Estimation of Heat Capacity of Ionic Liquids Using SÏ-profile

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Estimation of heat capacity of ionic liquids using S#-profile molecular descriptors Yongsheng Zhao, Shaojuan Zeng, Ying Huang, Raja Muhammad Afzal, and Xiangping Zhang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03576 • Publication Date (Web): 07 Dec 2015 Downloaded from http://pubs.acs.org on December 10, 2015

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Industrial & Engineering Chemistry Research

Estimation of heat capacity of ionic liquids using Sσ-profile molecular descriptors Yongsheng Zhao,†,‡ Shaojuan Zeng,† Ying Huang,† Raja Muhammad Afzal,† Xiangping Zhang*,† †

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

‡

School of Chemistry and Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

ABSTRACT: In order to estimate the heat capacity of ionic liquids (ILs), statistical models have been proposed using the quantum-chemical based charge distribution area (Sσ-profile) as the molecular descriptors for two different mathematical algorithms: multiple linear regression (MLR), and extreme learning machine (ELM). A total of 2416 experimental data points belonging to 46 ILs over a wide range of temperature (223.1-663 K) at atmospheric pressure, have been utilised to carry out validation. The average absolute relative deviation (AARD %) of the whole data set of the MLR and ELM is 2.72 % and 0.60 %, respectively. Although both two algorithms can be able to estimate the heat capacity of ILs well, the nonlinear model (ELM) shows more accurate ability, due to its capacity of determining complex nonlinear relationship. Moreover, the derived models can throw some light onto structural features that are related to the heat capacity, as well as could be a suitable option to decrease trial-and-error experiments. 1. Introduction Ionic liquids (ILs) are gaining much attention both in academic and industry communities, and widely applied in various fields because of their green and unique properties1-3. The heat capacity is one of the basic thermodynamic and thermophysical properties of ILs4, which is generally required in calculations of chemical thermodynamics, and is also the indispensable parameter in the chemical process of design. Using the heat capacities, we can calculate some other thermodynamic properties such as entropy, enthalpy, and Gibbs free energy, and so on5. Similarly, the heat capacity of a substance can generate a great influence on the heat transfer

*Corresponding author, Tel./Fax: +86 01062558174 E-mail address: [email protected] 1

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properties in a real industry process6. Usually, the heat capacity can be measured by various experimental methods such as the differential scanning calorimetry (DSC)7, adiabatic calorimetry8, hot-wire method9, and temperature oscillation calorimetry10. But in fact, the new or required certain compounds' heat capacity sometimes cannot be detected from the manual and databank of chemical thermodynamics, and due to the different experimental conditions and apparatuses, there are unavoidably some uncertainties in measurements11. In addition, because of the tunable properties of ILs, there are numerous potential combinations of cations and anions from current chemical database to create useful ILs, thus measuring the heat capacity of various ILs under a wide range of conditions through experimental techniques is impractical and costly. Accordingly, it is necessary to develop computational approaches to predict the heat capacity of ILs. Several valuable computational algorithms like multiple linear regression (MLR)12, artificial neural network (ANN)13-16, partial least-squares analysis (PLS)17, genetic function approximation (GFA)5, and support vector machine (SVM)18 have been reported for predicting the properties of organic compounds or ILs. Recently, some of the above-mentioned algorithms have been used to predict the heat capacity of ILs. Farahani et al19 applied the MLR algorithm to build a model for predicting the heat capacity of ILs using the atom counts and the number of groups as the model parameters. The global absolute average deviation of the obtained model is 2.5 %. Therefore, the proposed model could be safely used to predict the heat capacity of ILs. Valderrama et al20 employed the ANN algorithm to develop a model of heat capacity for 31 ILs with 477 data points at atmospheric pressure, and the overall average absolute relative deviation (AARD %) of the test set is probably as low as 0.22 %, which has good predictive performance. Recently, Sattari et al5 employed a GFA algorithm to predict the heat capacity of ILs at atmospheric pressure using 14 molecular parameters and one temperature parameter, and the overall AARD % is about 1.70 %. Among the previously mentioned methods, the MLR is one of the earliest methods for constructing models, and it is still one of the most commonly used ones to date. The advantage of the MLR is its simple form and easily interpretable mathematical expression21. The ANN is a computer-based system derived from the simplified concept of the human brain, which has good nonlinear mapping ability, self-learning ability22. So it provides a new way to solve the unknown nonlinear and control problem, and it is particularly suitable to deal with the problem that has complicated nonlinear relationship between input parameters and output parameters. As compared 2


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to the ANN algorithm, extreme learning machine (ELM) is a relative new algorithm which was firstly developed by Huang et al23, 24. It can effectively tend to reach a global optimum and only needs to learn a few parameters between the hidden layer and the output layer as compared with the traditional ANN, and thus can be used to predict properties because of its excellent efficiency and generalization performance25. However, to the best of our knowledge, the ELM has not yet been used for predicting the properties of ILs until now. Thus, we employed this relative new ELM algorithm to predict the heat capacity of ILs in this work. From the viewpoint of molecular scale, Sσ-profile is an a priori two-dimensional quantum chemical parameter, which can quantitatively characterize the electronic stucture and molecular size of ILs. It represents the molecule’s area with specific surface screening charge density, and is obtained from the histogram function σ-profile calculated by the Conductor-like Screening Model (COSMO-RS) computation. Sσ-profile has been successfully applied to predict the properties of the ILs, e.g., density26, toxicity27, and viscosity28. Likewise, it is also used in this study. The objective of this work is to establish two novel models by using the MLR and ELM algorithms, based on Sσ-profile molecular structure descriptors calculated by the COSMO-RS and large data gathered from the IL Thermo Database29. The characteristic descriptors which have important impact on heat capacity of the cations and anions have been screened and selected, and the predictive qualities of the two established models have been compared and investigated. 2. Methodology 2.1. Dataset and quantum chemical descriptors of ILs In this study, a large number of the experimental data points of 46 ILs is collected from IL Thermo Database29. The cations of the studied ILs are alkyl-substituted cations, such as imidazolium [Im]+, pyrrolidinium [Pyr]+, pyridinium [Py]+, phosphonium [P]+, and the anions are acetate [Ac]-, nitrate [NO3]-, tris(pentafluoroethyl)trifluorophosphate [FEP]-, hexafluorophosphate [PF6]-,

tetrafluoroborate

[BF4]-,

ethylsulfate

[EtSO4]-,

dicyanamide

[DCA]-,

bis(trifluoromethylsulfonyl)imide [BTI]-, octylsulfate [C8SO4]-, trifluoromethylsulfonate [TfO]-, methylsulfate [MeSO4]-, trifluoroacetate [TfA]-, halide [X]-, respectively. As shown in Table 1, the investigated data set consists of 2416 heat capacity data points (254.0-1805.7 J mol−1 K−1) over a wide range of temperature (223.1-663 K). The Sσ-profile of the investigated ILs in this work are 3



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taken from the COSMO IL database, which were calculated on the BP-TZVP quantum chemical level30 using the COSMOthermX program. The σ-profiles of four representative cations and anions

of

ILs,

namely

pyridinium

[Py]+,

1-butyl-3-methyl-imidazolium

[BMIM]+,

tetrafluoroborate [BF4]-, and trifluromethylfulfonate [TfO]- have been shown in Figure 1. The x axis in Figure 1 is screening charge density and y axis is the surface segment having a specific charge distribution. It should be noted that the positive charges of the cations cause negative screening charges and vice versa. Therefore, the caions are at the left side in Figure 1 and the anions are at the right side. The screening charge density range in Figure 1 can be divided into three regions, that is, the nonpolar region (-0.0082 ≤ σ ≤ +0.0082 e/Å2 ), the hydrogen bond donor region (σ < -0.0082 e/Å2) and the hydrogen bond acceptor region (σ > +0.0082 e/Å2). As depicted in Figure 1, both [Py]+ and [BMIM]+ are with screening charge density exceeding the hydrogen bond donor threshold (-0.0082 e/Å2), which means that they both have the ability to form hydrogen bond with hydrogen bond acceptor. The [Py]+ has more negative screening charge density than the [BMIM]+, which means that [Py]+ has the more strong ability to form hydrogen bond. This can be intuitively reflected by molecular color in Figure 1 (the darker the blue, the more polarity of cation). Both [BF4]- and [TfO]- are with the screening charge density exceeding the hydrogen bond acceptor threshold (+0.0082 e/Å2), and the [TfO]- has more deep red color on the molecular surface. This indicates the two anions both have the ability to form hydrogen bond with hydrogen bond donor as well as the [TfO]- has the stronger hydrogen bond acceptor ability. As described above, the σ-profiles have the rich information of molecules, and hence the charge distribution area (Sσ-profile) can be used as the descriptors to represent the relationship between micro-molecules and macro-properties. 2.2. MLR and ELM algorithms The MLR algorithm is one of the earliest and most commonly used algorithms to date, and its equation form is very simple and easy to use. The detailed introduction of the MLR algorithm can be found in our previous work

28

. Here, we only give a brief description of the ELM algorithm,

and the detailed introduction of the ELM theoretical basis was introduced in the literature25. The ELM is similar to the traditional single layer feed forward neural networks (SLFNs). However, its hidden nodes are randomly assigned, and fixed without iteratively tuning (independent of the training set). Unlike the traditional SLFNs, the ELM does not contain biases between the hidden 4


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layer and the output layer25, and only needs to learn the weights in a linear fashion. So, the ELM can effectively avoid the suboptimal problem of the traditional SLFNs, and has faster training speed and better generalization ability than the traditional SLFNs. The ELM employed in this study is depicted in Figure 2, which consists of three layers (topology of ELM), including input, hidden, and output layer, respectively (no biases to output neuron of hidden layer). Each layer linked by a certain number of small individual and highly interconnected processing elements called neurons or nodes. Signals are transmitted through the connection weights between neurons. In the ELM modeling, heat capacity (Cp) is the output variable. Molecular weight (M), temperature (T), and four Sσ-profile descriptors (selected by stepwise regression method) are the input variables. 2.3. Evaluation of the models’ performances The goodness-of-fit can be statically measured by the squared correlation coefficient (R2), which gives the degree of correlation between two variables for a data set, and the average absolute relative deviation (AARD), which are defined as follows: Np

Np

∑ (Cpi exp − CP )2 − ∑ (Cpical − Cpiexp )2 R2 =

i =1

i =1

(1)

Np

∑ (C

exp pi

− Cp )

2

i =1

Np

AARD (%) = 100 × ∑ i =1

Cpi cal − Cpi exp Cpi exp

/ Np

(2)

where C p represents the average experimental value of the heat capacity, Cpi exp represents the experimental value of the heat capacity, Cpi cal represents the prediction value of the heat capacity, and NP represents the number of ILs considered in this study. 3. Results and discussion In order to ensure the reliability of the results, all the data points are parted randomly into two groups, namely, training set and test set. As usually done in most literature, 80 % of the data points (1933 data points) are incorporated into the training set to develop the MLR and ELM models, and the rest of the 483 data points for the test set are used to verify the prediction performance. The 5



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detailed information of all the data points is presented in Supporting Information. 3.1. Results of the MLR model Linear model to predict the heat capacity of ILs was first carried out by the MLR algorithm based on the large collected data points. The MLR correlation equation (3) was established by comprehensive comparison of the correlation coefficient, and AARD % of the training set, and thus the optimal subset size of descriptor was selected as six (see below). Cp = 1.454M − 3142.507 S A-0.011 + 0.394T + 4.477 SC-0.003 + 6.490S A0.016 −7.862 SA0.018 − 192.002

(3)

(n=1933, R2=0.985, AARD %=2.58 %) where M is molecular weight (g mol-1), S is charge distribution area (Å2), subscript A means anion, C means cationic, T means temperature (K), and the number denotes the size of surface screening charge. The plus sign in equation (3) shows that the relationship between descriptors and heat capacity is positive correlation whereas the minus sign signifies a negative correlation. The importance of each descriptor increases in the order of t value, which means the most important descriptor is the headmost one of equation (3). Hereby, the most important descriptor is M, showing that the molecular weight has important effects on the heat capacity. The plus sign in front of M shows that the heat capacity of ILs increases with the increase of molecular weight of ILs. The heat capacity also increases with the increase of M of caitons or anions (when the counter ions are the same). This is similar to the results proposed by Soriano et al31. The second important descriptor is SA-0.011, which the -0.011 e/Å2 (screening charge density) located in the polar region. The minus sign before SA-0.011 means that the heat capacity of ILs decreases with the increase of the surface of anion with -0.011 e/Å2. The third important descriptor is T, heat capacity of ILs shows to increase with the increasing of temperature. The similar results can be found in several literature31-33. The fourth important descriptor is SC-0.003, and the -0.003 e/Å2 of the cations located in the non-polar range, showing that the electrostatic interaction has a positive influence on the heat capacity. The last two descriptors (SA0.016 and SA0.018) of the anion also have a certain influence on the heat capacity of ILs. These two descriptors are both at polar region (σ > +0.0082 e/Å2), which indicates that they both may form hydrogen bond with hydrogen bond donor. With R2 = 0.985, AARD % = 2.58 %, the MLR model based on the training set of 1933 data 6


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points shows a good result. Detailed statistics parameters of the MLR model are shown in Table 2. Calculated values are plotted against experimental values in Figure 3, Which shows that the computed values are well agreed with the experimental values. As shown in Figure 4, 86.3 % of absolute relative deviations of all the data points are within 5 %, and the AARD % of the entire data set is 2.72 % (Table 2). This suggests that the equation (3) (MLR model) can be employed for predicting the heat capacity of ILs, especially given that liquid heat capacity has the uncertainty between 3%-5% measured by power compensation differential scanning calorimetry (DSC).34 3.2. Results of the ELM model In order to get a more accurate prediction model, the same parameters used in MLR model are also employed as the input parameters to establish the ELM model. The triangular basis transfer function (tribas) was used to train the model based on the same training set mentioned above. The tribas transfer function could be described by equation (4): y = tribas (x)

= 1 – abs(x), if -1≤ x ≤ 1 = 0, otherwise

(4)

where y is the output value and x is the input parameter. In order to optimize and select the proper ELM model, only one parameter (the number of neurons) should be determined. Accordingly, based on the AARD % and R2 (the desirable AARD% and R2 are those closest to zero and unity, respectively), the best choice for the number of neurons was confirmed, and thus the optimal value of the number of neurons is 150. As shown in Figure 5, it is clear that the experimental vs. computed heat capacity values have an excellent correlation for the whole data set with the ELM algorithm. The AARD % of the whole data set is only 0.60 %, and the R2 of the entire data set is as high as 0.998. As displayed in Figure 6, 98.6 % of the absolute relative deviations of the whole data set are within 5 %, and distribute randomly around the zero line. In addition, the required time to train and test a single ELM model having 150 neurons of this study, was only 1.1040 seconds on an Intel 2.93 GHz desktop computer with 2 GB of RAM. These results indicate that the ELM model is effective. The detailed statistical parameters of the ELM model are summarized in Table 2. 3.3. Comparison of the MLR and ELM models The above work has established two models (MLR and ELM). In order to evaluate the performance of the two models, a wide comparison of their statistical assessments and their error 7



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distribution is summarized in Table 2 and Table 3. As shown in Table 2, considering the statistical results, the ELM model has better generalization capacity than the MLR model. Because the AARD % of the ELM of the training set, test set and the whole data set is less than the MLR model. As shown in Table 3, most of the absolute relative deviations are within 5% of the two models for the whole data set. There are 86.4 % of the absolute relative deviations within 1 % of the ELM model for the entire data set, whereas they are 38.9 % for the MLR model. Therefore, the ELM model can be better used to predict the heat capacity of ILs. The detailed error information of all the data points can be seen in Supporting Information. 4. Conclusions In this study, two novel models were established to predict the heat capacity based on the Sσ-profile molecular descriptor and 2416 experimental data points of 46 ILs. The reliability of the two models was verified by statistical analysis of the training set, test set, and total set. The results show that both the linear (MLR) and nonlinear (ELM) models can provide accurate results. In addition, the nonlinear (ELM) model has better performance than the linear MLR model. This means the heat capacity of ILs can be more accurately predicted by the ELM model with low AARD % (only 0.60 %), because of its capacity of determining complex nonlinear relationship between micro-structure and macro-property. It is observed that the molecular descriptor Sσ-profile can provide a wealth of information of micro-level, and the hydrogen bond and electrostatic interaction play an important role in the heat capacity of ILs. Moreover, the required time of this study was only 1.1040 seconds on an Intel 2.93 GHz desktop computer with 2 GB of RAM. Therefore, considering a series of advantages of the ELM algorithm (fast speed, good generalization ability and so on), we believe it could be extensively used to develop new models for predicting other properties of ILs containing systems. Supporting Information The investigated 2416 data points of 46 ionic liquids and predictive results were given here, including the name, reference, molar mass, temperature, calculated heat capacity, and absolute relative deviation (ARD %) of each piece of data by both the MLR model and ELM model. This material is available free of charge via the Internet at http://pubs.acs.org.

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Acknowledgements This work was financially supported by the National Basic Research Program of China (No. 2015CB251403), the National Natural Science Fund for Distinguished Young Scholars (No. 21425625), the key program of Beijing Municipal Natural Science Foundation (No. 2141003) and the National Natural Science Foundation of China (No. 21376242). The ELM program is supported by Binguang Huang team (Nanyang Technological University, Singapore). Reference: (1) Seddon, K. R. Ionic liquids - A taste of the future. Nature Mater. 2003, 2, 363-365. (2) Zhang, X.; Zhang, X.; Dong, H.; Zhao, Z.; Zhang, S.; Huang, Y. Carbon capture with ionic liquids: overview and progress. Energy Environ. Sci. 2012, 5, 6668-6681. (3) Roughton, B. C.; Christian, B.; White, J.; Camarda, K. V.; Gani, R. Simultaneous design of ionic liquid entrainers and energy efficient azeotropic separation processes. Comput. Chem. Eng. 2012, 42, 248-262. (4) Gardas, R. L.; Coutinho, J. A. P. A group contribution method for heat capacity estimation of ionic liquids. Ind. Eng. Chem. Res. 2008, 47, 5751-5757. (5) Sattari, M.; Gharagheizi, F.; Ilani-Kashkouli, P.; Mohammadi, A. H.; Ramjugernath, D. Estimation of the Heat Capacity of Ionic Liquids: A Quantitative Structure-Property Relationship Approach. Ind. Eng. Chem. Res. 2013, 52, 13217-13221. (6) Ceriani, R.; Gani, R.; Meirelles, A. J. Prediction of heat capacities and heats of vaporization of organic liquids by group contribution methods. Fluid Phase Equilib. 2009, 283, 49-55. (7) Straka, M.; Ruzicka, K.; Ruzicka, V. Heat capacities of chloroanilines and chloronitrobenzenes. J. Chem. Eng. Data 2007, 52, 1375-1380. (8) Kabo, G. J.; Blokhin, A. V.; Paulechka, Y. U.; Kabo, A. G.; Shymanovich, M. P.; Magee, J. W. Thermodynamic properties of 1-butyl-3-methylimidazolium hexafluorophosphate in the condensed state. J. Chem. Eng. Data 2004, 49, 453-461. (9) Giaretto, V.; Torchio, M. F. Two-wire solution for measurement of the thermal conductivity and specific heat capacity of liquids: Experimental design. Int. J. Thermophysics 2004, 25, 679-699. (10) Richner, G.; Neuhold, Y.-M.; Papadokonstantakis, S.; Hungerbuehler, K. Temperature oscillation calorimetry for the determination of the heat capacity in a small-scale reactor. Chem. Eng. Sci. 2008, 63, 3755-3765. (11) Shi, J.; Chen, L.; Chen, W. Prediction of the heat capacity for compounds based on the conjugate gradient and support vector machine methods. J. Chemometr. 2013, 27, 251-259. (12) Oliferenko, A. A.; Oliferenko, P. V.; Seddon, K. R.; Torrecilla, J. S. Prediction of gas solubilities in ionic liquids. Phys. Chem. Chem. Phys. 2011, 13, 17262-17272. (13) Torrecilla, J. S.; Rodríguez, F.; Bravo, J. L.; Rothenberg, G.; Seddon, K. R.; López-Martin, I. Optimising an artificial neural network for predicting the melting point of ionic liquids. Phys. Chem. Chem. Phys. 2008, 10, 5826-5831. (14) Díaz-Rodríguez, P.; Cancilla, J. C.; Plechkova, N. V.; Matute, G.; Seddon, K. R.; Torrecilla, J. S. Estimation of the refractive indices of imidazolium-based ionic liquids using their polarisability values. Phys. Chem. Chem. Phys. 2014, 16, 128-134. 9



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Table captions: Table 1. Temperature and heat capacity data points for different classes of ILs Table 2. Comparison of the statistical parameters for the MLR and ELM algorithms Table 3. Comparison of the ARD % for the MLR and ELM algorithms

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Table 1 Temperature and heat capacity data points for different classes of ILs Temperature range (K)

Heat capacity (J mol-1 K-1)

No.

Class

Data points

1

Imidazolium

223.1-663

254.0-743.7

2203

2

Pyridinium

290-425.15

343-665

62

3

Pyrrolidinium

283.15-358.15

544.2-661.22

29

4

Phosphonium

293-513.15

660.8-1805.7

122

Table 2. Comparison of the statistical parameters for the MLR and ELM algorithms Algorithms

Data set

No. of data points

R2

AARD %

Training

1933

0.985

2.58

Test

483

0.984

2.88

MLR

Total

2416

0.985

2.72

Training

1933

0.998

0.56

Test

483

0.998

0.74

Total

2416

0.998

0.60

ELM

Table 3. Comparison of the ARD % for the MLR and ELM algorithms Algorithms

Data points

ARD %< 1 %

1 % 5 %

MLR

2416

38.9

47.4

13.7

ELM

2416

86.4

12.2

1.4

ARD is the absolute relative deviation

13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure captions: Figure 1. The σ-profiles of four representative cations and anions of ILs Figure 2. Schematic illustration of the ELM employed in this study Figure 3. Calculated versus experimental heat capacity values using the MLR algorithm for all ionic liquids Figure 4. Relative deviation of calculated values versus experimental values with the MLR algorithm Figure 5. Calculated versus experimental heat capacity values using the ELM algorithm for all ionic liquids Figure 6. Relative deviation of calculated values versus experimental values with the ELM algorithm For Table of Contents Only

14


Page 14 of 17

Page 15 of 17

32 +

Pyridinium, [Py] + 1-butyl-3-methyl-imidazolium, [BMIM] Tetrafluoroborate, [BF4]

28 24

Trifluoromethylsulfonate, [TfO]

-

20 16

x

p (σ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


12 8 4 0 -0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

2

σ [e/Å ] Fig. 1. The σ-profiles of four representative cations and anions of ILs

Fig. 2. Schematic illustration of the ELM employed in this study

15



2000

Exp test MLR test

Exp train MLR train

1800 1600 1400

Heat capacity values

1200 1000 800 600 400 200 0 0

250

500

750

1000

1250

1500

1750

2000

2250

2500

Data number

Fig. 3. Calculated versus experimental heat capacity values using the MLR algorithm for all ionic liquids

60

training set test set

50 40 30

Relative deviation /%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 17

20 10 0 -10 -20 -30 -40 -50 -60 200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Data number

Fig. 4. Relative deviation of calculated values versus experimental values with the MLR algorithm

16


Page 17 of 17

2000

Exp test ELM test

Exp train ELM train

1800 1600 1400

Heat capacity values

1200 1000 800 600 400 200 0 0

250

500

750

1000

1250

1500

1750

2000

2250

2500

Data number

Fig. 5. Calculated versus experimental heat capacity values using the ELM algorithm for all ionic liquids

training set test set

30

20

Relative deviation /%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

0

-10

-20

-30 200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

Data number

Fig. 6. Relative deviation of calculated values versus experimental values with the ELM algorithm

For Table of Contents Only

17


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