NJC View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. PAPER Cite this: New J. Chem., 2021, 45, 18584 View Journal | View Issue Prediction of ionic conductivity of imidazoliumbased ionic liquids at different temperatures using multiple linear regression and support vector machine algorithms† Zi Kang Koi,a Wan Zaireen Nisa Yahya *ab and Kiki Adi Kurniac Ionic liquids (ILs) are well recognized as promising and environmentally friendly solvents owing to their remarkable features, which have captured the imagination of the global research community to expand ILs’ usage across various industrial processes and applications. Nevertheless, the formulation of ILs with desired properties requires strenuous effort in discovering the suitable combination of cations and anions. Hence, it is imperative to develop simple and accurate models to predict the physicochemical properties of ILs prior to experimentation. Ionic conductivity is one of the most significant intrinsic properties which affects the transport capabilities of ILs and it has been a limiting factor in the design of suitable ILs. In the present study, the conductivity of different imidazolium-based ILs has been estimated and correlated via the Quantitative Structure–Property Relationship (QSPR) approach using two different algorithms, namely multiple linear regression (MLR) and support vector machine (SVM) regression coupled with stepwise model-building. A set of descriptors, including interaction energies as well as dielectric energy of the ILs’ cation–anion pairs generated by the Conductor-like Screening Model for Real Solvents (COSMO-RS), were employed to derive the best-fit model. The models were developed using experimental data of imidazolium-based ionic liquids collected from the literature with conductivity in the range of 0.008–5.1 S m1 at temperatures between 268.15 K and 398.15 K. The coefficients of determination (R2) for the MLR and SVM model’s entire data set are 0.8556 and 0.9906, respectively, while the average absolute relative deviations (AARD) are 46.55% and 7.15%, respectively. Received 15th April 2021, Accepted 1st September 2021 This suggests that the non-linear model developed using the SVM regression algorithm fits better with DOI: 10.1039/d1nj01831k that conductivity is highly affected by van der Waals forces and temperature, followed by electrostatic the conductivity data set and is more reliable than the MLR algorithm. The stepwise approach reveals forces and dielectric energy to some extent. The prediction results from this work will aid the screening rsc.li/njc process of suitable ILs with desired conductivity for specific applications. Introduction Ionic liquids (ILs), which are molten salts at ambient temperature, represent an important class of materials which are currently widely investigated for numerous potential applications, such as extraction and separation processes, lubricants, waste recycling, catalysis, gas separation, CO2 capture, electrochemical energy a Department of Chemical Engineering, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia. E-mail: zaireen.yahya@utp.edu.my; Tel: +605-368 7584 b Center of Research in Ionic Liquids, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak Darul Ridzuan, Malaysia c Department of Chemical Engineering, Faculty of Industrial Technology, Institut Teknologi Bandung, Jl. Ganesha No. 10, Bandung 40132, Indonesia † Electronic supplementary information (ESI) available. See DOI: 10.1039/ d1nj01831k 18584 | New J. Chem., 2021, 45, 18584–18597 storage, and energy devices.1–3 These applications are driven by ILs’ desirable features of salts such as nonvolatility, superior electrochemical and thermal stability, high polarity, and high ionic conductivity.4–7 The common classes of cations encompass imidazolium, pyridinium, phosphonium, and ammonium, whereas the anions are usually inorganic in nature such as halides, sulfates, and phosphates.4 Their tunable nature and environmentally friendly characteristics offer numerous opportunities for improving existing processes and exploring new possibilities, thus making it essential to understand their behavior in the systems.8 Exemplarily, a study of the ILs’ properties and structure–property relationships for ILs is significant to provide valuable information on the design of suitable ILs. However, due to the immense number of ILs, one can envisage that possibly more than 108 ILs can be formed by combining different sets of anions and cations. The experimental This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. Paper NJC determination of ILs’ properties is time-consuming, expensive, and unrealistic.9,10 Therefore, methods for a priori prediction of ILs’ properties are highly desirable as they would provide a preliminary understanding that aids in the selection and design of suitable ILs for specific applications. To date, there have been several attempts at building predictive models via different approaches such as quantitative structure–property relationship (QSPR), group contribution method (GCM), ab initio molecular dynamics (AIMD), and machine learning.11,12 One of the critical properties that has drawn considerable attention from many researchers is ionic conductivity (s). Conductivity and its inverse, resistivity, represent the strength of cation–anion motion in ILs under an electric potential difference.13 Conductivity is also the measure of a material’s ability to allow the transport of free ions, which is a piece of crucial information in devising electrochemical applications.14–16 ILs with high conductivity at low temperatures are of extreme interest as they can replace organic solvents for charge transport in energy generators and batteries.17 Previously, Abbott18 successfully developed a model to predict the conductivity of ambient-temperature molten salts based on the Stokes–Einstein equation as follows: s¼ z2 Fer 1 Rþ þ R1 6pZMw (1) where s is the conductivity, z is the charge on the ion, F is the Faraday constant, e is the electronic charge, r is the density, Z is the viscosity, Mw is the molar mass of the IL, and R+ and R are the radii of the cation and anion respectively. The model pivots around the concept of ‘‘hole theory’’ in which the IL system is assumed to behave like an ideal gas. Its motion is limited by the availability of sites or holes for the migration of ions during charge transfer.19 Although the model shows a good correlation, this method has several drawbacks which limit its application for predicting the properties of unknown ILs. These include lengthy computational procedures, the need for some experimental data from the studied ILs and the fact that it is solely applicable for ambient-temperature ILs. Slattery et al.20 in a different approach proposed a simple volume-based method to predict ILs’ conductivity. They concluded that the conductivity decreases exponentially with increasing molecular volume and such a relationship can be interpreted in terms of ion mobility, whereby the conductivity is proportional to the motion of charge carriers in the ILs. The expression is as follows: s = cedVm (2) where c and d are empirical constants of best fit, and Vm is the molecular volume. It was found that the experimental and the predicted conductivity are highly correlated with an R2 value of 0.9871. Despite the simplicity, the caveat is that the model was developed based on pure ILs that are liquid at limited temperatures spanning from 293.15 to 295.15 K. Besides, the model does not account for generality as the empirical constant needs to be derived separately for different cation–anion pairs. For this equation to be temperature-dependent, Wileńska et al.21 introduced a T0/T term with T0 being set at 298.15 K, as shown below: T0 s ¼ cedVm T (3) However, it was reported that this equation only performs relatively well in the temperature range of 298.15–343.15 K, which could limit its predictive capability. From the experimental point of view, ionic conductivity data are commonly described using the Arrhenius model, which is correlated with temperature as follows: 1 s¼f (4) T Based on such temperature dependency, with 300 data points for 15 ILs, Coutinho and Gardas22 applied Vogel– Fulcher–Tammann (VFT) equation, which is also a function of temperature to predict the conductivity as follows: ln s ¼ ln As þ Bs ðT T0s Þ (5) where As, Bs and T0s are adjustable parameters, from which As and Bs can be obtained with a group contribution method (GCM). The GCM, also known as an additive method, is often used to develop a relationship between the chemical substructures and the desired physical property as the summation of the contributions of certain defined groups of atoms allowing prediction of the estimated property value.23,24 Their model indeed shows a good agreement between experimental and calculated conductivity values (R-squared (R2) = 0.9974, average absolute relative deviation (AARD) = 4.57%). However, an empirical fitting parameter T0s, also known as the Vogel temperature, is required. Estimation of this parameter is done by assuming that the glass transition temperature (Tg) of the IL is known; otherwise the VFT equation is not applicable for the prediction of the IL conductivity. Nevertheless, the VFT equation is widely used as the initial expression to generate models for the conductivity of ILs.11,21 With the reported success of previous work on the viscosity model,25 Chen et al. employed a similar GCM equation to predict the conductivity as follows:26 2 s 100 100 ln ¼ As þ Bs (6) þ Cs R0s T T where s is the electrical conductivity in S m1, T is the temperature in K, R0s is an adjustable parameter, also with a unit of S m1, while As, Bs and Cs are calculated from the group contribution method. They investigated 1578 experimental data points of conductivity, including 77 ILs covering 8 cation cores, 34 anions, and 4 side groups in a wide range of temperature (248.05–468.15 K) and conductivity (0.0017–9.167 S m1). Although the model has an acceptable AARD of 3.30%, the GCM heavily relies on the contribution values of the groups. Thus, its capability to estimate the conductivity for some ILs may be hindered due to the lack of some group contribution values.9,27 This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 New J. Chem., 2021, 45, 18584–18597 | 18585 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. NJC Paper Nilsson-Hallén et al.11 offered another thought-provoking approach by comparing two VFT based models for IL conductivity which were developed using volume, mass, and moment of inertia of the constituting ions and the energy of the interaction between cation and anion. Both equations are as follows: b Eint s¼ (7) exp c T T0 Vtot Mred Iþ b E int s¼ exp c Vtot Mred Iþ T Tg þ d ! (8) where Vtot is the sum of the cation and anion volumes, Mred is the reduced mass, I+ is the moment of inertia of the cation, and Eint is the interaction energy, while b, c, d and T0 are fitting parameters and Tg is the glass transition temperature from the literature. The difference between both models is that one is with the inclusion of experimental glass transition temperatures (R2 = 0.9600) while the other has T0 as a fitting parameter (R2 = 0.9508). They investigated a total dataset of 176 data points for 22 ILs and found that the inclusion of experimental glass transition temperatures did improve the fit but not to a large extent, and that it will narrow the temperature range that the model can predict. Despite the high R2 value, the models do not provide any valuable information on the relationship between each parameter and conductivity. The second approach attempted by Coutinho and Gardas22 was to correlate the molar conductivity of ILs with reciprocal of viscosity based on the Walden rule, which can be written as LZa = constant (9) where L is the molar conductivity and Z is the viscosity. The expression of molar conductivity is as follows: L = sM/d (10) 1 where M is the molecular weight (g mol ) and d is the density (g cm3) of the IL. The correlation was indicated in a log–log plot with the Walden line slope obtained as 0.935 0.008. According to Galiński et al.,28 they investigated and discovered that the Walden rule is applicable for a wide range of ILs while confirming the significant influence of viscosity on ionic liquid conductivity. Combining both the Walden rule and the Stokes–Einstein relation, the self-diffusivity can be correlated with conductivity through a Nernst–Einstein relation as follows:29 sNE ¼ Npair 2 qþ Dþ þ q2 D Vkb T (11) where Npair is the number of ion pairs, q+ and q are the cation and anion charges, and D+ and D are the self-diffusivities of the cations and anions, respectively. The difference between the actual ionic conductivity and the conductivity predicted by the Nernst–Einstein relation is usually expressed as follows:30 s = sNE(1 D) 18586 | New J. Chem., 2021, 45, 18584–18597 (12) where D is a Nernst–Einstein deviation parameter which is related to differences in cross-correlations of ionic velocities. Liu and Maginn29 employed the Nernst–Einstein model to study the conductivity of six different ionic liquids containing imidazolium, pyrrolidinium, and ammonium cations paired with bis(trifluoromethylsulfonyl)imide and bis(perfluoroethylsulfonyl) imide anions using molecular dynamics simulations. Although the model suggests that these ILs follow the Walden rule over the entire temperature range closely, the model prediction performance is subpar and all predicted ionic conductivity values were underestimated by a factor of 2 to 10. Additionally, the complex force-field parameters and intramolecular potential parameters need to be determined while electronic structure calculations need to be performed using special software such as Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).31 Essentially, a robust predictive model should preferably be user-friendly, non-empirical, and accurate. Another intriguing approach that has been widely used to correlate the conductivity of ILs is the quantity structure–property relationship (QSPR) approach. Tochigi and Yamamoto6 compared two different models that were generated via the polynomial expansion (PE) method and the multiple regression (MR) method, respectively, in predicting conductivity. The parameters used include dipole moment, ionization potential, lowest unoccupied molecular orbital (LUMO) energy, the charge on the nitrogen atom, area, volume, and ovality. Interestingly, they found that the PE method results in a higher R2 value (R2 = 0.9745, absolute average error = 0.457) as compared to the MR method (R2 = 0.9089, absolute average error = 0.928). Despite the high goodness of fit, the model is considerably complicated, with 25 input variables in the equation. Some variables are attributed to specific anions, which may confine its application to predicting the conductivity of other ILs with different anions. Additionally, the conductivity term in both PE and MR equations was not transformed into a logarithmic function. Recently, machine learning models such as the Artificial Neural Network (ANN), Fuzzy Logic System (FLS), Adaptive Network-based Fuzzy Inference System (ANFIS), and Support Vector Machine (SVM) have been recognized as the next frontier of statistical learning approaches.4,32–34 Kianfar et al.12 proposed an ANN model for predicting the conductivity of pyridinium-based hydrophobic ionic liquids using 36 data points for the network training and 12 data points for testing the neural network (R2 = 0.9999). It is undeniable that their model generates high goodness of fit. Nevertheless, the number of data points used to train the model is comparatively insufficient, and the predictive performance of this method is not fully established. Although the ANN has been successfully applied, there are some underlying concerns regarding its model architecture, for instance, over-fitting training, local minima, network optimization, low generalizability, as well as reproducibility of results, which may be attributed to the networks’ random initialization and variation of stopping criteria.35 SVM is a new popular supervised learning approach to address regression problems. It has attracted significant This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. Paper attention due to its extraordinary aptitude and generalization performance in interpreting the non-linear relationships between molecular structure and properties.35–37 One of the key advantages of the SVM algorithm is that the data overfitting can be effectively minimized as compared with the ANN algorithm.35 LIBSVM, a library for SVMs provided by Chang and Lin,38 has been successfully used to solve regression problems. Gharagheizi et al.39 established a least square support vector machine-group contribution (LSSVM-GC) model, which included an extensive set of 1077 experimental conductivity data for 54 ILs with temperature ranging from 238 to 480 K and conductivity ranging from 0.00009 to 20 S m1. Given that they have used an extensive database, an R2 of 0.997 and an overall AARD of 3.3% can be perceived as highly satisfactory. Nevertheless, as mentioned earlier, the data available for group contribution are limited, which may lead to an inability to estimate the conductivity of other ILs. Fayyaz et al.40 introduced an LSSVM model optimized by the coupled simulated annealing (CSA) algorithm for an accurate estimation of the conductivity of ILs in propylene carbonate as a function of molecular weight of the IL, temperature, and IL concentration in solution (R2 = 0.996). A total number of 828 data points covering 7 ILs with the temperature ranging from 258.15 to 363.15 K and the conductivity ranging from 0.142 to 10.48 S m1 were used for the model development. Their model has indeed proven its reliability and robustness; however, it does not provide molecular insights and understanding on the contribution of each parameter to conductivity. It is essential to develop a model that offers a valuable theoretical basis justifying each factor’s significance in affecting the conductivity. Following the drawbacks of these models, we find it meaningful to build a comprehensive QSPR model which possesses high accuracy of predictive capability yet offers simplicity and provides valuable insights in terms of the impact of each predictor, namely the molecular interaction energy of the ILs on the conductivity. In our previous work, we have developed a correlation model between viscosity and interaction energies via a stepwise multiple linear regression (MLR).41 In this work, we propose 2 different models, which are stepwise MLR and stepwise SVM regression, to compare both models’ predictive capability. The performance and accuracy of both models are evaluated by undertaking statistical error analyses of the results. Methodology Dataset A total of 239 experimental conductivity data points with a wide range of temperatures (268.15–398.15 K) for 25 ILs were used to build the predictive models.26,42–44 The cations include 1-ethyl3-methylimidazolium [C2C1im]+, 1-butyl-3-methylimidazolium [C4C1im]+, 1-propyl-3-methylimidazolium [C3C1im]+, 1-hexyl-3methylimidazolium [C6C1im]+ and 1-octyl-3-methylimidazolium [C8C1im]+, whereas the anions include bis(trifluoromethylsulfonyl) imide [N(CF3SO2)2], bis(pentafluoroethylsulfonyl)imide [N(C2F5SO2)2], methanesulfonate [CH3SO3], tetrafluoroborate NJC [BF4], acetate [CH3CO2], ethylsulfate [C2H5SO4], octylsulfate [C8H17SO4], hexafluorophosphate [PF6], methylsulfate [CH3SO4], tetracyanoborate [B(CN)4], thiocyanate [SCN], tricyanomethanide [C(CN)3], trifluoroacetate [CF3CO2], tris(pentafluoroethyl)trifluorophosphate [(C2F5)3PF3] and trifluoromethanesulfonate [CF3SO3]. Note that ILs with halide anions are not included in the data set as most of these ILs (for short alkyl chains) exist in the solid phase at room temperature due to higher melting points.45,46 The chemical structures of the cations and anions used are depicted in Fig. 1. By the rule of thumb, the data were randomly divided into training and test sets, with 190 data points (80%) chosen as the training set and the remaining 49 data points (20%) used as the test set, the latter of which consists of ILs at different temperatures as well as the ILs that were not used in the training set.47 The training set is used to develop the model, while the test set is used to validate and fine-tune the model. Both the training and test set data are provided in Table S1 in the ESI.† COSMO-RS Following our previous work on the correlation between viscosity and interaction energies,41 we aim to use similar parameters for the development of a predictive model that can estimate a priori conductivity and gather more in-depth insight into the mechanisms that impact the conductivity; thus the Conductor-like Screening Model for Real Solvents (COSMO-RS) was used herein. COSMO-RS is a thermodynamic model coined by Klamt48 with a quantum chemistry-based statistical framework that is used to predict the thermodynamic properties of fluid and liquid mixtures. In the molecular interaction approach, there are three intermolecular interaction energies, namely electrostatic or misfit (EMF), hydrogen-bonding (EHB) and van der Waals forces (EvdW), that can be estimated by COSMO-RS.49 These energies are described by eqn (13)–(15), respectively: a0 2 EMF ¼ aeff ðs þ s0 Þ 2 (13) EHB = aeffcHBmin(0;min(0;sdonor + sHB) max(0;sacceptor sHB)) (14) 0 EvdW ¼ aeff tvdW þ tvdW (15) where s and s 0 are the screening charge densities of two different segments; aeff, a 0 , cHB and sHB are the effective contact surface area, the misfit energy constant, the hydrogen bond coefficient, and the cut-off of the hydrogen bond, respectively; sdonor and sacceptor represent the screening charge densities of hydrogen bond donor and acceptor segments, respectively; and tvdW is the element-specific vdW interaction parameter. Additionally, these three interaction energies form the total interaction energy, EINT, as described in eqn (16): EINT = EMF + EHB + EvdW (16) In addition to these descriptors, here we introduced an additional descriptor, the dielectric energy, EDiel, which can This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 New J. Chem., 2021, 45, 18584–18597 | 18587 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. NJC Paper Fig. 1 Chemical structures of cations and anions composing the studied ILs. Cations: (a) methylimidazolium, (c) 1-butyl-3-methylimidazolium, (d) 1-hexyl-3-methylimidazolium, and bis(trifluoromethylsulfonyl)imide, (b) bis(pentafluoroethylsulfonyl)imide, (c) methanesulfonate, (d) (g) octylsulfate, (h) hexafluorophosphate, (i) methylsulfate, (j) tetracyanoborate, (k) thiocyanate, tris(pentafluoroethyl)trifluorophosphate and (o) trifluoromethanesulfonate. be described as half of the electrostatic interaction energies of the ideally screened and self-consistently polarized solutes with their screening charges based on eqn (17):50 EDiel ¼ 1X 1X Fv qv ¼ Fv sv sv 2 v 2 v (17) where Fv is the electrostatic potential, qv is the ideal screening charge, sv is the area, and sv is the ideal screening charge density on the v segment, respectively. Several researchers have made successful attempts at developing models based on these energy descriptors generated by COSMO-RS so as to predict the hydrogen-bond basicity of ILs,51 the ability of ILs as a thermodynamic hydrate inhibitor for methane hydrate,52 as well as the contact angles and wettability of ILs on polar and nonpolar surfaces.53 In this work, the COSMOthermX program with the parameter file BP_TZVP_C30_1201 was used in all the calculations. All the COSMO files required are available in the COSMOthermX database. The EMF, EHB, EvdW and EDiel values for the studied ILs are 18588 | New J. Chem., 2021, 45, 18584–18597 1-ethyl-3-methylimidazolium, (b) 1-propyl-3(e) 1-octyl-3-methylimidazolium. Anions: (a) tetrafluoroborate, (e) acetate, (f) ethylsulfate, (l) tricyanomethanide, (m) trifluoroacetate, (n) provided in Table S1 in the ESI.† Another descriptor is also considered in this model, which is 1/T as the conductivity is temperature dependent. QSPR models To select proper and suitable descriptors capable of forming a relationship with conductivity, a stepwise regression was used.53 The approach starts with a single input variable as an initial establishment of the correlation model. The model is then recurrently improved by adding a new variable or removing less significant variables until a satisfactory and accurate model is obtained. The MLR and SVM algorithms were employed to develop new models for the prediction of conductivity of ILs. MLR is a popular QSPR method because of its simplicity, transparency, reproducibility, and easy interpretability.47,54 This method correlates a set of data points of the desired property (y) with one or more descriptors (xn) in a linear form as described in This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 View Article Online Paper NJC Results and discussion eqn (18):55 y ¼ a0 þ n X an xn (18) Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. 1 where y represents the property value, xn is any molecular descriptor, and an is the regression coefficient. SVM is an intelligent and supervised algorithm initially developed by Cortes and Vapnik. It has been used for regression, clustering, and pattern recognition problems in various fields of science and engineering.4,56–59 SVM has been proven to be very effective in solving non-linear regression problems.35,60 Generally, the SVM function can be defined as follows: y = wTF(x) +b (19) where x represents the input variables with an N n matrix (N and n are the total number of data points and number of input variables, respectively), F(x) is the kernel function, wT is the output layer transposed vector, and b denotes the bias. Although SVM’s general equation is very similar to that of MLR, SVM allows the input variables to be mapped to a highdimensional feature space via a selected kernel function, and then the linear regression occurs in the feature space.61 Such robust non-linear feature mapping enables a non-linear problem to be solved in a linear space. The selection of the kernel function is very crucial as each type of function distributes the data points in the highdimensional feature space differently, thus generating different correlation coefficients. One of the most common kernel functions, which is the radial basis function (RBF), is used in this study because it is effective and fast in the training process.35 The RBF is described in eqn (20): K(x, xk) = exp(g8xk x82) (20) where K(x, xk) is the Kernel function calculated from the inner product of the two vectors x and xk in the feasible region and g is the tuning parameter. For a RBF kernel, there are 2 main tuning parameters, namely g and a cost function, C. C can be defined as a regularization constant that identifies the trade-off between minimization of the training error and maximization of the margin. The optimization of C and g is required to improve the accuracy of the model in predicting unknown data in the test set.62 For instance, if the C value is too small, insufficient stress will be placed on fitting the training data, which results in underfitting of the model. If the C value is too large, the model gets overfitted. The g parameter determines the distance of a single data sample that exerts influence. In our work, the best values of C and g were identified via a ‘‘gridsearch’’ method. The best MLR and SVM equations were selected based on the lowest Average Absolute Relative Deviation (AARD) and the highest R-squared (R2) value as screening criteria. The QSPR models’ accuracy was ascertained by further statistical analyses, including Standard Deviation Error (STDE) and Root Mean Square Error (RMSE). The electrical conductivity of ILs is one of the intrinsic properties that is critical, especially for electrochemical applications. Therefore, systematic knowledge of the effect of interaction energies on conductivity is of high importance. As all systems studied in this work are based on the imidazolium cation, it allows us to evaluate the impact of the alkyl chain length and anion on conductivity. The experimental and predicted conductivity values are given in Table S2 in the ESI.† Results of the stepwise MLR algorithm The correlations between selected descriptors and conductivity upon stepwise MLR regression are summarized in Table 1 and Fig. 2. A total of 190 experimental ionic conductivity data points of imidazolium-based ionic liquids, gathered from Chen et al.,26 were used as the training set data to build the predictive model. The first three equations (cf. eqn (21)–(23)) consist of (i) individual interaction energy that arises from each cation and anion and (ii) temperature. Table 1 shows that the hydrogen-bonding interaction has less influence on conductivity than the electrostatic interaction and van der Waals force, which is a similar outcome for viscosity property as presented in our previous work.41 This is likely to be attributed to the complexity and asymmetry of such polar and non-coordinating liquids.46,63 It was discovered that the contribution of dispersion force, which is part of the van der Waals forces, can outbalance the hydrogen-bonding energy with increasing temperature.64 The equation with EvdW produced the highest R2 value and the lowest AARD value when compared to other single interaction energy correlations. This elucidates that the van der Waals interaction energies between cation and anion of the ionic liquid have a pivotal impact on the electric potential of these fluids. Despite being simple, the yielded R2 value (0.5193) and AARD (72.81%) of the 3-descriptor equation are far below satisfactory. Therefore, a multidescriptor approach was then employed. Since the EvdW was identified as the interaction energy with the dominant contribution, extra descriptors were further added to eqn (23), resulting in a series of eqn (24)–(26) as listed in Table 1. The addition of EMF to eqn (23) results in a higher R2 value and a lower AARD as compared to the addition of EHB due to the smaller influence of hydrogen bonding. Interestingly, the combination of all three types of interaction energies in eqn (26) yields a nearly similar R2 value and AARD compared to eqn (25). This is in good agreement with the research outcome by Shi et al.65 in which the intermolecular attraction force in ionic liquids is mainly from the sum of electrostatic force and van der Waals force. According to Delhorbe et al.,66 both glass transition temperature and charge carrier density, which are associated with the polymer backbone’s segmental motion, are not the only factors that influence the charge transport in 1-alkyl3-vinylimidazolium bis-(trifluoromethane)sulfonimide-derived homopolymers. The charge mobility is also attributed to its self-assembling nanostructure, which is determined by the sum of Coulombic repulsion and van der Waals interactions. This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 New J. Chem., 2021, 45, 18584–18597 | 18589 View Article Online NJC Paper Table 1 Stepwise MLR to evaluate the relationship between the experimental conductivity values and the interaction energies (in kcal mol1) together with dielectric energy (in kcal mol1) estimated using COSMO-RS R2 AARD (%) Eqn lnðsÞ ¼ 6:5868 EHB;Cation þ ð6:5336Þ EHB;Anion 0.3427 99.13 (21) 1 þ 11:2667 T lnðsÞ ¼ ð0:2413Þ EMF; Cation þ ð0:0510Þ EMF;Anion 0.3931 92.81 (22) 1 þ 13:1135 T lnðsÞ ¼ 0:3495 EvdW;Cation þ 0:0192 EvdW;Anion 0.5193 72.81 (23) 1 þ 13:9012 T lnðsÞ ¼ ð11:0498Þ EHB;Cation þ 11:3014 EHB;Anion 0.5009 66.13 (24) 0.6783 64.56 (25) 0.7032 64.53 (26) 0.8653 45.86 (27) Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. þ ð3839:5942Þ þ ð4027:5787Þ þ ð3630:7134Þ þ 0:4244 EvdW;Cation þ 0:1003 EvdW;Anion 1 þ 14:1212 T lnðsÞ ¼ 0:0713 EMF;Cation þ ð0:6712Þ EMF; Anion þ ð3214:1704Þ þ 0:4112 EvdW; Cation þ ð0:2034Þ EvdW; Anion 1 þ 16:3842 T lnðsÞ ¼ 12:7664 EHB;Cation þ ð13:1097Þ EHB;Anion þ ð4121:3225Þ þ ð0:2606Þ EMF;Cation þ ð0:6731Þ EMF; Anion þ 0:3229 EvdW; Cation þ ð0:1776Þ EvdW;Anion 1 þ 18:5985 T lnðsÞ ¼ 0:9284 EMF; Cation þ ð0:9506Þ EMF; Anion þ ð4661:9406Þ þ 0:5266 EvdW;Cation þ ð0:3081Þ EvdW; Anion þ ð0:7667Þ EDiel; Cation þ 0:0983 EDiel; Anion þ ð3513:9528Þ 1 þ ð21:1878Þ T The linear model based on eqn (25) was then further improved with the addition of EDiel, which represents the energy needed for dielectric polarization, which explains its good correlation with ionic conductivity.67 Next, the test set’s conductivity was predicted using eqn (27) to evaluate its reliability and goodness of fit. The cross-plot of experimental data versus calculated/predicted data and the relative deviations for both training and test sets are presented in Fig. 4. The calculated statistical error parameters for s are shown in Table 3. As can be seen from Fig. 4(a), the calculated conductivity values were not in good agreement with the experimental conductivity values. As shown in Fig. 4(b), the AARD of the whole set is 46.55%, and almost 77% of the predicted ILs’ conductivity values have above 15% deviation. Thus, these results suggest that eqn (27) established by the MLR algorithm is not a suitable model. Hence, it is necessary to develop a non-linear regression model to fit the data. Results of the stepwise SVM regression algorithm The same descriptors selected for the MLR algorithm were applied as the input parameters to establish a non-linear model 18590 | New J. Chem., 2021, 45, 18584–18597 using the SVM algorithm. The correlations between selected descriptors and conductivity upon stepwise SVM regression are summarized in Table 2 and Fig. 3. Similarly, a stepwise approach was applied to evaluate the significance of each interaction energy parameter. Although the R2 value of the EvdW-based model (0.7596) is slightly lower than that of the EMF-based model (0.8435), van der Waals force was again identified as the principal contributor as its AARD of 28.17% is significantly lower than those of eqn (28) and (29), which are 72.12% and 53.54%, respectively. Also, the addition of EMF to eqn (30) results in a higher R2 value and a lower AARD as compared to the addition of EHB. The statistical result of eqn (32) is on par with the model which combines all three interaction energies, and thus the EDiel descriptor was added to eqn (32). When C = 1024, g = 0.0156 and epsilon = 0.0800 with 37 support vectors, the best model was obtained. The cross-plot of experimental data versus calculated/ predicted data and the relative deviations for both training and test sets are portrayed in Fig. 5. The calculated statistical error parameters for s are shown in Table 3. Based on Fig. 5(a), the results are concentrated on the unit slope line (line Y = X), This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. Paper NJC Fig. 2 Stepwise MLR models: (a) eqn (21), (b) eqn (22), (c) eqn (23), (d) eqn (24), (e) eqn (25), (f) eqn (26), and (g) eqn (27). R2 values: (a) 0.3427, (b) 0.3931, (c) 0.5193, (d) 0.5009, (e) 0.6783, (f) 0.7032, and (g) 0.8653. Table 2 Stepwise SVM to evaluate the relationship between the experimental conductivity values and the interaction energies (in kcal mol1) together with dielectric energy (in kcal mol1) estimated using COSMO-RS Parameter (x) EHB lnðsÞ ¼ n P 2 ai exp gkxi xnew k þ b EMF EvdW EDiel — — i — — — — — — — — — — — — — — 1 T — — — — — — — — g b C Epsilon nSVs R2 AARD (%) Eqn 0.3333 0.3333 0.3333 0.2000 0.2000 0.1429 0.1429 0.0156 0.3681 0.0066 0.3023 0.5790 0.1328 0.2066 0.3796 5.1408 1 1 1 1 1 1 1 1024 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.1000 0.0800 138 127 108 87 79 75 67 37 0.4488 0.8435 0.7596 0.7826 0.9657 0.9588 0.9788 0.9915 72.12 53.54 28.17 15.78 13.50 14.06 12.95 6.99 (28) (29) (30) (31) (32) (33) (34) (35) which elucidates that the SVM regression algorithm’s new model is robust and has a more superior prediction capability than the MLR algorithm. Moreover, the resulting AARD of the whole set is 7.15%, and more than 95% of the data points show deviations within 15%, which indicates a good accuracy for the imidazolium-based ILs. Some of the observed deviations may be due to impurities or water as it may improve the ionic conductivity.68 The mathematical expression of the SVM model is in the form of a Gaussian radial basis function kernel (RBF), which is expressed as eqn (36): lnðsÞ ¼ n X 2 ai exp 0:0156kxi xnew k 5:1408 (36) i where ai, xi, and xnew are the coefficients of the support vector, support vectors (SVs), and new input variables, respectively. ai and xi are provided in Table S6 in the ESI.† It is of high importance that normalization processing should be first carried out before using the model. Please note that to easily calculate the conductivity values of ILs in the MATLAB software, the LIBSVM toolbox should be initially installed (which can be downloaded online for free).38 Effect of the alkyl chain length on the ionic conductivity Understanding how the alkyl chain length might affect the transport properties of ILs is fundamentally important. Fig. 6 portrays the effect of the alkyl chain length on the conductivity of ILs. As shown in Fig. 6, the conductivity of imidazoliumbased ILs paired with the bis(trifluoromethylsulfonyl)imide anion decreases with increasing alkyl chain length, which can be explained by the increase in the viscosity of ILs due to the This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 New J. Chem., 2021, 45, 18584–18597 | 18591 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. NJC Paper Fig. 3 Stepwise SVM regression models: (a) eqn (28), (b) eqn (29), (c) eqn (30), (d) eqn (31), (e) eqn (32), (f) eqn (33), (g) eqn (34), and (h) eqn (35). R2 values: (a) 0.4488, (b) 0.8435, (c) 0.7596, (d) 0.7826, (e) 0.9657, (f) 0.9588, (g) 0.9788, and (h) 0.9915. Fig. 4 MLR plots using eqn (27): (a) experimental versus calculated conductivity with an R2 value of 0.8556 and (b) relative deviations between the experimental and calculated conductivity. Symbols: ( ), training set and ( ), test set. increase of the side chain length.26 In other words, an increase in the cationic size or –CH2– units will increase the van der Waals interactions in terms of the alkyl chain-ion inductive forces and the CH–CH bond interaction.70,71 This is consistent with the observations by Sun et al.72 in which the conductivity increases from [P2224]+ to [P2228]+-based ILs even at different temperatures due to the elongation. The ion-pairing interaction and ion mobility are slightly reduced for ILs with longer alkyl chain length which results in a lower threshold positive potential to oxidize the anion, thus leading to lower ionic conductivity. Hanabusa et al.73 deduced that the ionic 18592 | New J. Chem., 2021, 45, 18584–18597 conductivity is highly correlated with the viscosity upon discovering that the ionic conductivity of [DBUH]+-based protic ILs increases as the carbon number in the carboxylate ion increases to 8. In contrast, the viscosity decreases for the same carbon number range. Effect of different anions on the ionic conductivity Given the established SVM model’s reliable performance, eqn (35) was used to predict the conductivity values of other ILs not studied in this work (or ILs with no available experimental data). A database of conductivities comprising 7 This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. Paper NJC Fig. 5 SVM regression plots using eqn (35): (a) experimental versus calculated conductivity with an R2 value of 0.9906 and (b) relative deviations between the experimental and calculated conductivities. Symbols: ( ), training set and ( ), test set. Table 3 The statistical error parameters for s via the MLR and SVM approach Statistical parameter MLR SVM Training set R2 Average absolute relative deviation Standard deviation error Root mean square error No. of data points 0.8653 45.86% 0.4852 0.4868 190 0.9915 6.99% 0.0831 0.0851 190 Test set R2 Average absolute relative deviation Standard deviation error Root mean square error No. of data points 0.7717 49.21% 0.4034 0.3993 49 0.9900 7.76% 0.0575 0.0570 49 Total R2 Average absolute relative deviation Standard deviation error Root mean square error No. of data points 0.8556 46.55% 0.4695 0.4702 239 0.9906 7.15% 0.0787 0.0801 239 different 1-alkyl-3 methylimidazolium-based cations combined with 41 anions resulting in a total of 287 ILs was built. The full name, abbreviation, and cation or anion numbering of the ILs are given in Table S3 in the ESI.† The predicted conductivity values are provided in Table S4 in the ESI† and illustrated in Fig. 7. ILs paired with halide ions are not presented in this chart due to their high melting point properties, due to which they exist in crystalline form at room temperature.46 ILs that are paired with a larger anion such as [N(CN)3] (volume = 113.8148 Å3) display higher conductivity regardless of the alkyl chain length as compared to the smaller [BF4]-based (volume = 72.8506 Å3) ILs. The increase in anion size may decrease the interaction between anion and cation, mainly affected by the reduced hydrogen bond strength and Coulomb interaction.74 The decrease in interionic interaction results in reduced hindrance to the migration of charge, resulting in increased Fig. 6 Predicted vs. experimental conductivity value for [CNC1im][N(CF3SO2)2], where N = 2–9, at T = 298.15 K and P = 0.1 MPa. Symbols: (m), experimental value collated by Chen et al.;26 (K), experimental value by Papović et al.;7 (K), experimental value by Widegren et al.;69 and (m), predicted value using the SVM model. ionic conductivity. As the weakly coordinating or less symmetric anions such as [N(CF3SO2)2] and [N(C2F5SO2)2] have lower viscosities, the observed higher conductivities of these ILs is well justified.25 In general, the extent of this database can be as large as desired as the model established only requires two types of cation–anion interaction energies and dielectric energy that can be estimated using COSMO-RS. Thus, Fig. 7 can be used as an a priori tool to screen suitable ILs before running the experimental study. Comparison with existing models In this section, the performance of the developed SVM regression model in predicting the ionic conductivity of imidazolium-based ILs is evaluated graphically and statistically. Moreover, the results This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 New J. Chem., 2021, 45, 18584–18597 | 18593 View Article Online Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. NJC Paper Fig. 7 Predicted ionic conductivity values of 287 imidazolium-based ILs at T = 298.15 K and P = 0.1 MPa. of our model are compared with the existing models found in the literature for verification. Fig. 8 presents the experimental conductivity values and the predicted conductivity values from COSMOthermX, Chen et al.,26 Gharagheizi et al.,39 and our present work for [C4C1im]+ paired with [CH3CO2], while Fig. 9 presents the values for [C4C1im]+ paired with [CF3SO3]. The conductivity values are provided in Table S5 in the ESI.† As can be seen from Fig. 8 and 9, our model shows a far more superior prediction capability with less deviation from the experimental value as compared to the COSMO model, which was built with more than 50% of its training data being comprised of [N(CF3SO2)2]-based ILs.75 The GC-based model and the LSSVM-GC model proposed by Chen et al.26 and Gharagheizi et al.,39 respectively, show similar reliability in comparison to our model but the GCM is limited to the number of group functions used in the model, and thus cannot be Fig. 8 Comparison between experimental and predicted conductivity values from the COSMO model, Chen et al.,26 Gharagheizi et al.,39 and present work for 1-butyl-3-methylimidazolium acetate at P = 0.1 MPa. Symbols: (m), experimental value; (K), COSMO model; (K), Chen et al.; (K), Gharagheizi et al.; and (m), predicted value using the SVM model. 18594 | New J. Chem., 2021, 45, 18584–18597 Fig. 9 Comparison between experimental and predicted conductivity values from the COSMO model, Chen et al.,26 Gharagheizi et al.,39 and present work for 1-butyl-3-methylimidazolium trifluoromethanesulfonate at P = 0.1 MPa. Symbols: (m), experimental value; (K), COSMO model; (K), Chen et al.; (K), Gharagheizi et al.; and (m), predicted value using the SVM model. applied when a new group is introduced. Our model also provides a much simpler calculation with only 3 energy parameters that can be easily generated using the COSMO-RS software. There are only three simple steps required for the generation of data input. Firstly, in the COSMOthermX program, the user will need to select the cation and anion in the study. Next, under the properties tab, the chemical potential of the mixture is to be selected and then followed by inserting the corresponding temperature and equimolar mole fraction before running the simulation. In terms of the number of data points for the model development, Chen et al.26 and Gharagheizi et al.39 used a larger database as compared to our model. One can envisage that an extensive databank may contribute to the better understanding of a wider range of ILs and offer a higher degree of generality for the established model. However, in this case, there are always discrepancies in experimental values reported by two or more research groups due to sample impurities and difference in terms of instrument accuracy limit or calibration. The challenge would be to fit all data points and obtain a high goodness of fit or a low relative deviation. Therefore, in the model development process, training and validation steps play a pivotal role in identifying the outliers and anomalies. It is noteworthy that although our work has a smaller sampling size, every data point is unique and the test set consists of ILs at different temperatures as well as the ILs that were not used in the training set. In addition, the stepwise approach and the comparison analysis between linear and non-linear models in the present study have provided deeper insights and understanding of the contribution of interaction energies to conductivity and the suitable correlation between them. As compared to other machine learning models, SVM offers a significant advantage in that it is relatively simple to use as there are only a few userdefined parameters. In this work, since the RBF kernel is This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 View Article Online Paper Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. Table 4 NJC Comparisons of this work with models reported in the literature Ref. Method NIL D.P. T (K) P (MPa) R2 Coutinho and Gardas22 Chen et al.26 Gharagheizi et al.39 Tochigi and Yamamoto6 Tochigi and Yamamoto6 Eiden et al.75 (COSMO) This work This work GCM GCM GCM (LSSVM) QSPR (PE) QSPR (MLR) QSPR QSPR (MLR) QSPR (SVM) 15 77 54 79 79 142 25 25 300 1578 1077 150 150 713 239 239 258.15–433.15 248.05–468.15 238–480 243.15–338.15 243.15–338.15 238.15–468.15 268.15–398.15 268.15–398.15 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.9974 0.9973 0.9970 0.9676 0.8697 0.9100 0.8556 0.9906 selected, the user will only need to fine-tune the parameters for C and g. Moreover, the final results of SVM are reproducible and stable, unlike other methods such as neural networks, which may change in each iterative run due to the random initialization of weights.76 SVM model development can be performed across various computing platforms and programming languages, for instance, MATLAB, R, and Python. The optimization process of the SVM algorithm via grid-search is considerably fast during execution, and it works adequately with average computer system requirements. The statistical comparison in terms of R2 values between our models and other models reported in the literature is listed in Table 4. The result shows that the models established by the MLR algorithm do not provide good accuracy in predicting the conductivity of ILs in comparison with non-linear models. Our SVM model has a comparable statistical result as compared to the GCM models developed by Chen et al.26 and Gharagheizi et al.,39 which proves the prediction capability of our model. The R2 value of the COSMO model reported by Eiden et al.75 is 0.91, which is lower than that of our model (R2 = 0.9906). The PE model established by Tochigi and Yamamoto6 demonstrated a high R2 of 0.9676, but their model requires numerous quantum data inputs (more than 15 parameters), which might be excessive and cumbersome for users to obtain. In contrast, our predictive model applies a user-centric approach by offering simplicity with only 7 descriptors, and the algorithm can be easily computed using common spreadsheet software such as Microsoft Excel. Furthermore, although several molecular descriptors were used in Tochigi and Yamamoto’s model, the underlying insights were not provided. Our model not only works well for a variety of IL cation and anion types but also explains the theoretical deductions on the impact of interaction energy descriptors as the correlations are considerably built using a non-empirical approach. Based on the results, the proven capability of our model in predicting conductivity at different temperatures has overcome the limitation of the VFT model proposed by Coutinho and Gardas,22 which requires the determination of the Vogel temperature via trial and error. All these results confirmed the reliability and robustness of our QSPR-SVM model in describing the ionic conductivity of ILs at various temperatures. Following the success of the QSPR model development for the prediction of ionic conductivity of imidazolium-based ILs, the model can be further explored to predict the ionic conductivity of other non-imidazolium-based ILs. Moreover, a generalized model which can be applied to ILs with any type of cation can potentially be developed. Nonetheless, more descriptors may need to be considered in such context, for instance, ring energy, to improve the correlativity. Besides, the established models are built based on atmospheric pressure, and thus the models can be optimized with the addition of a pressure descriptor to allow the prediction of ILs at any pressure. This study has opened the research window to discover the correlation between interaction energies and other physicochemical properties of ILs, which may be useful for more applications. Conclusions In this study, 2 different QSPR models, MLR and SVM regression algorithms, were built and compared in terms of prediction capability for the ionic conductivity of imidazolium-based ionic liquids at different temperatures. A comprehensive data set of 239 ionic conductivity data points belonging to 25 ILs composed of 15 anions and 5 cations was employed to develop this model. Upon stepwise approach, eventually, both models were constructed with 4 parameters, including EMF, EvdW, EDiel and 1/T, in which the first three descriptors were calculated using COSMO-RS. We discovered that the MLR algorithm performed poorly for the entire data set, with the R2 and AARD values being 0.8556 and 46.55%, respectively. Comparatively, the model established by the SVM regression algorithm exhibited accuracy and correlativity for the whole data set, with the R2 and AARD values being 0.9906 and 7.15%, respectively. Herein the SVM model developed in this work is reliable and can be used to predict conductivity. In contrast to the general predictive models, we carried out stepwise regression to provide a valuable and exciting understanding of the impact of different interaction energies on conductivity. The van der Waals forces were identified to have the most significant impact on the conductivity of ILs followed by electrostatic interactions and hydrogen bonding interactions. Furthermore, dielectric energy is found to have a reasonable correlation with conductivity as well. It is noteworthy that this work provides valuable knowledge to the ionic liquid research community encompassing the impact of interaction energies on ILs’ conductivity for the screening and rational design of ILs. Conflicts of interest There are no conflicts to declare. This journal is © The Royal Society of Chemistry and the Centre National de la Recherche Scientifique 2021 New J. Chem., 2021, 45, 18584–18597 | 18595 View Article Online NJC Paper Acknowledgements Published on 02 September 2021. Downloaded by University of Rhode Island on 1/17/2022 8:04:32 AM. This work is funded under YUTP-FRG (015LC0-080) and received support from the Chemical Engineering Department and Centre of Research in Ionic Liquids of Universiti Teknologi PETRONAS. 23 24 25 26 Notes and references 27 1 M. Sattari, A. Kamari, H. Hashemi, A. H. Mohammadi and D. Ramjugernath, J. Fluorine Chem., 2016, 186, 19–27. 2 M. A. M. Al-Alwani, A. B. Mohamad, N. A. Ludin, A. A. H. Kadhum and K. 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