Prediction and verification of heat capacities for pure ionic liquids

Zhengxing Dai,Yifeng Chen,Chang Liu,Xiaohua Lu,Yanrong Liu*,Xiaoyan Ji*

1 State Key Laboratory of Material-Oriented Chemical Engineering,Nanjing Tech University,Nanjing 211816,China

2 Energy Engineering,Division of Energy Science,Lule? University of Technology,Lule?,Sweden

3 Swerim AB,Box 812,SE-97125 Lule?,Sweden

Keywords:Ionic liquids Heat capacity COSMO-RS

ABSTRACT The heat capacity of ionic liquids is an important physical property,and experimental measuring is usually used as a common method to obtain them.Owing to the huge number of ionic liquids that can be potentially synthesized,it is desirable to acquire theoretical predictions.In this work,the Conductor-like Screening Model for Real Solvents(COSMO-RS)was used to predict the heat capacity of pure ionic liquids,and an intensive literature survey was conducted for providing a database to verify the prediction of COSMO-RS.The survey shows that the heat capacity is available for 117 ionic liquids at temperatures ranging 77.66–520 K since 2004,and the 4025 data points in total with the values from 76.37 to 1484 J·mol-1·K-1 have been reported.The prediction of heat capacity with COSMO-RS can only be conducted at two temperatures(298 and 323 K).The comparison with the experimental data proves the prediction reliability of COSMO-RS,and the average relative deviation(ARD)is 8.54%.Based on the predictions at two temperatures,a linear equation was obtained for each ionic liquid,and the heat capacities at other temperatures were then estimated via interpolation and extrapolation.The acquired heat capacities at other temperatures were then compared with the experimental data,and the ARD is only 9.50%.This evidences that the heat capacity of a pure ionic liquid follows a linear equation within the temperature range of study,and COSMO-RS can be used to predict the heat capacity of ionic liquids reliably.

1.Introduction

Ionic liquid (IL) is an emerging ‘‘green solvent”with the merits of immeasurably low vapor pressure,excellent chemical and thermal stability,wide electrochemical window,nonflammability,and tunable properties [1].It has been widely developed in many research fields,such as gas capture/separation and conversion[2–4],biomaterial dissolution [5],battery [6],and absorption heat transformers[7].Due to the super tunable properties,1018kinds of ILs can be potentially formed through the combination of different anions and cations,resulting in different properties (e.g.,density,viscosity,heat capacity,surface tension,CO2solubility)and leading to their applications in a variety of areas.

Heat capacity is one of the important properties and also an indispensable parameter when estimating the energy balance in the processes with temperature as variable [8].The assessment of their values is essential for the reasonable tailoring of solvent properties.For example,ILs with low heat capacities are favorable in the CO2separation and absorption heat transformers because of low energy requirements [9].Compared with other properties,such as density,viscosity,surface tension,and CO2solubility,the study on heat capacity is insufficient [9].Measuring heat capacity with experimental techniques is not only costly but also impractical due to the large number of ILs.Therefore,it is essential to predict the heat capacities of ILs with theoretical methods and models.

Several articles on modeling the heat capacity of ILs have been published,and in general,adjustable parameters are needed.For instance,Müller et al.developed a model based on the temperature-dependent heat capacities of the constituent ions for each IL,and the parameters for 39 cations and 29 anions were obtained based on 104 ILs with 2443 data points,making it possible to predict the heat capacity of 1248 pure ILs[10].A deviation lower than 7.2%was acquired when modeling the ILs not used in parameter fitting at temperatures up to 425.15 K.Ge et al.combined the Joback group contribution(GC)method with the principle of corresponding states[11]to predict the heat capacity of ILs,and the GC parameters for three new groups of -SO-,B,and P were obtained.The developed model was used to predict the heat capacities of other ILs (51 ILs with 961 data points in a temperature range of 256–470 K),showing a 2.9% deviation [12].Later,the method was used to predict the heat capacity of 3-(alkoxymethyl)-1Himidazolium salicylate ([H-Im-C1OCn][Sal],n=3–11) up to 323.15 K by Jacquemin et al.[13],and a deviation about 3.2% was acquired.Sattari et al.[14]combined the GC method and genetic function approximation to predict the heat capacities,and the best prediction is for the dialkyl imidazolium-based ILs (ARD=1.51%),while the worst is for the phosphonium-based ILs(3.65%).Soriano et al.developed a group-additivity model with three adjustable parameters [15],and a deviation of 0.69% was achieved for 32 imidazolium-,pyridinium-,and pyrrolidinium-based ILs.The extreme learning machine(ELM,6 parameters)[16],multiple linear regression(MLR,5 parameters),and artificial neural network(ANN,5 parameters) were used to predict the heat capacity of imidazolium-,pyridinium-,pyrrolidinium-,and phosphoniumbased ILs for comparison [8].It was found that ELM (ARD=0.44%)is the best,followed by ANN (ARD=0.64%) and MLR(ARD=2.72%).Three chemical structural models (7 parameters),i.e.,coupled simulated annealing optimization algorithm (CSALSSVM),gene expression programming (GEP),and adaptive-neuro fuzzy inference system (ANFIS) optimized by the hybrid method(Hybrid-ANFIS),were also used for predicting the heat capacity of 56 ILs [17],evidencing that CSA-LSSVM (0.9%) is better than Hybrid-ANFIS (1.74%)and GEP(2.31%).

Recently,Conductorlike Screening Model for Real Solvents(COSMO-RS) has been strongly recommended for predicting the thermodynamic properties of ILs,as the molecular structural information is the only required input [18].As a prior and a rapid screening method,COSMO-RS has evidenced its prediction capability for the solubility (i.e.,cellulose,keratin,gas) [5,19,20],activity coefficient [21],Henry’s constant [22],viscosity [23],and density[24]of ILs.However,to the best of our knowledge,no research work has ever been conducted to investigate the prediction capacity of COSMO-RS for the heat capacities of ILs as well as its prediction reliability.

To fulfill this gap,in this work,the heat capacity of ILs was predicted with COSMO-RS,combined with the verification for both COSMO-RS predictions and their further linear correlations.A comprehensive survey of the experimental heat capacities of ILs was firstly carried out.COSMO-RS was used to predict the heat capacity of ILs at 298 and 323 K,and the predictions were compared with the experimental results for verification.Further,temperaturedependent linear correlations were obtained based on the results from COSMO-RS and then used to estimate the heat capacities at other temperatures,and the comparison with experimental results was also conducted for verification.

2.Computational Details

COSMO-RS calculations were performed using the software COSMOtherm(version 19.0.4,revision 5528,applied with parameterization BP_TZVP_19,COSMOlogic,Leverkusen,Germany),followed by the reported standard methods [25].All of the ILs were implemented in COSMOtherm software following the electroneutral approach,i.e.,each IL was treated as a separated cation and anion.To use COSMO-RS,the COSMOfiles for all the studied ILcations and anions are needed.In this work,those

(1) for the IL cations of [1B3Mpy]+,[1B4Mpy]+,[BAPY]+,[BENBIM]+,[BENMIM]+,[BIPIM]+,[BPDM]+,[BPHENIM]+,[BPIM]+,[C3MPIP]+,[C3MPy]+,[C3MPyrr]+,[C9MIM]+,[COPBIM]+,[EAPY]+,[EMPIP]+,[EMPyrr]+,[HAPY]+,[HOEtDMHA]+,[HOMEA]+,[N4441]+,[N7777]+,[N8888]+,and[P66614]+;

(2) for the IL anions of [1122FSO3]-,[AESO3]-,[C2COO]-,[C3-COO]-,[C4COO]-,[C6SO4]-,[Cys]-,[Deca]-,[MDEGSO4]-,[EtSO4]-,[HexO]-,[Lys]-,[OctO]-,[Oph]-,[Pro]-,[Ser]-,[Thr]-,[Tos]-,and [Val]-,

were calculated based on the procedures described in the computation details [25].The COSMOfiles for other IL-ions studied in this work were taken from the COSMO-RS database.The full and abbreviation names,the structures of cations and anions,as well as the COSMO-RS sigma surfaces are given in Tables S1 and S2.

By using COSMO-RS,the heat capacity of ILs can be acquired at 298 and 323 K.Then,a temperature-dependent linear equation was obtained for each IL,making it possible to estimate the heat capacity at different temperatures theoretically.The prediction results from COSMO-RS and those estimated with the obtained linear correlations were verified by comparing with the experimental heat capacities.The ARDs were calculated to quantify the model performance,and the expression is defined as

3.Results and Discussion

3.1.Literature survey

A comprehensive survey was conducted based on open publications since 2004.4025 experimental data points for 117 ILs (including imidazolium-,pyridinium-,pyrrolidinium-,morpholinium-,piperidinium-,ammonium-,phosphoniumbased)at temperatures ranging from 77.67 to 520 K were collected and used as the database for verifying the performance of COSMORS.The detailed results of the database are displayed in Tables 1 and S3,as well as Fig.1.Among these 117 ILs,for the ILs of[BMIM][Cl],[BMMIM][BF4],[BMMIM][PF6],and [PMMIM][Tf2N],only two experimental data points were reported at 298 and 323 K,respectively (Table 1).

Fig.1.Experimental heat capacities at different temperatures.

Table 1 ILs studied in this work

Table 1 (continued)

As shown in Fig.1,almost for all the studied ILs,their heat capacities at different temperatures follow a linear equation.The minimum heat capacity acquired from the survey (76.37 J·mol-1·K-1) belongs to [Epy][Br]at 77.66 K,while the maximum(1484 J·mol-1·K-1)affiliates to[P66614][FeCl4]at 418.19 K.The heat capacities for other ILs within the studied temperature range are between these two values.Except the linearly temperaturedependent,three other characteristics for the collected heat capacities can be observed from Table S3,i.e.,1)anions has a significant effect on the heat capacities of ILs compared with cations.For example,between [BMIM][Tf2N]and [BMIM][OTF]is 138.57 J·mol-1·K-1at 298 K,while,for different cations,it is 77.47 J·mol-1·K-1between [BMIM][Tf2N]and [C3MIM][Tf2N]at the same temperature;2)the heat capacity increases with increasing the alkyl chain length of cations,e.g.,the heat capacity increases from 489 to 971.7 J·mol-1·K-1for [C3-C14MIM][Tf2N],and it increases from 790 to 903 J·mol-1·K-1for [N7777-N8888]Br at 298 K;3) the heat capacity increases with increasing the number of alkyl chains in the imidazolium cation,but not for the pyridinium cation.For instance,for the heat capacity [BMMIM][Tf2N](591.9 J·mol-1·K-1) ＞[BMIM][Tf2N](566.47 J·mol-1·K-1),and [EMMIM][Tf2N](527 J·mol-1·K-1) ＞ [EMIM][Tf2N](524.3 J·mol-1·K-1) at 298 K,however,[EMPy][Tf2N](514 J·mol-1·K-1) ＜[EPy][Tf2N](J·mol-1·K-1) at 323 K.

3.2.Prediction and verification

3.2.1.COSMO-RS verification

The heat capacities of 117 ILs were predicted with COSMO-RS at 298 and 323 K.The results are listed in Table S4.It was found that COSMO-RS can be used for qualitative prediction.The predictions are consistent with the experimental results on 1) linear temperature-dependence,2) significant effect of anions than cations,3) effect of alkyl chain length in cations.However,for the effect of the number of alkyl chains in cations,the prediction tendency is not always correct.For example,the prediction tendency is correct for [EMMIM][Tf2N](518.10 J·mol-1·K-1) and[EMIM][Tf2N](490.17 J·mol-1·K-1),but incorrect for [EMPy][Tf2N](533.45 J·mol-1·K-1) and [EPy][[Tf2N](506.12 J·mol-1·K-1).

The comparison of the COSMO-RS predictions with the experimental results is illustrated in Fig.2.An acceptable ARD of 8.54%was acquired,indicating that COSMO-RS can also be used for quantitative predictions.The contribution to the ARD is mainly from the phosphonium-(1.06%–38.63%),ammonium-(9.55%–29.36%) and imidazolium-(3.4%–34.38%) based ILs,e.g.,the ARDs for [P4444][AESO3]and [N4441][AESO3]are 38.63% and 29.36%,respectively,and it is 34.50% for [BENMIM][BF4]at 298 K.The detailed results listed in Table S4 indicate that about 71%ILs(85 to 119)have ARDs lower than 10%,and the best is for[EMIM][OAc](ARD=0.28%).This implies that COSMO-RS can be used for quantitative prediction for most of ILs.Fig.3 shows 34 ILs with ARDs higher than 10%,and these ILs should be more beware when using COSMO-RS to predict their heat capacities.From Fig.3 it can be found that the ILs with the ARDs greater than 10% mainly have the features of 1)phosphonium-based ILs,including cations of [P4444]+and[P66614]+,and amino acid (e.g.,[Thr]-,[Ser]-,[Cys]-,[Lys]-,[Pro]-,[Val]-) and [AESO3]-anions;2) ammonium-based ILs structure with cation of [N4441]+and anions of [AESO3]-,[Thr]-,and [Lys]-;3) big size imidazolium cations,e.g.,[BENMIM]+together with anions of[BF4]-,[PF6]-,and[Tf2N]-;4)halogen anion-based ILs i.e.,[EPy][Br],[C3MPy][Br],[C3MIM][Br],and [BMIM][I].

Fig.2.Experimental heat capacity vs.COSMO-RS prediction at 298 and 323 K.

Fig.3.The ILs with the ARDs higher than 10% where the heat capacity was predicted with COSMO-RS.

In order to further illustrate the performance of COSMO-RS,[HMIM][Tf2N],[BMMIM][FAP],and [P4444][AESO3]were chosen as three representatives to show the minimum (0.22%),medium(8.58%),and maximum(38.63%)ARDs when compared with experimental results.It was further found that,as shown in Fig.4,no matter the deviation is large or small,the temperature effect on the heat capacity(i.e.,the slope of the heat capacity predicted with COSMO-RS) agrees well with the experimental observation.The investigation for other ILs not displayed in Fig.4 also evidenced the same results.Therefore,COSMO-RS can be used to predict the temperature effect on the heat capacity of ILs.

3.2.2.Extension of COSMO-RS predictions

Fig.4.Experimental and predicted heat capacities for three ILs with minimum([HMIM][Tf2 N]),medium ([BMMIM][FAP]) and maximum ([P4444 ][AESO3 ]) ARDs,respectively.

Based on the predicted heat capacities at 298 and 323 K,a linear correlation was conducted for each IL.The linear equations for 117 ILs are displayed in Table S5.Using the linear equations,the heat capacity at other temperatures were then estimated and compared with the available experimental data.Due to the availability of experimental data at temperatures other than 298 and 323 K,the comparison can only be conducted for 113 ILs with 3826 data points.The comparison is summarized in Fig.5,with details listed in Table S6.The comprehensive analysis of Table S6 shows that the correlated linear equations can be used to reliably estimate the heat capacity,being consistent with the performance of COSMORS combined with its reliable prediction on the temperature impact.

For quantitative prediction,an ARD of 9.50% was obtained for the correlations (Fig.5).Although the ARD is slightly larger than that of COSMO-RS (8.51%),this accuracy is within the acceptable range compared to the experimental uncertainty(10%)as reported by Müller et al.[10]The results listed in Table S5 further indicate that 74% (84–115) ILs have the ARDs lower than 10%,resulting in the best one (0.52%) for [BMPy][OTf].Therefore,COSMO-RS can be used to predict and further estimate the heat capacity at different temperatures.Among the ILs with ARDs higher than 10%(Fig.6),[Epy][Br]is the worst one (40.47%),and the ILs displayed in Fig.6 are also those with the ARDs higher than 10% in the COSMO-RS prediction.

In conclusion,original COSMO-RS can be used to predict the heat capacity at 298 and 323 K reliably,and the linear correlation makes it possible to reliably estimate the heat capacity at other temperatures.

3.2.3.Comparison of COSMO-RS with other models

Five ILs of [EMIM][BF4],[BMIM][BF4],[HMIM][Tf2N],[EMIM][Tf2N],[HMIM][BF4],which have the same prediction temperature(323 K)with other models of GC,MLR,ELM,group-additivity were selected for the comparison.The comparison shown in Fig.7 evidenced that COSMO-RS is the best one for [HMIM][Tf2N]and[HMIM][BF4]compared with the other four models,but the worst one for [EMIM][Tf2N].Additionally,for [EMIM][BF4],COSMO-RS is only better than the GC model,While for [BMIM][BF4],COSMO-RS is only worse than the group-additivity model.However,it should be pointed out that for COSMO-RS,the only needed input is the molecular structural information.Meanwhile,the prediction of COSMO-RS is always with the ARD less than 6%,while for other models,the ARD can be up to 22%.Therefore,it is strongly recommended to use COSMO-RS for the prediction.

Fig.5.Experimental heat capacity vs.linear correlation prediction at temperatures other than 298 and 323 K.

Fig.6.ARDs more than 10% predicted by linear correlations.

Fig.7.Comparison of ARDs for different models.

4.Conclusions

In this work,a heat capacity database including 117 ILs with 4025 experimental data points at 77.66–520 K was established based on open publications since 2004.COSMO-RS was used to predict the heat capacity of ILs,and its performance was verified based on the established database.The literature survey indicates that experimental heat capacity at different temperatures follows a linear equation within the scope of 76.37–1484 J·mol-1·K-1.The prediction and comparison show that COSMO-RS can provide reliable prediction at 298 and 323 K,and approximately 8.54% ARDs was acquired,evidencing that COSMO-RS can be used for quantitative prediction of the ILs heat capacity at these two temperatures.Linear equations were acquired for 117 ILs based on the COSMO-RS predicted results at 298 and 323 K,and used to estimate the heat capacity at temperatures other than 298 and 323 K.3826 experimental data points were further used to verify the correlations,and ARD is only 9.50%,indicating that the acquired linear equations can provide reliable estimations.Additionally,the comparison between COSMO-RS and other models further illustrates that COSMO-RS is a reliable tool for predicting the heat capacity of ILs.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work is financially supported by the Joint Research Fund for Overseas Chinese Scholars and Scholars in Hong Kong and Macao Young Scholars (No.21729601) and the National Natural Science Foundation of China (No.21838004).YL and XJ thank the financial support from Carl Tryggers Stiftelse foundation (No.18:175).XJ also thanks the financial support from Swedish Energy Agency (P50830-1).CL thanks the financial support from National Natural Science Foundation of China (No.21878143).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.10.040.