A Simple Group-Interaction Contribution Method for the Prediction of the Freezing Point of Ionic Liquids

 

Khadra Mokadem¹*, Belfar Mohemed Lakhdar¹, Kaniki Tumba²,

Abdulqader Saad Abed³, Mourad Korichi¹

¹Kasdi Merbah Ouargla University, B.P. 511, 30000, Ouargla, Algeria.

²Department of Chemical Engineering, Mangosuthu University of Technology, Durban, South Africa.

³Ministry of water Resources, State commission on Operation of Irrigation and Drainage projects,

Water Resources, El Anbar, Iraq.

*Corresponding Author E-mail: mo2kadem@gmail.com

A linear model based on group-interaction contributions is proposed for the estimation of the freezing temperature (Tf) of ionic liquids (ILs). This property is important for modelling solid-liquid equilibrium and selecting ionic liquids as reaction media among other things. A database of 66 experimental freezing points different ionic liquids was used to obtain all interaction contribution parameters and model constants. The database included various classes of ionic liquids and a wide range of cation and anion groups., with an average absolute relative deviation of 4,09% and a correlation coefficient of 0,93.

 

 

INTRODUCTION:

The characteristic temperature at which a liquid turn into liquid is termed as freezing point. The melting and freezing temperatures of the same compound are theoretically identical. However, small differences between the two properties have been observed for molecular liquids while surprisingly high differences, up to 100 K were reported in the case of ionic liquids¹. Practically, Differential Scanning Calorimetry (DSC) is the most commonly used technique for both melting and freezing points.

 

Ionic liquids are organic salts that can melt at low temperatures, generally below 373.15 K².

 

They have been attracting attention from the research community and industry as they have interesting properties that make them credible replacement for volatile organic solvents in industrial processes.

 

Properties which make ionic liquids attractive include:i) low or reduced flammability hazards³; ii) tunable properties⁴; iii) excellent solvation properties for a variety of organic and inorganic compounds⁴; iv) high electric conductivities⁵; v) high thermal stability⁶; vi) a wide liquid range and vii) a wide electrochemical window⁷.

 

In this study, a database of experimental measurements has been used to develop predictive models for the freezing point of ionic liquids based on group–interaction contributions (GIC). The present study is therefore the first account of the use of a GIC method for the estimation of the freezing point of ionic liquids. There is need for the development of predictive models for ionic liquids’ properties as experiments are time-consuming. Furthermore, such models can easily be implemented in process simulators for the design of processes incorporating ionic liquids.

 

It is interesting to note that group-interaction contribution (GIC) methods were derived to address the major limitation of conventional group contribution methods^8,9, i.e. inability to distinguish between isomers. Thus, the quest for more accurate predictions motivated the approach selected in the present study 66 ILs based on various cations and anions have been during model development.

 

METHODOLOGY:

Data set:

Lazzús, Zhang and co-researchers compiled experimental data for various properties of ionic liquids, including freezing point^10-12. Their publication was used to gather a total of 66 ionic liquids. Freezing Temperature were in the range from 185.15 to 466.15 K. Since some ionic liquids were associated with more than one source of experimental data, No data selection was performed prior to the modelling process. We were aware that in so doing, large discrepancies between experimental and calculated or predicted values using model can be expected. However, in the absence of any recommended standard procedure for Tf measurements, it is difficult to identify beyond any reasonable doubt, erroneous values that would be excluded from the database. Hence, all reported data for Freezing Temperature were considered when developing the new model.

 

Altogether, there were 5 cation types represented. Cations included Imidazolium ([IM]), Pyrrolidinium ([PY]), Phosphonium ([P]), Ammonium ([N]), Pyridinium ([py]). Anions contained in the investigated ionic liquids are hexafluorophosphate([PF6]), tetrafluoroborate ([BF₄]), bis (trifluoromethylsulfonyl)imide([BETI]), Halide ([X]), hexafluoroarsenate ([AsF₆]) carboxylates ([R1COO]), trifluoromethylsulfonate ([TfO]), 2,2,2-trifluoro-N (trifluoromethylsulfonyl) acetamide, bis((trifluoromethyl) sulfonyl) imide ([TFSI]), nitrate([NO₃]), borate ([R1R2R3R4B]).

 

The training set used for developing the models of this present study consisted of 59 ionic liquids. The validation set comprised 7 data points used to test the predictive ability of developed model. The correlation and the validation sets were selected randomly and care was taken to ensure a fair representation of all substructures in the selected ionic liquids.

 

Development of the method:

In the present study, molecular structure was related to the freezing point of ionic liquids through a three-level estimation: first-order contribution and second-order contribution. This was done according to principles outlined in previous works owed to Constantinou and Gani¹³, Marrero and Pardillo¹⁴ and as well as Mokadem et al.¹⁵. The method suggested by these researchers is articulated around the three points.

As shown in the literature, a property denoted Tm can be modelled via GIC by means of the following correlations:

 

       (1)

 

where n_j and m_k are the number of first and second-order groups of type j and k in the molecule respectively; and are the group-interaction contributions for the first and second-order group respectively.

 

The objective function, the average absolute deviation (AAD), the percent average relative deviation (%AARD) and the correlation coefficient (R²) were calculated as a means to assess the performance of the developed model, according to the following equation:

 

                                       (2)

 

                             (3)

 (4)

           (5)

 

As part of this study, the validation set comprised 66 data points used to test the developed model. Although the correlation and the validation sets were selected randomly, care was taken to ensure that during the modelling process, molecules were decomposed into fragments with all the groups found to have adequate frequency in the selected ILs.

 

RESULTS AND DISCUSSION:

The linear approach gave the best results for the studied property. After computing group interaction parameters from the experimental data using the computational scheme shown literature^15,16, the following equations were obtained:

 

                     (6)

All group group-interaction contribution parameters of first and second orders are reported in Table 1 and 2 respectively. A total of 49 first-order and 5 second order interaction parameters were obtained as part of this study.

 

 

Table 1: First-order structural groups and their interaction

 contributions.

 

Table 2: Second-order structural groups and their interaction contributions

 

A comparison between experimental and calculated freezing point temperatures is made in Figure 1 for the linear model. It can be seen that most of the points of the plot are close to the bisector. This indicates consistency between predicted or calculated and experimental data.

 

Figure 1: Comparison between experimental and predicted Tf using the linear model

 

The performance of the developed models can also be evaluated through statistical parameters provided in Tables 3. Due to the lack of similar work in the open literature, no comparison could be made between the presented models except method¹¹.

 

Table 3: The statistical parameters for the developed models

 

It is worth emphasising that as compared to conventional group contribution methods, GIC models have the advantage of differentiating between values related to isomers. Considering the large database used, the obtained results (R2 =0.93 as well as % AARD=4.09) suggest that the newly developed models are generally reliable as predictive tools for the freezing point of ionic liquids.

 

CONCLUSION:

New group-interaction contribution-based model linear is presented in this work for the estimation of the freezing point of ionic liquids. They rely on property estimation at three levels: first and second-orders parameters capturing structural features of ILs are determined along with a correction term. Unlike conventional group interaction methods, the new approach presented in this study takes isomerism into account. Its other merit is owed to diverse ionic liquids comprising the database, i.e. altogether 66 ionic liquids as well as the variety of cations and anions involved in the modelling process.

 

Supplementary Materials:

Table 4: Deviation between calculated and predicted Tf data for ILs using the linear GIC model. (RD: Relative deviation)

 

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Received on 08.08.2022                    Modified on 28.08.2022

Accepted on 19.09.2022                   ©AJRC All right reserved