Predicting the Viscosity of Ionic Liquids by the ELM Intelligence

Sep 1, 2017 - ABSTRACT: Predicting the viscosity of ionic liquids (ILs) is crucial for their applications in chemical and related industries. In this ...
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Predicting the Viscosity of Ionic Liquids by the ELM Intelligence Algorithm Xuejing Kang,† Zhijun Zhao,*,‡ Jianguo Qian,*,§ and Raja Muhammad Afzal§ †

College of Materials and Chemical Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China § Beijing Key Laboratory of Ionic Liquids Clean Process, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡

ABSTRACT: Predicting the viscosity of ionic liquids (ILs) is crucial for their applications in chemical and related industries. In this study, a large data set of experimental viscosity data of ILs with a wide range of viscosity (7.83−142 000 cP), pressure (1−3000 bar), and temperature (258.15−395.32 K) are employed to build predictive models. The structures of cations and anions for 89 ILs are optimized, and the Sσ‑profiles descriptors are calculated using the quantum chemistry method.Two new models are developed by using extreme learning machine (ELM) intelligence algorithm with the temperature, pressure, and a number of Sσ‑profiles descriptors as input parameters. The coefficient of determination (R2) and average absolute relative deviation (AARD %) of the total sets of the two predictive models are 0.982, 2.21% and 0.951, 4.10%, respectively. The results show that the two ELM models are reliable for predicting the viscosity of ILs.

1. INTRODUCTION Ionic liquids (ILs) have many unique characteristics, i.e., low vapor pressure, high chemical stability, wide liquid temperature range, high ionic conductivity, good solvents for many compounds, and tunable properties, and so on.1−6 Due to their special potential usages, the various applications of ILs have been applied recent years in diverse fields including organic synthesis,7−11 electrochemical industry,12,13 chemical and biological catalysis reactions,1,14 industrial extraction and separation processes,15−19 and so on. It is estimated that more than 1018 ILs systems can be potentially synthesized with the combinations of cations and anions as well as modification their side chains.16,20 Thus, using experimental methods to measure all of the properties of ILs is almost impossible. Therefore, many researchers have employed some different methods to build models and predict the properties of ILs to provide guidance for their applications. The viscosity of ILs is one of the vital physical properties, which has great influence on its practical applications. In general, the viscosity of ILs is 2−3 orders of magnitude higher than traditional organic compounds.21 For example, the viscosity of toluene at room temperature is only 0.6 cP, while the viscosity of [Hmim][Tf2N] is 70 cP,22 and the viscosity of [NHH,(C2OH)2][OAc] even as high as 5647 cP.23 The high viscosity of ILs can be applied as a stationary phase of gas and liquid chromatography, lubricants, and so on. However, the high viscosity can reduce the transfer rate in the process of reaction and separation as well as increase the energy consumption in the process of industrial production. In order © 2017 American Chemical Society

to design a suitable viscosity of ILs, the researchers implemented vast research works to establish a prediction model and deeply understand the structure−activity relationship. Tochigi et al.24 developed a quantitative structure−property relationship (QSPR) model to better predict the viscosity of ILs and provide some useful theoretical data for the reverse design. However, there were only 300 data points and the value of the coefficient of determination (R2) was lower than 0.9, and the correlation results between experimental and calculated values were inferior for some ILs. In Han’s study,25 four QSPR models were established with the CODESSA software, which only can be used to predict the viscosity of ILs at 298.15 K and had some defects such as each model was built by limited data of imidazolium-based ILs. The QSPR model of Mirkhani et al.26 had 435 data points of 293 ILs based on 36 anions and 146 cations. The data set contained a wide viscosity scale (5.7− 2824 cP) and temperature scale (253−373 K), but the R2 is only 0.8096 and the absolute average deviations (AAD) is 8.77%. Chen et al.27 utilized CODESSA software to establish eight QSPR correlation equations at different temperatures (283, 293, 298, 303, 313, 323, 333, and 343 K). Although all of the R2 of these models are over 0.82, they can only be suitable for [Tf2N]− based ILs, and thus more valuable viscosity Received: Revised: Accepted: Published: 11344

July 3, 2017 August 28, 2017 September 1, 2017 September 1, 2017 DOI: 10.1021/acs.iecr.7b02722 Ind. Eng. Chem. Res. 2017, 56, 11344−11351

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Industrial & Engineering Chemistry Research Table 1. Temperature, Pressure, Viscosity Range, and Data Points for Different ILs32 no.

class

temperature (K)

pressure (kPa)

viscosity (cP)

data points

1 2 3 4 5 6 7 8

imidazolium pyridinium pyrrolidinium phosphonium ammonium morpholinium piperidinium sulfonium

258.15−395.32 283−353.15 283.1−353.1 293.15−303.15 283.1−353.1 298.15 298.15 253.15−313.15

100−300000 101.325 101.325 101.325 101.325 101.325 101.325 101.325

7.83−142000 10−464.49 13.1−167.8 268.63−2077.91 14.1−1017 466−1035 102−456 12.1−120

1380 62 20 8 17 2 5 15

prediction models are desired. Chen et al.28 built a QSPR model which covered a wide range of viscosities (3−2300 cP) and temperatures (258.25−433.15 K) at constant pressure. However, the application of their model is relatively narrow though the R2 is 0.9888 with only nine alkyl imidazole-based cations and eight anions, and the constant pressure were considered in their model. All the above-mentioned studies developed the viscosity predictive models at constant pressure, and although the viscosity of ILs at low pressure is influenced mainly by temperature, the influence of pressure at higher ranges becomes crucial for particular purposes.29 Therefore, it is necessary to establish new models to predict the viscosity of ILs at wider pressure and temperature ranges. Recently, Zhao et al.30 constructed two models with the multiple linear regression (MLR) and support vector machine (SVM) algorithms to predict the viscosity of ILs which based on 1079 experimental data points of 45 imidazolium-based ILs under pressure (1−3000 bar) and temperature (273.15− 395.32K). Their results showed that the linear model developed by the MLR is more inferior to the nonlinear model built by the SVM, but the mean-square error (MSE), average absolute relative deviation (AARD %), and R2 of the nonlinear model are 0.009, 3.95%, and 0.977 respectively. Paduszynsk et al.31 used more than 13 000 viscosity data points of 1484 ILs at different pressures (0.06−350 MPa) and temperatures (253−573 K) to build a new model, which utilized a two-layer feedforward artificial neural network (FFANN) approach. In their work, the input variables include temperature, pressure, and group contributions while the output is the viscosity. The results of the neural network training, validation, and testing set are good with the R2 values of of 0.986, 0.973, and 0.972, respectively, but the relative deviations are a little higher with 11.1, 13.8, and 14.7%, respectively. Zhao et al.32 used MLR and SVM to develop two new QSPR models based on wide temperatures (0.1−300 MPa) and pressures (273.15−395.32K) using conductor-like screening model for real solvents (COSMO-RS) molecular descriptors (Sσ‑profile). The total set R2 of MLR and SVM models are 0.803 and 0.944 respectively, and the AARD values are 10.68 and 6.58%, respectively, which are suitable for predicting viscosity of ILs at different temperatures and pressures. However, FFANN and SVM intelligent algorithms both have some disadvantages such as being time-consuming and should be better substituted by a more effective intelligent algorithm. Extreme learning machine (ELM) is a relatively new intelligent algorithm, which is successfully employed by Zhao et al.33−35 to first predict the properties of ILs (such as heat capacity). Hence, the ELM intelligent algorithm was used for the first time to develop novel QSPR models, which can predict viscosity of ILs using the Sσ‑profile input descriptors calculated by quantum chemistry method. First, the qualitative analysis of the

influence of the temperature, pressure, cations, and anions on the viscosity of ILs was performed. Next, the structures of cations and anions of 89 ILs are optimized, and the σ-profiles were calculated by quantum chemistry. Last, two new QSPR models were established based on the ELM algorithm and Sσ‑profile descriptors, and the comprehensive comparison of our developed QSPR models and previous studies was conducted in detail.

2. DATA AND METHODOLOGY 2.1. Collection of Viscosity Data of ILs. The experimental data points of ILs in this work were collected from the work published by Zhao et al.32 All of the 89 ILs including 1502 experimental viscosity data points were investigated. The used ILs contain different alkyl-substituted cations, such as pyridinium [Py] + ,imidazolium [Im] + , pyrrolidinium[Pyr]+, sulfonium [S]+, ammonium [N]+, piperidinium [Pip]+, phosphonium [P]+, morpholinium [Mor]+, and different anions, including ethylsulfate [EtSO4]−, tetrafluoroborate [BF4]−, trifluoromethyltrifluoroborate [CF3BF3]−, acetate [Ac]−, n-butylsulfate [C4SO4]−, trifluoromethylsulfonate [TfO]−, pentafluoroethyltrifluoroborate[C2F5BF3]−, nitrate [NO3]−, bis(trifluoromethylsulfonyl)imide [BTI]−, hydrogensulfate [HSO4]−, methylsulfate [MeSO4]−, thiocyanate [SCN] − , octylsulfate [C 8 SO 4 ] − , halide [X] − , bis(pentafluoroethylsulfonyl)imide [BETI] − , dicyanamide [DCA]−, hexafluorophosphate [PF6]−, and trifluoroacetate [TfA]−. Furthermore, the collected viscosity data covered a wide range of temperatures (253.15−395.32 K), viscosities (7.83−142 000 cP), and pressure (1−3000 bar). In addition, in order to compare with the previous work in detail, the same training and test sets used by Zhao et al.32 was employed in this work, and the number of different ILs categorized by the cation type was presented in Table 1. In addition, 80% of the total data points were selected as the training set (1205 data points), while the others were used as the test set (297 data points). 2.2. Calculation of the Sσ‑profile Descriptors. First, all the geometric optimizations were performed at the B3LYP/6-31+ +G** theoretical level by means of the Gaussian 09 B.01 software.36 The vibrational frequencies of all the structures were calculated to confirm no imaginary frequency and thus ensure the existence of energy minimum. Then, Gaussian 03 software 37 was employed to calculate and obtain the COSMO files of cations and anions of ILs. Last, the σ-profiles were obtained by using the COSMOtherm program.38 In this work, the σ-profiles were treated in six regions based on the polarity σ (e/Å2). As shown in Figure 1a,b, both of the σprofiles of independent counterions (anions and cations) were divided into 6 different parts respectively (SC1−6 and SA1−6, subscripts A and C mean anions and cations, respectively) by integrating those segments over the σ; thus, there were 12 11345

DOI: 10.1021/acs.iecr.7b02722 Ind. Eng. Chem. Res. 2017, 56, 11344−11351

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descriptors altogether. As presented in Figure 1c, there were 6 descriptors (S1−6) of the single σ-profiles of the combined ILs with S1 = SC1 + SA1, S2 = SC2 + SA2, S3 = SC3 + SA3, S4 = SC4 + SA4, S5 = SC5 + SA5, and S6 = SC6 + SA6. 2.3. Extreme Learning Machine. ELM is an easy-to-use and effective single hidden layer feed-forward neural network (SLFNs) learning algorithm, which was first proposed by Huang et al.39−41 The traditional neural network learning algorithm (e.g., back-propagation (BP) algorithm) need to have artificially set a large amount of network training parameters; meanwhile, the local optimal solution is a problem of this BP algorithm. However, the ELM only need to set the number of hidden layer nodes of networks, and it need not to adjust the network’s input weights and bias of hidden neurons. And the optimal solution can be easily obtained, thus the ELM has advantages of fast learning speed and good generalization capability. Because of these advantages, the ELM as a new machine learning method has been widely used in many fields.40 As shown in Figure. 2, the ELM model structure was composed of three parts, which were the input layers, hidden layers and output layers. First, the temperature (T), pressure (P), and a number of Sσ‑profiles descriptors were made of the input layer parameters, while the viscosities of ILs were the output layer parameters. The function of f1 was activation function, and f 2 was linear function, respectively. After determining f1 and f 2, the coefficient from the input layer to hidden layer was randomly distributed (Figure. 2a), so it is only necessary to determine the coefficient of the hidden layer to output layer and the number of neurons (Figure. 2b), with 1205 groups of data for training and 297 groups of data for the external test in this study. At last, the number of neurons can be determined when the optimal ELM model was obtained. 2.4. Model Validation and Performance. In order to assess the effectiveness of the obtained ELM model, the different statistical parameters such as relative deviation (RD %), R2, AARD %, and mean-square error (MSE) were used. These statistical parameters were shown as below: RD % = 100 × (ηical /ηiexp − 1.0) N

R2 =

(1)

N

∑i =P1 (ηiexp − ηm̅ )2 − ∑i =P1 (ηical − ηiexp)2 N ∑i =P1 (ηiexp − ηm̅ )2 NP

AARD % = 100 ×

∑ i=1

ηical − ηiexp ηiexp

(2)

/NP (3)

NP

MSE =

∑ (ηical − ηiexp)2 /NP i=1

(4)

where NP represents the total number of the whole data set, η denotes the viscosity of ILs, ηm̅ denotes the average viscosity of the experimental data, and the superscripts “exp” and “cal” denote experimental data and predicted value, respectively.

Figure 1. Solvent theoretical descriptors defined by COSMO σprofiles areas (σ-profile of representative cation 1-(2-hydroxyethyl)-3methylimidazolium OHEMIM+ (a), anion hydrogensulfate Ace− (b), and ionic liquid [HEMIM][Ace] (c) are used for illustration) in this study. SC1: −0.03 eÅ2 < σ < −0.02 eÅ2; SC2: −0.02 eÅ2 < σ < −0.01 eÅ2; SC3: −0.01 eÅ2 < σ < 0.00 eÅ2; SC4: 0.00eÅ2 < σ < 0.01 eÅ2; SC5: 0.01 eÅ2 < σ < 0.02 eÅ2; SC6: 0.02 eÅ2 < σ < 0.03 eÅ2; SA1: −0.03 eÅ2 < σ < −0.02 eÅ2; SA2: −0.02 eÅ2 < σ < −0.01 eÅ2; SA3: −0.01 eÅ2 < σ < 0.00 eÅ2; SA4: 0.00eÅ2 < σ < 0.01 eÅ2; SA5: 0.01 eÅ2 < σ < 0.02 eÅ2; SA6: 0.02 eÅ2 < σ < 0.03 eÅ2; S1 = SC1 + SA1; S2 = SC2 + SA2; S3 = SC3 + SA3; S4 = SC4 + SA4; S5 = SC5 + SA5; S6 = SC6 + SA6; subscripts C and A mean cations and anions, respectively.

3. RESULT AND DISCUSSION 3.1. Qualitative Analysis of the Viscosity of ILs. As shown in Figure 3, the viscosities of ILs become lower as the temperatures increased, which means the inverse relationship is presented between temperature and viscosity, and it is same with the result of Chen et al.28 On the contrary, Figure 4 11346

DOI: 10.1021/acs.iecr.7b02722 Ind. Eng. Chem. Res. 2017, 56, 11344−11351

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Industrial & Engineering Chemistry Research

Figure 2. Network structure of the ELM model used in this study. y = − 0.017T − 9.377SA4 − 20.228SA5 + 3.97 × 10−6P − 31.391SA2 + 10.026SA3 + 1881.512SA1 + 22.985SC2 + 5.927SC3 − 6.555SA6 − 4152.905SC1 + 1.182SC4 + 0.266SC5 + 7.324 (n = 1502, R2 = 0.765, AARD % = 105.4%)

(5)

In this model, y is the viscosity of ILs, T is temperature, P is pressure, S is the charge distribution area, and the subscripts C and A denote cations and anions, respectively. In eq 5, the positive sign in front of the descriptors represents positive correlation, and the negative sign means negative correlation, respectively. In addition, the importance of descriptors sort according to the t value presents a descending order, and that means the first item of the eq 5 plays vital role in the determination of the most important descriptor. Consequently, the temperature is the most important descriptor, which is consistent with Zhao’s work,32 while the negative sign in the front reveals that the viscosity of ILs increases with the decrease of the T. The second and the third most important descriptors are SA4 in the nonpolar range (0.00 eÅ2 < σ < 0.01 eÅ2) and SA5 in the polar range (0.01 eÅ2 < σ < 0.02 eÅ2), and both of them have the negative sign which means that the inverse relationships are presented between them and viscosity. The reason may be that the negative charge of the anion cannot be effectively distributed; thus, the coulomb force increases which causes the increase of the viscosity.32 The fourth descriptor is P; the positive sign of this descriptor discloses that the pressure contributes positively to viscosity. The subsequent three descriptors are SA2, SA3, and SA1, followed by SC2, SC3, SA6, SC1, SC4, and SC5 in turn, which indicated that anions played more important roles than cations to the viscosity of ILs.32 Qualitative rules can be gotten by eq 5, but the quantitative results were poor due to the AARD % of the training set. Those of the whole data set were 108.8 and 105.4%, respectively. As depicted in Figure 5, the calculated viscosities were not in good agreement with the corresponding experimental viscosities. As shown in Figure 6, 13.1% of the relative deviation of the ILs is above 20%, and almost 40% of the ILs is above 10%, which indicated that the viscosity of ILs does not follow a simple linear rule. Therefore, it is needed to establish nonlinear predictive models. 3.2. Results of the ELM model based on independent counterions σ-profile. In order to obtain accurate quantitative results, the nonlinear model was established by ELM based on the subset of descriptors. The input descriptors were the T, P, SC1−6 of cations, and SA1−6 of anions, respectively.

Figure 3. Viscosity−temperature relationship for ILs.

Figure 4. Viscosity-pressure relationship of ILs.

illustrated that the viscosities of ILs become larger as the pressures increase. The above results were consistent with the general knowledge of chemical thermodynamics. In order to validate the importance of the descriptors, multiple linear regression (MLR) was used to establish a simple linear model using the enter method (eq 5). Because the SC6 descriptors of all the ILs in this study are zero; thus, there were 13 input descriptors left (T, P, SC1−5 of cations and SA1−6 of anions). 11347

DOI: 10.1021/acs.iecr.7b02722 Ind. Eng. Chem. Res. 2017, 56, 11344−11351

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Figure 7. AARD % and R2 of the ELM1 model versus the number of neurons for the training and test sets. Figure 5. Calculated versus experimental viscosities of the linear model in this study.

Figure 8. Calculated versus experimental viscosities of the ELM1 model in this study. Figure 6. Relative deviation of the linear model in this study.

In this model (called ELM1), the function of f1 used the sigmoid function, and f1 employed a linear function. The next step is to optimize the number of neurons between the input and hidden layers. In the process of optimizing, it can be seen in Figure 7 that the R2 of test set began to dramatically decrease and the AARD % of test set began to increase when the number of neurons over 200. Thus, the optimal model was obtained when the number of neurons was 200. The optimal network structure in this study is 13−200−1. The R2 and AARD of the test set and total data were 0.971, 0.983 and 2.53,2.21%, respectively. The Figure 8 indicated the calculated viscosity values (triangle points) were close to the experimental viscosity values (diamond points), which demonstrated the ELM1 model is reliable. As shown in Figure 9, 89.7% data points of the ELM1 model were calculated within 5% deviations, while only 0.2% of data points of over 20% deviations. These results also showed that the relationship between the ionic liquid viscosity and Sσ‑profile is not a simple linear relationship but the nonlinear relationship which can predict viscosity of ILs reasonably. 3.3. Results of the ELM Model Based on Single σProfile. On the basis of the training set and test set used above,

Figure 9. Relative deviation of the ELM1 model in this study.

using T, P, and the S1−6 (six descriptors shown in Figure 1c) as the input descriptors, a new model (here called ELM2) was established. First, the optimum number of neurons (125) was confirmed by the same optimizing process with ELM1. The 11348

DOI: 10.1021/acs.iecr.7b02722 Ind. Eng. Chem. Res. 2017, 56, 11344−11351

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Industrial & Engineering Chemistry Research calculated and experimental viscosities of the ELM2 model were shown in Figure. 10, and it is obvious that the calculated values

Table 2. Comparison of Different Models for Viscosities of ILs model ELM1

ELM2

SVM32

data set

no.

R2

MSE

AARD

training set test set total set training set test set total set training set test set total set

1205 297 1502 1205 297 1502 1205 297 1502

0.985 0.971 0.982 0.957 0.928 0.951 0.948 0.930 0.944

0.004 0.002 0.006 0.012 0.005 0.017 0.021 0.025 0.022

2.13 2.53 2.21 4.00 4.49 4.10 6.58 6.75 6.58

viscosity of ILs over wide temperature and pressure ranges. The reason may be that the input parameters of ELM1 model (Sσ‑profile) had more comprehensively represented molecular microstructure information than the ELM2 model and the SVM model established in the literature.32 The percent of values in different deviation ranges of these models were summarized in Figure 12. It can be seen that the Figure 10. Calculated versus experimental viscosities of the ELM2 model in this study.

(triangle points) and the experimental values (diamond points) were also close to each other in this model. The R2 of the test set and total data in this model are 0.928 and 0.951, respectively, and the AARD are 4.494 and 4.100%, respectively. As shown in Figure 11, 71.6% of data points of the ELM2

Figure 12. Percent of value in different deviation ranges of the different models.

deviations (89.7%) of total calculated viscosities of ELM1 and the deviations (71.6%) of ELM2 are within 0−5%, while there are only 42.1% of the deviations within the same range in SVM model. In contrast, the percent of deviations within 5−10% is 7.4% in ELM1 model and 9.5% in ELM2 model which is lower than that (35.2%) in SVM model. Similarly, the same results can be obtained in the range of over 10%. These results also indicated that ELM models are better than the SVM model32 for predicting the viscosity of ILs. The different predictive models from literature (GC, QSPR, ANN, SVM, etc.) were comprehensively summarized in Table 3. It can be observed that the ELM1 model has the minimum AARD %, while some of other models can only be used to predict the viscosity of ILs at constant pressure. Because of different input parameters in different models, we cannot directly compare with the above-mentioned models, but the two ELM models in this work both have relatively good results (low AARD, small amounts of input parameters, and wide temperature and pressure ranges). In addition, it is worth mentioning that the required time of the two ELM models was

Figure 11. Relative deviation of the ELM2 model in this study.

model were calculated within 5% deviations, and only 1.5% of data points of over 20% deviations, which means the ELM2 model using eight descriptors also can predict the viscosity of ILs effectively. 3.4. Comparison between This Work and the Previous Publications. The R2, MSE, and AARD % of the ELM1, ELM2 models in this work and the SVM model in the study of Zhao et al.32 were compared in Table 2. As shown in Table 1, the R2, MSE, and AARD % of the total set of ELM1 and ELM2 models are 0.982, 0.006, and 2.21% and 0.951, 0.017, and 4.10%, respectively, which are better than the SVM model. Therefore, the ELM models (especially ELM1) based on ELM algorithm and Sσ‑profile descriptors could be suitable for predicting the 11349

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Industrial & Engineering Chemistry Research Table 3. Comparison of Different Models for Viscosities of ILs

a

method

Npa

NILa

Trange/K

pressure/MPa

GC GC correlation QSPR+GC QSPR QSPR GC(ANN) QSPR+GC MLR SVM MLR SVM ELM1 ELM2

13 12

29 25 72 300b 125 293 1484 26 45 45 89 89 89 89

293−393 293−393 253−373 263−353 298 253−373 253−573 258.15−433.15 273.15−395.32 273.15−395.32 253.15−395.32 253.15−395.32 253.15−395.32 253.15−395.32

0.1 0.1 0.1 0.1 0.1 0.1 0.06−350 0.101 0.1−300 0.1−300 0.1−300 0.1−300 0.1−300 0.1−300

27 24 7 242 17 6 6 7 7 13 8

AARD % 7.7 7.7

a little poor 8.77 11.4 2.45 24.2 3.95 10.67 6.58 2.21 4.10

ref 42 43 44 24 45 26 31 28 30 30 32 32 this work this work

NIL is the number of ILs, and Np is the number of parameters. bData points. quantitative structure−activity relationship method. J. Hazard. Mater. 2014, 278, 320−329. (4) Zhao, Z. J.; Dong, H. F.; Zhang, X. P. The Research Progress of CO2 Capture with Ionic Liquids. Chin. J. Chem. Eng. 2012, 20 (1), 120−129. (5) Galán Sánchez, L. M.; Meindersma, G. W.; de Haan, A. B. Kinetics of absorption of CO2 in amino-functionalized ionic liquids. Chem. Eng. J. 2011, 166 (3), 1104−1115. (6) Lei, Z. G.; Dai, C. N.; Liu, X.; Xiao, L.; Chen, B. H. Extension of the UNIFAC Model for Ionic Liquids. Ind. Eng. Chem. Res. 2012, 51 (37), 12135−12144. (7) Dupont, J.; de Souza, R. F.; Suarez, P. A. Ionic liquid (molten salt) phase organometallic catalysis. Chem. Rev. 2002, 102 (10), 3667− 3692. (8) Li, G. H.; Zhang, S. J.; Li, Z. X.; Li, M. X.; Zhang, X. P. Effect of ionic liquid on the oxidative esterification from methacrolein to methyl methacrylate. Chem. J. Chin. Univ.-Chin. 2004, 25 (6), 1138−1140. (9) Zhang, S. J.; Chen, Y. H.; Ren, R. X.-F.; Zhang, Y. Q.; Zhang, J. M.; Zhang, X. P. Solubility of CO2 in sulfonate ionic liquids at high pressure. J. Chem. Eng. Data 2005, 50 (1), 230−233. (10) Zhang, S. J.; Li, X.; Chen, H. P.; Wang, J. F.; Zhang, J. M.; Zhang, M. L. Determination of physical properties for the binary system of 1-ethyl-3-methylimidazolium tetrafluoroborate+H2O. J. Chem. Eng. Data 2004, 49 (4), 760−764. (11) Biswas, A.; Shogren, R.; Stevenson, D.; Willett, J.; Bhowmik, P. K. Ionic liquids as solvents for biopolymers: Acylation of starch and zein protein. Carbohydr. Polym. 2006, 66 (4), 546−550. (12) Vila, J.; Gines, P.; Rilo, E.; Cabeza, O.; Varela, L. Great increase of the electrical conductivity of ionic liquids in aqueous solutions. Fluid Phase Equilib. 2006, 247 (1), 32−39. (13) Widegren, J. A.; Saurer, E. M.; Marsh, K. N.; Magee, J. W. Electrolytic conductivity of four imidazolium-based room-temperature ionic liquids and the effect of a water impurity. J. Chem. Thermodyn. 2005, 37 (6), 569−575. (14) Yang, Z.; Pan, W. B. Ionic liquids: Green solvents for nonaqueous biocatalysis. Enzyme Microb. Technol. 2005, 37 (1), 19− 28. (15) Han, X. X.; Armstrong, D. W. Ionic liquids in separations. Acc. Chem. Res. 2007, 40 (11), 1079−1086. (16) Huang, Y.; Dong, H. F.; Zhang, X. P.; Li, C. S.; Zhang, S. J. A new fragment contribution-corresponding states method for physicochemical properties prediction of ionic liquids. AIChE J. 2013, 59 (4), 1348−1359. (17) Huddleston, J. G.; Willauer, H. D.; Swatloski, R. P.; Visser, A. E.; Rogers, R. D. Room temperature ionic liquids as novel media for ‘clean’liquid−liquid extraction. Chem. Commun. 1998, 16, 1765−1766. (18) Nasir Shah, S.; Kallidanthiyil Chellappan, L.; Gonfa, G.; Mutalib, M. I. A.; Pilus, R. B. M.; Bustam, M. A. Extraction of naphthenic acid

only 1.0529 and 0.9363 s on an Intel 1.9 GHz laptop computer with 4 GB of RAM.

4. CONCLUSIONS Lots of experimental viscosity data points based on wide temperature and pressure ranges were selected first to predict the viscosity of ILs and provide some reliable models. Next, the multiple-linear model was made with the temperature, pressure, and a number of Sσ‑profiles descriptors as the dependent variables, and it is shown that the temperature, pressure, and the Sσ‑profiles of the anions have vital influence on the viscosity of ILs. Then, two nonlinear models (ELM1 and ELM2) were developed which included 13 and 8 input parameters, respectively. The ELM models have good performance based on both wider temperature and pressure ranges, and the AARD % of the total set of the ELM1 and ELM2 models were only 2.21 and 4.10%, respectively. By comparing with other models, it was verified that the models established by ELM have better correlativity and stability for the total data set. Thus, the two ELM models proposed in this work can be suitable to predict the viscosity of ILs.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Zhijun Zhao: 0000-0003-0203-9091 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Beijing Natural Science Foundation (No. 2164062), and State Key Laboratory of Chemical Engineering (No. SKL-ChE-15A01).

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