A simple correlation for determining ionic liquids surface tension
Introduction
Nowadays, Ionic Liquids (ILs) become new generation of solvents. ILs formerly used for electrochemical applications, then the other possible applications of them have been found [1]. ILs refer as green solvents because of their non-flammability, non-volatility properties and being fully recyclable [2,3]. They also have a wide range of liquidity, which can be very interesting for many applications. Extremely low vapor pressure, high concentration of ions (which cause good electrical and thermal conductivity), good thermal stability and wide electrochemical properties are some attractive properties that make ILs unique materials. Chemical diversity is one of their advantages but on the other hand, they are rather viscous (e.g., they are 50–1000 more viscous than water). As a disadvantage, impurities may effect their properties. The other disadvantages of ILs are being expensive in comparison with the molecular solvents, very few availability in commercial scale, being poorly biodegradable and potentially toxic [4]. Some of the applications of ILs are as follows: solvents for chemical and biochemical reactions, extraction media for natural product isolation, cleaning agents, storage media for unstable compounds, lubricants, electrochemical/battery materials [5].
Surface tension is an important parameter in process design, scientific and industrial applications of heterogeneous systems [6,7]. Surface tension affects the interface specification of two phases systems. The surface tension values of ILs can be measured experimentally or can be predicted using available correlations. Experimental data of ILs surface tension are rare and obtaining these data consume much cost, time and effort. Also the models for predicting these data are too limited in accuracy and number of ILs. Therefore, a general correlation for surface tension of ILs is needed to extent their applications. When it comes to the values of ILs surface tension, it should be noted that range of surface tension for known ILs is between values of alkanes and water's surface tension [8]. Surface tension caused by cohesive energies between molecules so information about surface tension of ILs is necessary to describe the energies, which are involved in ions interaction [9,10,11]. In addition, Surface tension value can be used as a way to circumvent an issue, which is hard to solve for the bulk fluid, but it is possible to access at the liquid-vacuum. Boundary-surface tension is a measure of cohesive forces between liquid molecules present at the surface and it represents the quantification of force per unit length of free energy per unit area. Therefore, measurement of ILs surface tension is one of the most effective ways to indirectly access the intrinsic energetics, which are involved in the ions interactions [12].
In comparison to other properties of ILs, surface tension didn't gain much attention. Some researchers tried to predict the surface tension of ionic liquids. F. Gharagheizi et al. tried to estimate the surface tension of ILs using Group Contribution model [13]. Their efforts reached to an average absolute relative deviation (AARD) 3.6% from experimental data. S.A. Mirkhani et al. proposed a molecular approach to predict the surface tension of ILs. They used 930 experimental data from 48 ILs for their approach and reached to an adequate accuracy [14]. Q. Shang et al. proposed a quantitative structure property relationship (QSPR) method using a topological index for predicting the surface tension of ILs. They used 930 experimental data from 115 ILs to develop a QSPR model with AARD 0.95% [15]. Some other researchers proposed methods for predicting the surface tension of ILs that are Parachor method with the AARD of 10.31% [16], Gardas and Coutinho with AARD 5.75% and Ghasemian and Zobeydi with AARD 8.5%.
Nowadays, strong techniques of soft computing such as artificial neural network (ANN), Genetic algorithm (GA) and genetic programing (GP) are powerful and reliable methods to simulate a system and to predict its behavior. Multi-Gene Genetic Programming (MGGP) is a kind of Genetic Programming (GP), which combines the model structure selection ability of standard MGGP with the parameter estimation power of classical regression to capture nonlinear interactions [17]. GP in artificial intelligence is an evolutionary algorithm-based methodology, which is based on biological evolution aim to find computer programs that perform a user-defined task. GP is a special form of Genetic Algorithm (GA) in which every individual is a computer program. As an optimization method, GP as a machine learning technique is used to optimize a population of computer programs according to a fitness landscape determined by a program's ability to perform a given computational task [18]. GP evolves computer programs, traditionally represented in memory as tree structures [19]. Trees can be easily evaluated in a recursive manner. Each tree node has an operator function, and each terminal node has an operand, making mathematical expressions easy to evolve and evaluate. Thus, traditionally, GP favors the use of programming languages that naturally embody tree structures [20].
In this paper, it has been tried to find a general correlation to predict surface tension of ILs using MGGP algorithm. The aim of this investigation was to derivate a simple correlation with minimum parameters and good accuracy, which can be usable for a wide range of conditions and many kinds of ILs.
Section snippets
Methodology
Four parameters have been introduced as input parameters to the MGGP for training a network to predict surface tension, as the output parameter. The input parameters were reduced temperature (Tr), reduced pressure (Pr), critical compatibility factor (ZC) and acentric factor (ω). 789 data related to 59 ILs were selected from the literature [[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]]. The
Results and discussion
Finding a general trend is very promising. The obtained correlation has 3 coefficients which should determine using GA, a simple fitting or Table 2 (containing these 3 coefficients of ILs used in this work). Using Table 2, one can find the coefficients of presented correlation with its precision (the index of precision was R2). However, the aim of this study is to present a simple correlation for surface tension of ILs, which can be used over a wide range of temperature. Using summation,
Conclusion
As it has been mentioned before, the purpose of this study was to determine a general correlation for obtaining the surface tension of ILs with good precision. Following this purpose, using MGGP, a general correlation for obtaining the values of ILs surface tension has been determined with R2 of 0.99 that shows a very good precision. The mentioned correlation has three coefficients. Six correlations have been presented (using MGGP) for determining these coefficients.
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