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A simple group contribution correlation for the prediction of ionic liquid heat capacities at different temperatures
Accepted Manuscript Title: A simple group contribution correlation for the prediction of ionic liquid heat capacities at different temperatures Author: Alireza Ahmadi Reza Haghbakhsh Sona Raeissi Vahid Hemmati PII: DOI: Reference:
S0378-3812(15)00328-3 http://dx.doi.org/doi:10.1016/j.fluid.2015.06.009 FLUID 10614
To appear in:
Fluid Phase Equilibria
Received date: Revised date: Accepted date:
22-3-2015 6-6-2015 8-6-2015
Please cite this article as: Alireza Ahmadi, Reza Haghbakhsh, Sona Raeissi, Vahid Hemmati, A simple group contribution correlation for the prediction of ionic liquid heat capacities at different temperatures, Fluid Phase Equilibria http://dx.doi.org/10.1016/j.fluid.2015.06.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A simple group contribution correlation for the prediction of ionic liquid heat capacities at different temperatures Alireza Ahmadi, Reza Haghbakhsh, Sona [email protected], Vahid Hemmati School of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Ave., Shiraz 71345, Iran. 1
Corresponding author at: School of Chemical and Petroleum Engineering, Shiraz University, 71345
Mollasadra Ave., Shiraz, Iran. Tel.: +98 71 36133707; Fax: +98 71 36474619.
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Abstract The heat capacities of pure ionic liquids (ILs) are among the thermophysical properties that are required for certain engineering calculations and designs. In this study, a simple correlation is presented for the prediction of the heat capacities of pure ionic liquids. This correlation is a temperature-dependent relation that uses temperature, molecular weight and the number of atoms (such as carbon, hydrogen, oxygen, nitrogen, etc.) in the structure of the IL as input parameters. A dataset of approximately 128 different ILs, consisting of 4822 data points, was used to develop and validate this general correlation, covering a temperature range from 190 to 663 K. Nearly three-quarters of the data were used for optimization and a quarter for validation. The resulting correlation gives good estimations for heat capacities, while having a number of advantages over previous literatures methods. These advantages include (a) being very simple; (b) not requiring any experimental data as input parameters; (c) being more global than previous literature models by having been constructed over a larger databank of ionic liquids; (d) being accurate. The Average Absolute Relative Deviation (AARD%) was calculated to be 5.8% for the optimization dataset, and 5.6% for the validation dataset. This is smaller than what is obtained for the literature atomic-contribution methods proposed by Farahani et al. and Sattari et al., with AARD% values of 14.2% and 6.6%, respectively, based on the validation dataset of this study. Keywords: physical property; thermophysical property; specific heat; estimation; ionic liquids.
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Symbols: AARD%: Average Absolute Relative Deviation B: boron Br: bromine C: carbon atom
(
Cp: heat capacity J .mol
−1
K −1
)
F: fluorine ILs: ionic liquids MW: molecular weight N: nitrogen n: number of data in equation (1) O: oxygen P: phosphorous S: sulfur T: temperature (K)
Subscripts and superscripts: A: anion C: cation cal: calculated exp: experimental
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1. Introduction Ionic liquids (ILs) are organic salts that consist completely of ions but are liquid at, or below, room temperature [1]. Because of their very unique properties, they have the potential to be used in a variety of industrial and chemical processes [2, 3]. However, highly accurate data regarding the physicochemical properties of ionic liquids are necessary for the design and operation of such processes [2, 4]. Heat capacity is among the important pure component properties in its own right, furthermore, the temperature-dependency of various thermodynamic properties, such as enthalpy, entropy, and Gibbs energy, can be calculated from the heat capacity of a compound [5]. For example, from a thermodynamic point of view, the heat capacity at constant pressure is the first derivative of enthalpy with respect to temperature. This further highlights the significance of accurate knowledge of heat capacity for many theoretical and engineering calculations. Numerous reports have now become available in literature on experimental measurements or the estimation and prediction techniques for determination of pure ionic liquid physicochemical properties. The most common experimental methods for measuring heat capacity, as reported in the literature, are differential scanning calorimetry and adiabatic calorimetry [6]. The heat capacities of some ionic liquids have also been measured with these methods [6-8]. However, such information is still lacking for many ionic liquids which have either not been measured yet, or are available at only limited temperatures. Only a limited number of publications are available on estimation methods of ionic liquid heat capacities at different temperatures and constant pressure. Valderrama et al. [9] presented a
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correlation for heat capacities of ionic liquids using the concept of mass conductivity index, which had recently been defined by the authors to estimate the critical properties of ionic liquids. This correlation also requires molar volume and the ratio of mass of the cation to that of the anion, as input data. Despite the high accuracy, the experimental molar volume at 298 K is unknown for yet-unsynthesized ionic liquids (as ionic liquids are considered to be designer solvents, and so, some research tasks are involved with feasibility predictions of yetunsynthesised ILs). Soriano et al. [1] applied a second-order group additive method to propose a model for the predication of heat capacities of ionic liquids. The database that they used consisted of 3149 data points from 32 ionic liquids, within a wide range of temperatures (188663 K). Since they used only large sub-structures as the groups in their derivation (consisting of the whole cation and anion segments) , their model is not able to estimate the heat capacities of ionic liquids for which either the specific cation or anion are not present in their own data set, for example the family of ammonium-based ionic liquids. Recently, Farahani et al. [10] proposed a structural method for the prediction of heat capacities of ionic liquids. Their databank contained 2940 data points from 56 ionic liquids, covering a temperature range of 188-663 K. Since they used only five input parameters, consisting of temperature, the atom count in both the anion and cation structures, the number of hydrogen atoms in the anion, and the number of methyl groups in the cation of the ionic liquids, they actually ignored the other elements such as oxygen, nitrogen, etc., which are often present in the structure of ionic liquids. Sattari et al. [11] proposed a new approach which combines a group-contribution method with the Genetic Function Approximation (GFA) for the prediction of atmospheric pressure liquid heat capacities for ionic liquids. The simplicity of their model was the advantage of their work. The dataset used comprised of 3,726 experimental data points from 82 ionic liquids. An overall average absolute
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relative deviation of 1.68 % was achieved in their work. In a different work, but with the same experimental database, Sattari et al. [12] developed a quantitative structure–property relationship (QSPR) to predict atmospheric pressure liquid heat capacities of ionic liquids. Instead of using non-linear modeling, such as Artificial Neural Network (ANN) or Support Vector Machine (SVM), the GFA method was applied to determine the model by a binary combination of descriptors rather than using single ones. Valderrama et al. [13] presented a simple and accurate group contribution method to estimate the heat capacities of ionic liquids. They considered a structural parameter known as the mass connectivity index. They used 469 heat capacity data points from 32 ionic liquids. In another work presented by Valderrama et al. [14], artificial neural networks were used with the concept of mass connectivity index to correlate and predict constant-pressure heat capacities of ionic liquids. They used 477 heat-capacity data at several temperatures from 31 ILs to train their network. In order to discriminate among the different substances, they considered the molecular masses of the anion and of the cation and the mass connectivity index as the independent variables. Gardas and Coutinho [15] developed a secondorder group contribution method for the estimation of the liquid heat capacities of imidazolium-, pyridinium-, and pyrrolidinium-based ionic liquids containing either the hexafluorophosphate (PF6), tetrafluoroborate (BF4), bis(trifluoromethanesulfonyl) amide (Tf2N), bromide (Br), ethyl sulfate (EtSO4), or trifluoromethane sulfonate (CF3SO3) anions, within the temperature range of 196.36 to 663.10 K, having liquid heat capacities ranging between 264.8 to 825.0 J. mol-1 K-1. Albert and Müller [16] used first order group contributions to describe the structure of the ions. They used 2419 experimental heat capacity data points from 106 ILs, divided into two separate subsets for parameter fitting and testing to allow for a reliable external validation. The testing group heat capacities were calculated by their model with the mean absolute error of 5.4 %. In
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another study, Müller and Albert [17] proposed temperature-dependent contributions to the heat capacity of ILs. They developed their model using 39 cations and 32 anions, from a database containing 2443 data points from 104 ILs. They reported that the experimental data in their test dataset could be reproduced with a mean relative error of 4.4%. In this study, we have attempted to introduce a simple correlation to cover a wider range of ionic liquids, for more extensive applications, than already available in literature. A temperaturedependent correlation based on the basic molecular parameters, including molecular weight and the number of elements such as carbon, hydrogen, oxygen, nitrogen, etc. in the structure of the ionic liquid, is presented to predict the heat capacities of ionic liquids.
2. Method Since the objective of this study was to present a very simple, yet general, correlation to predict the heat capacities of numerous ionic liquids, as the first step, the input parameters of the temperature-dependent correlation were chosen to be basic structural parameters such as molecular weight and the number of the various elements in the structure of the ionic liquid. These input parameters were chosen because they are readily known parameters and very simple to find. The proposal of any empirical correlation requires an adequate database of trustworthy experimental data. In this work, the physical property data of ionic liquids were obtained from various literature references [2, 6, 18-61]. A total of 4822 experimental heat capacity data points from a total of 128 different ILs, with a temperature range of (190–663.10 K) were considered. In this manner, the data covered a wide range of liquid heat capacities (93–1764 J mol−1 K−1). 7
The investigated ILs covered 54 different cations and 34 different anions. The names and structures of the cations and anions are presented in Tables S.1 and S.2 of the Supplementary section, respectively. Of the total of 128 ionic liquids investigated in this study, 100 were randomly considered for obtaining the correlation and the remaining 28 were set aside for validation of the suggested correlation. A complete list of all the 100 ILs used for optimizing the correlation is reported in Table 1, and the relevant information about the data is also provided, including the reference, the number of data for each IL, the molecular weight (MW), temperature range, and heat capacity range. Table 1 The optimization technique of Genetic Algorithm (GA) was used to obtain the constants of the correlation. GA is among the family of Evolutionary Algorithms (EA). It is a direct, parallel, stochastic method for global search and optimization, which imitates the evolution of living beings [62]. Genetic Algorithm works with a set of individuals, representing possible solutions of the task at hand. The selection principle is applied by using a criterion, giving an evaluation for the individual with respect to the desired solution. The best-suited individuals create the next generation [62]. Optimization on the coefficients of the correlation was carried out to minimize the objective function below, in the form of Average Absolute Relative Deviation (AARD%), in order to minimize the differences between the results of our equation and experimental data.
n
∑ AARD % =
C pexp − C pcal C pexp n
× 100
(1)
8
Where
cal −1 −1 C exp is the experimental heat capacity (J .mol K ) , C p is the calculated heat p
(
)
−1 −1 capacity J .mol K and n is number of data points.
For validation of the suggested correlation, the remaining 750 data points from 28 different ionic liquids, which were not used in the optimization, were selected and the predicted heat capacities were compared with experiment data. A list of the ILs making up the validation dataset is presented in Table 2, and the relevant information about the data is also provided in the table. Table 2
3. Results and discussion In order to propose a more general and comprehensive atomic contribution model with respect to literature models, a wide set of atoms commonly found in ILs has been considered in this study. The number of carbon atoms in the cation and anion, as well as other important atoms consisting of nitrogen, sulfur, phosphorous, oxygen, fluorine, bromine, chlorine and boron were found to be the most effective parameters to distinguish the behavior of different ILs from one another. The functionality for each of these atoms, similar to previous atomic-contribution models, was considered to be a simple additive term consisting of the number of that particular atom in the structure multiplied by a constant (weight) which is optimized. In this manner, by considering these atoms as the structure-related input parameters to the model and including a mathematical temperature functionality as well, various mathematical regressions were carried out on the 4072 training data of the different ionic liquids and the resulting optimized correlation for heat
(
capacity, in J .mol
−1
)
K − 1 , is suggested as follows: 9
C pcal = a1T a2 + a 3 ln (T ) + a 4 MW a5 + a 6 C A + a 7 C c + a 8 N + a 9 S + a10 O + a11 (F + Br + Cl ) + a12 B + a13 (2)
where T and MW are the temperature (K) and molecular weight, respectively. The remaining parameters are all structure-related and defined as the number of atoms of: carbon in the anion
(C A ) , carbon in the cation (C C ) , nitrogen (N ) , sulfur (S ) , oxygen (O ) , phosphorous (P ) , fluorine (F ) , bromine (Br ) , chlorine (Cl ) and boron (B ) . The global constants of Equation (2) are presented in Table 3. Table 3 The validation of the presented correlation was carried out using the remaining 750 data points, from 28 different ionic liquids that were not used in the optimization above. The heat capacities predicted with the correlation in this manner were compared to the corresponding experiment data. The resulting Average Absolute Relative Deviations (AARD%) are presented in Table 4. Table 4 Table 5 indicates that 82.5% of the optimization data and 71.7% of the validation data were estimated with errors of less than 10%, respectively. Since ionic liquids are very complex substances, having both hydrocarbon and ionic nature, such a range of error is acceptable. Table 5 Figure 1 indicates predicted heat capacity values versus the corresponding experimental values for the validation dataset. As shown in Fig. 1, the model is able to predict the experimental values successfully as the calculated values of heat capacities are in rather good agreement with the experimental ones. Figure 2 shows the average relative deviation (ARD%) of the predicted heat capacity values for the validation dataset. Of the total validation dataset, 71.7% of the data 10
are estimated with errors of less than 10%. Figure 3 shows the variations of heat capacities with temperature for different ionic liquids (both experimental data and model results). Additionally, Fig. 4 shows the predicted heat capacity values versus the corresponding experimental values for the optimization dataset by the proposed correlation in this work. Fig. 1 Fig. 2 Fig. 3 Fig.4 As mentioned earlier, other group contribution models are available in the literature for estimation of IL heat capacities. For an investigation of the accuracy of the proposed model in this study, results have been compared with some other literature methods [10, 11, 17]. In order to have a fair evaluation of the proposed model and those from literature, we have chosen the validation dataset of ionic liquids only for the comparisons below. In this manner, by excluding the ionic liquids which were directly used for optimizing the coefficients of our proposed model, unbiased and fair results of our method are compared with literature models. Table 6 presents the resulting AARD% values. As can be seen in this table, the Müller and Albert model [17] give the best results, with a total AARD% of 2.38%, but only for the ILs which could be calculated by this model (as some ILs could not be calculated since their ionic values were not listed in the model). This high accuracy was to be expected because the Müller and Albert model is one of ion contributions, in which a separate group is specifically dedicated to each anion and cation. Therefore, it is fine-tuned to each ionic liquid. However, the shortcoming of such an ion contribution model is its limitation of 11
use for a variety of different ionic liquids, i.e., it can only be used for those particular ionic liquid families for which the groups have been predetermined. Therefore, the Müller and Albert model is, in general, applicable to only the limited number ionic liquids proposed by the authors. However, by limiting the range of ionic liquids, more accurate results are obtained for those ionic liquids that do apply. The other two models compared in Table 6, i.e. the Sattari et al. [11] and the Farahani et al. [10] models, are both of the atomic-contribution type (combination of correlation and atomiccontribution for the Farahani et al. model), similar in principle to the proposed model in this study. These atomic models have no limitation of their usage for different ionic liquid families, as long as all the atoms present in the ionic liquid are available among the atomic contributions of the model. A comparison of the accuracies of the atomic group contribution models in Table 6, shows that the proposed model gives the better results with respect to those of literature, with a total AARD% of 5.64% for all of the validation ILs. The Sattari et al. atomic model has a total AARD% of 6.57% and the Farahani et al. model, a combination of correlation and an atomic model, has a total AARD% of 14.20%. Also, a graphical presentation of the accuracy of the Müller and Albert [17], Sattari et al. [11] and Farahani et al. [10] methods, based on the validation data set, are presented in the Supplementary section as Figure S.1-3. These figures can be compared with that of the proposed model in this work, as given in Figure 1, since they all represent the same dataset. It may be observed that the method presented in this work has reliable results with respect to experimental data. Table 6
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4.
Conclusions
Various approaches can be used to estimate the heat capacities of ILs based on different principles. Such approaches include the empirical-based models such as correlations, group contributions, artificial intelligence methods, etc., while others can be more theoretically-based, such as computational methods or derivations from equations of states [10-17]. The methodology of each of these models involves certain advantages, as well as specific concerns and limitations over the others. For instance, the use of empirical correlations, although very simple, requires either experimental physical property data as the input necessary to distinguish the IL of concern, or else a large databank of component-specific constants to be used in the pre-optimized mathematical equation. Group contribution methods alleviate the necessity of any experimental data or component-specific correlation constants. All that is required in true group contribution models is knowledge of molecular structure, so they can be considered to be more global than correlations. However, generality often comes at the price of lower accuracy. They are also slightly more difficult to use than the very simple empirical correlations, although calculations are still in the category of hand-held calculators. Artificial intelligence methods, which have gained some popularity among scholars in the past decade, for example neural networks, suffer from the lack of any theoretical background as they are merely blind interpolative tools. Perhaps their greatest drawback is their necessity to extensive experimental data banks for their construction, a severely limiting issue, especially in the case of ILs which still suffer from the limited amount of available experimental information. However, the use of thousands of data points for construction, often makes the correlative results rather accurate.
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Such artificial intelligence methods, in contrast to the previous two methods, rely on computer calculations and are not common engineering tools to be accepted and popularized by the general engineering community. Since all of the three approaches mentioned above are correlative, they have the added shortcoming that they cannot be used outside of the ranges of components, temperatures, and pressures for which they were correlated and optimized. The other category of ionic liquid heat capacity estimation models are the theoretically-based approaches. Such methods, although potentially powerful models, sometimes lack the theoretical depth and knowledge to treat the various mechanisms and complexities involved on microscopic levels, which are required for the accurate estimation of a macroscopic property. Therefore, because of such shortcomings, they often revert to using experimental data to fit or simplify the lacking information. Another drawback is that some of these methods require extensive computational time and expertise, which make them unattractive to the engineering community. However, when extrapolation of heat capacity is necessary, these methods are far more advantageous over the correlative methods. Such theoretical routes to estimating the heat capacities of ionic liquids have not yet been given attention by the scientific community and remain to be investigated. With the explanations above, the place of the atomic contribution model of this study, among the selection of approaches, is somewhat clearer. It is a very simple method that can be adopted for fast and easy-to-use engineering calculations. It has the advantage that it requires absolutely no experimental data as input, which is particularly beneficial in the case of ionic liquids which are still greatly deficient in many physical property data. It is only necessary to know the structure of the desired ionic liquid to predict the heat capacity. In addition, among the group contribution family of methods, this purely atomic contribution approach has priority to the others available in literature for IL heat capacity estimations because the “groups” are presented only as atoms, 14
making our model applicable to a wider range of ionic liquids than currently possible with the other literature models which are limited to families containing only the specifies groups of their methods. The result of this work was a very simple correlation for the estimation of heat capacities of ionic liquids covering a wide range of anion and cation structures, as well as a wide range of temperatures. The proposed correlation had an average absolute relative deviations of 5.83% for the optimization dataset consisting of 4072 data from 100 different ionic liquids and 5.61% for the validation dataset consisting of 750 data of new ionic liquids, which were not used in the optimization. Different literature models were compared with the proposed model, based on the validation dataset. The Müller and Albert model had a total AARD% of 2.38%, but for only those ILs which could be calculated by their model (some ILs could not be calculated because their ions were not listed in the model of Müller and Albert). If we exclude the Müller and Albert model because of its different ionic nature and type, our proposed model has the best results among the atomic-contribution models, with a total AARD% of 5.64% for all of the validation ILs. The atomic-contribution model of Sattari et al. [11] had a total AARD% of 6.57%, while the Farahani et al. [10] model, a combination of correlation and atomic-contribution, had a total AARD% of 14.20%. Therefore, simplicity and ease of use, availability of input parameters, generality, and acceptable errors, are the advantages of this correlation over previously reported methods for ionic liquid heat capacity.
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[55] Fredlake, C. P.; Crosthwaite, J. M.; Hert, D. G.; Aki, S. N. V. K.; Brennecke, J. F. J. Chem. Eng. Data. 49(2004) 954-964. [56] Freire, M. G.; Teles, A. R. R.; Rocha, M. A. A.; Schroder, B.; Neves, C. M. S. S.; Carvalho, P. J.; Evtuguin, D. V.; Santos, L. M. N. B. F.; Coutinho, J. A. P. J. Chem. Eng. Data. 56(2011) 4813-4822. [57] Rocha, M. A. A.; Bastos, M.; Coutinho, J. A. P.; Santos, J. M. N. B. F. J. Chem. Thermodyn. 53(2012) 140-143
18
[58] Verevkin, S. P.; Zaitsau, D. H.; Emel'yanenko, V. N.; Ralys, R. V.; Schick, C. Thermochim. Acta 562(2013) 84-95. [59] Waliszewski, D.; Stepniak, I.; Piekarski, H.; Lewandowski, A.; Thermochim. Acta 433 (2005) 149-152. [60]
Krolikowska, M.; Paduszynski, K.; Zawadzki, M.; J. Chem. Eng. Data. 58(2) (2013) 285-293.
[61]
Shin, C.; Worsley, I.; Criss, C. M. J. Solution Chem. 5(1976) 867-879.
[62] Popov A., GENETIC ALGORITHMS FOR OPTIMIZATION Programs for MATLAB User Manual, Hamburg, 2005, www.tuhh.de.
19
Figure Captions Fig 1: Predicted heat capacity versus experimental values for the validation dataset Fig 2: The Average Relative Deviation (ARD%) of the predicted heat capacities by the proposed model from experimental values, for the validation dataset Fig 3: The variations of heat capacities with temperature for different ionic liquids (experimental data and model) Fig 4: Predicted heat capacity versus experimental values for the optimization dataset by the proposed correlation in this work.
20
Fig 1
21
Fig 2
22
Fig 3
23
Fig.4
24
Tables Table 1: List of investigated ionic liquids and their references No. of No.
1
Ionic liquid
Reference
data
Temperature MW range
(K )
CPexp range
(Jmol
−1
K
−1
)
1-butyl-3-methylimidazolium hexafluorophosphate
[18]
1528
284.18
300.05-524.87
409.20-510.00
1-ethyl-3-methylimidazolium ethyl sulfate
[19]
170
236.29
196.36-389.95
346.80-399.90
3
1-hexyl-3methylimidazoliumtrifluoromethylsulfonylimide
[20]
174
447.42
196.00-418.13
589-719
4
Trihexylphosphonium pentafluoroethyltrifluorophosphate
[21]
143
928.87
338.15-513.15
1540-1810
1-hexyl-3-methylimidazolium tetrafluoroborate
[22]
117
254.08
283.15-323.15
422.80-444.50
trihexylphosphonium trifluoromethyl)sulfonylimide
[21]
110
764.00
328.15-463.15
1360-1570
1-methyl-3-propylimidazolium bromide
[22]
91
205.10
212.20-366.73
259.70-305.50
1-hexylquinolinium trifluoromethylsulfonylamide
[23]
77
494.47
322,72-370.13
578-599
1-hexyl-3-methylimidazolium oxalate borate
[24]
80
354.12
239.33-397.44
575.80-656.70
1-butyl-3-methylimidazolium dicyanamide
[25]
78
205.26
235.80-367.14
355.90-403.20
11
1-ethyl-3-methylimidazolium trifluoromethyl)sulfonylimide
[21]
75
391.31
283.15-463.15
502.30-559.0
12
1-butyl-1-methylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide
[25]
72
422.41
237.44-368.40
546.8-638.0
tetradecyl(trihexyl)phosphonium dicyanamide
[21]
63
549.90
313.15-413.15
1060-1240
14
3-methyl-1-propyl-1H-imidazolium(S)-2-amino-4carboxybutanoate
[26]
58
271.31
244.24-357.68
471.00-568.10
15
1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate
[27]
51
612.28
293.15-343.15
726-768.
1-hexyl-3-methylimidazolium hexafluorophosphate
[27]
62
312.24
293.15-453.10
422-553
1-tetradecyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide
[25]
50
559.63
309.98-368.07
896.30-953.30
1-butyl-3-methylimidazolium bis(oxalato)borate
[24]
50
326.07
244.30-292.74
528.7-551.9
19
N-(2-hydroxyethyl)-N,N-dimethylpropanaminium bromid
[28]
48
212.13
382.50-429.9
370.7-392.6
20
Butyltrimethylammonium bis(trifluoromethylsulfonyl)imide
[25]
48
396.37
278.32-367.93
547.5-600.9
1-butylpyridinium tetrafluoroborate
[29]
40
223.02
286.06-389.03
377.18-427.76
22
1-butyl-3-methylpyridinium1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide
[30]
41
430.39
293.10-333.10
541-582
23
1-ethyl-3-methylpyridinium bis((trifluoromethyl)sulfonyl)amide
[30]
41
402.33
293.10-333.10
484-522
24
3-methyl-1-propylpyridinium bis(trifluoromethylsulfonyl)imide
[6, 30]
41
416.36
293.10-331.10
510-549
2
5 6 7 8 9 10
13
16 17 18
21
25
AARD%
0.85 2.64 2.23 3.10 0.33 3.84 17.45 34.36 1.63 0.65 1.42 1.44 6.14 6.60 17.83 10.46 1.26 0.44 2.76 5.90 0.53 10.68 10.61 11.30
25
22.71
1-butyl-1-methylpyrrolidinium dicyanamide
[31]
41
208.30
293.15-333.15
490-554
1,2-dimethyl-3-propylimidazolium bis[(trifluoromethyl)sulfonyl]imide
[32]
35
419.40
323.15-663.10
473.50-631.0
1-butyl-3-methylpyridinium trifluoromethanesulfonate
[30]
31
299.31
323.10-353.10
461.0-496.0
1-propylpyridinium tetrafluoroborate
[33]
25
208.99
278.15-338.15
352.0-385.0
29
n-butyl-4-(n',n'-dimethylammonium)pyridinium bis(trifluoromethylsulfonyl)imid
[6]
23
459.43
315.15-425.15
673-739
30
n-ethyl-4-(n',n'-dimethylammonium)pyridiium bis(trifluoromethylsulfonyl)imide
[6]
23
431.37
315.15-425.15
603-659
31
1-hexyl-3-methylimidazolium trifluoromethanesulfonate
[6]
23
316.34
313.14-423.17
517-572
1-ethyl-3-methylimidazolium trifluoromethanesulfonate
[6]
23
260.23
313.13-423.14
384-422
1-octyl-3-methylimidazoliumtrifluoromethanesulfonate
[6]
23
344.39
313.17-423.14
588-651
N-octyl-3-methylpyridinium tetrafluoroborate
[34]
20
293.15
278.15-325.65
434-472
1-ethyl-3-methylimidazolium thiocyanate
[35]
20
169.25
296.20-372.20
340.7-404.7
1-ethyl-3-methylimidazolium dicyanamide
[35]
20
177.21
296.20-372.20
323.8-376.7
1-butyl-3-methylimidazolium thiocyanate
[35]
20
197.3
296.20-372.20
383.0-457.3
N-(2-hydroxyethyl)-N,N-dimethylbutanaminium bromide
[28]
19
226.15
409.71-438.26
382.5-407.0
39
1-octyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide
[36]
18
475.47
281.99-372.66
694-780
1.94
40
1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide
[37]
17
419.36
293.15-453.1
436-575
18.57
41
N-ethyl-N-(2-hydroxyethyl)-N,N-dimethylammonium ethyl sulfate
[38]
16
243.32
300.15-375.15
451-507
17.53
42
trihexyltetradecylphosphonium bis(2,4,4trimethylpentyl)phosphinate
[39]
15
773.27
293.15-363.15
1619-1764
2.07
43
1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate
[40]
14
587.27
293.00-358.00
767-812
6.49
44
1H-imidazolium octanoate
[41]
7
212.29
298.15-313.15
769-788.2
47.42
45
1-octylpyridinium bis((trifluoromethyl)sulfonyl)amide
[42]
13
472.47
265.04-385.13
583-756
9.34
46
1-methyl-1-octylpyrrolidinium bis(trifluoromethylsulfonyl)amide
[42]
13
478.51
265.06-385.14
606-732
9.74
47
N-(2-hydroxyethyl)-N,N-dimethylhexan-1-aminium bromide
[28]
13
254.21
386.41-403.35
465-475
2.19
48
1-butyl-3-methylimidazolium chloride
[2]
13
174.67
343.20-403.20
337.2-376.8
1.94
49
1-ethyl-3-methylimidazolium bromide
[43]
12
191.07
347.66-367.50
265.30-272.60
22.22
50
1-butyl-3-methylimidazolium methylsulfate
[44]
12
250.32
303.20-358.20
375.5-400.5
6.98
51
1-ethyl-3-methylimidazolium hexafluorophosphate
[37]
11
256.13
353.15-453.10
289-346
25.76
52
1-butyl-3-methylimidazolium trifluoroacetate
[45]
11
252.23
190-290
367.4-403.8
3.32
53
N-ethyl-2-hydroxy-N,N-dimethylethanaminium 1butanesulfonate
[38]
10
255.37
355.15-400.15
93.00-104.00
369.97
26 27 28
32 33 34 35 36 37 38
26
18.14 3.84 3.7 1.25 0.25 3.45 0.64 4.11 19.16 18.86 4.57 13.18 9.46
54
4,6-dimethyl-N-phenylpyrimidin-2-amine dodecanoate
[46]
10
399.57
323.46-339.26
830.6-872.9
2.01
55
N,N-dibutyl-N-methylbutanaminium L-serinate
[47]
9
304.47
293.15-363.15
632-681
8.16
56
etrabutylphosphonium L-prolinate
[47]
9
373.55
293.15-363.15
838—939
13.58
57
tetrabutylphosphonium L-threoninate
[47]
9
377.54
293.15-363.15
952-1100
26.19
58
tetrabutylphosphonium L-valinate
[47]
9
375.57
293.15-363.15
744-811
1.54
59
tetrabutylphosphonium L-serinate
[47]
9
363.52
293.15-363.15
742-815
11.80
60
N,N-dibutyl-N-methyl-1-butanaminium 2aminoethanesulfonate
[47]
9
324.52
293.15-363.15
822-892
30.38
61
N,N-dibutyl-N-methyl-1-butanaminium L-lysinate
[47]
9
345.56
293.15-363.15
817-925
19.87
[48]
9
383.57
293.15-363.15
990-1090
30.93
62
tetrabutylphosphonium 2-aminoethanesulfonate
63
N-ethyl-2-hydroxy-N,N-dimethylethanaminium methanesulfonate
[38]
9
213.30
355.15-395.15
406-435
13.05
64
2-hydroxy-N,N,N-trimethyl-ethanaminium 1butanesulfonate
[38]
9
241.35
360.15-400.15
518.0-529.0
17.60
65
N,N,N-trimethyl-1-butanaminium 1butanesulfonate
[38]
9
253.40
360.15-400.15
701-741
33.74
66
1-butyl-3-methylimidazolium nitrate
[48]
8
201.22
309.16-370.00
357.7-383.0
2.54
67
1H-imidazolium, 1-ethyl-3-methyl-, salt with trifluoroacetic acid (1:1)
[49]
7
224.18
283.15-343.15
308-337
13.12
68
1-ethyl-3-methylimidazolium methanesulfonate
[50]
7
206.26
283.15-343.15
327-350
1.95
69
1-ethyl-3-methylimidazolium diethylphosphate
[50]
7
264.26
283.15-343.15
517-557
16.13
70
1-ethyl-3-methylimidazolium hydrogen sulfate
[50]
7
208.24
283.15-343.15
290-324
3.44
71
1-(2-hydroxyethyl)-3-methyl-1H-imidazolium 2,2,2trifluoroacetate
[50]
7
240.18
283.15-343.15
362-394
1.25
72
1-ethyl-3-methylimidazolium methylsulfate
[50]
7
222.26
283.15-343.15
324-354
2.14
73
N-ethyl-N,N-dimethyl-N-butylammonium ethyl sulfate
[38]
7
255.37
360.15-390.15
451-500
4.33
74
1-butyl-3-methylimidazolium tosylate
[51]
5
310.41
343.89-380
543.4-569.8
6.8
75
1-butyl-1-methylpyrrolidinium trifluoromethanesulfonate
[52]
3
291.33
288.15-308.15
424-441
5.03
76
1-methylpyridinium methylsulfate
[52]
3
205.23
288.15-308.15
288-305
8.68
77
1,2-diethylpyridinium ethylsulfate
[52]
3
261.34
288.15-308.15
399-420
9.44
78
1-butyl-3-methylpyridinium tetrafluoroborate
[53]
2
237.05
298.15-323.15
405-421
1.45
79
1-hexylpyridinium bis(trifluromethylsulfonyl)imide
[53]
2
444.41
298.15-323.15
612-632
5.16
80
1-hexyl-2,3-dimethylimidazolium
[53]
2
461.44
298.15-323.15
686-705
3.53
81
3-hexyl-1-methyl-1H-imidazolium bromide
[53]
2
247.18
298.15-323.15
344-357
23.56
82
1-butyl-3-methylimidazolium 2-(2methoxyethoxy)ethyl sulfate
[53]
2
338.42
298.15-323.15
643-652
12.46
27
83 84
85 86
1-octyl-3-methylpydridinium bis(trifluoromethylsulfonyl)imide 1-hexyl-3-methyl-4-(dimethylamino)pyridinium 1,1,1trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 1-hexyl-4-(4-methyl-1-piperidinyl)pyridinium 1,1,1trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 3,5-diethyl-1-hexyl-2-propylpyridinium 1,1,1-trifluoroN-[(trifluoromethyl)sulfonyl]methanesulfonamide
[53]
2
486.49
298.15-323.15
669-693
10.32
[53]
2
501.51
298.15-323.15
725-764
2.90
[53]
2
541.57
298.15-323.15
628-650
34.76
[53]
2
542.60
298.15-323.15
766-799
12.64
87
1-hexyl-3,5-dimethylpyridinium bis(trifluoromethylsulfonyl)imide
[53]
2
472.47
298.15-323.15
620-665
11.97
88
1-ethyl-3-methylpyridinium ethylsulfate
[53]
2
247.31
298.15-323.15
389-402
35.45
89
1-methyl-3-octylimidazolium bromide
[53]
2
275.23
298.15-323.15
392-408
24.11
90
17-hydroxy-N-(17-hydroxy-3,6,9,12,15pentaoxaheptadec-1-yl)-N-methyl-N-tetradecyl3,6,9,12,15-pentaoxaheptadecan-1-aminium methyl sulfate
[53]
2
868.16
298.15-323.15
1070-1100
49.03
91
tetrabutylammonium docusate
[53]
2
664.03
298.15-323.15
1320-1380
2.47
92
1-methyl-3-(3,3,4,4,5,5,6,6,6-nonafluorohexyl)-1Himidazolium 1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide
[53]
2
611.35
298.15-323.15
725 -752
7.33
93
1-hexyl-3-methylpyridinium bromide
[54]
2
258.20
298.15-323.15
343-358
37.08
[54]
2
265.12
298.2-323.2
495-524
1.95
94
1-butyl-3-methylpyridinium tetracyanoborate
95
1-butyl-1-methylpyrrolidinium tetracyanoborate
[54]
2
257.14
298.2-323.2
471-498
2.05
96
1-n-butyl-3-methylimidazolium bromide
[55]
2
219.12
298.15-323.15
330-338
10.80
97
1-butyl-2,3-dimethylimidazolium hexafluorophosphate
[55]
2
298.21
298.15-323.15
442.3-458.1
0.55
98
1-ethyl-3-methyl-1H-imidazolium hydrogen methylphosphonate
[56]
1
206.18
298.15
344.7
3.01
99
1-pentyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide
[57]
1
433.39
298.15
596
0.79
1
202.72
298
100
1-hexyl-3-methylimidazolium chloride
[58]
28
381
0.53
Table 2: List of investigated ionic liquids for validation Temperature No.
Ionic liquid
Reference
MW range
(K )
CPexp range
(Jmol
−1
K −1
)
AARD%
1
1-methyl-3-octylimidazolium tetrafluoroborate
[22]
282.13
283.15-323.15
489.2-514.5
1.55
2
1-ethyl-3-methylimidazolium tetrafluoroborate
[22]
197.97
283.15-323.15
300.2-315.1
0.47
3
trihexyl(tetradecyl)phosphonium chloride
[21]
519.31
338.15-463.15
834-970
15.07
4
1-butyl-3-methylimidazolium tetrafluoroborate
[22]
226.02
283.15-323.15
360.20-378.1
0.07
5
tributylmethylphosphonium methylsulphate
[21]
328.45
343.15-463.15
661-757
12.7
6
1-butyl-3-methylimidazolium octyl sulfate
[59]
348.5
298.15-343.15
635-698
4.79
7
1-butyl-3-methylimidazolium trifluoromethanesulfonate
[25]
288.29
292.86-367.78
425-465
0.54
8
4-(dimethylamino)-1-hexyl-pyridinium 1,1,1-trifluoroN[(trifluoromethyl)sulfonyl]methanesulfonamide
[6]
487.48
315.15-425.15
750-825
3.46
9
1-ethyl-3-methyl-1H-imidazolium tricyanomethanide
[35]
201.23
296.2-368.2
357.2-399.2
2.91
10
1-methyl-1-propylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide
[59]
408.38
288.15-358.15
547.5-594
0.74
11
2-octylisoquinolinium thiocyanate
[60]
300.46
278.15-343.15
510-540
14.30
12
1-ethyl-1-octylpiperidinium bis((trifluoromethyl)sulfonyl)amide
[42]
506.57
265.01-385.02
704-904
4.99
13
1-butyl-3-methylimidazolium acetate
[45]
198.26
210-300
352.4-384.1
3.84
14
tetrabutylphosphonium L-cysteinate
[47]
379.58
293.15-363.15
914-1020
21.37
15
tetrabutylphosphonium L-lysinate
[47]
404.61
293.15-363.15
990-1110
22.41
16
N,N-dibutyl-N-methyl-1-butanaminium L-threoninate
[47]
318.5
293.15-363.15
748-821
19.23
17
N-ethyl-2-hydroxy-N,N-dimethylethanaminium 1octanesulfonate
[38]
311.48
355.15-395.15
711-748
19.53
18
tributylethylphosphonium diethylphosphate
[50]
384.47
283.15-343.15
683-768
3.71
19
tetrapropylammonium bromide
[61]
266.26
283.01-348.43
333-393
36.57
20
1-hexyl-3-methylimidazolium dicyanamide
[52]
233.31
288.15-308.15
510-548
17.05
21
3-(ethoxycarbonyl)-1-ethylpyridinium ethylsulfate
[54]
305.35
298-323
513-530
0.89
[54]
458.44
298-323
624-644
8.27
[55]
405.34
309.15-323.15
502.6 - 509
7.59
22 23
1-hexyl-3-methylpyridinium 1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 1-ethyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide
24
1-butyl-2,3-dimethylimidazolium tetrafluoroborate
25
1-butyl-nicotinic acid butyl ester bis[(trifluoromethyl)sulfonyl]imide
[55] [53]
29
240.05
330.15-372.15
382.8-414.6
5.78
516.48
298-323
778-800
0.7035
26
1-ethyl-3-methylimidazolium acetate
[56]
170.21
298.15
314.4
0.47
27
1-methyl-3-octylimidazolium chloride
[58]
230.78
298
445
0.72
28
1-dodecyl-3-methyl-1H-imidazolium bis(trifluoromethylsulfonyl)amide
[57]
531.58
298.15
820
0.93
30
Table 3: The constants of Equation (2)
Constant
Value
a1
0.2808
a2
1.0854
a3
-17.5066
a4
0.6593
a5
1.0793
a6
15.9932
a7
16.1292
a8
-2.8956
a9
-11.7667
a10
-1.3729
a11
-4.1977
a12
6.7438
a13
-12.3990
31
Table 4: The Average Absolute Relative Deviation (AARD%) on the optimization and validation datasets Proposed method Method Optimization dataset
Validation dataset
Number of data
4072
750
Error (AARD%)
5.83 %
5.61 %
32
Table 5: The number of datapoints which have error less than 2.5, 5, 10, 25, 50 and 75 % Percent of data with errors less than:
Optimization dataset
Validation dataset
2.5 %
61.9 %
57.6 %
5%
73.9 %
66.7%
10 %
82.5 %
71.7 %
25 %
96.4 %
98.9 %
50 %
99.7 %
100.0%
75 %
99.8%
100.0 %
33
Table 6: Comparison the AARD% values of the proposed model with different literature models based on the validation dataset.
No.
Müller and
Sattari et al.
Farahani et al.
Albert [17]
[11]
[10]
Proposed model
Ionic liquid
1
1-methyl-3-octylimidazolium tetrafluoroborate
0.59
1.78
5.66
1.55
2
1-ethyl-3-methylimidazolium tetrafluoroborate
1.74
10.92
20.82
0.47
3
trihexyl(tetradecyl)phosphonium chloride
-
5.39
15.62
15.07
4
1-butyl-3-methylimidazolium tetrafluoroborate
6.39
8.05
13.07
0.07
5
tributylmethylphosphonium methylsulphate
0.30
8.27
26.25
12.70
6
1-butyl-3-methylimidazolium octyl sulfate
0.04
1.55
7.33
4.79
7
1-butyl-3-methylimidazolium trifluoromethanesulfonate
1.76
2.10
12.22
0.54
8
4-(dimethylamino)-1-hexyl-pyridinium 1,1,1-trifluoroN[(trifluoromethyl)sulfonyl]methanesulfonamide
-
7.53
8.78
3.46
9
1-ethyl-3-methyl-1H-imidazolium tricyanomethanide
-
14.48
21.61
2.91
10
1-methyl-1-propylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide
0.00
5.72
4.00
0.74
11
2-octylisoquinolinium thiocyanate
0.08
2.16
2.54
14.30
12
1-ethyl-1-octylpiperidinium bis((trifluoromethyl)sulfonyl)amide
0.23
5.04
5.42
4.99
13
1-butyl-3-methylimidazolium acetate
0.49
3.09
17.26
3.84
14
tetrabutylphosphonium L-cysteinate
0.15
19.69
32.34
21.37
15
tetrabutylphosphonium L-lysinate
0.65
7.40
26.81
22.41
16
N,N-dibutyl-N-methyl-1-butanaminium L-threoninate
15.22
4.90
26.12
19.23
17
N-ethyl-2-hydroxy-N,N-dimethylethanaminium 1octanesulfonate
-
4.23
11.54
19.53
18
tributylethylphosphonium diethylphosphate
0.31
10.91
15.86
3.71
19
tetrapropylammonium bromide
-
25.23
5.59
36.57
20
1-hexyl-3-methylimidazolium dicyanamide
13.75
9.95
32.79
17.05
21
3-(ethoxycarbonyl)-1-ethylpyridinium ethylsulfate
-
5.15
18.06
0.89
-
21.17
2.37
8.27
15.53
2.96
16.29
7.59
1.61
12.4
18.73
5.78
22 23 24
1-hexyl-3-methylpyridinium 1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 1-ethyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-butyl-2,3-dimethylimidazolium tetrafluoroborate
34
-
16.71
11.79
0.70
1-ethyl-3-methylimidazolium acetate
7.02
7.68
21.97
0.47
27
1-methyl-3-octylimidazolium chloride
-
8.92
11.26
0.72
28
1-dodecyl-3-methyl-1H-imidazolium bis(trifluoromethylsulfonyl)amide
-
6.16
6.77
0.93
2.38
6.57
14.20
5.64
25
1-butyl-nicotinic acid butyl ester bis[(trifluoromethyl)sulfonyl]imide
26
Total
35
S0378-3812(15)00328-3 http://dx.doi.org/doi:10.1016/j.fluid.2015.06.009 FLUID 10614
To appear in:
Fluid Phase Equilibria
Received date: Revised date: Accepted date:
22-3-2015 6-6-2015 8-6-2015
Please cite this article as: Alireza Ahmadi, Reza Haghbakhsh, Sona Raeissi, Vahid Hemmati, A simple group contribution correlation for the prediction of ionic liquid heat capacities at different temperatures, Fluid Phase Equilibria http://dx.doi.org/10.1016/j.fluid.2015.06.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A simple group contribution correlation for the prediction of ionic liquid heat capacities at different temperatures Alireza Ahmadi, Reza Haghbakhsh, Sona [email protected], Vahid Hemmati School of Chemical and Petroleum Engineering, Shiraz University, Mollasadra Ave., Shiraz 71345, Iran. 1
Corresponding author at: School of Chemical and Petroleum Engineering, Shiraz University, 71345
Mollasadra Ave., Shiraz, Iran. Tel.: +98 71 36133707; Fax: +98 71 36474619.
1
Abstract The heat capacities of pure ionic liquids (ILs) are among the thermophysical properties that are required for certain engineering calculations and designs. In this study, a simple correlation is presented for the prediction of the heat capacities of pure ionic liquids. This correlation is a temperature-dependent relation that uses temperature, molecular weight and the number of atoms (such as carbon, hydrogen, oxygen, nitrogen, etc.) in the structure of the IL as input parameters. A dataset of approximately 128 different ILs, consisting of 4822 data points, was used to develop and validate this general correlation, covering a temperature range from 190 to 663 K. Nearly three-quarters of the data were used for optimization and a quarter for validation. The resulting correlation gives good estimations for heat capacities, while having a number of advantages over previous literatures methods. These advantages include (a) being very simple; (b) not requiring any experimental data as input parameters; (c) being more global than previous literature models by having been constructed over a larger databank of ionic liquids; (d) being accurate. The Average Absolute Relative Deviation (AARD%) was calculated to be 5.8% for the optimization dataset, and 5.6% for the validation dataset. This is smaller than what is obtained for the literature atomic-contribution methods proposed by Farahani et al. and Sattari et al., with AARD% values of 14.2% and 6.6%, respectively, based on the validation dataset of this study. Keywords: physical property; thermophysical property; specific heat; estimation; ionic liquids.
2
Symbols: AARD%: Average Absolute Relative Deviation B: boron Br: bromine C: carbon atom
(
Cp: heat capacity J .mol
−1
K −1
)
F: fluorine ILs: ionic liquids MW: molecular weight N: nitrogen n: number of data in equation (1) O: oxygen P: phosphorous S: sulfur T: temperature (K)
Subscripts and superscripts: A: anion C: cation cal: calculated exp: experimental
3
1. Introduction Ionic liquids (ILs) are organic salts that consist completely of ions but are liquid at, or below, room temperature [1]. Because of their very unique properties, they have the potential to be used in a variety of industrial and chemical processes [2, 3]. However, highly accurate data regarding the physicochemical properties of ionic liquids are necessary for the design and operation of such processes [2, 4]. Heat capacity is among the important pure component properties in its own right, furthermore, the temperature-dependency of various thermodynamic properties, such as enthalpy, entropy, and Gibbs energy, can be calculated from the heat capacity of a compound [5]. For example, from a thermodynamic point of view, the heat capacity at constant pressure is the first derivative of enthalpy with respect to temperature. This further highlights the significance of accurate knowledge of heat capacity for many theoretical and engineering calculations. Numerous reports have now become available in literature on experimental measurements or the estimation and prediction techniques for determination of pure ionic liquid physicochemical properties. The most common experimental methods for measuring heat capacity, as reported in the literature, are differential scanning calorimetry and adiabatic calorimetry [6]. The heat capacities of some ionic liquids have also been measured with these methods [6-8]. However, such information is still lacking for many ionic liquids which have either not been measured yet, or are available at only limited temperatures. Only a limited number of publications are available on estimation methods of ionic liquid heat capacities at different temperatures and constant pressure. Valderrama et al. [9] presented a
4
correlation for heat capacities of ionic liquids using the concept of mass conductivity index, which had recently been defined by the authors to estimate the critical properties of ionic liquids. This correlation also requires molar volume and the ratio of mass of the cation to that of the anion, as input data. Despite the high accuracy, the experimental molar volume at 298 K is unknown for yet-unsynthesized ionic liquids (as ionic liquids are considered to be designer solvents, and so, some research tasks are involved with feasibility predictions of yetunsynthesised ILs). Soriano et al. [1] applied a second-order group additive method to propose a model for the predication of heat capacities of ionic liquids. The database that they used consisted of 3149 data points from 32 ionic liquids, within a wide range of temperatures (188663 K). Since they used only large sub-structures as the groups in their derivation (consisting of the whole cation and anion segments) , their model is not able to estimate the heat capacities of ionic liquids for which either the specific cation or anion are not present in their own data set, for example the family of ammonium-based ionic liquids. Recently, Farahani et al. [10] proposed a structural method for the prediction of heat capacities of ionic liquids. Their databank contained 2940 data points from 56 ionic liquids, covering a temperature range of 188-663 K. Since they used only five input parameters, consisting of temperature, the atom count in both the anion and cation structures, the number of hydrogen atoms in the anion, and the number of methyl groups in the cation of the ionic liquids, they actually ignored the other elements such as oxygen, nitrogen, etc., which are often present in the structure of ionic liquids. Sattari et al. [11] proposed a new approach which combines a group-contribution method with the Genetic Function Approximation (GFA) for the prediction of atmospheric pressure liquid heat capacities for ionic liquids. The simplicity of their model was the advantage of their work. The dataset used comprised of 3,726 experimental data points from 82 ionic liquids. An overall average absolute
5
relative deviation of 1.68 % was achieved in their work. In a different work, but with the same experimental database, Sattari et al. [12] developed a quantitative structure–property relationship (QSPR) to predict atmospheric pressure liquid heat capacities of ionic liquids. Instead of using non-linear modeling, such as Artificial Neural Network (ANN) or Support Vector Machine (SVM), the GFA method was applied to determine the model by a binary combination of descriptors rather than using single ones. Valderrama et al. [13] presented a simple and accurate group contribution method to estimate the heat capacities of ionic liquids. They considered a structural parameter known as the mass connectivity index. They used 469 heat capacity data points from 32 ionic liquids. In another work presented by Valderrama et al. [14], artificial neural networks were used with the concept of mass connectivity index to correlate and predict constant-pressure heat capacities of ionic liquids. They used 477 heat-capacity data at several temperatures from 31 ILs to train their network. In order to discriminate among the different substances, they considered the molecular masses of the anion and of the cation and the mass connectivity index as the independent variables. Gardas and Coutinho [15] developed a secondorder group contribution method for the estimation of the liquid heat capacities of imidazolium-, pyridinium-, and pyrrolidinium-based ionic liquids containing either the hexafluorophosphate (PF6), tetrafluoroborate (BF4), bis(trifluoromethanesulfonyl) amide (Tf2N), bromide (Br), ethyl sulfate (EtSO4), or trifluoromethane sulfonate (CF3SO3) anions, within the temperature range of 196.36 to 663.10 K, having liquid heat capacities ranging between 264.8 to 825.0 J. mol-1 K-1. Albert and Müller [16] used first order group contributions to describe the structure of the ions. They used 2419 experimental heat capacity data points from 106 ILs, divided into two separate subsets for parameter fitting and testing to allow for a reliable external validation. The testing group heat capacities were calculated by their model with the mean absolute error of 5.4 %. In
6
another study, Müller and Albert [17] proposed temperature-dependent contributions to the heat capacity of ILs. They developed their model using 39 cations and 32 anions, from a database containing 2443 data points from 104 ILs. They reported that the experimental data in their test dataset could be reproduced with a mean relative error of 4.4%. In this study, we have attempted to introduce a simple correlation to cover a wider range of ionic liquids, for more extensive applications, than already available in literature. A temperaturedependent correlation based on the basic molecular parameters, including molecular weight and the number of elements such as carbon, hydrogen, oxygen, nitrogen, etc. in the structure of the ionic liquid, is presented to predict the heat capacities of ionic liquids.
2. Method Since the objective of this study was to present a very simple, yet general, correlation to predict the heat capacities of numerous ionic liquids, as the first step, the input parameters of the temperature-dependent correlation were chosen to be basic structural parameters such as molecular weight and the number of the various elements in the structure of the ionic liquid. These input parameters were chosen because they are readily known parameters and very simple to find. The proposal of any empirical correlation requires an adequate database of trustworthy experimental data. In this work, the physical property data of ionic liquids were obtained from various literature references [2, 6, 18-61]. A total of 4822 experimental heat capacity data points from a total of 128 different ILs, with a temperature range of (190–663.10 K) were considered. In this manner, the data covered a wide range of liquid heat capacities (93–1764 J mol−1 K−1). 7
The investigated ILs covered 54 different cations and 34 different anions. The names and structures of the cations and anions are presented in Tables S.1 and S.2 of the Supplementary section, respectively. Of the total of 128 ionic liquids investigated in this study, 100 were randomly considered for obtaining the correlation and the remaining 28 were set aside for validation of the suggested correlation. A complete list of all the 100 ILs used for optimizing the correlation is reported in Table 1, and the relevant information about the data is also provided, including the reference, the number of data for each IL, the molecular weight (MW), temperature range, and heat capacity range. Table 1 The optimization technique of Genetic Algorithm (GA) was used to obtain the constants of the correlation. GA is among the family of Evolutionary Algorithms (EA). It is a direct, parallel, stochastic method for global search and optimization, which imitates the evolution of living beings [62]. Genetic Algorithm works with a set of individuals, representing possible solutions of the task at hand. The selection principle is applied by using a criterion, giving an evaluation for the individual with respect to the desired solution. The best-suited individuals create the next generation [62]. Optimization on the coefficients of the correlation was carried out to minimize the objective function below, in the form of Average Absolute Relative Deviation (AARD%), in order to minimize the differences between the results of our equation and experimental data.
n
∑ AARD % =
C pexp − C pcal C pexp n
× 100
(1)
8
Where
cal −1 −1 C exp is the experimental heat capacity (J .mol K ) , C p is the calculated heat p
(
)
−1 −1 capacity J .mol K and n is number of data points.
For validation of the suggested correlation, the remaining 750 data points from 28 different ionic liquids, which were not used in the optimization, were selected and the predicted heat capacities were compared with experiment data. A list of the ILs making up the validation dataset is presented in Table 2, and the relevant information about the data is also provided in the table. Table 2
3. Results and discussion In order to propose a more general and comprehensive atomic contribution model with respect to literature models, a wide set of atoms commonly found in ILs has been considered in this study. The number of carbon atoms in the cation and anion, as well as other important atoms consisting of nitrogen, sulfur, phosphorous, oxygen, fluorine, bromine, chlorine and boron were found to be the most effective parameters to distinguish the behavior of different ILs from one another. The functionality for each of these atoms, similar to previous atomic-contribution models, was considered to be a simple additive term consisting of the number of that particular atom in the structure multiplied by a constant (weight) which is optimized. In this manner, by considering these atoms as the structure-related input parameters to the model and including a mathematical temperature functionality as well, various mathematical regressions were carried out on the 4072 training data of the different ionic liquids and the resulting optimized correlation for heat
(
capacity, in J .mol
−1
)
K − 1 , is suggested as follows: 9
C pcal = a1T a2 + a 3 ln (T ) + a 4 MW a5 + a 6 C A + a 7 C c + a 8 N + a 9 S + a10 O + a11 (F + Br + Cl ) + a12 B + a13 (2)
where T and MW are the temperature (K) and molecular weight, respectively. The remaining parameters are all structure-related and defined as the number of atoms of: carbon in the anion
(C A ) , carbon in the cation (C C ) , nitrogen (N ) , sulfur (S ) , oxygen (O ) , phosphorous (P ) , fluorine (F ) , bromine (Br ) , chlorine (Cl ) and boron (B ) . The global constants of Equation (2) are presented in Table 3. Table 3 The validation of the presented correlation was carried out using the remaining 750 data points, from 28 different ionic liquids that were not used in the optimization above. The heat capacities predicted with the correlation in this manner were compared to the corresponding experiment data. The resulting Average Absolute Relative Deviations (AARD%) are presented in Table 4. Table 4 Table 5 indicates that 82.5% of the optimization data and 71.7% of the validation data were estimated with errors of less than 10%, respectively. Since ionic liquids are very complex substances, having both hydrocarbon and ionic nature, such a range of error is acceptable. Table 5 Figure 1 indicates predicted heat capacity values versus the corresponding experimental values for the validation dataset. As shown in Fig. 1, the model is able to predict the experimental values successfully as the calculated values of heat capacities are in rather good agreement with the experimental ones. Figure 2 shows the average relative deviation (ARD%) of the predicted heat capacity values for the validation dataset. Of the total validation dataset, 71.7% of the data 10
are estimated with errors of less than 10%. Figure 3 shows the variations of heat capacities with temperature for different ionic liquids (both experimental data and model results). Additionally, Fig. 4 shows the predicted heat capacity values versus the corresponding experimental values for the optimization dataset by the proposed correlation in this work. Fig. 1 Fig. 2 Fig. 3 Fig.4 As mentioned earlier, other group contribution models are available in the literature for estimation of IL heat capacities. For an investigation of the accuracy of the proposed model in this study, results have been compared with some other literature methods [10, 11, 17]. In order to have a fair evaluation of the proposed model and those from literature, we have chosen the validation dataset of ionic liquids only for the comparisons below. In this manner, by excluding the ionic liquids which were directly used for optimizing the coefficients of our proposed model, unbiased and fair results of our method are compared with literature models. Table 6 presents the resulting AARD% values. As can be seen in this table, the Müller and Albert model [17] give the best results, with a total AARD% of 2.38%, but only for the ILs which could be calculated by this model (as some ILs could not be calculated since their ionic values were not listed in the model). This high accuracy was to be expected because the Müller and Albert model is one of ion contributions, in which a separate group is specifically dedicated to each anion and cation. Therefore, it is fine-tuned to each ionic liquid. However, the shortcoming of such an ion contribution model is its limitation of 11
use for a variety of different ionic liquids, i.e., it can only be used for those particular ionic liquid families for which the groups have been predetermined. Therefore, the Müller and Albert model is, in general, applicable to only the limited number ionic liquids proposed by the authors. However, by limiting the range of ionic liquids, more accurate results are obtained for those ionic liquids that do apply. The other two models compared in Table 6, i.e. the Sattari et al. [11] and the Farahani et al. [10] models, are both of the atomic-contribution type (combination of correlation and atomiccontribution for the Farahani et al. model), similar in principle to the proposed model in this study. These atomic models have no limitation of their usage for different ionic liquid families, as long as all the atoms present in the ionic liquid are available among the atomic contributions of the model. A comparison of the accuracies of the atomic group contribution models in Table 6, shows that the proposed model gives the better results with respect to those of literature, with a total AARD% of 5.64% for all of the validation ILs. The Sattari et al. atomic model has a total AARD% of 6.57% and the Farahani et al. model, a combination of correlation and an atomic model, has a total AARD% of 14.20%. Also, a graphical presentation of the accuracy of the Müller and Albert [17], Sattari et al. [11] and Farahani et al. [10] methods, based on the validation data set, are presented in the Supplementary section as Figure S.1-3. These figures can be compared with that of the proposed model in this work, as given in Figure 1, since they all represent the same dataset. It may be observed that the method presented in this work has reliable results with respect to experimental data. Table 6
12
4.
Conclusions
Various approaches can be used to estimate the heat capacities of ILs based on different principles. Such approaches include the empirical-based models such as correlations, group contributions, artificial intelligence methods, etc., while others can be more theoretically-based, such as computational methods or derivations from equations of states [10-17]. The methodology of each of these models involves certain advantages, as well as specific concerns and limitations over the others. For instance, the use of empirical correlations, although very simple, requires either experimental physical property data as the input necessary to distinguish the IL of concern, or else a large databank of component-specific constants to be used in the pre-optimized mathematical equation. Group contribution methods alleviate the necessity of any experimental data or component-specific correlation constants. All that is required in true group contribution models is knowledge of molecular structure, so they can be considered to be more global than correlations. However, generality often comes at the price of lower accuracy. They are also slightly more difficult to use than the very simple empirical correlations, although calculations are still in the category of hand-held calculators. Artificial intelligence methods, which have gained some popularity among scholars in the past decade, for example neural networks, suffer from the lack of any theoretical background as they are merely blind interpolative tools. Perhaps their greatest drawback is their necessity to extensive experimental data banks for their construction, a severely limiting issue, especially in the case of ILs which still suffer from the limited amount of available experimental information. However, the use of thousands of data points for construction, often makes the correlative results rather accurate.
13
Such artificial intelligence methods, in contrast to the previous two methods, rely on computer calculations and are not common engineering tools to be accepted and popularized by the general engineering community. Since all of the three approaches mentioned above are correlative, they have the added shortcoming that they cannot be used outside of the ranges of components, temperatures, and pressures for which they were correlated and optimized. The other category of ionic liquid heat capacity estimation models are the theoretically-based approaches. Such methods, although potentially powerful models, sometimes lack the theoretical depth and knowledge to treat the various mechanisms and complexities involved on microscopic levels, which are required for the accurate estimation of a macroscopic property. Therefore, because of such shortcomings, they often revert to using experimental data to fit or simplify the lacking information. Another drawback is that some of these methods require extensive computational time and expertise, which make them unattractive to the engineering community. However, when extrapolation of heat capacity is necessary, these methods are far more advantageous over the correlative methods. Such theoretical routes to estimating the heat capacities of ionic liquids have not yet been given attention by the scientific community and remain to be investigated. With the explanations above, the place of the atomic contribution model of this study, among the selection of approaches, is somewhat clearer. It is a very simple method that can be adopted for fast and easy-to-use engineering calculations. It has the advantage that it requires absolutely no experimental data as input, which is particularly beneficial in the case of ionic liquids which are still greatly deficient in many physical property data. It is only necessary to know the structure of the desired ionic liquid to predict the heat capacity. In addition, among the group contribution family of methods, this purely atomic contribution approach has priority to the others available in literature for IL heat capacity estimations because the “groups” are presented only as atoms, 14
making our model applicable to a wider range of ionic liquids than currently possible with the other literature models which are limited to families containing only the specifies groups of their methods. The result of this work was a very simple correlation for the estimation of heat capacities of ionic liquids covering a wide range of anion and cation structures, as well as a wide range of temperatures. The proposed correlation had an average absolute relative deviations of 5.83% for the optimization dataset consisting of 4072 data from 100 different ionic liquids and 5.61% for the validation dataset consisting of 750 data of new ionic liquids, which were not used in the optimization. Different literature models were compared with the proposed model, based on the validation dataset. The Müller and Albert model had a total AARD% of 2.38%, but for only those ILs which could be calculated by their model (some ILs could not be calculated because their ions were not listed in the model of Müller and Albert). If we exclude the Müller and Albert model because of its different ionic nature and type, our proposed model has the best results among the atomic-contribution models, with a total AARD% of 5.64% for all of the validation ILs. The atomic-contribution model of Sattari et al. [11] had a total AARD% of 6.57%, while the Farahani et al. [10] model, a combination of correlation and atomic-contribution, had a total AARD% of 14.20%. Therefore, simplicity and ease of use, availability of input parameters, generality, and acceptable errors, are the advantages of this correlation over previously reported methods for ionic liquid heat capacity.
15
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19
Figure Captions Fig 1: Predicted heat capacity versus experimental values for the validation dataset Fig 2: The Average Relative Deviation (ARD%) of the predicted heat capacities by the proposed model from experimental values, for the validation dataset Fig 3: The variations of heat capacities with temperature for different ionic liquids (experimental data and model) Fig 4: Predicted heat capacity versus experimental values for the optimization dataset by the proposed correlation in this work.
20
Fig 1
21
Fig 2
22
Fig 3
23
Fig.4
24
Tables Table 1: List of investigated ionic liquids and their references No. of No.
1
Ionic liquid
Reference
data
Temperature MW range
(K )
CPexp range
(Jmol
−1
K
−1
)
1-butyl-3-methylimidazolium hexafluorophosphate
[18]
1528
284.18
300.05-524.87
409.20-510.00
1-ethyl-3-methylimidazolium ethyl sulfate
[19]
170
236.29
196.36-389.95
346.80-399.90
3
1-hexyl-3methylimidazoliumtrifluoromethylsulfonylimide
[20]
174
447.42
196.00-418.13
589-719
4
Trihexylphosphonium pentafluoroethyltrifluorophosphate
[21]
143
928.87
338.15-513.15
1540-1810
1-hexyl-3-methylimidazolium tetrafluoroborate
[22]
117
254.08
283.15-323.15
422.80-444.50
trihexylphosphonium trifluoromethyl)sulfonylimide
[21]
110
764.00
328.15-463.15
1360-1570
1-methyl-3-propylimidazolium bromide
[22]
91
205.10
212.20-366.73
259.70-305.50
1-hexylquinolinium trifluoromethylsulfonylamide
[23]
77
494.47
322,72-370.13
578-599
1-hexyl-3-methylimidazolium oxalate borate
[24]
80
354.12
239.33-397.44
575.80-656.70
1-butyl-3-methylimidazolium dicyanamide
[25]
78
205.26
235.80-367.14
355.90-403.20
11
1-ethyl-3-methylimidazolium trifluoromethyl)sulfonylimide
[21]
75
391.31
283.15-463.15
502.30-559.0
12
1-butyl-1-methylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide
[25]
72
422.41
237.44-368.40
546.8-638.0
tetradecyl(trihexyl)phosphonium dicyanamide
[21]
63
549.90
313.15-413.15
1060-1240
14
3-methyl-1-propyl-1H-imidazolium(S)-2-amino-4carboxybutanoate
[26]
58
271.31
244.24-357.68
471.00-568.10
15
1-hexyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate
[27]
51
612.28
293.15-343.15
726-768.
1-hexyl-3-methylimidazolium hexafluorophosphate
[27]
62
312.24
293.15-453.10
422-553
1-tetradecyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide
[25]
50
559.63
309.98-368.07
896.30-953.30
1-butyl-3-methylimidazolium bis(oxalato)borate
[24]
50
326.07
244.30-292.74
528.7-551.9
19
N-(2-hydroxyethyl)-N,N-dimethylpropanaminium bromid
[28]
48
212.13
382.50-429.9
370.7-392.6
20
Butyltrimethylammonium bis(trifluoromethylsulfonyl)imide
[25]
48
396.37
278.32-367.93
547.5-600.9
1-butylpyridinium tetrafluoroborate
[29]
40
223.02
286.06-389.03
377.18-427.76
22
1-butyl-3-methylpyridinium1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide
[30]
41
430.39
293.10-333.10
541-582
23
1-ethyl-3-methylpyridinium bis((trifluoromethyl)sulfonyl)amide
[30]
41
402.33
293.10-333.10
484-522
24
3-methyl-1-propylpyridinium bis(trifluoromethylsulfonyl)imide
[6, 30]
41
416.36
293.10-331.10
510-549
2
5 6 7 8 9 10
13
16 17 18
21
25
AARD%
0.85 2.64 2.23 3.10 0.33 3.84 17.45 34.36 1.63 0.65 1.42 1.44 6.14 6.60 17.83 10.46 1.26 0.44 2.76 5.90 0.53 10.68 10.61 11.30
25
22.71
1-butyl-1-methylpyrrolidinium dicyanamide
[31]
41
208.30
293.15-333.15
490-554
1,2-dimethyl-3-propylimidazolium bis[(trifluoromethyl)sulfonyl]imide
[32]
35
419.40
323.15-663.10
473.50-631.0
1-butyl-3-methylpyridinium trifluoromethanesulfonate
[30]
31
299.31
323.10-353.10
461.0-496.0
1-propylpyridinium tetrafluoroborate
[33]
25
208.99
278.15-338.15
352.0-385.0
29
n-butyl-4-(n',n'-dimethylammonium)pyridinium bis(trifluoromethylsulfonyl)imid
[6]
23
459.43
315.15-425.15
673-739
30
n-ethyl-4-(n',n'-dimethylammonium)pyridiium bis(trifluoromethylsulfonyl)imide
[6]
23
431.37
315.15-425.15
603-659
31
1-hexyl-3-methylimidazolium trifluoromethanesulfonate
[6]
23
316.34
313.14-423.17
517-572
1-ethyl-3-methylimidazolium trifluoromethanesulfonate
[6]
23
260.23
313.13-423.14
384-422
1-octyl-3-methylimidazoliumtrifluoromethanesulfonate
[6]
23
344.39
313.17-423.14
588-651
N-octyl-3-methylpyridinium tetrafluoroborate
[34]
20
293.15
278.15-325.65
434-472
1-ethyl-3-methylimidazolium thiocyanate
[35]
20
169.25
296.20-372.20
340.7-404.7
1-ethyl-3-methylimidazolium dicyanamide
[35]
20
177.21
296.20-372.20
323.8-376.7
1-butyl-3-methylimidazolium thiocyanate
[35]
20
197.3
296.20-372.20
383.0-457.3
N-(2-hydroxyethyl)-N,N-dimethylbutanaminium bromide
[28]
19
226.15
409.71-438.26
382.5-407.0
39
1-octyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide
[36]
18
475.47
281.99-372.66
694-780
1.94
40
1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide
[37]
17
419.36
293.15-453.1
436-575
18.57
41
N-ethyl-N-(2-hydroxyethyl)-N,N-dimethylammonium ethyl sulfate
[38]
16
243.32
300.15-375.15
451-507
17.53
42
trihexyltetradecylphosphonium bis(2,4,4trimethylpentyl)phosphinate
[39]
15
773.27
293.15-363.15
1619-1764
2.07
43
1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl)trifluorophosphate
[40]
14
587.27
293.00-358.00
767-812
6.49
44
1H-imidazolium octanoate
[41]
7
212.29
298.15-313.15
769-788.2
47.42
45
1-octylpyridinium bis((trifluoromethyl)sulfonyl)amide
[42]
13
472.47
265.04-385.13
583-756
9.34
46
1-methyl-1-octylpyrrolidinium bis(trifluoromethylsulfonyl)amide
[42]
13
478.51
265.06-385.14
606-732
9.74
47
N-(2-hydroxyethyl)-N,N-dimethylhexan-1-aminium bromide
[28]
13
254.21
386.41-403.35
465-475
2.19
48
1-butyl-3-methylimidazolium chloride
[2]
13
174.67
343.20-403.20
337.2-376.8
1.94
49
1-ethyl-3-methylimidazolium bromide
[43]
12
191.07
347.66-367.50
265.30-272.60
22.22
50
1-butyl-3-methylimidazolium methylsulfate
[44]
12
250.32
303.20-358.20
375.5-400.5
6.98
51
1-ethyl-3-methylimidazolium hexafluorophosphate
[37]
11
256.13
353.15-453.10
289-346
25.76
52
1-butyl-3-methylimidazolium trifluoroacetate
[45]
11
252.23
190-290
367.4-403.8
3.32
53
N-ethyl-2-hydroxy-N,N-dimethylethanaminium 1butanesulfonate
[38]
10
255.37
355.15-400.15
93.00-104.00
369.97
26 27 28
32 33 34 35 36 37 38
26
18.14 3.84 3.7 1.25 0.25 3.45 0.64 4.11 19.16 18.86 4.57 13.18 9.46
54
4,6-dimethyl-N-phenylpyrimidin-2-amine dodecanoate
[46]
10
399.57
323.46-339.26
830.6-872.9
2.01
55
N,N-dibutyl-N-methylbutanaminium L-serinate
[47]
9
304.47
293.15-363.15
632-681
8.16
56
etrabutylphosphonium L-prolinate
[47]
9
373.55
293.15-363.15
838—939
13.58
57
tetrabutylphosphonium L-threoninate
[47]
9
377.54
293.15-363.15
952-1100
26.19
58
tetrabutylphosphonium L-valinate
[47]
9
375.57
293.15-363.15
744-811
1.54
59
tetrabutylphosphonium L-serinate
[47]
9
363.52
293.15-363.15
742-815
11.80
60
N,N-dibutyl-N-methyl-1-butanaminium 2aminoethanesulfonate
[47]
9
324.52
293.15-363.15
822-892
30.38
61
N,N-dibutyl-N-methyl-1-butanaminium L-lysinate
[47]
9
345.56
293.15-363.15
817-925
19.87
[48]
9
383.57
293.15-363.15
990-1090
30.93
62
tetrabutylphosphonium 2-aminoethanesulfonate
63
N-ethyl-2-hydroxy-N,N-dimethylethanaminium methanesulfonate
[38]
9
213.30
355.15-395.15
406-435
13.05
64
2-hydroxy-N,N,N-trimethyl-ethanaminium 1butanesulfonate
[38]
9
241.35
360.15-400.15
518.0-529.0
17.60
65
N,N,N-trimethyl-1-butanaminium 1butanesulfonate
[38]
9
253.40
360.15-400.15
701-741
33.74
66
1-butyl-3-methylimidazolium nitrate
[48]
8
201.22
309.16-370.00
357.7-383.0
2.54
67
1H-imidazolium, 1-ethyl-3-methyl-, salt with trifluoroacetic acid (1:1)
[49]
7
224.18
283.15-343.15
308-337
13.12
68
1-ethyl-3-methylimidazolium methanesulfonate
[50]
7
206.26
283.15-343.15
327-350
1.95
69
1-ethyl-3-methylimidazolium diethylphosphate
[50]
7
264.26
283.15-343.15
517-557
16.13
70
1-ethyl-3-methylimidazolium hydrogen sulfate
[50]
7
208.24
283.15-343.15
290-324
3.44
71
1-(2-hydroxyethyl)-3-methyl-1H-imidazolium 2,2,2trifluoroacetate
[50]
7
240.18
283.15-343.15
362-394
1.25
72
1-ethyl-3-methylimidazolium methylsulfate
[50]
7
222.26
283.15-343.15
324-354
2.14
73
N-ethyl-N,N-dimethyl-N-butylammonium ethyl sulfate
[38]
7
255.37
360.15-390.15
451-500
4.33
74
1-butyl-3-methylimidazolium tosylate
[51]
5
310.41
343.89-380
543.4-569.8
6.8
75
1-butyl-1-methylpyrrolidinium trifluoromethanesulfonate
[52]
3
291.33
288.15-308.15
424-441
5.03
76
1-methylpyridinium methylsulfate
[52]
3
205.23
288.15-308.15
288-305
8.68
77
1,2-diethylpyridinium ethylsulfate
[52]
3
261.34
288.15-308.15
399-420
9.44
78
1-butyl-3-methylpyridinium tetrafluoroborate
[53]
2
237.05
298.15-323.15
405-421
1.45
79
1-hexylpyridinium bis(trifluromethylsulfonyl)imide
[53]
2
444.41
298.15-323.15
612-632
5.16
80
1-hexyl-2,3-dimethylimidazolium
[53]
2
461.44
298.15-323.15
686-705
3.53
81
3-hexyl-1-methyl-1H-imidazolium bromide
[53]
2
247.18
298.15-323.15
344-357
23.56
82
1-butyl-3-methylimidazolium 2-(2methoxyethoxy)ethyl sulfate
[53]
2
338.42
298.15-323.15
643-652
12.46
27
83 84
85 86
1-octyl-3-methylpydridinium bis(trifluoromethylsulfonyl)imide 1-hexyl-3-methyl-4-(dimethylamino)pyridinium 1,1,1trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 1-hexyl-4-(4-methyl-1-piperidinyl)pyridinium 1,1,1trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 3,5-diethyl-1-hexyl-2-propylpyridinium 1,1,1-trifluoroN-[(trifluoromethyl)sulfonyl]methanesulfonamide
[53]
2
486.49
298.15-323.15
669-693
10.32
[53]
2
501.51
298.15-323.15
725-764
2.90
[53]
2
541.57
298.15-323.15
628-650
34.76
[53]
2
542.60
298.15-323.15
766-799
12.64
87
1-hexyl-3,5-dimethylpyridinium bis(trifluoromethylsulfonyl)imide
[53]
2
472.47
298.15-323.15
620-665
11.97
88
1-ethyl-3-methylpyridinium ethylsulfate
[53]
2
247.31
298.15-323.15
389-402
35.45
89
1-methyl-3-octylimidazolium bromide
[53]
2
275.23
298.15-323.15
392-408
24.11
90
17-hydroxy-N-(17-hydroxy-3,6,9,12,15pentaoxaheptadec-1-yl)-N-methyl-N-tetradecyl3,6,9,12,15-pentaoxaheptadecan-1-aminium methyl sulfate
[53]
2
868.16
298.15-323.15
1070-1100
49.03
91
tetrabutylammonium docusate
[53]
2
664.03
298.15-323.15
1320-1380
2.47
92
1-methyl-3-(3,3,4,4,5,5,6,6,6-nonafluorohexyl)-1Himidazolium 1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide
[53]
2
611.35
298.15-323.15
725 -752
7.33
93
1-hexyl-3-methylpyridinium bromide
[54]
2
258.20
298.15-323.15
343-358
37.08
[54]
2
265.12
298.2-323.2
495-524
1.95
94
1-butyl-3-methylpyridinium tetracyanoborate
95
1-butyl-1-methylpyrrolidinium tetracyanoborate
[54]
2
257.14
298.2-323.2
471-498
2.05
96
1-n-butyl-3-methylimidazolium bromide
[55]
2
219.12
298.15-323.15
330-338
10.80
97
1-butyl-2,3-dimethylimidazolium hexafluorophosphate
[55]
2
298.21
298.15-323.15
442.3-458.1
0.55
98
1-ethyl-3-methyl-1H-imidazolium hydrogen methylphosphonate
[56]
1
206.18
298.15
344.7
3.01
99
1-pentyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide
[57]
1
433.39
298.15
596
0.79
1
202.72
298
100
1-hexyl-3-methylimidazolium chloride
[58]
28
381
0.53
Table 2: List of investigated ionic liquids for validation Temperature No.
Ionic liquid
Reference
MW range
(K )
CPexp range
(Jmol
−1
K −1
)
AARD%
1
1-methyl-3-octylimidazolium tetrafluoroborate
[22]
282.13
283.15-323.15
489.2-514.5
1.55
2
1-ethyl-3-methylimidazolium tetrafluoroborate
[22]
197.97
283.15-323.15
300.2-315.1
0.47
3
trihexyl(tetradecyl)phosphonium chloride
[21]
519.31
338.15-463.15
834-970
15.07
4
1-butyl-3-methylimidazolium tetrafluoroborate
[22]
226.02
283.15-323.15
360.20-378.1
0.07
5
tributylmethylphosphonium methylsulphate
[21]
328.45
343.15-463.15
661-757
12.7
6
1-butyl-3-methylimidazolium octyl sulfate
[59]
348.5
298.15-343.15
635-698
4.79
7
1-butyl-3-methylimidazolium trifluoromethanesulfonate
[25]
288.29
292.86-367.78
425-465
0.54
8
4-(dimethylamino)-1-hexyl-pyridinium 1,1,1-trifluoroN[(trifluoromethyl)sulfonyl]methanesulfonamide
[6]
487.48
315.15-425.15
750-825
3.46
9
1-ethyl-3-methyl-1H-imidazolium tricyanomethanide
[35]
201.23
296.2-368.2
357.2-399.2
2.91
10
1-methyl-1-propylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide
[59]
408.38
288.15-358.15
547.5-594
0.74
11
2-octylisoquinolinium thiocyanate
[60]
300.46
278.15-343.15
510-540
14.30
12
1-ethyl-1-octylpiperidinium bis((trifluoromethyl)sulfonyl)amide
[42]
506.57
265.01-385.02
704-904
4.99
13
1-butyl-3-methylimidazolium acetate
[45]
198.26
210-300
352.4-384.1
3.84
14
tetrabutylphosphonium L-cysteinate
[47]
379.58
293.15-363.15
914-1020
21.37
15
tetrabutylphosphonium L-lysinate
[47]
404.61
293.15-363.15
990-1110
22.41
16
N,N-dibutyl-N-methyl-1-butanaminium L-threoninate
[47]
318.5
293.15-363.15
748-821
19.23
17
N-ethyl-2-hydroxy-N,N-dimethylethanaminium 1octanesulfonate
[38]
311.48
355.15-395.15
711-748
19.53
18
tributylethylphosphonium diethylphosphate
[50]
384.47
283.15-343.15
683-768
3.71
19
tetrapropylammonium bromide
[61]
266.26
283.01-348.43
333-393
36.57
20
1-hexyl-3-methylimidazolium dicyanamide
[52]
233.31
288.15-308.15
510-548
17.05
21
3-(ethoxycarbonyl)-1-ethylpyridinium ethylsulfate
[54]
305.35
298-323
513-530
0.89
[54]
458.44
298-323
624-644
8.27
[55]
405.34
309.15-323.15
502.6 - 509
7.59
22 23
1-hexyl-3-methylpyridinium 1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 1-ethyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide
24
1-butyl-2,3-dimethylimidazolium tetrafluoroborate
25
1-butyl-nicotinic acid butyl ester bis[(trifluoromethyl)sulfonyl]imide
[55] [53]
29
240.05
330.15-372.15
382.8-414.6
5.78
516.48
298-323
778-800
0.7035
26
1-ethyl-3-methylimidazolium acetate
[56]
170.21
298.15
314.4
0.47
27
1-methyl-3-octylimidazolium chloride
[58]
230.78
298
445
0.72
28
1-dodecyl-3-methyl-1H-imidazolium bis(trifluoromethylsulfonyl)amide
[57]
531.58
298.15
820
0.93
30
Table 3: The constants of Equation (2)
Constant
Value
a1
0.2808
a2
1.0854
a3
-17.5066
a4
0.6593
a5
1.0793
a6
15.9932
a7
16.1292
a8
-2.8956
a9
-11.7667
a10
-1.3729
a11
-4.1977
a12
6.7438
a13
-12.3990
31
Table 4: The Average Absolute Relative Deviation (AARD%) on the optimization and validation datasets Proposed method Method Optimization dataset
Validation dataset
Number of data
4072
750
Error (AARD%)
5.83 %
5.61 %
32
Table 5: The number of datapoints which have error less than 2.5, 5, 10, 25, 50 and 75 % Percent of data with errors less than:
Optimization dataset
Validation dataset
2.5 %
61.9 %
57.6 %
5%
73.9 %
66.7%
10 %
82.5 %
71.7 %
25 %
96.4 %
98.9 %
50 %
99.7 %
100.0%
75 %
99.8%
100.0 %
33
Table 6: Comparison the AARD% values of the proposed model with different literature models based on the validation dataset.
No.
Müller and
Sattari et al.
Farahani et al.
Albert [17]
[11]
[10]
Proposed model
Ionic liquid
1
1-methyl-3-octylimidazolium tetrafluoroborate
0.59
1.78
5.66
1.55
2
1-ethyl-3-methylimidazolium tetrafluoroborate
1.74
10.92
20.82
0.47
3
trihexyl(tetradecyl)phosphonium chloride
-
5.39
15.62
15.07
4
1-butyl-3-methylimidazolium tetrafluoroborate
6.39
8.05
13.07
0.07
5
tributylmethylphosphonium methylsulphate
0.30
8.27
26.25
12.70
6
1-butyl-3-methylimidazolium octyl sulfate
0.04
1.55
7.33
4.79
7
1-butyl-3-methylimidazolium trifluoromethanesulfonate
1.76
2.10
12.22
0.54
8
4-(dimethylamino)-1-hexyl-pyridinium 1,1,1-trifluoroN[(trifluoromethyl)sulfonyl]methanesulfonamide
-
7.53
8.78
3.46
9
1-ethyl-3-methyl-1H-imidazolium tricyanomethanide
-
14.48
21.61
2.91
10
1-methyl-1-propylpyrrolidinium bis[(trifluoromethyl)sulfonyl]imide
0.00
5.72
4.00
0.74
11
2-octylisoquinolinium thiocyanate
0.08
2.16
2.54
14.30
12
1-ethyl-1-octylpiperidinium bis((trifluoromethyl)sulfonyl)amide
0.23
5.04
5.42
4.99
13
1-butyl-3-methylimidazolium acetate
0.49
3.09
17.26
3.84
14
tetrabutylphosphonium L-cysteinate
0.15
19.69
32.34
21.37
15
tetrabutylphosphonium L-lysinate
0.65
7.40
26.81
22.41
16
N,N-dibutyl-N-methyl-1-butanaminium L-threoninate
15.22
4.90
26.12
19.23
17
N-ethyl-2-hydroxy-N,N-dimethylethanaminium 1octanesulfonate
-
4.23
11.54
19.53
18
tributylethylphosphonium diethylphosphate
0.31
10.91
15.86
3.71
19
tetrapropylammonium bromide
-
25.23
5.59
36.57
20
1-hexyl-3-methylimidazolium dicyanamide
13.75
9.95
32.79
17.05
21
3-(ethoxycarbonyl)-1-ethylpyridinium ethylsulfate
-
5.15
18.06
0.89
-
21.17
2.37
8.27
15.53
2.96
16.29
7.59
1.61
12.4
18.73
5.78
22 23 24
1-hexyl-3-methylpyridinium 1,1,1-trifluoro-N[(trifluoromethyl)sulfonyl]methanesulfonamide 1-ethyl-2,3-dimethylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-butyl-2,3-dimethylimidazolium tetrafluoroborate
34
-
16.71
11.79
0.70
1-ethyl-3-methylimidazolium acetate
7.02
7.68
21.97
0.47
27
1-methyl-3-octylimidazolium chloride
-
8.92
11.26
0.72
28
1-dodecyl-3-methyl-1H-imidazolium bis(trifluoromethylsulfonyl)amide
-
6.16
6.77
0.93
2.38
6.57
14.20
5.64
25
1-butyl-nicotinic acid butyl ester bis[(trifluoromethyl)sulfonyl]imide
26
Total
35