Prediction of Henry's law constant of CO2 in ionic liquids based on SEP and Sσ-profile molecular descriptors

Accepted Manuscript Prediction of Henry's law constant of CO2 in ionic liquids based on SEP and Sσ-profile molecular descriptors

Xuejing Kang, Chunjiang Liu, Shaojuan Zeng, Zhijun Zhao, Jianguo Qian, Yongsheng Zhao PII: DOI: Reference:

S0167-7322(17)35901-9 doi:10.1016/j.molliq.2018.04.026 MOLLIQ 8929

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

11 December 2017 27 March 2018 6 April 2018

Please cite this article as: Xuejing Kang, Chunjiang Liu, Shaojuan Zeng, Zhijun Zhao, Jianguo Qian, Yongsheng Zhao , Prediction of Henry's law constant of CO2 in ionic liquids based on SEP and Sσ-profile molecular descriptors. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Molliq(2017), doi:10.1016/j.molliq.2018.04.026

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ACCEPTED MANUSCRIPT Prediction of Henry’s law constant of CO2 in ionic liquids based on SEP and Sσ-profile molecular descriptors Xuejing Kanga,1, Chunjiang Liub,1, Shaojuan Zengc,*, Zhijun Zhaod,*, Jianguo Qianc, Yongsheng Zhaoa,e a

Key Laboratory for Thin Film and Microfabrication of Ministry of Education, Department of

b

Department of Mathematics, Reed College, Portland, Oregon, 97202, USA

Department Beijing Key Laboratory of Ionic Liquids Clean Process, Key Laboratory of Green Process and

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c

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Micro/Nano-electronics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

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Engineering, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, 100190, China State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University,

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d

Beijing, 100084, China

Department of Chemical Engineering, University of California, Santa Barbara, California

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e

93106-5080, USA

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Abstract: Nowadays, greenhouse gas CO2 emissions have caused serious global warming

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problems. Unique properties of ionic liquids (ILs), such as negligible vapor pressure, good thermal and chemical stability, high gas dissolution capacity, etc., have made them highly promising in

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capturing CO2 . Although researchers have done a lot of experimental work using ILs to capture

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CO2, time-consuming and high experimental economic costs have led to a strong interest in establishing predictive models. In this work, 297 experimental data points including 16 cations and 9 anions for 34 ILs are collected and the structures of cations and anions are optimized by quantum chemistry. Then the electrostatic potential surface area (SEP) and charge distribution area (Sσ-profile) descriptors are calculated and used to predict the Henry’s law constant (HLC) of CO2 in ILs. Three new models, namely, the multiple linear regression (MLR), support vector machine 

Corresponding author, Tel./Fax: 8058374996 E-mail addresses: [email protected], [email protected], [email protected] 1 The authors contributed equally. 1

ACCEPTED MANUSCRIPT (SVM), and extreme learning machine (ELM) are finally developed based on the above-calculated descriptors. Results show that the ELM model with AARD=3.22% for the entire data set is the most valid and powerful one to predict the HLC of CO2. Keywords: Energy gases; Quantum chemistry; Ionic liquids; CO2; Extreme learning machine

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1. Introduction

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Emissions of greenhouse gases[1, 2] (mainly carbon dioxide or CO2) have caused a serious

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problem-global warming, which has resulted in great concern from the international community. The data released by the International Energy Agency show that global CO2 emissions are about

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32.1 billion tons in 2016[3]. In addition, there is a certain amount of CO2 impurities in many

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energy sources (such as natural gas, shale gas, biogas, syngas, etc.), which reduces the heating values of the energy gases, resulting in a significant increase in the cost of transportation, storage

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and use of the gases[4]. Therefore, the development of efficient CO2 capture and separation

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method is a common concern of the scientific community, and is one of the hot topics in the field of chemical engineering[5-7]. Solvent scrubbing is one of the most commonly CO2 capture and

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separation approaches used in industry[8]. However, the commercial absorbents (such as

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methyldiethanolamine) generally suffer from the disadvantages of high energy consumption, high economic cost, and easy volatilization that pollutes the environment and products[9, 10]. In order to solve the above problems, the use of new green solvent is urgently desired. Ionic liquids (ILs) have been widely concerned by many researchers and are generally considered to be green solvents because of their unique physical and chemical properties, particularly their low vapor pressure and adjustable structures and properties, which show a huge potential for application in CO2 capture[11-13] and separation[14-17]. 2

ACCEPTED MANUSCRIPT Considerable research efforts have been devoted to capturing CO2 with ILs, however, owing to the huge number of ILs which can be synthesized[18, 19], it is uneconomic and time-consuming to obtain the ideal ILs with high performance only using experimental methods[20-22], and thus it is imperative to be estimated via establishing a prediction mode.

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Currently, the common property prediction models involve empirical correlation model,

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UNIQUAC model, COSMO-RS model, artificial neural network(ANN) model[23] and

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quantitative structure–property relationship (QSPR)[24]. Among them, the QSPR approach has the advantage of high prediction accuracy, which has been intensively employed to predict the

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viscosity, toxicity, heat capacity and H2S solubility in ILs and so on[25-28]. Because the ILs are

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extensively used in gas capture and separation fields, a few studies about predicting the Henry’s law constant (HLC) of CO2 in ILs have been done[29, 30]. Eike et al.[29] correlated values of

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infinite-dilution activity coefficients for 38 solutes in three ILs: [bmpyr][BF4], [emim][Tf2N], and

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[emmim][Tf2N]. The octanol-water partition coefficients, dipole moments, and other calculated descriptors were used as input parameters. In addition, they predicted the HLC in [emim][Tf2N]),

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and [emmim][Tf2N] at two different temperatures (283 and 298 K). However, the average

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deviation was higher than 20%. Recently, Ghaslani et al.[30] developed two QSPR models for predicting the HLC of CO2 in 32 ILs using multiple linear regression (MLR) and support vector machines (SVM) algorithms. The absolute relative deviations of the two QSPR models for the test set were 6.33% and 4.42%, respectively. The results indicated the two QSPR models are reliable, predictive and stable, however, the nonlinear model (SVM) has higher accuracy than the linear one (MLR). Compared with the SVM, another powerful intelligence algorithm, namely, extreme learning 3

ACCEPTED MANUSCRIPT machine (ELM) has received much attention[31, 32]. This algorithm was firstly proposed by Huang et al.[33, 34], and has lots of advantages such as fast prediction speed, high prediction accuracy, and good generalization ability, etc. In addition, many investigations have demonstrated the critical importance of molecular descriptors, which are known to have more significant effect

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than the choice of machine learning algorithm[35]. Charge distribution area (Sσ-profile) descriptors

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are calculated by the conductor-like screening model (COSMO)[36], have been effectively used to

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predict the properties of ILs[37]. In our recent work, electrostatic potential surface area (SEP) descriptors have been successfully used to predict the toxicity of ILs[38]. Thus, in this work, the

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SEP and Sσ-profile descriptors, as well as ELM algorithm would be employed together to predict the

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HLC of CO2 in ILs.

In this study, 16 cations and 9 anions for 34 ILs were collected and the structures of them

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were optimized firstly. Then the Sσ-profile and SEP molecular descriptors were calculated using the

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quantum chemistry method. By using the above-obtained descriptors, three QSPR models were developed based on the MLR, SVM, and ELM algorithms. In order to define the applicability

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domain (AD) of the established models, the Williams plots were used to visualize the AD and

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check the presence of outliers. 2. Theory and algorithms 2.1 Multiple linear regression (MLR) MLR is an algorithm often used for predicting models[39, 40], which can express the relationship between input variables(x) and the output variables (y). The general equation of MLR model is presented as follows: y  1 x1  2 x2  n xn  0 4

(1)

ACCEPTED MANUSCRIPT where βi (i=0, 1, …, n) represents the parameters of the input variables, and the number of n is determined by screening in the modeling process. 2.2 Support Vector Machine (SVM) SVM, a machine learning approach, was proposed by Vapnik and co-workers[41] and has

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been widely utilized to effectively deal with nonlinear regression problems[42]. The independent

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variables in the SVM[43, 44] are firstly mapped into a high-dimensional or infinite-dimensional

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characteristic space using kernel function, and subsequently the linear regression is developed in the characteristic space. The nonlinear problem can be solved in the linear space by the nonlinear

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characteristic mapping. The option of kernel function and its parameters are the key factors for the

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generalization performance of SVM. Therefore, it is very important to select the kernel function and determine the corresponding parameters. The Gaussian radical basis function (RBF) kernel

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with the efficient and fast advantages is commonly used for solving regression problems and also

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employed in this work (shown in equation 2).



k  u, v   exp r  u  v

2



(2)

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where r stands for the parameter of kernel, u and v represent two independent variables.

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2.3 Extreme learning machine (ELM) ELM was proposed by Huang et al.[34, 45-47]. Compared to the conventional neural network, such as artificial neural network (ANN), and SVM, one of the most important features of ELM is that it is faster than the conventional learning algorithm while ensuring the accuracy of learning. The output function of ELM[34, 47-50] is fL(x) as shown in equation (3), where T   1 , 2 ,......, L  is the weight vector between the hidden layer and the output layer,

h x   h1 , h2 ,......, hL  is a nonlinear feature mapping, for example, the input vector of the hidden 5

ACCEPTED MANUSCRIPT layer is x, h(x) is the output of the hidden layer node. Different hidden nodes are allowed to have different activation functions. In practical applications, h(x) is the same function, G(ai, bi, x) ( as shown in equation (4)), and this function is a nonlinear piecewise continuous function that satisfies the universal approximation ability theorem. In general, ELM training is divided into two

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stages: random feature mapping and linear parameter solving. In the first stage, the ELM

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randomly initializes the hidden layer and maps the input data to the feature space by a nonlinear

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mapping function. In the second stage, the connection weight between the hidden layer and the output layer is solved by the equations (5) and (6), where H is the randomization matrix and T is

L

f L  x    i hi  h( x)

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i 1

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the target matrix of the training data (equations (7) and (8)).

h( x)  G (a i , bi , x ), a i  R d , bi  R 2

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min H  T

  H'T

(3) (4) (5)

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(6) (7)

 t1T   t11 ... t1m    T   ...    ... ... ...  t NT  t N 1 ... t Nm   

(8)

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 h( x1 )   h( x1 ) ... hL ( x1 )  H   ...    ... ... ...   h( xN )   h( xN ) ... hL ( xN ) 

3. Materials and methods 3.1 Data preparation and analysis The accuracy of the established models is directly affected by the reliability of the experimental data points. Experimental HLC values for CO2 were collected from the literature at different temperatures. If the experimental values have multiple data sources, the HLC values that 6

ACCEPTED MANUSCRIPT differ significantly from other literature reports will not be used. For example, as shown in Figure S1 in supporting information, only the HLC values for [BMIM][BF4] from the references in Table 1 were employed in this work. After carefully analysis, 34 ILs for CO2 capture were finally selected to build the QSPR models. The dataset contains 297 data points for HLC of CO2 in ILs,

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which includes 16 cations and 9 anions. The abbreviations of ILs, range of temperatures, and the

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number of data points for each IL coupled with their references are presented in Table 1. The

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structures of cations and anions were geometrically optimized by the Gaussian 09 B.01 software[51] at the theoretical level of B3LYP/6-31++G** and provided in Figure 1.

HLC

Range (K)

[1,3BMPY][Tf2N]

283.15-323.15

[BMIM][BF4]

283.15-323.15

ILs

1 2

Data

AARD%

AARD%

AARD%

Range(MPa)

Points

(MLR)

(SVM)

(ELM)

2.60-4.60

6

14.65

2.25

1.37

[52]

4.18-8.86

3

17.25

6.85

2.74

[53]

6.16-12.34

11

11.51

4.48

0.87

[54]

4.19-8.40

6

19.59

5.47

2.47

[52]

303.00-323.00

6.60-9.16

3

4.81

5.01

6.06

[55]

298.15-323.15

5.58-8.77

3

12.74

1.56

1.74

[56]

294.00-363.00

5.13-15.74

10

13.37

1.00

0.17

[57]

303.00

5.90

1

7.74

2.29

4.11

[58]

298.15-333.15

5.34-8.13

2

12.05

8.94

8.62

[59]

283.15-323.15

3.87-8.13

3

9.10

1.76

1.86

[60]

283.15-323.15

3.88-8.13

3

9.00

1.84

1.95

[53]

298.00-393.15

4.71-18.91

6

13.22

4.57

3.00

[61]

283.15-343.04

3.78-10.96

14

7.83

1.22

1.26

[62]

313.15

4.10

1

2.97

2.94

3.88

[63]

298.15-333.15

3.30-4.87

2

22.10

9.47

9.92

[59]

298.15

3.70

1

31.42

12.18

9.59

[64]

283.15-323.15

2.53-4.87

3

27.04

4.46

2.85

[53]

313.15

3.70

1

7.50

14.07

15.11

[65]

283.15-323.15

2.80-5.10

6

27.13

7.88

4.94

[52]

303.00-323.00

3.34-4.77

3

5.70

3.93

5.18

[55]

283.36-343.79

2.39-6.70

14

12.02

1.84

1.88

[66]

400.00-500.00

12.10-22.40

3

1.34

1.01

0.07

[67]

303.38-344,27

[BMIM][DCA]

4

[BMIM][PF6]

5

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3

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283.15-323.15

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Temperature

No.

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Table 1. The temperature range, data points and AARD% in different models for each IL

[BMIM][Tf2N]

References

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[BMIM][TFA]

294.00-363.00

3.40-13.57

10

20.46

11.93

4.42

[68]

7

[BMPYR][eFAP]

283.50-323.30

2.03-4.45

3

27.97

12.04

1.26

[69]

8

[BMPYR][Tf2N]

283.15-323.15

3.02-5.61

3

18.90

12.85

7.79

[53]

7

ACCEPTED MANUSCRIPT 298.15

6.39

1

19.24

1.57

0.00

[70]

10

[BPY][Tf2N]

298.15-333.15

3.20-5.17

3

14.87

5.96

7.74

[70]

11

[BPY][TFA]

298.15

5.69

1

2.91

1.76

0.01

[70]

12

[BzMIM][Tf2N]

298.15-313.15

3.99-6.35

2

15.31

18.76

1.91

[71]

13

[C5MIM][Tf2N]

298.15-363.15

2.88-9.43

9

8.97

9.32

6.85

[72]

14

[C7MIM][Tf2N]

313.15

3.60

1

18.97

2.78

0.02

[65]

15

[DMIM][BF4]

298.15-323.15

2.90-4.34

3

63.39

53.41

2.37

[56]

16

[DMIM][Tf2N]

313.15

3.70

1

52.02

2.71

0.06

[65]

17

[EMIM][BF4]

298.20-313.20

9.74-13.02

2

21.11

20.50

10.19

[73]

298.15-343.15

8.00-16.00

4

10.74

3.09

[74]

303.00

7.80

1

11.00

11.06

0.13

[58]

313.15

9.60

1

0.33

6.08

2.03

[56]

8.36

19

[EMIM][EtSO4]

303.15

9.78-17.90

6

8.25

1.30

1.88

[75]

20

[EMIM][eFAP]

283.00-363.00

2.24-7.71

9

15.48

2.05

1.03

[76]

21

[EMIM][Tf2N]

303.00

3.90

1

9.94

0.15

0.67

[58]

313.15

4.80

1

9.63

2.09

3.37

[63]

313.15-333.15

4.66-6.40

3

12.76

1.02

0.47

[72]

303.45

3.95-3.96

2

9.51

0.67

1.26

[77]

283.43-343.07

2.49-7.30

5

10.60

2.70

4.81

[66]

303.63-344.23

3.81-7.29

14

15.14

3.65

3.08

[78]

3.77

1

1.39

6.27

5.77

[79]

3.40-26.20

5

8.84

4.95

3.19

[67]

3.90-7.80

4

4.50

6.14

6.31

[74]

3.90

1

1.99

9.40

8.91

[71]

298.15 300.00-500.00

298.15

D

298.15-343.15

[EMIM][TfO]

3.59-5.71

3

8.66

1.84

2.42

[56]

303.00

7.30

1

33.87

35.08

0.32

[58]

313.15

7.12

1

18.51

20.60

0.34

[56]

303.15-353.15

10.80-19.80

6

14.89

2.24

0.22

[75]

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298.15-323.15 22

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[EMIM][DCA]

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18

SC

PT

[BPY][DCA]

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9

[HEMIM][BF4]

24

[HEMIM][PF6]

303.15-353.15

8.94-16.50

6

6.90

0.83

1.42

[75]

25

[HEMIM][Tf2N]

303.15-353.15

4.42-7.69

6

40.76

1.23

0.94

[75]

26

[HEMIM][TfO]

303.15-353.15

6.14-9.73

6

14.09

1.67

0.76

[75]

27

[HMIM][eFAP]

298.15-333.15

2.52-4.20

2

29.05

2.83

1.37

[59]

283.50-323.30

1.85-3.66

3

48.36

10.41

3.90

[69]

313.15

4.00

1

4.13

1.75

1.12

[63]

298.15

3.50

1

31.60

12.58

7.05

[64]

288.48-343.20

2.46-5.82

11

18.38

2.28

6.58

[80]

300.00-500.00

2.90-19.10

5

13.54

4.93

3.75

[67]

298.15-343.5

3.40-6.40

4

11.45

7.92

6.46

[73]

298.15

4.40

1

45.57

30.46

26.06

[71]

298.15-313.15

3.16-4.56

2

20.06

8.49

7.12

[81]

313.15

4.03

1

4.85

2.48

0.37

[56]

283.15-333.15

2.42-4.56

3

36.99

7.70

6.73

[59]

283.15-333.15

2.54-4.62

3

26.92

6.77

3.51

[59]

29

AC

28

CE

23

[HMIM][Tf2N]

[HMPY][Tf2N]

8

ACCEPTED MANUSCRIPT 298.15-313.15

3.28-4.62

2

4.04

6.84

6.64

[81]

30

[N4,1,1,1][Tf2N]

290.17-343.07

2.79-7.00

11

5.35

1.90

1.35

[66]

31

[OMIM][BF4]

303.00-323.00

5.39-7.56

3

2.45

2.72

0.65

[55]

32

[OMIM][Tf2N]

298.15

3.00

1

81.27

3.34

0.03

[64]

300.00-500.00

2.20-18.50

5

17.94

8.46

8.66

[67]

[OPY][Tf2N]

298.15-333.15

2.79-4.22

3

27.49

3.34

0.29

[70]

34

[P6,6,6,14][MeSO3]

307.45-322.15

2.04-2.65

4

14.30

2.66

1.58

[82]

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33

Figure 1. The structures of cations and anions in this study

3.2 Calculation of the SEP and Sσ-profile descriptors 9

ACCEPTED MANUSCRIPT The option of descriptors has vital effects on the performance of predictive models. In this work, the SEP and Sσ-profile descriptors are employed for the development models. Based on the obtained optimal structures of isolated cations and anions, the SEP and Sσ-profile were calculated by different programs. Firstly, the COSMO files of isolated cations and anions were obtained using

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Gaussian 03 software[83], and then the σ-profiles of them were calculated by a MATLAB code

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(rewritten by our group) which was got via referring the σ-profiles generation program[84, 85].

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The range of each σ-profile is from -0.03 to 0.03 e/Å2 and the step size is 0.001 e/Å2, thus there are 61 segments for each ion. Figure 2 shows the σ-profiles and their corresponding COSMO

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surfaces of representative cation (1-decyl-3-methy-imidazolium) and anion (ethylsulfate). As seen

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from Figure 2, the darker color (blue or red) means the stronger polarity of the cation or anion. The calculations of SEP for isolated cations and anions are achieved using the Multiwfn

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software[86] with the ranges of 0 ~ 200 kcal/mol for cations, -200 ~ 0 kcal/mol for anions (the

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step size is 0.5 kcal/mol). The electrostatic potential surfaces of the same representative

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1-decyl-3-methy-imidazolium cation and ethylsulfate anion are presented in Figure 3.

10

ACCEPTED MANUSCRIPT

50

1-decyl-3-methyl-imidazolium ethylsulfate

40

x

p (s)

30

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20

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10

-0.03

-0.02

-0.01

0.00 2

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0

0.01

0.02

0.03

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[e/Å ]

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Figure 2. The Sσ-profile of a representative cation and anion of ILs used in this study.

1-decyl-3-methyl-imidazolium ethylsulfate

6

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4

3

2

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2

Surface area(Å )

5

AC

1

0

-150

-100

-50

0

50

100

150

Electrostatic potential (kcal/mol)

Figure 3. The SEP of a representative cation and anion of ILs used in this study.

3.3 Model development and validation In this study, three algorithms, namely, MLR, SVM, and ELM have been utilized for calculating HLC in diverse ILs. The dataset was randomly divided into two parts which are 11

ACCEPTED MANUSCRIPT training set (238 data points, 80% of the total set) and test set (59 data points, 20% of the total data). The next important step is to determine the input parameters for the establishment models from a number of SEP and Sσ-profile descriptors along with the corresponding temperature using stepwise linear regression method. Through the process of regression and analysis of the outcomes,

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eight vital parameters were selected to develop the predictive models, which are listed in Table 2.

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implies that the linear relationship between them is weak.

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All the values for the linear correlation coefficient of any two descriptors are below 0.5, which

In order to evaluate the predictability and validity of the established models, five general

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parameters were employed. They are squared correlation coefficient (R2), average absolute relative

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deviation (AARD%), absolute relative deviation (ARD%), root-mean-square error (RMSE), and mean-square error (MSE), respectively. The calculation equations are presented as follows.

i 1

i

 ym

   y exp

i 1

i

Np

i 1

CE



 ym

AARD (%) = 100  

cal

i

i 1

 y NP

NP

2

PT E

R2 

exp

D

 y NP

 yiexp



2

(9)

2

yical  yiexp / Np yiexp

(10)

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ARD (%)  100  ( yical / yiexp  1.0) RMSE 

 NP

i 1

NP



yical  yiexp

MSE   yi  yi i 1

cal

exp





(11)

2

(12)

/ NP

2

/ NP

(13)

Table 2. Correlation matrix of eight descriptors T

SEP-C 57.25

T

1

SEP-C 57.25

-0.060

1

SEP-A-86.75

0.064

-0.177

SEP-A-86.75

SEP-C 116.75

1 12

SEP-A -46.25

SEP-C35.25

Sσ-A 0.009

Sσ-C 0.006

ACCEPTED MANUSCRIPT SEP-C 116.75

0.117

0.026

-0.021

1

SEP-A -46.25

0.027

-0.185

-0.121

0.041

1

SEP-C35.25

0.096

0.363

-0.061

0.113

-0.039

1

Sσ-A 0.009

-0.020

0.066

-0.444

-0.010

-0.082

-0.105

1

Sσ-C 0.006

0.055

-0.308

-0.113

-0.573

-0.043

-0.081

0.108

1

Williams plot can be utilized to visualize the applicability domain (AD) of models[87-89],

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and the horizontal axe represents leverage value (h), which is calculated as follows (Eq. (14)):

hi  xiT ( X T X ) 1 xi (i  1, , n)

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(14)

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where xi represents the row vector of the descriptors for ILs, X is the p × n matrix, p is the number of variable parameters, and n is the number of data points utilized to develop the model. The

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vertical axe denotes standardized residuals (σ). The critical value is h∗= 3(p + 1)/n, which is the

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leverage threshold. A compound which has standardized residual over three standard deviation units (>3σ), should be considered as an outlier compound which is wrongly calculated. A chemical

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with a high leverage (h>h∗) in the test set is structurally far from the training set chemical and

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therefore should be considered beyond the AD of the predictive models. 4 Results and discussion

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4.1 Results of the MLR model

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The MLR model was established using the above-selected descriptors based on the stepwise algorithm. As shown in Eq. (15), the descriptors were arranged in order of importance.

HLC  0.096T  3.383S EP  A-86.25  0.948S EP  C57.25 +8.666S EP  A-46.25  0.610S EP  C35.25 0.849S C0.006  0.019S A0.009  0.944S EP  C116.75  19.826

（15）

where T is temperature, S means surfaces, subscript EP and σ indicate electrostatic potential and screening charge density, C and A are cation and anion, respectively. According to Eq. (15), the most important descriptor is T, and the HLC values increase as the temperature increases. This is consistent with the common sense of chemical thermodynamics, 13

ACCEPTED MANUSCRIPT which means that the solubility of CO2 in ILs decreases with the increasing temperature. The second important descriptor is SEP-A-86.25, which is related to the structure of anion. The negative sign before it indicates that as the surfaces of this descriptor increases, the CO2 solubility in ILs increases. For example, it can be found that the SEP-A-86.25 of different anions with same cation,

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following the order of [BF4]-<[NTf2]-<[eFAP]-, which is consistent with experimental CO2

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solubility trend[69]. The third important descriptor is SEP-C57.25, which relates to cation. Similar to

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the first descriptor, there is a negative correlation between CO2 solubility and SEP-C57.25. For instance, when the anion is the same, CO2 solubility increases with the increase of the alkyl chain

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length on the cation[90]. The following fourth, fifth and eighth parameters belong to the SEP

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descriptors, and the sixth and seventh parameters belong to the Sσ-profile descriptors, respectively, which means that these descriptors also have a certain influence on CO2 solubility. In addition, it

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can be concluded that the anion has more important effect on CO2 solubility in IL than the cation,

30

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25

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which agrees with the previous research results[6, 91].

training set test set

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20

Pre.

15

10

5

0 0

5

10

15

20

25

30

Exp. Figure 4. Calculated versus experimental HLC values of CO2 in ILs from MLR model 14

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Figure 5. Percent of HLC values for the MLR model in different ARD% range

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Predicted HLC values of the MLR model and their ARD% for the ILs are summarized in

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Table 1. The R2, AARD%, MSE, and RMSE values of the MLR model for total set are 0.920, 15.44, 1.346 and 1.160, respectively, and more detailed statistical results are presented in Table 2.

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Figure 4 shows the estimated and experimental values of the MLR model. In addition, the percent

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of HLC values in different ARD% range of the MLR model is depicted in Figure 5. It can be seen that only 41.14% of the ARD% values for the predicted data points are within the range of 0-10%,

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and 22.9% of the values are beyond 20%. The above results show that the performance of the

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linear model is not good enough. Therefore, it is necessary to establish the nonlinear models to calculate the HLC of CO2 in ILs. 4.2 Results of the SVM and ELM models

15

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30

training set test set

25

20

Pre.

15

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10

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5

0

5

10

15

20

25

30

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Exp.

SC

0

30

training set test set

D

25

Pre.

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10

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20

15

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Figure 6. Calculated versus experimental HLC values of CO2 in ILs from SVM model.

5

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0

0

5

10

15

20

25

30

Exp.

Figure 7. Calculated versus experimental HLC values of CO2 in ILs from ELM model

In order to establish more accurate models, the SVM and ELM algorithms were employed to build new nonlinear models based on the same input parameters used in the MLR model. When C =58.9, ε=0.0182, r=0.106, with 169 support vectors, the best SVM model is obtained. The R2, AARD%, MSE and RMSE values of the total set for the SVM model are 0.983, 5.16, 0.281 and 16

ACCEPTED MANUSCRIPT 0.530, respectively. The best ELM model is acquired when the training function is ‘sin’ and the number of neurons is 90, and the R2, AARD%, MSE and RMSE values of the total set for it are 0.995, 3.22, 0.089 and 0.298, respectively. The values of the predictive HLC of CO2 in ILs versus the experimental values for the SVM and ELM models are shown in Figure 6 and Figure 7,

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respectively. The detailed parameters for the training set and test set of each developed models are

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given in the Table 2 and the detailed ARD% of each IL for the models are also summarized in

SC

Table 1. It can be seen that most of the HLC values can be well predicted by the SVM and ELM models.

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Figure 8 shows the predictive values from the SVM models in different ARD% range. 85.86%

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of SVM model predictions are in the ARD% range of 0-10%, and only 4.38% exceeds 20%. By contrast, according to the Figure 9, 92.93% of the ARD% values for the ELM model are within

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0-10% and only 0.67% are over 20%. The above results illustrate that both of the SVM and ELM

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models are reliable and valid to predict the HLC of CO2 in ILs and the ELM model has better

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performance.

Figure 8. Percent of ARD% value in different deviation range of the SVR model

17

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Figure 9. Percent of value in different deviation range of the ELM model

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The applicability domain is demonstrated as Williams plot in Figure 10 and 11 to illustrate the validity of the models. It can be seen that there are 8 data points of the SVM model and 11

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data points of the ELM model are response outliers (>3σ), however in this case, they are within the AD of the model, with the leverage below the critical hat value (h*). Therefore, according to

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the Williams plot method, this erroneous prediction is most likely due to the wrong experimental rather than to molecular structure[38, 92]. As can be seen from Figure 10 and Figure 11, ten data

6

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points exceed the critical hat value and are influential in the model established.

10

training set test set

197

2

246

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standardized residuals

4

22

123

268

0

258

147 129 190

86 175 104 124 83

-2

-4

225 252 156

-6 0.00

0.05

0.10

Hat 18

h*

0.15

0.20

ACCEPTED MANUSCRIPT Figure 10. Williams plot of the SVM model for the train and test sets 6 10

training set test set

246 1 248

4

250

2

86 268

0

-2 15 251

-4

5

2

-6 0.00

104 175 124 83

RI

240

258 129 147

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190

0.05

0.10

h*

0.15

0.20

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Hat

SC

standardized residuals

22

Figure 11. Williams plot of the ELM model for the train and test sets

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4.3 Comparison with the MLR, SVM, and ELM models

Comparison with the MLR, SVM, and ELM models has been performed in this section, and

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the detailed statistical parameters were summarized in Table 3. In the established three models, the

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same types and number of ILs and same descriptors were employed in their train set, test set and thus they can be straightly compared. According to the Table 3, the outcomes of ELM model are

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the best because of the greatest R2 and the lowest AARD%, MSE, and RMSE, which indicated

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that the ELM method is the most suitable model to predict the HLC of CO2 in ILs. It also can be concluded that the SEP and Sσ-profile descriptors contain abundant molecular information and could be utilized to well predict the properties of ILs. Table 3 Comparison of the statistical parameters by different QSAR models

Model

MLR

SVM

Dataset

No.

R2

AARD%

MSE

RMSE

Train

238

0.921

15.02

1.283

1.133

Test

59

0.918

17.12

1.598

1.264

Total

297

0.920

15.44

1.346

1.160

Train

238

0.983

5.11

0.278

0.527

Test

59

0.986

5.35

0.293

0.541

19

ACCEPTED MANUSCRIPT

ELM

Total

297

0.983

5.16

0.281

0.530

Train

238

0.995

2.97

0.072

0.269

Test

59

0.992

4.24

0.154

0.392

Total

297

0.995

3.22

0.089

0.298

5. Conclusion In the present work, for the sake of quickly and accurately calculating the HLC of CO2

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dissolution in ILs, the SEP and Sσ-profile descriptors were employed to construct predictive models.

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Initially, 297 data points belonging to 34 ILs (containing 16 cations and 9 anions) for HLC of CO2

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were collected and the structures of cations and anions were geometrically optimized by quantum

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chemistry method. Then the SEP and Sσ-profile descriptors for the cations and anions were calculated and employed to build the predictive models. The performance of the nonlinear models (SVM and

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ELM models) is greater than that of the linear model (MLR model) and the ELM model is the best with the R2 (0.995) and AARD% (3.22) for the total set. Finally, the applicability domain of the

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SVM and ELM models was demonstrated via William plot. Results show that the proposed

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models (SVM and ELM models) are reliable and robust, and the HLC of CO2 in ILs can be well predicted using the molecular descriptors of SEP and Sσ-profile.

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Acknowledgement

the

China

Postdoctoral

Science

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We are grateful for the financial support provided by

Foundation (2017M621477), the National Natural Science Foundation of China (No. 201506219, U1662122, 51574215, 21436010), the Beijing Natural Science Foundation (No.2164062), and the State Key Laboratory of Chemical Engineering (No.SKL-ChE-15A01). Reference [1] E.S. Sanz-Pérez, C.R. Murdock, S.A. Didas, C.W. Jones, Direct capture of CO 2 from ambient air, Chem Rev, 116 (2016) 11840-11876. [2] M. Pera-Titus, Porous inorganic membranes for CO 2 capture: present and prospects, Chem Rev, 114 (2013) 1413-1492. 20

ACCEPTED MANUSCRIPT [3] International Energy Outlook 2016 - EIA, 2016. [4] S. Zeng, X. Zhang, L. Bai, X. Zhang, H. Wang, J. Wang, D. Bao, M. Li, X. Liu, S. Zhang, Ionic-Liquid-Based CO2 Capture Systems: Structure, Interaction and Process, Chem. Rev., 117 (2017) 9625-9673. [5] X. Zhang, X. Zhang, H. Dong, Z. Zhao, S. Zhang, Y. Huang, Carbon capture with ionic liquids: overview and progress, Energy Environ. Sci., 5 (2012) 6668-6681. [6] Z. Lei, C. Dai, B. Chen, Gas Solubility in Ionic Liquids, Chem. Rev., 114 (2014) 1289-1326. [7] Z. Zhao, X. Xing, Z. Tang, Y. Zheng, W. Fei, X. Liang, E. Ataeivarjovi, D. Guo, Experiment and simulation

study

of

CO2

solubility

in

dimethyl

carbonate,

PT

tetrafluoroborate and their mixtures, Energy, 143 (2018) 35-42.

1-octyl-3-methylimidazolium

[8] S. Babamohammadi, A. Shamiri, M.K. Aroua, A review of CO 2 capture by absorption in ionic

RI

liquid-based solvents, Rev Chem Eng, 31 (2015) 383-412.

[9] J.F. Brennecke, E.J. Maginn, Ionic liquids: innovative fluids for chemical processing, AIChE Journal,

SC

47 (2001) 2384-2389.

[10] Z. Feng, F. Cheng-Gang, W. You-Ting, W. Yuan-Tao, L. Ai-Min, Z. Zhi-Bing, Absorption of CO2 in the aqueous solutions of functionalized ionic liquids and MDEA, Chem Eng J, 160 (2010) 691-697.

NU

[11] Q. Yang, Z. Wang, Z. Bao, Z. Zhang, Y. Yang, Q. Ren, H. Xing, S. Dai, New Insights into CO2 Absorption Mechanisms with Amino‐Acid Ionic Liquids, ChemSusChem, 9 (2016) 806-812. [12] H. Xing, Y. Yan, Q. Yang, Z. Bao, B. Su, Y. Yang, Q. Ren, Effect of Tethering Strategies on the Surface

MA

Structure of Amine-Functionalized Ionic Liquids: Inspiration on the CO2 Capture, The Journal of Physical Chemistry C, 117 (2013) 16012-16021.

[13] Z.J. Zhao, H.F. Dong, X.P. Zhang, The Research Progress of CO 2 Capture with Ionic Liquids, Chin. J. Chem. Eng, 20 (2012) 120-129. CO2, Nature, 399 (1999) 28.

D

[14] L.A. Blanchard, D. Hancu, E.J. Beckman, J.F. Brennecke, Green processing using ionic liquids and

PT E

[15] K. Huang, D.N. Cai, Y.L. Chen, Y.T. Wu, X.B. Hu, Z.B. Zhang, Thermodynamic validation of 1‐alkyl‐3‐ methylimidazolium carboxylates as task‐specific ionic liquids for H2S absorption, AIChE J, 59 (2013) 2227-2235.

[16] C. Wang, X. Luo, H. Luo, D.e. Jiang, H. Li, S. Dai, Tuning the basicity of ionic liquids for equimolar

CE

CO2 capture, Angew Chem Int Edit, 50 (2011) 4918-4922. [17] D. Fu, P. Zhang, Investigation of the absorption performance and viscosity for CO2 capture process 165-172.

AC

using [Bmim][Gly] promoted MDEA (N-methyldiethanolamine) aqueous solution, Energy, 87 (2015) [18] V. Venkatraman, B.K. Alsberg, Predicting CO2 capture of ionic liquids using machine learning, J CO2 Util, 21 (2017) 162-168. [19] R.D. Rogers, K.R. Seddon, Ionic liquids--solvents of the future?, Science, 302 (2003) 792-793. [20] Y. Huang, H. Dong, X. Zhang, C. Li, S. Zhang, A new fragment contribution‐corresponding states method for physicochemical properties prediction of ionic liquids, AIChE J, 59 (2013) 1348-1359. [21] J.M. Slattery, C. Daguenet, P.J. Dyson, T.J. Schubert, I. Krossing, How to predict the physical properties of ionic liquids: a volume‐based approach, Angewandte Chemie, 119 (2007) 5480-5484. [22] I. Krossing, J.M. Slattery, C. Daguenet, P.J. Dyson, A. Oleinikova, H. Weingärtner, Why are ionic liquids liquid? A simple explanation based on lattice and solvation energies, J Am Chem Soc, 128 (2006) 13427-13434. [23] M.A. Sedghamiz, A. Rasoolzadeh, M.R. Rahimpour, The ability of artificial neural network in 21

ACCEPTED MANUSCRIPT prediction of the acid gases solubility in different ionic liquids, J CO2 Util, 9 (2015) 39-47. [24] Y. Zhao, R. Gani, R.M. Afzal, X. Zhang, S. Zhang, Ionic liquids for absorption and separation of gases: An extensive database and a systematic screening method, AIChE J, 63 (2017) 1353-1367. [25] Y. Zhao, J. Gao, Y. Huang, R.M. Afzal, X. Zhang, S. Zhang, Predicting H 2S solubility in ionic liquids by the quantitative structure–property relationship method using Sσ-profile molecular descriptors, RSC Adv, 6 (2016) 70405-70413. [26] Y. Zhao, Y. Huang, X. Zhang, S. Zhang, A quantitative prediction of the viscosity of ionic liquids using S σ-profile molecular descriptors, Phys Chem Chem Phys, 17 (2015) 3761-3767. [27] Y. Zhao, S. Zeng, Y. Huang, R.M. Afzal, X. Zhang, Estimation of heat capacity of ionic liquids using

PT

Sσ-profile molecular descriptors, Ind Eng Chem Res, 54 (2015) 12987-12992.

[28] Y. Zhao, J. Zhao, Y. Huang, Q. Zhou, X. Zhang, S. Zhang, Toxicity of ionic liquids: database and

RI

prediction via quantitative structure–activity relationship method, Journal of Hazardous Materials, 278 (2014) 320-329.

SC

[29] D.M. Eike, J.F. Brennecke, E.J. Maginn, Predicting infinite-dilution activity coefficients of organic solutes in ionic liquids, Ind Eng Chem Res, 43 (2004) 1039-1048.

[30] D. Ghaslani, Z.E. Gorji, A.E. Gorji, S. Riahi, Descriptive and predictive models for Henry’s law

NU

constant of CO 2 in ionic liquids: A QSPR study, Chemical Engineering Research and Design, 120 (2017) 15-25.

[31] C. Deng, G. Huang, J. Xu, J. Tang, Extreme learning machines: new trends and applications, SCI

MA

CHINA INFORM SCI, 58 (2015) 1-16.

[32] X. Kang, Z. Zhao, J. Qian, R. Muhammad Afzal, Predicting the Viscosity of Ionic Liquids by the ELM Intelligence Algorithm, Ind Eng Chem Res, 56 (2017) 11344-11351. [33] G.-B. Huang, Q.-Y. Zhu, C.-K. Siew, Extreme learning machine: a new learning scheme of

D

feedforward neural networks, Neural Networks, 2 (2004) 985-990. [34] G.-B. Huang, Q.-Y. Zhu, C.-K. Siew, Extreme learning machine: theory and applications,

PT E

Neurocomputing, 70 (2006) 489-501.

[35] O. Isayev, C. Oses, C. Toher, E. Gossett, S. Curtarolo, A. Tropsha, Universal fragment descriptors for predicting properties of inorganic crystals, Nature Communications, 8 (2017). [36] A. Klamt, V. Jonas, T. Bürger, J.C. Lohrenz, Refinement and parametrization of COSMO-RS, J PHYS

CE

CHEM A, 102 (1998) 5074-5085.

[37] J.S. Torrecilla, J. Palomar, J. Lemus, F. Rodríguez, A quantum-chemical-based guide to analyze/quantify the cytotoxicity of ionic liquids, Green Chem, 12 (2010) 123-134. predict

AC

[38] L. Cao, P. Zhu, Y. Zhao, J. Zhao, Using machine learning and quantum chemistry descriptors to the

toxicity

of

ionic

liquids,

Journal

of

Hazardous

Materials,

DOI

10.1016./j.jhzmat.2018.03.025. [39] S. Tiryaki, A. Aydın, An artificial neural network model for predicting compression strength of heat treated woods and comparison with a multiple linear regression model, Constr Build Mater, 62 (2014) 102-108. [40] S. Sousa, F. Martins, M. Alvim-Ferraz, M.C. Pereira, Multiple linear regression and artificial neural networks based on principal components to predict ozone concentrations, Environ Modell Softw, 22 (2007) 97-103. [41] V. Vapnik, C. Cortes, Support Vector Networks, machine learning 20, 273-297, Kunwer Acedemic Publisher, 1995. [42] Y. Ren, H. Liu, X. Yao, M. Liu, Prediction of ozone tropospheric degradation rate constants by 22

ACCEPTED MANUSCRIPT projection pursuit regression, Anal Chim Acta, 589 (2007) 150-158. [43] B. Schölkopf, A.J. Smola, Learning with kernels: support vector machines, regularization, optimization, and beyond, MIT press2002. [44] A.M. Andrew, AN INTRODUCTION TO SUPPORT VECTOR MACHINES AND OTHER KERNEL-BASED LEARNING METHODS by Nello Christianini and John Shawe-Taylor, Cambridge University Press, Cambridge, 2000, xiii+ 189 pp., ISBN 0-521-78019-5 (Hbk,£ 27.50), Robotica, 18 (2000) 687-689. [45] Q.-Y. Zhu, A.K. Qin, P.N. Suganthan, G.-B. Huang, Evolutionary extreme learning machine, Pattern Recogn, 38 (2005) 1759-1763. [46] G.-B. Huang, C.-K. Siew, Extreme learning machine with randomly assigned RBF kernels,

PT

International Journal of Information Technology, 11 (2005) 16-24.

[47] G.-B. Huang, D.H. Wang, Y. Lan, Extreme learning machines: a survey, INT J MACH LEARN CYB, 2

RI

(2011) 107-122.

[48] G.-B. Huang, X. Ding, H. Zhou, Optimization method based extreme learning machine for

SC

classification, Neurocomputing, 74 (2010) 155-163.

[49] G.-B. Huang, L. Chen, Convex incremental extreme learning machine, Neurocomputing, 70 (2007) 3056-3062.

NU

[50] G.-B. Huang, M.-B. Li, L. Chen, C.-K. Siew, Incremental extreme learning machine with fully complex hidden nodes, Neurocomputing, 71 (2008) 576-583.

[51] M. Frisch, Gaussian 09 Revision B. 01, Gaussian, Inc Wallingford, CT, 2010

MA

[52] Y. Hou, R.E. Baltus, Experimental measurement of the solubility and diffusivity of CO 2 in room-temperature ionic liquids using a transient thin-liquid-film method, Ind Eng Chem Res, 46 (2007) 8166-8175.

[53] J.L. Anthony, J.L. Anderson, E.J. Maginn, J.F. Brennecke, Anion effects on gas solubility in ionic

D

liquids, J PHYS CHEM B, 109 (2005) 6366-6374.

[54] J. Jacquemin, M.F.C. Gomes, P. Husson, V. Majer, Solubility of carbon dioxide, ethane, methane,

PT E

oxygen, nitrogen, hydrogen, argon, and carbon monoxide in 1-butyl-3-methylimidazolium tetrafluoroborate between temperatures 283K and 343K and at pressures close to atmospheric, The Journal of Chemical Thermodynamics, 38 (2006) 490-502. [55] J. Zhang, Q. Zhang, B. Qiao, Y. Deng, Solubilities of the gaseous and liquid solutes and their

CE

thermodynamics of solubilization in the novel room-temperature ionic liquids at infinite dilution by gas chromatography, J Chem Eng Data, 52 (2007) 2277-2283. [56] D. Camper, J. Bara, C. Koval, R. Noble, Bulk-fluid solubility and membrane feasibility of

AC

Rmim-based room-temperature ionic liquids, Ind Eng Chem Res, 45 (2006) 6279-6283. [57] P.J. Carvalho, V.H. Álvarez, I.M. Marrucho, M. Aznar, J.A. Coutinho, High pressure phase behavior of carbon dioxide in 1-butyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide and 1-butyl-3-methylimidazolium dicyanamide ionic liquids, The Journal of Supercritical Fluids, 50 (2009) 105-111. [58] D. Camper, P. Scovazzo, C. Koval, R. Noble, Gas solubilities in room-temperature ionic liquids, Ind Eng Chem Res, 43 (2004) 3049-3054. [59] M.J. Muldoon, S.N. Aki, J.L. Anderson, J.K. Dixon, J.F. Brennecke, Improving carbon dioxide solubility in ionic liquids, J PHYS CHEM B, 111 (2007) 9001-9009. [60] J.L. Anthony, E.J. Maginn, J.F. Brennecke, Solubilities and thermodynamic properties of gases in the ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate, J PHYS CHEM B, 106 (2002) 7315-7320. 23

ACCEPTED MANUSCRIPT [61] I. Urukova, J. Vorholz, G. Maurer, Solubility of CO 2, CO, and H2 in the Ionic Liquid [bmim][PF6] from Monte Carlo Simulations, J PHYS CHEM B, 109 (2005) 12154-12159. [62] J. Jacquemin, P. Husson, V. Majer, M.F.C. Gomes, Low-pressure solubilities and thermodynamics of solvation of eight gases in 1-butyl-3-methylimidazolium hexafluorophosphate, Fluid Phase Equilibr, 240 (2006) 87-95. [63] T.K. Carlisle, J.E. Bara, C.J. Gabriel, R.D. Noble, D.L. Gin, Interpretation of CO 2 solubility and selectivity in nitrile-functionalized room-temperature ionic liquids using a group contribution approach, Ind Eng Chem Res, 47 (2008) 7005-7012. [64] R.E. Baltus, B.H. Culbertson, S. Dai, H. Luo, D.W. DePaoli, Low-pressure solubility of carbon dioxide

PT

in room-temperature ionic liquids measured with a quartz crystal microbalance, J PHYS CHEM B, 108 (2004) 721-727.

RI

[65] J.E. Bara, C.J. Gabriel, S. Lessmann, T.K. Carlisle, A. Finotello, D.L. Gin, R.D. Noble, Enhanced CO 2 separation selectivity in oligo (ethylene glycol) functionalized room-temperature ionic liquids, Ind Eng

SC

Chem Res, 46 (2007) 5380-5386.

[66] J. Jacquemin, P. Husson, V. Majer, M.F.C. Gomes, Influence of the cation on the solubility of CO 2 and H2 in ionic liquids based on the bis (trifluoromethylsulfonyl) imide anion, J Solut Chem, 36 (2007)

NU

967-979.

[67] D. Kerlé, R. Ludwig, A. Geiger, D. Paschek, Temperature dependence of the solubility of carbon dioxide in imidazolium-based ionic liquids, J PHYS CHEM B, 113 (2009) 12727-12735.

MA

[68] P.J. Carvalho, V.H. Álvarez, B. Schröder, A.M. Gil, I.M. Marrucho, M. Aznar, L.M. Santos, J.A. Coutinho, Specific solvation interactions of CO2 on acetate and trifluoroacetate imidazolium based ionic liquids at high pressures, J PHYS CHEM B, 113 (2009) 6803-6812. [69] X. Zhang, Z. Liu, W. Wang, Screening of ionic liquids to capture CO 2 by COSMO‐RS and

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experiments, AIChE J, 54 (2008) 2717-2728.

[70] N.M. Yunus, M.A. Mutalib, Z. Man, M.A. Bustam, T. Murugesan, Solubility of CO 2 in pyridinium

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based ionic liquids, Chem Eng J, 189 (2012) 94-100. [71] S.M. Mahurin, T. Dai, J.S. Yeary, H. Luo, S. Dai, Benzyl-functionalized room temperature ionic liquids for CO2/N2 separation, Ind Eng Chem Res, 50 (2011) 14061-14069. [72] P.J. Carvalho, V.H. Álvarez, J.J. Machado, J. Pauly, J.-L. Daridon, I.M. Marrucho, M. Aznar, J.A.

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Coutinho, High pressure phase behavior of carbon dioxide in 1-alkyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide ionic liquids, J Supercrit Fluid, 48 (2009) 99-107. [73] Z. Lei, J. Yuan, J. Zhu, Solubility of CO 2 in propanone, 1-ethyl-3-methylimidazolium

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tetrafluoroborate, and their mixtures, J Chem Eng Data, 55 (2010) 4190-4194. [74] A. Finotello, J.E. Bara, D. Camper, R.D. Noble, Room-temperature ionic liquids: temperature dependence of gas solubility selectivity, Ind Eng Chem Res, 47 (2008) 3453-3459. [75] A.H. Jalili, A. Mehdizadeh, M. Shokouhi, A.N. Ahmadi, M. Hosseini-Jenab, F. Fateminassab, Solubility and diffusion of CO2 and H2S in the ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate, The Journal of Chemical Thermodynamics, 42 (2010) 1298-1303. [76] M. Althuluth, M.T. Mota-Martinez, M.C. Kroon, C.J. Peters, Solubility of carbon dioxide in the ionic liquid 1-ethyl-3-methylimidazolium tris (pentafluoroethyl) trifluorophosphate, J Chem Eng Data, 57 (2012) 3422-3425. [77] D. Camper, C. Becker, C. Koval, R. Noble, Diffusion and solubility measurements in room temperature ionic liquids, Ind Eng Chem Res, 45 (2006) 445-450. [78] G. Hong, J. Jacquemin, P. Husson, M. Costa Gomes, M. Deetlefs, M. Nieuwenhuyzen, O. Sheppard, 24

ACCEPTED MANUSCRIPT C. Hardacre, Effect of Acetonitrile on the Solubility of Carbon Dioxide in 1-Ethyl-3-methylimidazolium Bis (trifluoromethylsulfonyl) amide, Ind Eng Chem Res, 45 (2006) 8180-8188. [79] S.M. Mahurin, J.S. Yeary, S.N. Baker, D.-e. Jiang, S. Dai, G.A. Baker, Ring-opened heterocycles: Promising ionic liquids for gas separation and capture, J Membrane Sci, 401 (2012) 61-67. [80] M. Costa Gomes, Low-pressure solubility and thermodynamics of solvation of carbon dioxide, ethane, and hydrogen in 1-hexyl-3-methylimidazolium bis (trifluoromethylsulfonyl) amide between temperatures of 283 K and 343 K, J Chem Eng Data, 52 (2007) 472-475. [81] J.L. Anderson, J.K. Dixon, E.J. Maginn, J.F. Brennecke, Measurement of SO 2 solubility in ionic liquids, J PHYS CHEM B, 110 (2006) 15059-15062.

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[82] S. Zhang, Y. Chen, R.X.-F. Ren, Y. Zhang, J. Zhang, X. Zhang, Solubility of CO2 in sulfonate ionic liquids at high pressure, Journal of Chemical & Engineering Data, 50 (2005) 230-233.

RI

[83] M. Frisch, G. Trucks, H. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, J. Montgomery Jr, T. Vreven, K. Kudin, J. Burant, Gaussian 03, revision B. 03, Gaussian Inc., Pittsburgh, PA, 2003.

SC

[84] E. Mullins, Y. Liu, A. Ghaderi, S.D. Fast, Sigma profile database for predicting solid solubility in pure and mixed solvent mixtures for organic pharmacological compounds with COSMO-based thermodynamic methods, Ind Eng Chem Res, 47 (2008) 1707-1725.

NU

[85] E. Mullins, R. Oldland, Y. Liu, S. Wang, S.I. Sandler, C.-C. Chen, M. Zwolak, K.C. Seavey, Sigma-profile database for using COSMO-based thermodynamic methods, Ind Eng Chem Res, 45 (2006) 4389-4415.

MA

[86] T. Lu, F. Chen, Multiwfn: a multifunctional wavefunction analyzer, Journal of computational chemistry, 33 (2012) 580-592.

[87] P. Gramatica, Principles of QSAR models validation: internal and external, Molecular Informatics, 26 (2007) 694-701.

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[88] D. Ghaslani, Z.E. Gorji, A.E. Gorji, S. Riahi, Descriptive and predictive models for Henry’s law constant of CO2 in ionic liquids: A QSPR study, Chemical Engineering Research and Design, 120 (2017)

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15-25.

[89] S. Buratti, D. Ballabio, S. Benedetti, M. Cosio, Prediction of Italian red wine sensorial descriptors from electronic nose, electronic tongue and spectrophotometric measurements by means of Genetic Algorithm regression models, Food Chem, 100 (2007) 211-218.

CE

[90] Y.-F. Hu, Z.-C. Liu, C.-M. Xu, X.-M. Zhang, The molecular characteristics dominating the solubility of gases in ionic liquids, Chem Soc Rev, 40 (2011) 3802-3823. [91] C. Cadena, J.L. Anthony, J.K. Shah, T.I. Morrow, J.F. Brennecke, E.J. Maginn, Why is CO 2 so soluble

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in imidazolium-based ionic liquids?, J Am Chem Soc, 126 (2004) 5300-5308. [92] P. Gramatica, Principles of QSAR models validation: internal and external, Molecular Informatics, 26 (2007) 694-701.

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ACCEPTED MANUSCRIPT Highlights 297 experimental data points including 16 cations and 9 anions for 34 ILs are collected.

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The structures of cations and anions of ILs are optimized by quantum chemistry.

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The descriptors are used to predict the Henry’s law constant (HLC) of CO2 in ILs.

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The ELM model with AARD=3.22% for the entire data set is powerful to predict the HLC of

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CO2.

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