Elsevier

Fluid Phase Equilibria

Volume 314, 25 January 2012, Pages 128-133
Fluid Phase Equilibria

Using artificial neural network to predict the ternary electrical conductivity of ionic liquid systems

https://doi.org/10.1016/j.fluid.2011.10.028Get rights and content

Abstract

The unique physical properties of ionic liquids play a decisive part in many of their applications. Therefore, the ability to predict the physical properties of ionic liquids is extremely important for the rational design of proper ionic liquids with specific properties. In practice, the processes involving ionic liquids usually contain other components, in addition to the ionic liquids. Therefore, in addition to pure component properties, knowledge of the physical properties of mixtures are also crucial for various applications. In the present study, the feasibility of using a feed-forward multi-layer perceptron neural network (MLPNN) model was investigated to predict the electrical conductivity of the ternary mixtures of 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF6]) + water + ethanol and [bmim][PF6] + water + acetone in the temperature range from 288.15 K to 308.15 K, consisting of 104 data points. Not only were different networks, namely the linear and the hyperbolic tangent sigmoid transfer functions, considered in this study, but also the effects of the number of hidden layers, hidden neurons and the training algorithm were investigated on the accuracy of the results using 78 data points as training data to minimize the average absolute relative deviation percent (AARD%), mean square error (MSE) and correlation coefficient (R2). Among the various cases studies, statistical analyses indicated the best configuration of the network to include one hidden layer and seven neurons in the hidden layer. The optimum network was then validated using 26 data points (test data) not used in the training stage which indicated the good interpolative ability of the trained network with AARD% = 1.44, MSE = 2.87 × 10−8 and R2 = 0.9981.

Highlights

► The use of artificial neural networks to predict electrical conductivity was studied. ► Complex ternary mixtures with one component being an ionic liquid were investigated. ► Artificial neural networks (ANNs) are excellent tools for correlations of such systems. ► ANNs are also accurate for prediction of electrical conductivity of ternary systems.

Introduction

Room-temperature ionic liquids (RTILs) are novel organic salts composed of anions and cations. Owing to their unique chemical and physical properties, such as lack of vapor pressure, wide liquid range, high thermal stability, low melting temperature, and excellent solubility in many polar and nonpolar organic substances, they have been recognized as alternative solvents for specific applications such as solvents, lubricants, pump oils, phase change media, propellants, and for separations [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. In addition, RTILs are important in the field of energy, especially as electrolytes for lithium batteries, fuel cells, and high-temperature fuel cells, which greatly benefit from the switch to non-volatile, non-flammable, ionic liquid-based electrolytes [12], [13], [14], [15]. They have better energy efficiency compared to other electrochemical storage systems. It has been found that ionic liquids based on the NTf2, BF4 and PF6 anions, exhibiting wide and stable electrochemical windows, in some cases, can even reach below the Li/Li + reductive potential region [16].

Lu et al. [17] experimentally showed that using 1-butyl-3-methyl imidazolium cations together with anions such as hexafluorophosphate (PF6) can significantly enhance the π-conjugated polymers’ lifetime in electrochemical devices without failure (up to 1 million cycles) with fast cycle switching speeds (100 ms).

The increasing research on using ionic liquids in solar batteries [18], [19], electrochemical capacitors [20], superoxide electrochemistry [21], [22], and electrochemical synthesis [23], [24] is due to the wide electrochemical voltage windows of ionic liquids (ILs) [16].

The selection of the most suitable ionic liquid for a given application requires knowledge of some physical, chemical, and thermodynamic properties. Although some progress has been made in this area, there is still ample space for research, in particular, in the area of property measurement, correlation, and prediction. More and more publications are being reported on the physicochemical properties of some ILs, but the overall amount of property data measured by experimental methods is still not fulfilling the requirements for their broad potential applications [16].

Some of the examples of experimentally measured physical property and thermodynamic data of mixtures with ILs include the phase behavior of supercritical CO2 + IL [14], [25], water + IL [26], and ethanol + water + [bmim][PF6] [27], [28], the conductivity [29] and the viscosity [30] of supercritical CO2 + [bmim][PF6], and the effect of impurities on the viscosity of [bmim][PF6] [31]. Up till now, most studies on ILs are limited to pure ILs or binary mixtures. Experimental data on ternary systems are scare, yet crucial [32].

It is also of importance to develop characterization techniques to correlate the thermodynamic and physicochemical properties of pure ILs, as well as mixtures involving ILs. In addition, there is a critical necessity to develop techniques to predict properties of unknown ionic liquids for process design and performance optimization in order to increase their future applications.

Therefore, in response to the need to design and synthesize ILs with predefined, task-specific properties, a number of papers have appeared that present different predictive methods which allow the prediction of some of the fundamental physical properties of ILs, including conductivity [33], [34], [35], [36], [37], [38]. Although most of these methods have good predictive ability, they involve complicated models, and require extended data and considerable computer time [39]. In order to reduce expensive computer time, simple and reliable predictive methods are desirable.

In this respect, using predictive tools, such as artificial neural network (ANN) programming to easily estimate the transport properties of pure ILs, as well as their binary and ternary mixtures, can be useful. Successful applications of neural networks to predict mixture properties, such as solid solubilities in supercritical fluids, vapor liquid equilibria, and activity coefficients among others, have been published in the literature [40], [41], [42], [43]. To the best of the authors’ knowledge, there are no publications on the application of ANN for the prediction of electrical conductivity of ionic liquids, neither for pure ILs nor their mixtures.

In this study, the applicability of artificial neural network in predicting the electrical conductivities of ternary systems involving ionic liquids is investigated. The two mixtures studied are [bmim][PF6] + water + ethanol and [bmim][PF6] + water + acetone.

Section snippets

Ternary electrical conductivity data

The electrical conductivity data of ternary mixtures of [bmim][PF6] (1) + water (2) + ethanol (3) and [bmim][PF6] (1) + water (2) + acetone (3) were collected from the literature [32]. All in all, a total of 104 ternary data points were obtained with mole fractions of the solvents in the mixtures ranging up to 0.48, within the temperature range from 288.15 K to 308.15 K. The physico-chemical properties of compounds involved in the ternary systems are given in Table 1.

Artificial neural networks

The concept of neural network models (NNMs) is a rather recent development. Artificial neural networks (ANNs) are nonlinear learning mathematical models that are designed by simulation of human brain procedures and have been used in many scientific disciplines by now [44], [45], [46], [47], [48]. A neural network consists of a number of simple processing elements, called the neurons. Each neuron of the neural network is connected to others by means of direct communication links, each with an

Results and discussion

Table 2 shows the results of the topological studies to find the optimal ANN configuration. The bold numbers refer to the best number of neurons in the hidden layer based on the minimum AARD% for the test data set. These results show that among the different training parameters considered, the optimal network configuration consists of one hidden layer and seven hidden neurons, giving the smallest overall values of MSE (1.11 × 10−8), AARD% (1.01) and an acceptable value of R2 (0.9994). In

Conclusions

In the present study, an ANN approach was applied to ternary systems of ILs in order to investigate the applicability of the ANN tool to predict the electrical conductivities of complex ternary systems. The model was applied to the only IL ternary electrical conductivity data set available in the literature. A total of 104 data points, on two systems containing [bmim][PF6], were used which were divided into two separate sets, one intended for training data, and the other as test data to check

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