4.7608 4.0087
[C4mim]+ 6.1040 5.0832
[C6mim]+ 7.4623 6.1698
[C8mim]+ 8.8143 7.2515
[C4mmim]+ 6.7595 5.6076
[C4py]+ 5.9737 4.9790
[C4mpyrr]+ 6.6061 5.4849
[P66614]+ 23.0213 18.6171
[N1114]+ 5.6947 4.7558
[BF4]- 2.2421 1.9937
[C1SO4]- 3.1995 2.7596
[NTf2]- 6.7937 5.6350
[PF6]- 3.1900 2.7520
[DCA]- 2.5346 2.2277
[SCN]- 2.1410 1.9128
[OAc]- 2.2192 1.9754
[OTf]- 3.9625 3.3700
[C2SO4]- 3.8506 3.2805
Cl- 1.1105 1.0884
Organic Group R Q
CH2, CH2cy 0.6744 0.54
CH3 0.9011 0.848
CHar 0.5313 0.4
C=O 0.7713 0.64
COO 1.002 0.88
OH 1 1.2
CH3OH 1.4311 1.432
H2O 0.92 1.4
HCOO 1.242 1.188
CF3 1.406 1.38
CHCl3 2.87 2.41
CH2Cl2 2.2564 1.988
NH2 0.6948 0.696
CHO 0.998 0.948
CO3 0.9565 0.664
NH 0.5326 0.396
C≡N 0.969 0.876
N 0.2854 0.092
S=O 1.0244 0.776
HCON 1.2834 1.04
CON 1.0567 0.732
C5H5N 2.9993 2.113
C4H4S 2.8569 2.14
CH2=CH 1.3454 1.176
FCH2O 0.9183 1.1
CH2=C 1.1173 0.988
Table S3. Binary interaction parameters 𝜶𝜶𝒎𝒎𝒎𝒎 used in this work
group 𝒎𝒎 group 𝒎𝒎 𝜶𝜶𝒎𝒎𝒎𝒎 𝜶𝜶𝒎𝒎𝒎𝒎
[BF4]- [C2mim]+ -130.81 -222.19 [BF4]- [C4mim]+ -464.73 -0.06
[C1mim]- CH2 2755.75 -249.24 [C1mim]- CH3 4442.6 -75.06 [C1mim]- H2O 42369.7 -349.35 [C1mim]- OH 4162.0 -351.81 [C1SO4]- [C1mim]- -54.69 -158.3 [C1SO4]- [C4mim]+ -365.32 112.45 [C1SO4]- CH2 -1131.64 -445.58 [C1SO4]- CH3 211.77 2345.01 [C1SO4]- H2O -443.6 -453.99 [C1SO4]- OH -214.55 10955.7 [C2SO4]- [C2mim]+ 423.56 355.51
[C4mmim]+ [BF4]- -105.01 -768.66 [C4mmim]+ C≡N -422.48 5925.57 [C4mmim]+ CH3 -311.35 5867.63 [C4mmim]+ S=O -21.71 22064.4 [C4mpyrro]+ [DCA]- -208.95 -53.51 [C4mpyrro]+ [NTf2]- -127.47 -29.34 [C4mpyrro]+ C≡N -223.08 -694.76 [C4mpyrro]+ CH2 272 -264.33 [C4mpyrro]+ CH2cy -51.14 -350.44 [C4mpyrro]+ CH3 129.44 -9.25 [C4mpyrro]+ CH3OH 21865.6 -445.35 [C4mpyrro]+ CO3 229.2 -43.83 [C4mpyrro]+ COO 4696.8 -191.81 [C4mpyrro]+ H2O -357.73 -341.98 [C4mpyrro]+ HCON 1665.9 -18.93
[C4py]+ [BF4]- -404.47 7644.6 [C4py]+ [NTf2]- 86.82 417.64 [C4py]+ CH2Cl2 -236.74 -257.19 [C4py]+ CH3OH 13201.0 -428.91 [C4py]+ H2O -458.8 -96.22
[C6mim]+ [BF4]- -155.98 -414.47 [C6mim]+ [NTf2]- -251.08 415.53 [C6mim]+ CH2 -529.85 5450.54 [C6mim]+ CH2cy -37.54 -35.83 [C6mim]+ CH3 -15.98 -424.08 [C6mim]+ CHCl3 -206.11 -283 [C6mim]+ CO 8076.6 -36.15 [C6mim]+ COO -88.4 5700.3
[C6mim]+ H2O -637.39 -243.64 [C6mim]+ N 82 46249.1 [C6mim]+ OH -133.01 110929 [C8mim]+ [BF4]- -443.32 29.73 [C8mim]+ [NTf2]- 80.21 36.46 [C8mim]+ CH2 216.65 -258.36 [C8mim]+ CH3 -31.65 -249.61 [C8mim]+ CH3OH -178.38 -350.45 [C8mim]+ CO 183.85 -202.14 [C8mim]+ COO 11328.4 -160.51 [C8mim]+ OH 348.37 -365.94
[DCA]- [C2mim]+ -260.54 9765.3 [DCA]- [C4mim]+ -291.3 361 [DCA]- CH2 -997.96 67.89 [DCA]- CH2cy 251.21 -18.21 [DCA]- CH3 3839.42 1.67 [DCA]- COO -135.26 -75.25 [DCA]- H2O 3484.2 -159.32 [DCA]- OH 3625.2 0.37 [N1114]+ [NTf2]- -3.97 -9.63 [N1114]+ CH2 5500.75 -176.73 [N1114]+ OH 128.13 -263.54 [NTf2]- [C2mim]+ 1978.2 -322.07 [NTf2]- [C4mim]+ -228.33 322.36 [OAc]- [C2mim]+ 6394.8 -611.17 [OAc]- [C4mim]+ -712.86 4669.6 [OAc]- C≡N -374.36 -574.77 [OAc]- CH2 -89.48 1643.36 [OAc]- CH3 108.66 -358.97 [OAc]- H2O -807.64 -468.65 [OAc]- HCON 1817.1 -7.43 [OAc]- N -1791 140.3 [OAc]- OH -139.48 -322.65 [OTf]- [C2mim]+ -465.92 1717.39 [OTf]- [C4mim]+ -14.04 -280.5 [OTf]- CHar -9.24 -571.67 [OTf]- H2O -745.52 45.35
[P66614]+ [NTf2]- 1463.7 -403.99 [P66614]+ H2O -508.19 -235.65
[PF6]- [C4mim]+ -544.06 1248.42 [PF6]- C≡N -202.55 -197.1 [PF6]- CF3 2262192 400.24 [PF6]- CH2 -578.15 4472.24 [PF6]- CH2Cl2 25.3 -59.88
[PF6]- CH2cy -56.69 66.86 [PF6]- CH3 1739.04 -232.68 [PF6]- CH3OH -406.41 -97.15 [PF6]- CHCl3 -218.31 2.12 [PF6]- CO -353.95 47692.3 [PF6]- COO -810.94 6218.1 [PF6]- FCH2O -10.18 431.86 [PF6]- H2O -817.72 36606.1 [PF6]- HCON 212.85 15771 [PF6]- N 22 19974.5 [PF6]- NH2 -80 4476.82 [PF6]- OH -276.85 -230.22 [PF6]- S=O -26.65 -163.08 [SCN]- [C4mim]+ 346530 57.26 [SCN]- [C4mpyrro]+ -18.69 -42.61 [SCN]- C4H4S -816.13 67.15 [SCN]- CH2 -742.38 119.26 [SCN]- CH3 491.06 24184.6 [SCN]- CH3OH 1898.6 156.03 [SCN]- CHar 17.61 -196.58 [SCN]- H2O -55.17 -368.48 [SCN]- OH 3821.4 6904.3 C≡N [BF4]- -767.13 6716.13 C≡N [C4mim]+ -20.97 -162.2 C≡N [NTf2]- 279.70 81.14 C≡N CH3 -227.94 3702.29
C4H4S [C4mim]+ 149.42 35434.7 C4H4S [NTf2]- -80.05 -584.29 C5H5N [BF4]- -18.77 344.29 C5H5N [C4mim]+ -550.65 92.64
CF3 [C4mim]+ 5714.51 344.45 CF3 [NTf2]- -29.12 -139.53 CF3 CH2 12410.6 135358 CF3 OH 12087.5 379.63 CH2 [BF4]- -419.6 14669.4 CH2 [C2mim]+ 90710.2 8370.44 CH2 [C2SO4]- 5724.1 -666.97 CH2 [C4mim]+ 257.06 8822.1 CH2 [NTf2]- 698.48 -93.01
CH2=C [C4mim]+ 188015 8.31 CH2=C [PF6]- 61150.1 788516 CH2=C CH3 21326.5 -289.2 CH2=C COO 10787.9 -6.35
CH2=CH [C6mim]+ -456.74 27086.7
CH2=CH [NTf2]- 5003.01 -532.76 CH2=CH CH2 -323.47 15430.2 CH2=CH CH3 -24996.6 437.6 CH2Cl2 [BF4]- -334.46 212.74 CH2Cl2 [C4mim]+ -501.2 -140.92 CH2cy [BF4]- 2544.1 -365.8 CH2cy [C2mim]+ -37 -50.58 CH2cy [C4mim]+ -578.45 529.74 CH2cy [NTf2]- -52.98 78495.1 CH2cy CH2 -538.1 224.9 CH3 [BF4]- 12.92 66.65 CH3 [C2mim]+ -128.38 -36.82 CH3 [C2SO4]- 56484 5161.41 CH3 [C4mim]+ -308.3 -94.47 CH3 [NTf2]- -256.33 -89.2 CH3 CH2 -709.5 66.53 CH3 CH2cy -130.7 187.3
CH3OH [BF4]- -498.06 -109.06 CH3OH [C2mim]+ -32.43 -225.65 CH3OH [C2SO4]- -314.26 -34.42 CH3OH [C4mim]+ -275.33 -199.81 CH3OH [NTf2]- -484.28 -94.26 CH3OH CH2 -526.1 -219.7 CH3OH CH2cy 751.3 -381.53 CH3OH CH3 653.1 -228.7 CH3OH CHar 51.31 -88.81 CH3OH CO -22.59 -22.59 CH3OH COO -286.2 69.62 CH3OH OH -23.91 416.4
CHar [C2mim]+ -6.04 -33.86 CHar [C4mim]+ -38.77 -124.23 CHar [NTf2]- 281.92 -416.13 CHar CH2 -623.7 406.7 CHar CH2cy 50.89 8.96 CHar CH3 237.2 -119.5
CHCl3 [BF4]- -360.67 -51.04 CHCl3 [C4mim]+ -383.07 -222.43 CHCl3 [NTf2]- 5.6 -130.29
Cl- [C8mim]+ -1499.7 35183 Cl- CH2 -0.92 9.4 Cl- CH3 -764.47 4.01 Cl- CH3OH -863.26 -157.06 Cl- OH -654.08 -35.32 CO [BF4]- -704.52 -400.48
CO [C4mim]+ -35.23 10.1 CO CH2 586.2 859.5 CO CH2cy 740.6 -125.4 CO CH3 -21.56 11.86 CO CHar -117.9 128.4 CO3 [NTf2]- -923.26 114.01 CO3 CH2 582.68 -175.59 CO3 CH2cy -4202.6 -114.37 CON [BF4]- -16.89 -6.32 CON [C2mim]+ -312.37 19461 CON [C4mim]+ 4125.82 4719.65 CON [NTf2]- 4275.94 -176.55 CON CH2cy -390.78 308.95 CON CH3 9311.5 5345.3 COO [BF4]- -494.06 -729.32 COO [C4mim]+ 4390.79 98.43 COO [NTf2]- -525.55 -59.82 COO CH2 541.6 1172 COO CH2cy 416.2 -165.7 COO CH3 -44.25 -172.4 COO CHar -36.17 -49.85 COO CO 22.92 29.2 COO OH 186.8 68.35
FCH2O [BF4]- -878.54 -151.48 FCH2O [C4mim]+ -659.08 -36.92 FCH2O [C6mim]+ 8057.32 -460.42 FCH2O CH2cy 28.27 27.43
H2O [BF4]- -254.39 13052.7 H2O [C2mim]+ -196.69 -390.26 H2O [C2SO4]- -66.88 -411.54 H2O [C4mim]+ -338.52 -447.15 H2O [NTf2]- -404.72 -347.69
HCON [BF4]- -579.41 134.33 HCON [C2mim]+ -1.33 736.57 HCON [C4mim]+ 3271.35 6380.07 HCON [NTf2]- -102.77 11.23 HCON CH3 8624.7 8095.8 HCOO [BF4]- -257.25 -53.12 HCOO [C4mim]+ -462.72 -154.48 HCOO CH2 -843.85 378.6 HCOO CH3 63590.8 -281.4
N [BF4]- -1228.14 -1.89 N [C4mim]+ -1021.2 2837.17 N [NTf2]- 7160.7 80.00
N CH2 10500 -18358.2 N CH3 -1663.1 8.49 N OH 6687.6 -365.39
NH [C4mim]+ -174.05 6046.42 NH [OAc]- 112.22 710.53 NH CH2 31.29 9102.59 NH OH 12008.4 -58236.2 NH2 [BF4]- 3645.69 -172368 NH2 [C4mim]+ -942.43 100 NH2 [C6mim]+ -380.31 -504.41 NH2 CH2 5502.38 -171672 NH2 CH3 4842.6 3565.5 NH2 OH -905.02 5179.22 OH [BF4]- -515.88 5753.64 OH [C2mim]+ -243.5 74.33 OH [C2SO4]- -256.19 46718.9 OH [C4mim]+ 56.2 -21.6 OH [NTf2]- -394.53 13909.4 OH CH2 -634.5 498.6 OH CH2cy -138 694.4 OH CH3 1209 594.4 OH CHar 197.7 419.3 OH CO 664.1 221.5 S=O [BF4]- -709.88 78.68 S=O [C2mim]+ -209.34 4718.6 S=O [C4mim]+ 4352.2 14921 S=O CH3 4634.4 174.65
Table S4. Experimental density 𝝆𝝆𝒆𝒆𝒆𝒆𝒆𝒆, viscosity 𝜼𝜼𝒆𝒆𝒆𝒆𝒆𝒆, excess molar volume 𝑽𝑽𝑬𝑬 [18], ideal molar volume 𝑽𝑽𝒎𝒎, real molar volume 𝑽𝑽,
calculated viscosity 𝜼𝜼𝒄𝒄𝒄𝒄𝒄𝒄𝒊𝒊𝒊𝒊𝒆𝒆𝒄𝒄𝒄𝒄−𝒗𝒗𝒗𝒗𝒄𝒄𝒗𝒗𝒎𝒎𝒆𝒆 using 𝑽𝑽𝒎𝒎, and calculated viscosity 𝜼𝜼𝒄𝒄𝒄𝒄𝒄𝒄𝒓𝒓𝒆𝒆𝒄𝒄𝒄𝒄−𝒗𝒗𝒗𝒗𝒄𝒄𝒗𝒗𝒎𝒎𝒆𝒆 using 𝑽𝑽 of [C2mim][C2SO4] and 1-propanol.
T
(K) 𝒆𝒆𝒔𝒔
𝝆𝝆𝒆𝒆𝒆𝒆𝒆𝒆
(𝒈𝒈 ∙ 𝒄𝒄𝒎𝒎−𝟑𝟑)
𝜼𝜼𝒆𝒆𝒆𝒆𝒆𝒆
(𝒎𝒎𝒎𝒎𝒄𝒄 ∙ 𝒔𝒔)
𝑽𝑽𝑬𝑬
(𝒄𝒄𝒎𝒎𝟑𝟑 ∙ 𝒎𝒎𝒗𝒗𝒄𝒄−𝟏𝟏)
𝑽𝑽𝒎𝒎
(𝒄𝒄𝒎𝒎𝟑𝟑 ∙ 𝒎𝒎𝒗𝒗𝒄𝒄−𝟏𝟏)
𝑽𝑽
(𝒄𝒄𝒎𝒎𝟑𝟑 ∙ 𝒎𝒎𝒗𝒗𝒄𝒄−𝟏𝟏)
𝜼𝜼𝒄𝒄𝒄𝒄𝒄𝒄𝒊𝒊𝒊𝒊𝒆𝒆𝒄𝒄𝒄𝒄−𝒗𝒗𝒗𝒗𝒄𝒄𝒗𝒗𝒎𝒎𝒆𝒆
(𝒎𝒎𝒎𝒎𝒄𝒄 ∙ 𝒔𝒔)
𝜼𝜼𝒄𝒄𝒄𝒄𝒄𝒄𝒓𝒓𝒆𝒆𝒄𝒄𝒄𝒄−𝒗𝒗𝒗𝒗𝒄𝒄𝒗𝒗𝒎𝒎𝒆𝒆
(𝒎𝒎𝒎𝒎𝒄𝒄 ∙ 𝒔𝒔)
298.15 0.1619 1.2081 60.85 -0.209 172.18 171.97 62.13 62.20
298.15 0.2104 1.1979 52.11 -0.263 166.57 166.31 33.58 53.86
298.15 0.336 1.1674 34.41 -0.334 152.03 151.69 20.32 36.28
298.15 0.5159 1.1116 18.01 -0.406 131.20 130.79 53.78 19.32
298.15 0.7298 1.0155 7.296 -0.380 106.44 106.06 29.53 8.06
298.15 0.8046 0.9700 5.491 -0.334 97.78 97.44 18.07 5.70
298.15 0.8894 0.9077 3.577 -0.287 87.96 87.67 36.20 3.73
298.15 0.9401 0.8625 2.776 -0.180 82.09 81.91 20.71 2.84
298.15 0.9727 0.8298 2.419 -0.097 78.32 78.22 13.04 2.37
313.15 0.1619 1.1979 33.73 -0.250 173.69 173.44 19.26 33.63
313.15 0.2104 1.1876 29.56 -0.306 168.05 167.75 11.69 29.59
313.15 0.336 1.1571 20.72 -0.418 153.46 153.04 7.66 20.77
313.15 0.5159 1.1008 11.73 -0.484 132.56 132.08 8.03 11.73
313.15 0.7298 1.0044 5.125 -0.483 107.71 107.23 5.22 5.25
313.15 0.8046 0.9586 3.918 -0.419 99.02 98.60 3.59 3.80
313.15 0.8894 0.8959 2.58 -0.342 89.17 88.83 5.68 2.56
313.15 0.9401 0.8506 1.997 -0.223 83.28 83.06 3.79 1.98
313.15 0.9727 0.8178 1.729 -0.125 79.49 79.37 2.64 1.66
328.15 0.1619 1.1876 20.84 -0.271 175.21 174.94 3.72 20.35
328.15 0.2104 1.1773 18.59 -0.348 169.56 169.22 2.55 18.11
328.15 0.336 1.1467 13.61 -0.497 154.93 154.43 1.81 13.08
328.15 0.5159 1.0902 8.159 -0.606 133.97 133.36 2.84 7.69
328.15 0.7298 0.9932 3.774 -0.606 109.04 108.44 1.97 3.61
328.15 0.8046 0.9472 2.918 -0.540 100.33 99.79 1.42 2.66
328.15 0.8894 0.8840 1.923 -0.425 90.45 90.02 2.36 1.82
328.15 0.9401 0.8385 1.482 -0.286 84.54 84.26 1.66 1.42
328.15 0.9727 0.8055 1.272 -0.163 80.74 80.58 1.20 1.20
Table S5. Parameters [18] fitted to the Redlich-Kister equation for the excess molar
volume of the binary system ([C2mim][C2SO4] and 1-propanol).
T/K 𝑩𝑩𝟎𝟎 𝑩𝑩𝟏𝟏 𝑩𝑩𝟐𝟐 𝑩𝑩𝟑𝟑 𝑩𝑩𝟒𝟒
298.15 -3.0405 -2.1161 0.0081 -3.6345 -4.3987
313.15 -3.4271 -2.2571 -0.4171 -4.1579 -4.5898
328.15 -3.8769 -2.6370 -0.3710 -4.4694 -5.6886