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Development of a group contribution method for estimating surface tension of ionic liquids over a wide range of temperatures
Development of a group contribution method for estimating surface tension of ionic liquids over a wide range of temperatures Juan A. Lazz´us, Geraldo Pulgar-Villarroel, Fernando Cuturrufo, Pedro Vega PII: DOI: Reference:
S0167-7322(17)30678-5 doi: 10.1016/j.molliq.2017.05.095 MOLLIQ 7387
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
14 February 2017 15 May 2017 21 May 2017
Please cite this article as: Juan A. Lazz´ us, Geraldo Pulgar-Villarroel, Fernando Cuturrufo, Pedro Vega, Development of a group contribution method for estimating surface tension of ionic liquids over a wide range of temperatures, Journal of Molecular Liquids (2017), doi: 10.1016/j.molliq.2017.05.095
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Development of a group contribution method for estimating surface tension of ionic liquids over a wide range of temperatures Juan A. Lazz´ us∗ , Geraldo Pulgar-Villarroel, Fernando Cuturrufo, Pedro Vega
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Departamento de F´ısica y Astronom´ıa, Universidad de La Serena, Casilla 554, La Serena, Chile
Abstract
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A group contribution methods for estimating the surface tension of ionic liquids as a function of the absolute temperature, is presented. A total of 2286 experimental data points from 226 data sets of 154 ionic liquids were collected from the specialized literature. This database covers a temperature range of 263–533 K and a surface tension range of 0.015–0.062 N·m−1 , for a heterogeneous set of ionic liquid-types such as imidazolium, ammonium, phosphonium, pyridinium, pyrrolidinium, and piperidinium. A correlation set containing the 75% of the overall database was used in order to calculate the contribution values of 10 structural cation groups and 30 structural anion groups. Then, a prediction set containing the other 25% of the overall database with data sets not used in the correlation phase was used in order to test the capabilities and accuracy of the proposed method. The results show that the proposed method can estimate the surface tension of several ionic liquids with a better accuracy than other methods available in the literature, with an average absolute relative deviation of 2.8% and a correlation coefficient of 0.98. Keywords: Ionic liquids, Surface tension, Group contribution method, Genetic algorithm, Parameter estimation.
∗ Tel.: +56 51 2204128; fax: +56 51 2206658. [email protected]
Preprint submitted to Journal of Molecular Liquids
May 22, 2017
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1. Introduction
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Ionic liquids (ILs) are a class of salts that have been of great interest in recent years due to its unique physical and chemical properties [1]. ILs typically consist of one anion and one cation, which allows the most suitable anion-cation combination for a specific IL to adapt to a specific applications demands [2] (for a theoretical description of ILs, see [3]). In order to maximize its use and design, a knowledge of its physical and chemical properties is required. In particular, the knowledge of the interfacial and surface tensions is highly relevant [1]. The surface tension (σ) of ILs is an important physical property. It is used to access the intrinsic energetics that are involved in the interactions between ions [4]. Thus, σ in ILs directly indicates the cohesive forces between liquid molecules present at the surface [5]. Unfortunately, the knowledge of the σ of ILs, is still limited, inconsistent, and discrepant [6]. The available experimental data for the σ of ILs is very lacking and essentially restricted to imidazolium-based ionic liquids [7]. So it is important to collect a large database, not only for process and product design but also for the development of new predictive methods and generalized correlations [6]. In this way, the estimation of σ of ILs has been carried out by parachors [6, 8, 9, 10], corresponding states theory [11, 12], group contribution methods [5], and quantitative structure-property relationships [13, 14]. Parachor models are an empirical method, which relates density with the σ via a temperature-independent relationship [15]. Deetlefs et al. [8] were the first who proposed a parachor model for estimating σ of ILs. Also, Gardas and Coutinho [9] proposed the estimation of the σ of ILs applying a parachor approach by using 361 data points of 38 imidazolium-based ILs. Later, this above parachor model was extended for new ILs cation [6]. Next, Lemraski and Zobeydi [10] applied a new parachor method in order to estimate the σ of imidazolium-based ILs. Corresponding states theory (CST) provides the single most important basis for the development of correlations and estimation methods for unknown properties of many fluids from the known properties of a few [15]. Mousazadeh and Faramarzi [11] applied CST methodology to derive a model for σ of ILs by compiling 30 ILs. Next, Wu et al. [12] developed other CST model for estimating σ of ILs based on 224 experimental data points of 105 ILs. Group contribution method (GCM) is a technique to estimate thermody2
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namics properties of a compound from the sum of the contributions from the parts of molecules that form it [15]. Gharagheizi et al. [5] proposed a GCM for estimating σ of ILs using 920 experimental data points for 51 ILs. Quantitative structure-property relationships (QSPR) is an analytical method for breaking down a molecule into a series of numerical values describing their physico-chemical properties [15]. Mirkhani et al. [13] developed a QSPR model based on seven molecular descriptors for estimating the σ of ILs by compiling 930 experimental data points for 48 ILs. Also, Shang et al. [14] proposed a QSPR model based on topological indices in order to predict the σ of ILs by compiling 930 data points for 115 ILs. In other methods, Ghatee et al. [16] proposed a linear relation between the logarithm of σ and the fluidity by involving a characteristic exponent for 19 imidazolium-based ILs. Ghasemian and Zobeydi [17] present a simple equation in order to predict the σ of ILs based on the enthalpy of vaporization. On the other hand, Llovell et al. [18, 19] show the possibility of describing the σ of ILs by using the soft-SAFT equation-of-state. And for mixtures, Lemraski and Pouyanfar [20] used three thermodynamic models in order to predict the σ of ionic liquid binary mixtures based on a corresponding-states group-contribution method, an extended Guggenheim’s ideal solution model, and a parachor model. Note that, the current development state of methods for estimating σ of IL fails mainly in a poor quantity of represented ILs and in a narrow temperature range considered. In this study, a new group contribution method is applied in order to estimate the σ of several IL-types as a function of the temperature, where the proposed GCM is decomposed in structural groups for the cationanion parts. 2. The proposed GCM For a given liquid, the σ decreases with the temperature, since the cohesion forces decrease with increasing the thermal agitation, causing a lower intensity in the intermolecular forces [21]. Then, a linear approximation can be applied [15] as follows: σ(T ) = A − B · T
(1)
where A and B are constants, and T is the absolute temperature. In addition, this equation can be decomposed into the cation and anion parts of one IL, as follows: 3
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σ(T ) = a+ − b+ · T + a− − b− · T
(2)
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where a+ and b+ are the adjustable constants of the cation part, and a− and b− are the adjustable constants for the anion part associated with σ. The method here proposed employs a GCM to estimate the cation and anion parameters. For this equation A = a+ + a− , and B = b+ + b− . The mathematical formulation of GCM is based on the multilinear regression method [22]. This technique fits a set of data points of a property of interest (y) as a linear combination of one or more selected descriptors (xl ) [23]: X nk xl (3) y= k=1, l=0
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where y represents the value of the property, nk is the number of occurences of each molecular group, and xl is the value of the contribution of each group obtained by the regression analysis. Then, for the σ of ILs was obtained the following equation: X X X X (4) ni ga+i + nj ga−j − T ni gb+i + nj gb−j σ(T ) = i
j
i
j
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where ni and nj are the occurrences of the groups i and j in the ILs, ga+ and gb+ are the contributions of the cation groups, and ga− and gb− are the contributions of the anion groups. This equation P represent the proposed P ngb GCM to correlate σ(T ). For this equation a = nga , and b = (with their respective ionic charges). Note that the absolute values for the total contribution were added in order to prevent that if the sum of the contributions is negative, the slope doesn’t change (as is suggested by [24]). 3. Database and regression method A total of 2286 σ(T )-experimental data points from 226 data sets of 154 ILs were collected from the specialized literature [25], by considering that experimental protocol measurements were clearly described (as is suggested by [26]). The total data set was divided into a correlation set with 1804 experimental data points (∼75% of the overall database), and a prediction set with 482 experimental data points (∼25% of the overall database), where 4
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all data for one IL were assigned to one same data set. Table S1 shows the experimental values of σ(T ) considered in this study (see, Supplementary material). In our database, σ(T )-properties cover wide ranges, such as: 263–533 K for the temperature, and 0.015–0.062 N·m−1 for the surface tension. The heterogeneous set of ILs of our study includes IL-types such as imidazolium, ammonium, phosphonium, pyrrolidinium, piperidinium and pyridinium. Figure 1 shows a general picture of the wide ranges of σ and ILs considered. These values are of especial importance in order to verify that an acceptable range of σ was covered in this study. Note that, ILs included in this database have very different physico-chemical characteristics, e.g. low molecular weight substances such as propylammonium formate (M W = 105.14) [27], or high molecular weight substances such as trihexyl(tetradecyl)phosphonium tris(pentafluoroethyl)trifluorophosphate (M W = 928.88) [28], and low σ value for 1tetradecyl-3-methylimidazolium bis(trifluo-romethylsulfonyl)imide (σ = 0.0155 N·m−1 at 512.9 K) [29], and high σ value for 1-ethyl-3-methylimi-dazolium dicyanamide (σ = 0.06196 N·m−1 at 278.16 K) [30]. In order to estimate the σ of ILs as a function of the temperature, the contributions of the structural groups were calculated using the ∼75% of the overall database (correlation set). The occurrence of a structural group was defined as: 0, when the group does not appear in the IL and n, when the group appears n-times in the IL, according to the methodology described in [22]. To improve the accuracy of the correlation in determining the contribution values of each structural group, a GCM was defined for each IL-type. Thus, over these correlation sets was applied a regression method for estimating the contribution values of each structural group associated with Eq. 4. The regression method was optimized by genetic algorithms (GA) [31] in order to minimize the difference between calculated and experimental σ(T ). This procedure was based on the following objective function (OF ): OF =
ND X
σ(T )calc − σ(T )exp
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2 z
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where the merit function minimized is the sum of the square distances between the regression values (calc) and the experimental (exp) data points. The full methodology was programmed in C++. Table 1 shows the selected parameters used in our GA optimization. 5
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4. Results and discussion
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At the end of the regression process, the optimum contribution values were obtained for the correlation set associated to each IL-type. Table 2 shows the occurrence of each group (in the correlation set) and the contribution values determined for each IL-type. In this Table, the cation groups included 10 substituted-groups for 6 IL-types, such as: imidazolium, ammonium, phosphonium, pyridinium, pyrrolidinium, and piperidinium, while the anion groups included 25 functional structural groups plus other 5 functional ring groups for different anion-types, such as halides, sulfonates, tosylates, imides, amides, cyanides, borates, phosphates, sulfates, acetates, amino acids, and metal complexes, among others. Once the correlation process was successfully done and the optimum contribution values for the groups were obtained, the other ∼25% of the overall experimental data for σ not used in the correlation set were used in order to test the proposed GCM. Note that, correlation and prediction sets were selected randomly, with the consideration that in the group contribution methods, the molecules are decomposed into fragments and that all fragments are present with a suitable frequency in the correlation set [22]. In addition, the accuracy of the proposed GCM was checked between the calculated values of σ(T ) and the experimental data taken from the literature by using the average absolute relative deviation for each data point (ARD) and for the individual sets (AARD), and by using the coefficient of determination (R2 ). These statistical parameters were calculated as follows: σ(T )calc − σ(T )exp · 100 (6) ARD = σ(T )exp ND σ(T )calc − σ(T )exp 100 X AARD = ND z=1 σ(T )exp z P ND 2 calc − σ(T )exp z z=1 σ(T ) 2 R =1− P h i exp 2 ND calc − σ(T ) z=1 σ(T )
(7)
(8)
z
where (exp) denotes the experimental value, (calc) the calculated value via the GCM, ND is the total data points in a data set, z is a particular data point, and σ(T ) is the mean of the experimental data of σ(T ).
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Table 3 summarizes the statistical deviations obtained in the prediction step and its comparison with the correlation process results. As shown the accuracy of the proposed GCM is very good, with ARDmax of 14.20%, an AARD from 0.07% to ∼4%, and R2 between 0.91 and 0.99. For the overall correlation set, AARD was 2.69% and the R2 was 0.986, while for the overall prediction set, AARD was 3.36% and R2 was 0.981. For the total set the overall AARD was 2.81% and the overall R2 was 0.984. In order to verify the correct interpretation of our results, Figure 2 shows the experimental surface tension versus the relative deviation (RD) obtained for all 2286 σ(T )experimental data points. This Figure offers a better understanding of the prediction capability of our proposed GCM. Here, RDmax was 13.90%, RDmin was −14.20%, and RDmean was −0.06%, which illustrate that our method generated homogeneous deviations. Table 4 presents the final equations obtained for the proposed GCM. For these Equations (9 to 14), ni and nj are the occurrences of the groups i and j in the ILs; ga+ , gb+ are the contribution of the cation groups and ga− , gb− are the contribution of the anion groups for σ(T ). In this equation, T is in units of K, the contributions ga+ and ga− are calculated in terms of the unit N·m−1 , and gb+ and gb− are calculated in units of N·m−1 ·K−1 , finally σ(T ) is obtained in unit of N·m−1 . Figure 3 shows the comparison between experimental and calculated values by Eqs. 9 to 14 (Table 4) in the estimation of σ(T ), where black dots represent the correlation set, red dots represent the prediction set, and the solid line is the expected value. This Figure shows a general picture of the accuracy and capabilities of our proposed GCM, and it ratifies the good results presented above, however, we will clarify the specific results for each IL-type. Figure 3a shows the Imidazolium’s GCM accuracy in the estimation of σ(T ). For this case, correlation set shows a R2 of 0.982 and a slope of the curve (m) of 0.954 (expected to be 1.0), while the prediction set shows a R2 of 0.978 and m of 1.004 (also expected to be 1.0). Figure 3b illustrates the accuracy of the Ammonium’s GCM. In this Figure, correlation set presents a R2 of 0.952 and a m of 0.908, while the prediction set presents a R2 of 0.915 and a m of 0.901. Figure 3c presents the accuracy of the Phosphonium’s GCM. Here, correlation phase exhibits a R2 of 0.997 and a m of 0.994, while the prediction phase exhibits a R2 of 0.999 and a m of 1.010. Figure 3d shows the Pyridinium’s GCM accuracy. For this Figure, correlation set shows a R2 of 0.990 and a m of 0.966, while the prediction set shows a R2 of 0.996 and a m of 1.018. Figure 3e shown the accuracy of the Pyrrolidinium’s GCM. 7
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Where the correlation phase presents a R2 of 0.998 and a m of 0.980, while the prediction set presents a R2 of 0.999 and a m of 0.998. Finally, Figure 3f illustrates the accuracy of the Piperidinium’s GCM. Here, correlation phase exhibits a R2 of 0.998 and a m of 0.996, while the prediction set exhibits a R2 of 0.999 and a m of 0.999. An example of the use of Eq. 9 (Table 4) and the Imidazolium’s GCM, is shown in Table 5. This Table details the procedure to calculate σ(T ) via the calculated values for our Imidazolium’s GCM (columns 3 and 4 in Table 2) for 1-ethyl-3-methylimidazolium tosylate (C13 H18 N2 O3 S; M W = 282.36) [32], that was selected randomly from the predicion set. For this example, our GCM shows a higher accuracy, such as ARDmax of 0.39%, an AARD of 0.21%, and a R2 of 0.993. These results show that the correlation set for the Imidazolium’s GCM was correctly selected as shown in Table 3. Note that the highest ARD obtained was 14.20% for the σ=0.0374 N·m−1 at 293.15 K of the 1-butyl-2,3-dimethyl-1H-imidazolium bis(trifluoromethylsulfonyl)amide (C11 H17 F6 N3 O4 S2 ; M W = 433.39) [6], however lower than 20% of the overall data points obtained an ARD higher than 5%, while only the 3% of the overall data points obtained an ARD higher than 10% (see, Table S1). More examples of the use of GCM can be found in Tables S2 to S6 (see, Supplementary material). Table S2 presents an example of the use of Eq. 10 (Table 4) to calculate σ(T ) for the propylammonium acetate (C5 H13 NO2 ; M W = 119.16) [27] randomly selected from the ammonium’s dataset. For this IL, ARDmax = 0.11%, AARD= 0.07%, and R2 = 0.999. Note that for the overall ammonium’s dataset the highest ARD obtained was 13.04% for a σ = 0.0308 N·m−1 at 293.30 K for the tributylmethylammonium bis[(trifluoromethyl)sulfonyl]imide (C15 H30 F6 N2 O4 S2 ; M W = 480.53) [33] (see, Table S1). Table S3 illustrates the use of Eq. 11 (Table 4) to calculate σ(T ) for the tributylmethylphosphonium methylsulphate (C14 H33 O4 PS; M W = 328.45) [34] randomly selected from the phosphonium’s dataset. Here, ARDmax = 0.95%, AARD= 0.41%, and R2 = 0.991. From the overall phosphonium’s dataset the highest ARD obtained was 1.99% for a σ=0.02967 N·m−1 at 313.21 K for the tetradecyl(trihexyl)phosphonium dicyanamide (C34 H68 N3 P; M W = 549.90) [35] (see, Table S1). Table S4 illustrates the use of Eq.12 (Table 4) for estimating the σ(T ) of the 1-butylpyridinium tetrafluoroborate (C9 H14 BF4 N; M W = 223.02) [36] randomly selected from the pyridinium’s dataset. These results present an ARDmax = 2.01%, with an AARD= 1.02%, and a R2 = 0.999. In addition for the overall pyridinium’s dataset the highest ARD obtained was 6.94% for a σ=0.0377 N·m−1 at 288.15 8
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K for the 1-ethylpyridinium bis[(trifluoromethyl)sulfonyl]imide (C9 H10 F6 N2 O4 S2 ; M W = 388.31) [37] (see, Table S1). Also, Table S5 illustrates the use of Eq. 13 (Table 4) to estimate the σ(T ) for the 1-butyl-1-methylpyrrolidinium dicyanamide (C11 H20 N4 ; M W = 208.30) [38] randomly selected from the pyrrolidinium’s dataset. In this example the proposed GCM shows an ARDmax of 1.24%, with an AARD of 0.70%, and a R2 of 0.980. For the overall pyrrolidinium’s dataset the highest ARD obtained was 6.65% for the estimation of σ=0.0421 N·m−1 at 341.35 K for the 1-butyl-1-methylpyrrolidinium thiocyanate (C10 H20 N2 S; M W = 200.34) [38] (See, Table S1). Finally, Table S6 illustrates the application of Eq. 14 (Table 4) for estimating the σ(T ) for the 1-butyl-1-methylpiperidinium bis(trifluoromethanesulfonyl)imide (C12 H22 F6 N2 O4 S2 ; M W = 436.43) [39]. In this example our proposed GCM presents an ARDmax of 0.14%, with an AARD of 0.09%, and a R2 of 0.999. Note that, for the overall pyrrolidinium’s dataset the highest ARD obtained was 0.50% for the estimation of σ=0.03589 N·m−1 at 263.08 K for the 1-(2-methoxyethyl)-1methylpiperidinium trifluorotris(perfluoroethyl)phosphate (C15 H20 F18 NOP; M W = 603.27) [40] (See, Table S1).
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4.1. Cation-anion effects The results obtained by the proposed GCM shows differences in the estimation of σ(T ) for the different IL-types studied (see, Supplementary material). These results show the impact of the cation size on the correlationprediction performance and its accuracy. For example, imidazolium ILs present the following AARD ranges in the estimation of σ(T ): ∼3% > N, N -alkyl-imidazolium > N, N, N -alkyl-imidazolium > amino-imidazolium > 0.5%, while ammonium ILs show the following AARD ranges: ∼3% > N, N, N, N -alkyl-ammonium > choline-ammonium > 0.3, and while pyridinium ILs show the following AARD ranges: 2.7% > N -alkyl-pyridinium∼cyanopyridinium > N, N -alkyl-pyridinium>1%. In addition, for all IL-types studied the AARD values increase with increasing alkyl chain length in the cation. This fact can be associated with the general trend toward lower σ(T ) values when increasing alkyl chain length in the cation [41], such as those reported experimentally (see, Table S1). Note that, the van der Waals interactions have a remarkable effect on the alkyl chain length because molecular dynamics simulations show that the longer the alkyl chain, the stronger the attractive Lennard-Jones contribution [42]. On the other hand, also AARD values increase when increasing cation asymmetry. Recent experimental studies
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show that σ(T ) depends greatly on the asymmetrical/symmetrical structure of IL [43]. Remarkable differences in the estimation of σ(T ) (via AARD) were also observed for several anion sizes. Our results show also the impact of the anion type on the accuracy of the correlation and prediction of σ(T ). For example our proposed GCM presents the following AARD ranges in the estimation of σ(T ) (for the most common anion types): bromide (0.3%) < chloride, trifluoroacetate (0.5%) < tris(pentafluoroethyl)trifluorophosphate (1.5%) < tosylate (1.8%) < tetrafluoroborate (2.3%) < alkyl-phosphate (2.4%) < alkylsulphate (2.9%) < bis[(trifluoromethyl)sulfonyl]imide, dicyanamide, hexafluorophosphate, trifluoromethanesulfonate (3.4%) < acetate (3.9%) < iodide (4.7%), while the others anions (such as formate, nitrate, amino acid, metal complex, among others) show an AARD ∼2%. Our heterogeneous set of ILs contain small-sized anions (such as bromide, chloride, iodide, tetrafluoroborate), medium-sized (such as hexafluorophosphate, trifluoromethanesulfonate), and large-sized (such as tris(pentafluoroethyl)trifluorophosphate, bis[(trifluoromethyl)sulfonyl]imide). Experimental studies have suggested that σ(T ) decreases for ILs with increasing anion size, which was attributed to the higher charge delocalization in larger anions and a decrease in hydrogenbonding ability [44]. From this fact, we would expect the estimation of σ(T ) via the proposed GCM to be difficult when increasing/decreasing the anion size, but our results do not exhibit this behavior, and our accuracy in the estimation of σ(T ) was independent of the anion size. However, most recent studies show that this behavior can not be generalized, since in the literature there are different statements concerning the dependence of σ(T ) on the anion size, where with respect to selected anions it is found that the σ(T ) either increases or decreases with increasing anion size, or that there is no dependence at all [38, 41, 45]. 4.2. Comparative analysis In the literature, many models has been used in order to estimate σ(T ) of ILs (see, Section 1). Coutinho et al. [7] discussed a variety of correlation and prediction methods for estimating σ(T ), such as: parachor methods [6, 8, 9, 10], corresponding states methods [11, 12], group contribution methods [5], and quantitative structure-property relationship models [13, 14]. Due to the complexity of these linear or non-linear models, the IL molecule and their properties can be described in many different ways [46]. In order to evaluate the estimation accuracy and capability of our proposed GCM, we compare it 10
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directly with others three reported analytical methods for estimating σ(T ) of ILs, such as Gharagheizi’GCM [5], Mirkhani’s QSPR [13], and Wu’s CST [12]. Gharagheizi et al. [5] proposed a GCM for estimating σ(T ) of ILs using 920 experimental data for 51 ILs collected from various references. They employ a total of 19 sub-structures to predict the σ(T ) with an AARD of 3.6% from experimental data. Although, Mirkhani et al. [13] developed a QSPR model to predict σ(T ) of ILs making use of 930 experimental data points for 40 ILs by using 7 molecular descriptors, and obtaining an AARD of 4.9%. But, Wu et al. [12] employed a CST-group contribution method in order to estimate σ(T ) of ILs by using 1224 data points of 105 ILs with an AARD of 5.0%. While our proposed GCM for estimating σ(T ) was developed using 2286 experimental data of 154 ILs in order to obtain 40 structural groups and to predict the σ(T ) with an AARD of 2.8% from experimental data. It is worth pointing out that these methods obtained their results from different databases with different correlation and prediction sets (or training and prediction sets) and based on very different methodologies, then their results cannot be compared directly with one another. However, a comparison can be made for some selected datasets for common ILs for these methods. Table 6 shows a comparison between the proposed GCM versus Gharagheizi’s GCM [5], Mirkhani’s QSPR [13], and Wu’s CST [12] for estimating σ(T ) of ILs. This Table contains 30 datasets of ILs in common taken from [30, 38, 44, 47, 48, 49, 50, 51, 28]. Based on these results, Gharagheizi’s GCM showed an AARDtotal of 4.7% and R2 of 0.912; Mirkhani’s QSPR exhibited an AARDtotal of 5.6% with R2 of 0.891; Wu’s CST presented AARDtotal of 5.3% and R2 of 0.897; while our proposed GCM resulted in an AARDtotal of 2.3% with a R2 of 0.983. Note that the results of this comparative analysis also evidence some advantages and disadvantages that can be found in these models. For example, both Parachor’s methods [6, 8, 9, 10] and CST’s methods [11, 12] require the use of additional physicochemical properties such as density, melting and boiling points, and hypothetical critical properties, so that the uncertainties associated with these estimates are necessarily very large, e.g. some studies report methods with R2 lower than 0.8 for the density and the melting point of ILs [7]. Furthermore, QSPR’ methods (such as [13, 14]) are very difficult of apply due to the complex calculations for obtaining their molecular descriptors. These descriptors are computed from molecular mechanics or quantum mechanical analysis of the substance mainly by using of commercial softwares 11
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[15]. These problems severely limit the applicability of similar approaches such as parachor, CST, and QSPR to the prediction of the physicochemical properties of ILs. On the other hand, GCM-based models are easy to apply only with the knowledge of the molecular structure of the substance [22]. From these methods, a macroscopic property can be related directly and analytically to molecular structure and the bonds between atoms, which determine the magnitude of the intermolecular forces [15]. Due to the simplicity of the GCM and its direct relation between macroscopic property-molecular structure, it can obtain a better correlation and a more accuracy estimation of the physicochemical properties of an IL. Note that, the results in Table 6 evidence this fact, and show better accuracy among GCM-based models. In this point, Gharagheizi’s GCM shows higher deviations for small-sized ILs than our GCM, while for medium-sized ILs both GCMs present similars deviation (approx.), but for large-sized ILs our GCM was also better than Gharagheizi’s GCM. Also, our proposed method shows a higher accuracy than Gharagheizi’s GCM when is applied to ILs composed of anions such as bis[(trifluoromethyl)sulfonyl]imide and dicyanamide. But in general, the proposed GCM presented a higher accuracy with statistical deviations of ARDmax of 14%, an AARD of 2.8% and a R2 of 0.98. Note that, the incorporation of cation-types, such as imidazolium, ammonium, phosphonium, pyridinium, pyrrolidinium, and piperidinium is very important for the current applications of ILs as solvents in organic synthesis, catalysis, electrochemistry, chemical separation, metal extraction and nanoparticle formation [52]. Also, the incorporation of groups for ILs with cyanide and hydroxyl containing cations, and metal complexes groups for the anion, transforms our GCM in one of the most complete for estimating σ(T ) of ILs that has been reported so far. 5. Conclusions Based on the results and discussion, the following main conclusions were obtained: (i) The proposed GCM allows the σ estimation of different IL-types composed of 10 cation groups and 30 anion groups in a wide range of temperatures (263–533 K), and surface tension (0.015–0.062 N·m−1 ). For a database consisting of 2286 experimental data points from 226 data sets of 154 ILs. The great differences in the chemical structure and the physical properties of the ILs considered in the study impose additional difficulties to the problems that the proposed GCM has been able to handle; (ii) The accuracy of 12
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Acknowledgments
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the proposed GCM was tested by comparing calculated and experimentally measured σ(T ) values from the literature, resulting in a AARD=2.8% and R2 =0.98. Our results show that the proposed GCM can estimate the σ(T ) of ILs at different temperatures with low deviations and it is also applicable to a temperature range that is higher than those methods referenced by other authors and mentioned in this study. Note that the proposed method should be able to estimate σ(T ) of a larger range of ILs as data for these to become available; (iii) A comparative analysis between our GCM method and others methods such as corresponding states methods and quantitative structure-property relationship methods evidenced the simplicity, better correlation and more accuracy of our GCM in the estimation of σ(T ) of ILs; and (iv) The values calculated using the proposed model are considered to be accurate enough for engineering calculations, for generalized correlations and for equations of state methods, among other uses.
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The authors thank the Direction of Research and Development of the University of La Serena (DIDULS) through the research projects PEQ16141 and P116141, and the Department of Physics and Astronomy of the University of La Serena (DFULS) for the special support that made possible the preparation of this paper. Supplementary material Supplementary material to this article can be found online at http://dx.doi.org/xxxxxx.
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Table 1: Parameters of the genetic algorithm used for minimizing Eq. 5.
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GA Parameter Number of generations (Gen) Number of individuals (Ni ) Length of chromosome (L) Length of an individuals (Li) Crossover probability (Cros) Mutation probability (M ut) Crossover operador (CO) Mutation operador (M O) Objetive function (OF )
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Value 500 200 20 80 0.8 0.1 Multipoint Binary Eq. 5
Occ.
1250 1804 1794 6 9 12 21 16 12 13
Occ.
160 83 7 29 63 138 201 45 41 37 848 134 210 711 29 8 15 31 530 56 45 248 327 767 11 7 7 12 12 7
Groups+
–H –CH3 –CH2 − –CH< –CN >C=O –O– –OH –NH– –NH2
Groups−
–CH3 –CH2 − >C= >C< [>C–] >CH– [–CH–] –COO– [–COO] –O– [–O] =O –OH –HCOO –CF3 –CF2 –CN >N– [–N–] [>N<] –NH2 –NO3 –Br –Cl –F –I –S –B [>B<] –P [>P<] [> – P<] – –SO2 − >In< –CH2 − (ring) >CH– (ring) =CH– (ring) >C= (ring) –NH– (ring)
ga− [N·m−1 ] 2.3701E-03 -3.3387E-03 -8.2696E-02 8.3516E-05 -1.8872E-03 1.1581E-02 6.0961E-03 2.8934E-02 7.2778E-04 2.6177E-02 -8.7959E-03 1.5481E-02 7.1981E-03 1.8202E-02 3.3701E-02 NA 1.9703E-02 6.6650E-03 8.6654E-03 2.2708E-02 2.5196E-02 -1.7082E-02 -3.8646E-02 3.8429E-03 2.8828E-05 -7.5034E-04 -2.2510E-03 -1.0888E-03 5.6300E-03 -2.2510E-03
ga+ [N·m ] 1.7397E-02 1.5873E-02 -2.0941E-03 NA NA 2.3680E-03 NA NA 2.3680E-03 2.8136E-02 −1
−1
gb− [N·m−1 ·K−1 ] 4.9420E-05 2.4056E-06 -2.6686E-04 2.6878E-07 4.9427E-07 -3.4135E-06 -8.1082E-05 8.6386E-05 -1.1906E-05 7.5863E-05 -4.3027E-06 1.2095E-05 -2.0336E-05 -4.5065E-05 1.3034E-04 NA -5.5328E-05 -1.9668E-05 -2.3869E-05 -5.3496E-05 -7.4501E-05 4.1448E-05 1.0406E-04 5.4988E-05 5.0146E-07 5.4171E-06 1.6251E-05 8.8384E-07 -5.1822E-05 1.6246E-05
gb+ [N·m ·K ] 2.7002E-06 4.1968E-06 -3.1427E-06 NA NA 7.5426E-06 NA NA 7.5548E-06 -1.5107E-05
Imidazolium −1
ga− [N·m−1 ] 4.0251E-02 1.1011E-02 NA NA NA -1.4372E-03 -4.5365E-03 NA NA 4.2241E-02 5.4035E-03 4.1123E-04 NA 1.1109E-02 NA NA NA NA NA NA NA NA NA 5.4049E-03 NA NA NA NA NA NA
ga+ [N·m ] 4.3051E-03 4.0811E-03 1.0075E-03 NA NA NA NA -1.3532E-02 NA NA
−1 −1
gb− [N·m−1 ·K−1 ] 1.7688E-04 -2.2332E-06 NA NA NA -1.3075E-04 -5.7748E-05 NA NA 4.9132E-05 9.8628E-07 3.2356E-06 NA 3.8788E-06 NA NA NA NA NA NA NA NA NA 9.8167E-07 NA NA NA NA NA NA
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−1
−1
gb− [N·m−1 ·K−1 ] NA NA NA NA NA NA NA NA NA NA -2.6780E-07 3.7676E-06 NA -2.5988E-05 NA NA NA NA 3.7676E-06 NA NA NA 1.1303E-05 -1.2994E-05 NA NA NA NA NA NA
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ga− [N·m−1 ] NA NA NA NA NA NA NA NA NA NA 3.9230E-03 2.3884E-03 NA 1.7514E-02 NA NA NA NA 2.3884E-03 NA NA NA 7.1652E-03 8.7570E-03 NA NA NA NA NA NA
gb+ [N·m−1 ·K−1 ] NA -2.1202E-06 2.7941E-06 NA NA NA 1.1304E-05 NA NA NA
Piperidinium ga+ [N·m−1 ] NA 5.7386E-03 -1.9005E-03 NA NA NA 7.1652E-03 NA NA NA
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gb− [N·m−1 ·K−1 ] NA NA NA NA NA -8.6882E-05 NA NA NA NA -1.0350E-05 NA -3.8412E-05 -7.4567E-05 NA NA NA NA NA NA -1.2132E-04 NA NA -1.3796E-06 NA NA NA NA NA NA
gb+ [N·m ·K ] NA -3.2904E-05 4.2015E-05 NA NA NA NA NA NA NA
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ga− [N·m−1 ] NA NA NA NA NA 4.5291E-02 NA NA NA NA 4.9623E-03 NA 2.2930E-02 4.1042E-02 NA NA NA NA NA NA 5.9685E-02 NA NA -1.1605E-03 NA NA NA NA NA NA
−1
Pyrrolidinium ga+ [N·m ] NA 1.7470E-02 -1.2897E-02 NA NA NA NA NA NA NA
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Phosphonium Pyridinium Cation contributions −1 −1 −1 −1 ga+ [N·m ] gb+ [N·m ·K ] ga+ [N·m ] gb+ [N·m−1 ·K−1 ] NA NA 1.8783E-02 2.1688E-05 3.4791E-03 -5.9693E-07 1.1332E-02 1.0572E-06 5.0573E-04 8.3142E-08 -1.8017E-03 8.5965E-07 1.2233E-03 1.5919E-05 NA NA NA NA 8.4310E-03 -1.0118E-04 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA Anion contributions −1 −1 −1 −1 ga− [N·m ] gb− [N·m ·K ] ga− [N·m ] gb− [N·m−1 ·K−1 ] 1.2642E-02 -2.1610E-05 NA NA -5.1607E-03 4.6611E-05 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3.8563E-02 -5.3641E-05 1.1311E-02 -2.8592E-05 4.8240E-02 -1.8437E-05 -1.0321E-02 9.3221E-05 NA NA NA NA NA NA NA NA NA NA 1.3884E-03 9.0593E-06 6.9338E-03 5.2156E-05 2.1943E-03 -1.1065E-06 -9.3007E-03 -1.3467E-05 9.2997E-03 2.3098E-05 7.7065E-03 1.2711E-05 9.2554E-03 3.5822E-05 4.1127E-02 -1.3484E-04 NA NA NA NA NA NA 3.8214E-02 -9.5572E-05 2.3065E-02 -7.3242E-05 NA NA 2.9041E-02 -7.9244E-05 NA NA 2.1943E-03 -1.1065E-06 2.5811E-03 7.9133E-07 NA NA NA NA NA NA 9.9110E-02 -2.6784E-04 NA NA 3.9723E-02 6.3322E-05 -1.7876E-04 3.3877E-05 3.1537E-02 -7.4563E-05 4.0322E-03 3.3460E-06 -1.0921E-02 4.0159E-05 NA NA NA NA NA NA NA NA NA NA NA NA 9.1746E-04 1.1940E-05 NA NA 1.8349E-03 2.3879E-05 NA NA NA NA NA NA
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−1
gb+ [N·m ·K ] -4.8626E-05 7.4630E-06 4.6419E-06 NA NA NA NA -1.9420E-05 NA NA
Ammonium
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Table 2: Group contribution values obtained in the correlation process for each IL-class. (NA: group not available for the IL).
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ND ARDmin ARDmax AARD R2
Stat. Dev.
Imidazolium Correlation Prediction 1123 325 0.01 0.02 14.20 11.41 3.13 4.03 0.982 0.978
Ammonium Correlation Prediction 178 41 0.00 0.01 13.04 10.75 2.84 3.73 0.952 0.915
Phosphonium Correlation Prediction 115 17 0.00 0.03 1.99 1.07 0.48 0.39 0.997 0.999
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Piperidinium Correlation Prediction 29 7 0.01 0.00 0.50 0.14 0.19 0.07 0.998 0.999
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Pyrrolidinium Correlation Prediction 50 29 0.01 0.00 6.65 3.19 1.80 0.94 0.998 0.999
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Pyridinium Correlation Prediction 309 63 0.00 0.01 6.94 6.05 2.19 1.97 0.990 0.996
Table 3: Summary of statistical deviations obtained for the proposed GCM during the correlation and prediction processes.
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IL type σ(T )imi
Equation P P P29 P 6 − = i=1 ni ga+i + j=1 nj ga−j − T 6i=1 ni gb+i + 29 n g j bj j=1
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Imidazolium
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Table 4: Final equations obtained for the proposed GCM. Here, equations are individualized for each IL type.
(9)
σ(T )amm
P P9 4 i=1 ni gb+i + j=1 nj gb−j
(10)
Phosphonium
P P − σ(T )phos = 3i=1 ni ga+i + 15 n g j=1 j aj − T
P P15 3 + − + n g n g i=1 i bi j=1 j bj
(11)
P P − σ(T )pyri = 4i=1 ni ga+i + 12 n g j=1 j aj − T
P P12 4 i=1 ni gb+i + j=1 nj gb−j
(12)
P P P P σ(T )pyrr = 2i=1 ni ga+i + 6j=1 nj ga−j − T 2i=1 ni gb+i + 6j=1 nj gb−j
(13)
P P6 3 i=1 ni gb+i + j=1 nj gb−j
(14)
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Pyridinium
PT
Ammonium
P P9 4 = i=1 ni ga+i + j=1 nj ga−j − T
Pyrrolidinium Piperidinium
σ(T )pipe
P P6 3 = i=1 ni ga+i + j=1 nj ga−j − T
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Table 5: Example of application of the proposed Imidazolium’s GCM in the estimation of σ(T ) of ILs.
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ni ga+ [N·m−1 ] gb+ [N·m−1 ·K−1 ] 1 1.7397E-02 2.7002E-06 2 1.5873E-02 4.1968E-06 1 -2.0941E-03 -3.1427E-06 nj ga− [N·m−1 ] gb− [N·m−1 ·K−1 ] 1 2.3701E-03 4.9420E-05 1 6.0961E-03 -8.1082E-05 1 3.8429E-03 5.4988E-05 4 -1.0888E-03 8.8384E-07 2 5.6300E-03 -5.1822E-05 Eq. 9: σ(T )=6.6263E-02−6.8832E-05·T Data set [32]: exp ARD σ(T ) [N·m−1 ] σ(T )calc [N·m−1 ] 0.0452 0.0451 0.32 0.0442 0.0444 0.39 0.0436 0.0437 0.12 0.0430 0.0430 0.05 0.0427 0.0426 0.14 0.21 0.993
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Cation group –H –CH3 –CH2 − Anion group –CH3 –O –SO2 − =CH– (ring) >C= (ring)
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IL: 1-ethyl-3-methylimidazolium tosylate
T [K] 308.10 318.00 328.50 338.30 343.20 AARD R2
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[47] [47] [47] [47] [48] [49] [30] [30] [48] [38] [44] [47] [47] [47] [44] [48] [44] [47] [47] [38] [38] [38] [50] [38] [48] [38] [51] [51] [49] [28]
Ref.
T
Wu’s CST [12] AARD [%] 7.54 7.58 5.30 5.32 2.00 2.81 8.64 8.28 5.37 5.45 5.33 1.24 1.29 1.27 1.28 3.22 3.25 7.55 7.60 3.32 3.28 4.74 2.64 9.38 5.20 6.14 4.61 4.64 9.60 10.70 5.3% 0.897
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Mirkhani’s QSPR [13] AARD [%] 6.18 6.39 3.49 3.41 19.70 19.85 7.57 8.25 0.53 0.77 0.55 1.31 1.64 1.27 0.98 14.43 13.52 1.27 1.33 9.39 5.98 1.44 8.95 6.00 1.27 3.76 1.99 2.08 20.52 12.54 5.6% 0.891
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Gharagheizi’GCM [5] AARD [%] 5.89 6.11 3.78 3.35 6.20 7.01 13.03 13.69 1.50 1.65 1.17 1.68 1.80 1.31 1.75 2.09 2.66 1.94 1.90 2.96 10.12 1.12 0.11 11.49 15.74 2.00 3.21 4.19 0.31 0.36 4.7% 0.912
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0.050–0.055 0.050–0.055 0.038–0.041 0.038–0.041 0.033–0.037 0.034–0.037 0.056–0.062 0.056–0.062 0.041–0.045 0.041–0.045 0.042–0.045 0.033–0.035 0.033–0.035 0.033–0.035 0.033–0.036 0.031–0.033 0.031–0.034 0.035–0.040 0.035–0.040 0.045–0.050 0.038–0.048 0.051–0.056 0.034–0.036 0.036–0.044 0.029–0.032 0.029–0.032 0.031–0.035 0.031–0.035 0.025–0.028 0.027–0.029
∆σ [N·m−1 ]
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288–356 288–356 268–356 268–356 283–352 279–328 278–356 278–348 284–351 294–352 293–341 292–353 293–356 292–353 293–343 284–352 293–343 269–356 269–356 303–344 303–342 293–353 300–333 293–350 283–351 298–362 284–354 284–354 279–328 299–343
∆T [K]
PT
1-ethyl-3-methylimidazolium tetrafluoroborate 1-ethyl-3-methylimidazolium tetrafluoroborate 1-ethyl-3-methylimidazolium trifluoromethanesulfonate 1-ethyl-3-methylimidazolium trifluoromethanesulfonate 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-ethyl-3-methylimidazolium dicyanamide 1-ethyl-3-methylimidazolium dicyanamide 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-hexyl-3-methylimidazolium tetrafluoroborate 1-hexyl-3-methylimidazolium tetrafluoroborate 1-butyl-1-methylpyrrolidinium thiocyanate 1-butyl-4-methylpyridinium thiocyanate 1-butyl-1-methylpyrrolidinium dicyanamide hexyltrimethylammonium bis[(trifluoromethyl)sulfonyl]imide N-butyl-3-methylpyridinium dicyanamide 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-methyl-3-octylimidazolium tetrafluoroborate 1-octyl-3-methylimidazolium hexafluorophosphate 1-octyl-3-methylimidazolium hexafluorophosphate 1-butyl-3-methylimidazolium octyl sulfate trihexyl(tetradecyl)phosphonium tris(pentafluoroethyl)trifluorophosphate Overall R2
IL
Table 6: Comparison between three available methods ([5, 12, 13]) and the proposed GCM for estimating σ(T ) of ILs. This work AARD [%] 5.31 5.09 3.14 3.15 0.90 0.68 7.04 6.22 1.72 2.05 1.39 1.14 1.57 1.35 1.36 2.30 1.51 1.39 1.43 2.56 2.79 0.45 0.16 1.61 0.10 0.55 2.68 2.76 1.94 0.09 2.3% 0.983
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0.08 0.06 0.04 0.02 0
−1 σ [N⋅m ]
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(a)
400
MW
600
800
0
200
0
200
400
MW
1000
(b)
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0.08 0.06 0.04 0.02 0
0
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0.08 0.06 0.04 0.02 0
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−1 σ [N⋅m ]
−1 σ [N⋅m ]
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Highlights
• The GCM was divided into individual GCMs according to the IL-type.
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• The GCM employs 10 structural cation groups and 30 structural anion groups.
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• The results show an AARD of 1.8% and a R2 of 0.98.
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S0167-7322(17)30678-5 doi: 10.1016/j.molliq.2017.05.095 MOLLIQ 7387
To appear in:
Journal of Molecular Liquids
Received date: Revised date: Accepted date:
14 February 2017 15 May 2017 21 May 2017
Please cite this article as: Juan A. Lazz´ us, Geraldo Pulgar-Villarroel, Fernando Cuturrufo, Pedro Vega, Development of a group contribution method for estimating surface tension of ionic liquids over a wide range of temperatures, Journal of Molecular Liquids (2017), doi: 10.1016/j.molliq.2017.05.095
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.
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Development of a group contribution method for estimating surface tension of ionic liquids over a wide range of temperatures Juan A. Lazz´ us∗ , Geraldo Pulgar-Villarroel, Fernando Cuturrufo, Pedro Vega
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Departamento de F´ısica y Astronom´ıa, Universidad de La Serena, Casilla 554, La Serena, Chile
Abstract
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A group contribution methods for estimating the surface tension of ionic liquids as a function of the absolute temperature, is presented. A total of 2286 experimental data points from 226 data sets of 154 ionic liquids were collected from the specialized literature. This database covers a temperature range of 263–533 K and a surface tension range of 0.015–0.062 N·m−1 , for a heterogeneous set of ionic liquid-types such as imidazolium, ammonium, phosphonium, pyridinium, pyrrolidinium, and piperidinium. A correlation set containing the 75% of the overall database was used in order to calculate the contribution values of 10 structural cation groups and 30 structural anion groups. Then, a prediction set containing the other 25% of the overall database with data sets not used in the correlation phase was used in order to test the capabilities and accuracy of the proposed method. The results show that the proposed method can estimate the surface tension of several ionic liquids with a better accuracy than other methods available in the literature, with an average absolute relative deviation of 2.8% and a correlation coefficient of 0.98. Keywords: Ionic liquids, Surface tension, Group contribution method, Genetic algorithm, Parameter estimation.
∗ Tel.: +56 51 2204128; fax: +56 51 2206658. [email protected]
Preprint submitted to Journal of Molecular Liquids
May 22, 2017
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1. Introduction
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Ionic liquids (ILs) are a class of salts that have been of great interest in recent years due to its unique physical and chemical properties [1]. ILs typically consist of one anion and one cation, which allows the most suitable anion-cation combination for a specific IL to adapt to a specific applications demands [2] (for a theoretical description of ILs, see [3]). In order to maximize its use and design, a knowledge of its physical and chemical properties is required. In particular, the knowledge of the interfacial and surface tensions is highly relevant [1]. The surface tension (σ) of ILs is an important physical property. It is used to access the intrinsic energetics that are involved in the interactions between ions [4]. Thus, σ in ILs directly indicates the cohesive forces between liquid molecules present at the surface [5]. Unfortunately, the knowledge of the σ of ILs, is still limited, inconsistent, and discrepant [6]. The available experimental data for the σ of ILs is very lacking and essentially restricted to imidazolium-based ionic liquids [7]. So it is important to collect a large database, not only for process and product design but also for the development of new predictive methods and generalized correlations [6]. In this way, the estimation of σ of ILs has been carried out by parachors [6, 8, 9, 10], corresponding states theory [11, 12], group contribution methods [5], and quantitative structure-property relationships [13, 14]. Parachor models are an empirical method, which relates density with the σ via a temperature-independent relationship [15]. Deetlefs et al. [8] were the first who proposed a parachor model for estimating σ of ILs. Also, Gardas and Coutinho [9] proposed the estimation of the σ of ILs applying a parachor approach by using 361 data points of 38 imidazolium-based ILs. Later, this above parachor model was extended for new ILs cation [6]. Next, Lemraski and Zobeydi [10] applied a new parachor method in order to estimate the σ of imidazolium-based ILs. Corresponding states theory (CST) provides the single most important basis for the development of correlations and estimation methods for unknown properties of many fluids from the known properties of a few [15]. Mousazadeh and Faramarzi [11] applied CST methodology to derive a model for σ of ILs by compiling 30 ILs. Next, Wu et al. [12] developed other CST model for estimating σ of ILs based on 224 experimental data points of 105 ILs. Group contribution method (GCM) is a technique to estimate thermody2
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namics properties of a compound from the sum of the contributions from the parts of molecules that form it [15]. Gharagheizi et al. [5] proposed a GCM for estimating σ of ILs using 920 experimental data points for 51 ILs. Quantitative structure-property relationships (QSPR) is an analytical method for breaking down a molecule into a series of numerical values describing their physico-chemical properties [15]. Mirkhani et al. [13] developed a QSPR model based on seven molecular descriptors for estimating the σ of ILs by compiling 930 experimental data points for 48 ILs. Also, Shang et al. [14] proposed a QSPR model based on topological indices in order to predict the σ of ILs by compiling 930 data points for 115 ILs. In other methods, Ghatee et al. [16] proposed a linear relation between the logarithm of σ and the fluidity by involving a characteristic exponent for 19 imidazolium-based ILs. Ghasemian and Zobeydi [17] present a simple equation in order to predict the σ of ILs based on the enthalpy of vaporization. On the other hand, Llovell et al. [18, 19] show the possibility of describing the σ of ILs by using the soft-SAFT equation-of-state. And for mixtures, Lemraski and Pouyanfar [20] used three thermodynamic models in order to predict the σ of ionic liquid binary mixtures based on a corresponding-states group-contribution method, an extended Guggenheim’s ideal solution model, and a parachor model. Note that, the current development state of methods for estimating σ of IL fails mainly in a poor quantity of represented ILs and in a narrow temperature range considered. In this study, a new group contribution method is applied in order to estimate the σ of several IL-types as a function of the temperature, where the proposed GCM is decomposed in structural groups for the cationanion parts. 2. The proposed GCM For a given liquid, the σ decreases with the temperature, since the cohesion forces decrease with increasing the thermal agitation, causing a lower intensity in the intermolecular forces [21]. Then, a linear approximation can be applied [15] as follows: σ(T ) = A − B · T
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σ(T ) = a+ − b+ · T + a− − b− · T
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where a+ and b+ are the adjustable constants of the cation part, and a− and b− are the adjustable constants for the anion part associated with σ. The method here proposed employs a GCM to estimate the cation and anion parameters. For this equation A = a+ + a− , and B = b+ + b− . The mathematical formulation of GCM is based on the multilinear regression method [22]. This technique fits a set of data points of a property of interest (y) as a linear combination of one or more selected descriptors (xl ) [23]: X nk xl (3) y= k=1, l=0
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where ni and nj are the occurrences of the groups i and j in the ILs, ga+ and gb+ are the contributions of the cation groups, and ga− and gb− are the contributions of the anion groups. This equation P represent the proposed P ngb GCM to correlate σ(T ). For this equation a = nga , and b = (with their respective ionic charges). Note that the absolute values for the total contribution were added in order to prevent that if the sum of the contributions is negative, the slope doesn’t change (as is suggested by [24]). 3. Database and regression method A total of 2286 σ(T )-experimental data points from 226 data sets of 154 ILs were collected from the specialized literature [25], by considering that experimental protocol measurements were clearly described (as is suggested by [26]). The total data set was divided into a correlation set with 1804 experimental data points (∼75% of the overall database), and a prediction set with 482 experimental data points (∼25% of the overall database), where 4
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all data for one IL were assigned to one same data set. Table S1 shows the experimental values of σ(T ) considered in this study (see, Supplementary material). In our database, σ(T )-properties cover wide ranges, such as: 263–533 K for the temperature, and 0.015–0.062 N·m−1 for the surface tension. The heterogeneous set of ILs of our study includes IL-types such as imidazolium, ammonium, phosphonium, pyrrolidinium, piperidinium and pyridinium. Figure 1 shows a general picture of the wide ranges of σ and ILs considered. These values are of especial importance in order to verify that an acceptable range of σ was covered in this study. Note that, ILs included in this database have very different physico-chemical characteristics, e.g. low molecular weight substances such as propylammonium formate (M W = 105.14) [27], or high molecular weight substances such as trihexyl(tetradecyl)phosphonium tris(pentafluoroethyl)trifluorophosphate (M W = 928.88) [28], and low σ value for 1tetradecyl-3-methylimidazolium bis(trifluo-romethylsulfonyl)imide (σ = 0.0155 N·m−1 at 512.9 K) [29], and high σ value for 1-ethyl-3-methylimi-dazolium dicyanamide (σ = 0.06196 N·m−1 at 278.16 K) [30]. In order to estimate the σ of ILs as a function of the temperature, the contributions of the structural groups were calculated using the ∼75% of the overall database (correlation set). The occurrence of a structural group was defined as: 0, when the group does not appear in the IL and n, when the group appears n-times in the IL, according to the methodology described in [22]. To improve the accuracy of the correlation in determining the contribution values of each structural group, a GCM was defined for each IL-type. Thus, over these correlation sets was applied a regression method for estimating the contribution values of each structural group associated with Eq. 4. The regression method was optimized by genetic algorithms (GA) [31] in order to minimize the difference between calculated and experimental σ(T ). This procedure was based on the following objective function (OF ): OF =
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4. Results and discussion
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At the end of the regression process, the optimum contribution values were obtained for the correlation set associated to each IL-type. Table 2 shows the occurrence of each group (in the correlation set) and the contribution values determined for each IL-type. In this Table, the cation groups included 10 substituted-groups for 6 IL-types, such as: imidazolium, ammonium, phosphonium, pyridinium, pyrrolidinium, and piperidinium, while the anion groups included 25 functional structural groups plus other 5 functional ring groups for different anion-types, such as halides, sulfonates, tosylates, imides, amides, cyanides, borates, phosphates, sulfates, acetates, amino acids, and metal complexes, among others. Once the correlation process was successfully done and the optimum contribution values for the groups were obtained, the other ∼25% of the overall experimental data for σ not used in the correlation set were used in order to test the proposed GCM. Note that, correlation and prediction sets were selected randomly, with the consideration that in the group contribution methods, the molecules are decomposed into fragments and that all fragments are present with a suitable frequency in the correlation set [22]. In addition, the accuracy of the proposed GCM was checked between the calculated values of σ(T ) and the experimental data taken from the literature by using the average absolute relative deviation for each data point (ARD) and for the individual sets (AARD), and by using the coefficient of determination (R2 ). These statistical parameters were calculated as follows: σ(T )calc − σ(T )exp · 100 (6) ARD = σ(T )exp ND σ(T )calc − σ(T )exp 100 X AARD = ND z=1 σ(T )exp z P ND 2 calc − σ(T )exp z z=1 σ(T ) 2 R =1− P h i exp 2 ND calc − σ(T ) z=1 σ(T )
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Table 3 summarizes the statistical deviations obtained in the prediction step and its comparison with the correlation process results. As shown the accuracy of the proposed GCM is very good, with ARDmax of 14.20%, an AARD from 0.07% to ∼4%, and R2 between 0.91 and 0.99. For the overall correlation set, AARD was 2.69% and the R2 was 0.986, while for the overall prediction set, AARD was 3.36% and R2 was 0.981. For the total set the overall AARD was 2.81% and the overall R2 was 0.984. In order to verify the correct interpretation of our results, Figure 2 shows the experimental surface tension versus the relative deviation (RD) obtained for all 2286 σ(T )experimental data points. This Figure offers a better understanding of the prediction capability of our proposed GCM. Here, RDmax was 13.90%, RDmin was −14.20%, and RDmean was −0.06%, which illustrate that our method generated homogeneous deviations. Table 4 presents the final equations obtained for the proposed GCM. For these Equations (9 to 14), ni and nj are the occurrences of the groups i and j in the ILs; ga+ , gb+ are the contribution of the cation groups and ga− , gb− are the contribution of the anion groups for σ(T ). In this equation, T is in units of K, the contributions ga+ and ga− are calculated in terms of the unit N·m−1 , and gb+ and gb− are calculated in units of N·m−1 ·K−1 , finally σ(T ) is obtained in unit of N·m−1 . Figure 3 shows the comparison between experimental and calculated values by Eqs. 9 to 14 (Table 4) in the estimation of σ(T ), where black dots represent the correlation set, red dots represent the prediction set, and the solid line is the expected value. This Figure shows a general picture of the accuracy and capabilities of our proposed GCM, and it ratifies the good results presented above, however, we will clarify the specific results for each IL-type. Figure 3a shows the Imidazolium’s GCM accuracy in the estimation of σ(T ). For this case, correlation set shows a R2 of 0.982 and a slope of the curve (m) of 0.954 (expected to be 1.0), while the prediction set shows a R2 of 0.978 and m of 1.004 (also expected to be 1.0). Figure 3b illustrates the accuracy of the Ammonium’s GCM. In this Figure, correlation set presents a R2 of 0.952 and a m of 0.908, while the prediction set presents a R2 of 0.915 and a m of 0.901. Figure 3c presents the accuracy of the Phosphonium’s GCM. Here, correlation phase exhibits a R2 of 0.997 and a m of 0.994, while the prediction phase exhibits a R2 of 0.999 and a m of 1.010. Figure 3d shows the Pyridinium’s GCM accuracy. For this Figure, correlation set shows a R2 of 0.990 and a m of 0.966, while the prediction set shows a R2 of 0.996 and a m of 1.018. Figure 3e shown the accuracy of the Pyrrolidinium’s GCM. 7
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Where the correlation phase presents a R2 of 0.998 and a m of 0.980, while the prediction set presents a R2 of 0.999 and a m of 0.998. Finally, Figure 3f illustrates the accuracy of the Piperidinium’s GCM. Here, correlation phase exhibits a R2 of 0.998 and a m of 0.996, while the prediction set exhibits a R2 of 0.999 and a m of 0.999. An example of the use of Eq. 9 (Table 4) and the Imidazolium’s GCM, is shown in Table 5. This Table details the procedure to calculate σ(T ) via the calculated values for our Imidazolium’s GCM (columns 3 and 4 in Table 2) for 1-ethyl-3-methylimidazolium tosylate (C13 H18 N2 O3 S; M W = 282.36) [32], that was selected randomly from the predicion set. For this example, our GCM shows a higher accuracy, such as ARDmax of 0.39%, an AARD of 0.21%, and a R2 of 0.993. These results show that the correlation set for the Imidazolium’s GCM was correctly selected as shown in Table 3. Note that the highest ARD obtained was 14.20% for the σ=0.0374 N·m−1 at 293.15 K of the 1-butyl-2,3-dimethyl-1H-imidazolium bis(trifluoromethylsulfonyl)amide (C11 H17 F6 N3 O4 S2 ; M W = 433.39) [6], however lower than 20% of the overall data points obtained an ARD higher than 5%, while only the 3% of the overall data points obtained an ARD higher than 10% (see, Table S1). More examples of the use of GCM can be found in Tables S2 to S6 (see, Supplementary material). Table S2 presents an example of the use of Eq. 10 (Table 4) to calculate σ(T ) for the propylammonium acetate (C5 H13 NO2 ; M W = 119.16) [27] randomly selected from the ammonium’s dataset. For this IL, ARDmax = 0.11%, AARD= 0.07%, and R2 = 0.999. Note that for the overall ammonium’s dataset the highest ARD obtained was 13.04% for a σ = 0.0308 N·m−1 at 293.30 K for the tributylmethylammonium bis[(trifluoromethyl)sulfonyl]imide (C15 H30 F6 N2 O4 S2 ; M W = 480.53) [33] (see, Table S1). Table S3 illustrates the use of Eq. 11 (Table 4) to calculate σ(T ) for the tributylmethylphosphonium methylsulphate (C14 H33 O4 PS; M W = 328.45) [34] randomly selected from the phosphonium’s dataset. Here, ARDmax = 0.95%, AARD= 0.41%, and R2 = 0.991. From the overall phosphonium’s dataset the highest ARD obtained was 1.99% for a σ=0.02967 N·m−1 at 313.21 K for the tetradecyl(trihexyl)phosphonium dicyanamide (C34 H68 N3 P; M W = 549.90) [35] (see, Table S1). Table S4 illustrates the use of Eq.12 (Table 4) for estimating the σ(T ) of the 1-butylpyridinium tetrafluoroborate (C9 H14 BF4 N; M W = 223.02) [36] randomly selected from the pyridinium’s dataset. These results present an ARDmax = 2.01%, with an AARD= 1.02%, and a R2 = 0.999. In addition for the overall pyridinium’s dataset the highest ARD obtained was 6.94% for a σ=0.0377 N·m−1 at 288.15 8
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K for the 1-ethylpyridinium bis[(trifluoromethyl)sulfonyl]imide (C9 H10 F6 N2 O4 S2 ; M W = 388.31) [37] (see, Table S1). Also, Table S5 illustrates the use of Eq. 13 (Table 4) to estimate the σ(T ) for the 1-butyl-1-methylpyrrolidinium dicyanamide (C11 H20 N4 ; M W = 208.30) [38] randomly selected from the pyrrolidinium’s dataset. In this example the proposed GCM shows an ARDmax of 1.24%, with an AARD of 0.70%, and a R2 of 0.980. For the overall pyrrolidinium’s dataset the highest ARD obtained was 6.65% for the estimation of σ=0.0421 N·m−1 at 341.35 K for the 1-butyl-1-methylpyrrolidinium thiocyanate (C10 H20 N2 S; M W = 200.34) [38] (See, Table S1). Finally, Table S6 illustrates the application of Eq. 14 (Table 4) for estimating the σ(T ) for the 1-butyl-1-methylpiperidinium bis(trifluoromethanesulfonyl)imide (C12 H22 F6 N2 O4 S2 ; M W = 436.43) [39]. In this example our proposed GCM presents an ARDmax of 0.14%, with an AARD of 0.09%, and a R2 of 0.999. Note that, for the overall pyrrolidinium’s dataset the highest ARD obtained was 0.50% for the estimation of σ=0.03589 N·m−1 at 263.08 K for the 1-(2-methoxyethyl)-1methylpiperidinium trifluorotris(perfluoroethyl)phosphate (C15 H20 F18 NOP; M W = 603.27) [40] (See, Table S1).
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4.1. Cation-anion effects The results obtained by the proposed GCM shows differences in the estimation of σ(T ) for the different IL-types studied (see, Supplementary material). These results show the impact of the cation size on the correlationprediction performance and its accuracy. For example, imidazolium ILs present the following AARD ranges in the estimation of σ(T ): ∼3% > N, N -alkyl-imidazolium > N, N, N -alkyl-imidazolium > amino-imidazolium > 0.5%, while ammonium ILs show the following AARD ranges: ∼3% > N, N, N, N -alkyl-ammonium > choline-ammonium > 0.3, and while pyridinium ILs show the following AARD ranges: 2.7% > N -alkyl-pyridinium∼cyanopyridinium > N, N -alkyl-pyridinium>1%. In addition, for all IL-types studied the AARD values increase with increasing alkyl chain length in the cation. This fact can be associated with the general trend toward lower σ(T ) values when increasing alkyl chain length in the cation [41], such as those reported experimentally (see, Table S1). Note that, the van der Waals interactions have a remarkable effect on the alkyl chain length because molecular dynamics simulations show that the longer the alkyl chain, the stronger the attractive Lennard-Jones contribution [42]. On the other hand, also AARD values increase when increasing cation asymmetry. Recent experimental studies
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show that σ(T ) depends greatly on the asymmetrical/symmetrical structure of IL [43]. Remarkable differences in the estimation of σ(T ) (via AARD) were also observed for several anion sizes. Our results show also the impact of the anion type on the accuracy of the correlation and prediction of σ(T ). For example our proposed GCM presents the following AARD ranges in the estimation of σ(T ) (for the most common anion types): bromide (0.3%) < chloride, trifluoroacetate (0.5%) < tris(pentafluoroethyl)trifluorophosphate (1.5%) < tosylate (1.8%) < tetrafluoroborate (2.3%) < alkyl-phosphate (2.4%) < alkylsulphate (2.9%) < bis[(trifluoromethyl)sulfonyl]imide, dicyanamide, hexafluorophosphate, trifluoromethanesulfonate (3.4%) < acetate (3.9%) < iodide (4.7%), while the others anions (such as formate, nitrate, amino acid, metal complex, among others) show an AARD ∼2%. Our heterogeneous set of ILs contain small-sized anions (such as bromide, chloride, iodide, tetrafluoroborate), medium-sized (such as hexafluorophosphate, trifluoromethanesulfonate), and large-sized (such as tris(pentafluoroethyl)trifluorophosphate, bis[(trifluoromethyl)sulfonyl]imide). Experimental studies have suggested that σ(T ) decreases for ILs with increasing anion size, which was attributed to the higher charge delocalization in larger anions and a decrease in hydrogenbonding ability [44]. From this fact, we would expect the estimation of σ(T ) via the proposed GCM to be difficult when increasing/decreasing the anion size, but our results do not exhibit this behavior, and our accuracy in the estimation of σ(T ) was independent of the anion size. However, most recent studies show that this behavior can not be generalized, since in the literature there are different statements concerning the dependence of σ(T ) on the anion size, where with respect to selected anions it is found that the σ(T ) either increases or decreases with increasing anion size, or that there is no dependence at all [38, 41, 45]. 4.2. Comparative analysis In the literature, many models has been used in order to estimate σ(T ) of ILs (see, Section 1). Coutinho et al. [7] discussed a variety of correlation and prediction methods for estimating σ(T ), such as: parachor methods [6, 8, 9, 10], corresponding states methods [11, 12], group contribution methods [5], and quantitative structure-property relationship models [13, 14]. Due to the complexity of these linear or non-linear models, the IL molecule and their properties can be described in many different ways [46]. In order to evaluate the estimation accuracy and capability of our proposed GCM, we compare it 10
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directly with others three reported analytical methods for estimating σ(T ) of ILs, such as Gharagheizi’GCM [5], Mirkhani’s QSPR [13], and Wu’s CST [12]. Gharagheizi et al. [5] proposed a GCM for estimating σ(T ) of ILs using 920 experimental data for 51 ILs collected from various references. They employ a total of 19 sub-structures to predict the σ(T ) with an AARD of 3.6% from experimental data. Although, Mirkhani et al. [13] developed a QSPR model to predict σ(T ) of ILs making use of 930 experimental data points for 40 ILs by using 7 molecular descriptors, and obtaining an AARD of 4.9%. But, Wu et al. [12] employed a CST-group contribution method in order to estimate σ(T ) of ILs by using 1224 data points of 105 ILs with an AARD of 5.0%. While our proposed GCM for estimating σ(T ) was developed using 2286 experimental data of 154 ILs in order to obtain 40 structural groups and to predict the σ(T ) with an AARD of 2.8% from experimental data. It is worth pointing out that these methods obtained their results from different databases with different correlation and prediction sets (or training and prediction sets) and based on very different methodologies, then their results cannot be compared directly with one another. However, a comparison can be made for some selected datasets for common ILs for these methods. Table 6 shows a comparison between the proposed GCM versus Gharagheizi’s GCM [5], Mirkhani’s QSPR [13], and Wu’s CST [12] for estimating σ(T ) of ILs. This Table contains 30 datasets of ILs in common taken from [30, 38, 44, 47, 48, 49, 50, 51, 28]. Based on these results, Gharagheizi’s GCM showed an AARDtotal of 4.7% and R2 of 0.912; Mirkhani’s QSPR exhibited an AARDtotal of 5.6% with R2 of 0.891; Wu’s CST presented AARDtotal of 5.3% and R2 of 0.897; while our proposed GCM resulted in an AARDtotal of 2.3% with a R2 of 0.983. Note that the results of this comparative analysis also evidence some advantages and disadvantages that can be found in these models. For example, both Parachor’s methods [6, 8, 9, 10] and CST’s methods [11, 12] require the use of additional physicochemical properties such as density, melting and boiling points, and hypothetical critical properties, so that the uncertainties associated with these estimates are necessarily very large, e.g. some studies report methods with R2 lower than 0.8 for the density and the melting point of ILs [7]. Furthermore, QSPR’ methods (such as [13, 14]) are very difficult of apply due to the complex calculations for obtaining their molecular descriptors. These descriptors are computed from molecular mechanics or quantum mechanical analysis of the substance mainly by using of commercial softwares 11
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[15]. These problems severely limit the applicability of similar approaches such as parachor, CST, and QSPR to the prediction of the physicochemical properties of ILs. On the other hand, GCM-based models are easy to apply only with the knowledge of the molecular structure of the substance [22]. From these methods, a macroscopic property can be related directly and analytically to molecular structure and the bonds between atoms, which determine the magnitude of the intermolecular forces [15]. Due to the simplicity of the GCM and its direct relation between macroscopic property-molecular structure, it can obtain a better correlation and a more accuracy estimation of the physicochemical properties of an IL. Note that, the results in Table 6 evidence this fact, and show better accuracy among GCM-based models. In this point, Gharagheizi’s GCM shows higher deviations for small-sized ILs than our GCM, while for medium-sized ILs both GCMs present similars deviation (approx.), but for large-sized ILs our GCM was also better than Gharagheizi’s GCM. Also, our proposed method shows a higher accuracy than Gharagheizi’s GCM when is applied to ILs composed of anions such as bis[(trifluoromethyl)sulfonyl]imide and dicyanamide. But in general, the proposed GCM presented a higher accuracy with statistical deviations of ARDmax of 14%, an AARD of 2.8% and a R2 of 0.98. Note that, the incorporation of cation-types, such as imidazolium, ammonium, phosphonium, pyridinium, pyrrolidinium, and piperidinium is very important for the current applications of ILs as solvents in organic synthesis, catalysis, electrochemistry, chemical separation, metal extraction and nanoparticle formation [52]. Also, the incorporation of groups for ILs with cyanide and hydroxyl containing cations, and metal complexes groups for the anion, transforms our GCM in one of the most complete for estimating σ(T ) of ILs that has been reported so far. 5. Conclusions Based on the results and discussion, the following main conclusions were obtained: (i) The proposed GCM allows the σ estimation of different IL-types composed of 10 cation groups and 30 anion groups in a wide range of temperatures (263–533 K), and surface tension (0.015–0.062 N·m−1 ). For a database consisting of 2286 experimental data points from 226 data sets of 154 ILs. The great differences in the chemical structure and the physical properties of the ILs considered in the study impose additional difficulties to the problems that the proposed GCM has been able to handle; (ii) The accuracy of 12
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the proposed GCM was tested by comparing calculated and experimentally measured σ(T ) values from the literature, resulting in a AARD=2.8% and R2 =0.98. Our results show that the proposed GCM can estimate the σ(T ) of ILs at different temperatures with low deviations and it is also applicable to a temperature range that is higher than those methods referenced by other authors and mentioned in this study. Note that the proposed method should be able to estimate σ(T ) of a larger range of ILs as data for these to become available; (iii) A comparative analysis between our GCM method and others methods such as corresponding states methods and quantitative structure-property relationship methods evidenced the simplicity, better correlation and more accuracy of our GCM in the estimation of σ(T ) of ILs; and (iv) The values calculated using the proposed model are considered to be accurate enough for engineering calculations, for generalized correlations and for equations of state methods, among other uses.
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The authors thank the Direction of Research and Development of the University of La Serena (DIDULS) through the research projects PEQ16141 and P116141, and the Department of Physics and Astronomy of the University of La Serena (DFULS) for the special support that made possible the preparation of this paper. Supplementary material Supplementary material to this article can be found online at http://dx.doi.org/xxxxxx.
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Table 1: Parameters of the genetic algorithm used for minimizing Eq. 5.
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GA Parameter Number of generations (Gen) Number of individuals (Ni ) Length of chromosome (L) Length of an individuals (Li) Crossover probability (Cros) Mutation probability (M ut) Crossover operador (CO) Mutation operador (M O) Objetive function (OF )
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Value 500 200 20 80 0.8 0.1 Multipoint Binary Eq. 5
Occ.
1250 1804 1794 6 9 12 21 16 12 13
Occ.
160 83 7 29 63 138 201 45 41 37 848 134 210 711 29 8 15 31 530 56 45 248 327 767 11 7 7 12 12 7
Groups+
–H –CH3 –CH2 − –CH< –CN >C=O –O– –OH –NH– –NH2
Groups−
–CH3 –CH2 − >C= >C< [>C–] >CH– [–CH–] –COO– [–COO] –O– [–O] =O –OH –HCOO –CF3 –CF2 –CN >N– [–N–] [>N<] –NH2 –NO3 –Br –Cl –F –I –S –B [>B<] –P [>P<] [> – P<] – –SO2 − >In< –CH2 − (ring) >CH– (ring) =CH– (ring) >C= (ring) –NH– (ring)
ga− [N·m−1 ] 2.3701E-03 -3.3387E-03 -8.2696E-02 8.3516E-05 -1.8872E-03 1.1581E-02 6.0961E-03 2.8934E-02 7.2778E-04 2.6177E-02 -8.7959E-03 1.5481E-02 7.1981E-03 1.8202E-02 3.3701E-02 NA 1.9703E-02 6.6650E-03 8.6654E-03 2.2708E-02 2.5196E-02 -1.7082E-02 -3.8646E-02 3.8429E-03 2.8828E-05 -7.5034E-04 -2.2510E-03 -1.0888E-03 5.6300E-03 -2.2510E-03
ga+ [N·m ] 1.7397E-02 1.5873E-02 -2.0941E-03 NA NA 2.3680E-03 NA NA 2.3680E-03 2.8136E-02 −1
−1
gb− [N·m−1 ·K−1 ] 4.9420E-05 2.4056E-06 -2.6686E-04 2.6878E-07 4.9427E-07 -3.4135E-06 -8.1082E-05 8.6386E-05 -1.1906E-05 7.5863E-05 -4.3027E-06 1.2095E-05 -2.0336E-05 -4.5065E-05 1.3034E-04 NA -5.5328E-05 -1.9668E-05 -2.3869E-05 -5.3496E-05 -7.4501E-05 4.1448E-05 1.0406E-04 5.4988E-05 5.0146E-07 5.4171E-06 1.6251E-05 8.8384E-07 -5.1822E-05 1.6246E-05
gb+ [N·m ·K ] 2.7002E-06 4.1968E-06 -3.1427E-06 NA NA 7.5426E-06 NA NA 7.5548E-06 -1.5107E-05
Imidazolium −1
ga− [N·m−1 ] 4.0251E-02 1.1011E-02 NA NA NA -1.4372E-03 -4.5365E-03 NA NA 4.2241E-02 5.4035E-03 4.1123E-04 NA 1.1109E-02 NA NA NA NA NA NA NA NA NA 5.4049E-03 NA NA NA NA NA NA
ga+ [N·m ] 4.3051E-03 4.0811E-03 1.0075E-03 NA NA NA NA -1.3532E-02 NA NA
−1 −1
gb− [N·m−1 ·K−1 ] 1.7688E-04 -2.2332E-06 NA NA NA -1.3075E-04 -5.7748E-05 NA NA 4.9132E-05 9.8628E-07 3.2356E-06 NA 3.8788E-06 NA NA NA NA NA NA NA NA NA 9.8167E-07 NA NA NA NA NA NA
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gb− [N·m−1 ·K−1 ] NA NA NA NA NA NA NA NA NA NA -2.6780E-07 3.7676E-06 NA -2.5988E-05 NA NA NA NA 3.7676E-06 NA NA NA 1.1303E-05 -1.2994E-05 NA NA NA NA NA NA
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ga− [N·m−1 ] NA NA NA NA NA NA NA NA NA NA 3.9230E-03 2.3884E-03 NA 1.7514E-02 NA NA NA NA 2.3884E-03 NA NA NA 7.1652E-03 8.7570E-03 NA NA NA NA NA NA
gb+ [N·m−1 ·K−1 ] NA -2.1202E-06 2.7941E-06 NA NA NA 1.1304E-05 NA NA NA
Piperidinium ga+ [N·m−1 ] NA 5.7386E-03 -1.9005E-03 NA NA NA 7.1652E-03 NA NA NA
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gb− [N·m−1 ·K−1 ] NA NA NA NA NA -8.6882E-05 NA NA NA NA -1.0350E-05 NA -3.8412E-05 -7.4567E-05 NA NA NA NA NA NA -1.2132E-04 NA NA -1.3796E-06 NA NA NA NA NA NA
gb+ [N·m ·K ] NA -3.2904E-05 4.2015E-05 NA NA NA NA NA NA NA
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ga− [N·m−1 ] NA NA NA NA NA 4.5291E-02 NA NA NA NA 4.9623E-03 NA 2.2930E-02 4.1042E-02 NA NA NA NA NA NA 5.9685E-02 NA NA -1.1605E-03 NA NA NA NA NA NA
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Pyrrolidinium ga+ [N·m ] NA 1.7470E-02 -1.2897E-02 NA NA NA NA NA NA NA
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Phosphonium Pyridinium Cation contributions −1 −1 −1 −1 ga+ [N·m ] gb+ [N·m ·K ] ga+ [N·m ] gb+ [N·m−1 ·K−1 ] NA NA 1.8783E-02 2.1688E-05 3.4791E-03 -5.9693E-07 1.1332E-02 1.0572E-06 5.0573E-04 8.3142E-08 -1.8017E-03 8.5965E-07 1.2233E-03 1.5919E-05 NA NA NA NA 8.4310E-03 -1.0118E-04 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA Anion contributions −1 −1 −1 −1 ga− [N·m ] gb− [N·m ·K ] ga− [N·m ] gb− [N·m−1 ·K−1 ] 1.2642E-02 -2.1610E-05 NA NA -5.1607E-03 4.6611E-05 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 3.8563E-02 -5.3641E-05 1.1311E-02 -2.8592E-05 4.8240E-02 -1.8437E-05 -1.0321E-02 9.3221E-05 NA NA NA NA NA NA NA NA NA NA 1.3884E-03 9.0593E-06 6.9338E-03 5.2156E-05 2.1943E-03 -1.1065E-06 -9.3007E-03 -1.3467E-05 9.2997E-03 2.3098E-05 7.7065E-03 1.2711E-05 9.2554E-03 3.5822E-05 4.1127E-02 -1.3484E-04 NA NA NA NA NA NA 3.8214E-02 -9.5572E-05 2.3065E-02 -7.3242E-05 NA NA 2.9041E-02 -7.9244E-05 NA NA 2.1943E-03 -1.1065E-06 2.5811E-03 7.9133E-07 NA NA NA NA NA NA 9.9110E-02 -2.6784E-04 NA NA 3.9723E-02 6.3322E-05 -1.7876E-04 3.3877E-05 3.1537E-02 -7.4563E-05 4.0322E-03 3.3460E-06 -1.0921E-02 4.0159E-05 NA NA NA NA NA NA NA NA NA NA NA NA 9.1746E-04 1.1940E-05 NA NA 1.8349E-03 2.3879E-05 NA NA NA NA NA NA
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Ammonium
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Table 2: Group contribution values obtained in the correlation process for each IL-class. (NA: group not available for the IL).
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ND ARDmin ARDmax AARD R2
Stat. Dev.
Imidazolium Correlation Prediction 1123 325 0.01 0.02 14.20 11.41 3.13 4.03 0.982 0.978
Ammonium Correlation Prediction 178 41 0.00 0.01 13.04 10.75 2.84 3.73 0.952 0.915
Phosphonium Correlation Prediction 115 17 0.00 0.03 1.99 1.07 0.48 0.39 0.997 0.999
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Piperidinium Correlation Prediction 29 7 0.01 0.00 0.50 0.14 0.19 0.07 0.998 0.999
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Pyrrolidinium Correlation Prediction 50 29 0.01 0.00 6.65 3.19 1.80 0.94 0.998 0.999
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Pyridinium Correlation Prediction 309 63 0.00 0.01 6.94 6.05 2.19 1.97 0.990 0.996
Table 3: Summary of statistical deviations obtained for the proposed GCM during the correlation and prediction processes.
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IL type σ(T )imi
Equation P P P29 P 6 − = i=1 ni ga+i + j=1 nj ga−j − T 6i=1 ni gb+i + 29 n g j bj j=1
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Table 4: Final equations obtained for the proposed GCM. Here, equations are individualized for each IL type.
(9)
σ(T )amm
P P9 4 i=1 ni gb+i + j=1 nj gb−j
(10)
Phosphonium
P P − σ(T )phos = 3i=1 ni ga+i + 15 n g j=1 j aj − T
P P15 3 + − + n g n g i=1 i bi j=1 j bj
(11)
P P − σ(T )pyri = 4i=1 ni ga+i + 12 n g j=1 j aj − T
P P12 4 i=1 ni gb+i + j=1 nj gb−j
(12)
P P P P σ(T )pyrr = 2i=1 ni ga+i + 6j=1 nj ga−j − T 2i=1 ni gb+i + 6j=1 nj gb−j
(13)
P P6 3 i=1 ni gb+i + j=1 nj gb−j
(14)
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Pyridinium
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Ammonium
P P9 4 = i=1 ni ga+i + j=1 nj ga−j − T
Pyrrolidinium Piperidinium
σ(T )pipe
P P6 3 = i=1 ni ga+i + j=1 nj ga−j − T
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Table 5: Example of application of the proposed Imidazolium’s GCM in the estimation of σ(T ) of ILs.
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ni ga+ [N·m−1 ] gb+ [N·m−1 ·K−1 ] 1 1.7397E-02 2.7002E-06 2 1.5873E-02 4.1968E-06 1 -2.0941E-03 -3.1427E-06 nj ga− [N·m−1 ] gb− [N·m−1 ·K−1 ] 1 2.3701E-03 4.9420E-05 1 6.0961E-03 -8.1082E-05 1 3.8429E-03 5.4988E-05 4 -1.0888E-03 8.8384E-07 2 5.6300E-03 -5.1822E-05 Eq. 9: σ(T )=6.6263E-02−6.8832E-05·T Data set [32]: exp ARD σ(T ) [N·m−1 ] σ(T )calc [N·m−1 ] 0.0452 0.0451 0.32 0.0442 0.0444 0.39 0.0436 0.0437 0.12 0.0430 0.0430 0.05 0.0427 0.0426 0.14 0.21 0.993
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Cation group –H –CH3 –CH2 − Anion group –CH3 –O –SO2 − =CH– (ring) >C= (ring)
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IL: 1-ethyl-3-methylimidazolium tosylate
T [K] 308.10 318.00 328.50 338.30 343.20 AARD R2
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[47] [47] [47] [47] [48] [49] [30] [30] [48] [38] [44] [47] [47] [47] [44] [48] [44] [47] [47] [38] [38] [38] [50] [38] [48] [38] [51] [51] [49] [28]
Ref.
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Wu’s CST [12] AARD [%] 7.54 7.58 5.30 5.32 2.00 2.81 8.64 8.28 5.37 5.45 5.33 1.24 1.29 1.27 1.28 3.22 3.25 7.55 7.60 3.32 3.28 4.74 2.64 9.38 5.20 6.14 4.61 4.64 9.60 10.70 5.3% 0.897
RI P
Mirkhani’s QSPR [13] AARD [%] 6.18 6.39 3.49 3.41 19.70 19.85 7.57 8.25 0.53 0.77 0.55 1.31 1.64 1.27 0.98 14.43 13.52 1.27 1.33 9.39 5.98 1.44 8.95 6.00 1.27 3.76 1.99 2.08 20.52 12.54 5.6% 0.891
SC
NU
Gharagheizi’GCM [5] AARD [%] 5.89 6.11 3.78 3.35 6.20 7.01 13.03 13.69 1.50 1.65 1.17 1.68 1.80 1.31 1.75 2.09 2.66 1.94 1.90 2.96 10.12 1.12 0.11 11.49 15.74 2.00 3.21 4.19 0.31 0.36 4.7% 0.912
MA
0.050–0.055 0.050–0.055 0.038–0.041 0.038–0.041 0.033–0.037 0.034–0.037 0.056–0.062 0.056–0.062 0.041–0.045 0.041–0.045 0.042–0.045 0.033–0.035 0.033–0.035 0.033–0.035 0.033–0.036 0.031–0.033 0.031–0.034 0.035–0.040 0.035–0.040 0.045–0.050 0.038–0.048 0.051–0.056 0.034–0.036 0.036–0.044 0.029–0.032 0.029–0.032 0.031–0.035 0.031–0.035 0.025–0.028 0.027–0.029
∆σ [N·m−1 ]
ED
288–356 288–356 268–356 268–356 283–352 279–328 278–356 278–348 284–351 294–352 293–341 292–353 293–356 292–353 293–343 284–352 293–343 269–356 269–356 303–344 303–342 293–353 300–333 293–350 283–351 298–362 284–354 284–354 279–328 299–343
∆T [K]
PT
1-ethyl-3-methylimidazolium tetrafluoroborate 1-ethyl-3-methylimidazolium tetrafluoroborate 1-ethyl-3-methylimidazolium trifluoromethanesulfonate 1-ethyl-3-methylimidazolium trifluoromethanesulfonate 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-ethyl-3-methylimidazolium dicyanamide 1-ethyl-3-methylimidazolium dicyanamide 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium tetrafluoroborate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium trifluoromethanesulfonate 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-hexyl-3-methylimidazolium tetrafluoroborate 1-hexyl-3-methylimidazolium tetrafluoroborate 1-butyl-1-methylpyrrolidinium thiocyanate 1-butyl-4-methylpyridinium thiocyanate 1-butyl-1-methylpyrrolidinium dicyanamide hexyltrimethylammonium bis[(trifluoromethyl)sulfonyl]imide N-butyl-3-methylpyridinium dicyanamide 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide 1-methyl-3-octylimidazolium tetrafluoroborate 1-octyl-3-methylimidazolium hexafluorophosphate 1-octyl-3-methylimidazolium hexafluorophosphate 1-butyl-3-methylimidazolium octyl sulfate trihexyl(tetradecyl)phosphonium tris(pentafluoroethyl)trifluorophosphate Overall R2
IL
Table 6: Comparison between three available methods ([5, 12, 13]) and the proposed GCM for estimating σ(T ) of ILs. This work AARD [%] 5.31 5.09 3.14 3.15 0.90 0.68 7.04 6.22 1.72 2.05 1.39 1.14 1.57 1.35 1.36 2.30 1.51 1.39 1.43 2.56 2.79 0.45 0.16 1.61 0.10 0.55 2.68 2.76 1.94 0.09 2.3% 0.983
ACCEPTED MANUSCRIPT
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0.08 0.06 0.04 0.02 0
−1 σ [N⋅m ]
SC 200
MA
NU
(a)
400
MW
600
800
0
200
0
200
400
MW
1000
(b)
ED
0.08 0.06 0.04 0.02 0
0
PT
0.08 0.06 0.04 0.02 0
AC CE
−1 σ [N⋅m ]
−1 σ [N⋅m ]
RI P
T
ACCEPTED MANUSCRIPT
600
800
1000
(c)
400
MW
600
800
1000
Figure 1: Surface tension as a function of the molecular weight for all ionic liquids used in this study. (a) Cation distribution, (b) anion distribution, and (c) total mass distribution.
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SC
RI P
T
ACCEPTED MANUSCRIPT
NU
30
MA
20
ED
0
PT
RD
10
AC CE
−10
−20
−30 0.015
0.02
0.025
0.03
0.035
0.04
σ [N⋅m−1]
0.045
0.05
0.055
0.06
0.065
Figure 2: Experimental surface tension versus the relative deviation obtained for the proposed method.
25
26
0.02
0.04
]
−1
σ (exp) [N⋅m
(d)
]
0.05
−1
σ (exp) [N⋅m
0.03
0.06
0.07
0.035
0.02
0.045
]
0.05 −1
0.045
0.055
0.06
0.031 0.031
0.032
0.033
0.034
0.035
0.036
0.037
0.025 0.025
0.03
0.035
0.04
0.032
0.035
0.035
T
0.034
−1 σ (exp) [N⋅m ]
0.033
(f)
−1 σ (exp) [N⋅m ]
0.03
(c)
RI P
SC
NU
0.04
MA
]
0.035
−1
σ (exp) [N⋅m
0.04
(e)
0.03
σ (exp) [N⋅m
0.025
ED
(b)
Figure 3: Accuracy in the estimation of σ(T ) of ILs using the proposed GCM for: (a) imidazolium, (b) ammonium (c) phophonium, (d) pyridinium, (e) pyrrolidinium, and (f ) piperidinium ILs. For all cases, black points is the correlation set, red points is the prediction set, and solid line is the expected value.
0.03 0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.015 0.015
0.02
0.025
PT
0.03
0.035
0.04
0.045
AC CE
0.02 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
0.01 0.01
0.02
0.03
0.04
0.05
0.06
)
(a
σ (calc) [N⋅m−1]
σ (calc) [N⋅m−1]
σ (calc) [N⋅m−1]
−1 σ (calc) [N⋅m ]
−1 σ (calc) [N⋅m ] −1 σ (calc) [N⋅m ]
0.07
0.036
0.037
0.04
ACCEPTED MANUSCRIPT
T
ACCEPTED MANUSCRIPT
RI P
Highlights
• The GCM was divided into individual GCMs according to the IL-type.
SC
• The GCM employs 10 structural cation groups and 30 structural anion groups.
AC CE
PT
ED
MA
NU
• The results show an AARD of 1.8% and a R2 of 0.98.
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