Introduction
Ionic liquids (ILs) are a kind of common low melting point organic salts. Recently, ILs have attracted much attention for their unique physical and chemical properties, such as good thermal stability, conductivity, wide electrochemical window, incombustibility and recyclability.1,2 Because of these characteristics, ILs have been successfully applied in the fields of electrochemistry,3-5 separation and extraction procedures,6-8 biological field9,10 and chemical engineering.2,11
The thermodynamic properties of ILs basically determine and affect their applications. Density (ρ ) is indispensable in the process design of material science and chemical engineering. In particular, the density of ILs can be used to calculate other properties (viscosity, surface tension, thermal conductivity, etc.). The viscosity (η ) of ILs can be used to determine the feasible operation conditions of the actual chemical process, such as fluids pumping and stirring, liquid-liquid extraction, distillation process.12 Thermal conductivity (λ ) is very important for obtaining the heat transfer coefficient of fluid, which is essential for the design of heat transfer fluid and equipment.13,14 Until now, large amount of ILs have been synthesized by a variety of cations, anions and substituents.15 However, the existing experimental properties data of ILs cannot meet the requirements for guiding chemical industrial applications. Moreover, density, viscosity and thermal conductivity are significantly affected by the temperature and the pressure, and it is even impossible for obtaining all these experiment data under different temperatures and pressures through the time-consuming and expensive experimental methods. Therefore, it is urgent to provide a model to calculate these characteristics of ILs under variable temperature and pressure as an alternative to the experimental measurement.
To date, different methods have been reported in literatures to calculate the properties of ILs.16-20 These methods are mainly based on: (i) the group contribution model (GCM), and (ii) the quantitative structure−property relationship (QSPR). GCM is a very important method to predict various physical and thermodynamic properties with satisfy prediction results21. For the thermal conductivity of ionic liquids, Lazzús 22established a GCM with 400 data point of 41 ILs at a wide range of temperature (253-395 K) and pressure (0.1-20 MPa) (R 2=0.9843, AARD =2.12 %). Recently, Chen et al.16 developed a GCM model to calculate properties at variable temperatures of ILs including the density (7360 data points,143 ILs) and the viscosity (1090 data points, 76 ILs) with good prediction results. It is undeniable that these models provide accurate predictions for the physical properties of ILs. However, GCM depends on the group contribution value, and due to the lack of some group contribution values, the properties of some ILs cannot be calculated for some ILs.
In the last decade, QSPR has been profusely employed to study the properties of ILs, such as heat capacity,23-25viscosity,26-29 thermal conductivity,30,31 surface tension,32,33 and toxicity.34-37Lazzús38 estimated the density in a wide of temperature (253-473 K) and pressure (0.1-250 MPa) range with satisfactory results (AARD =2.00 %). Yan et al.39 established a QSPR model to predict the density of ILs under variable temperature and pressure by using topological index with AARD of 0.42 %. Recently, AguirrePaduszyński40 established a reference term model and a modified QSPR model to predict the density (temperature (217−473 K) and pressure (0.1−250 MPa)) of ILs, and good results could be obtained with AARD of 0.9 %. Paduszyński41has proposed a new QSPR method for calculating ILs density and viscosity with temperature (217-473 K) and pressure (0.1-250 MPa) by MLR and LSSVM with good results.
Beckner et al. 42 used neural networks to get a high-precision model to predict the ILs viscosity at variable temperatures and pressure with satisfactory results (AARD= 7.10 %). Zhao et al.43 established a new QSPR model using multiple linear regression (MLR) and support vector machine (SVM) algorithm to predict the viscosity of ILs at variable temperature (253.15-395.32 K) and pressure (0.1-300 MPa) with the overallAARD of 6.58 %. Yan et al.29 predicted the viscosity of ILs under a wide range of temperature (253.15-573 K) and pressure (0.06-300 MPa), and obtained satisfactory prediction results with AARD of 4.62 %.
In case of thermal conductivity of ILs, Chen et al.44and Lazzus et al.45 proposed a QSPR model to predict the thermal conductivity of ILs under the condition of variable temperature (273.15-390 K) with AARD of 2.0 %-2.3 %. He et al.46 presents a linear QSPR model based on the norm-indexes for predicting ILs thermal conductivity in a wide temperature (273.15-355.07 K) and pressure range (0.1-20.0 MPa) withAARD of 1.45 %.
Indeed, the above QSPR and GCM reference methods have achieved good results in predicting the properties of ILs. However, in their modelling process, the descriptors used to build the model were made up of anion and cation descriptors, and their interactions were often neglected to some extent. In order to study the interaction between cations and anions, our previous work regarded the interaction between cations and anions as a mathematical formula composed of ion descriptors.37,47Compared with the results in the above literatures, the accuracy of our previous works on the interaction between anions and cations have been significantly improved. Recently, Yan et al.25,48proposed a new method to express the interaction between anions and cations by calculating descriptors from ILs molecule, which have been successfully applied for QSPR modelling for predicting the heat capacity and the eco-toxicity of ILs. The improved prediction accuracy and stability of the model further suggests that the interaction between anion and anion has an important impact on the properties of ILs, which is essential in the construction of the prediction model.
At present, there are hundreds of common cations and about 100 anions, and the combination of these anions and anions thus can produce tens of thousands of ILs. Although many literatures have reported QSPR models to predict thermodynamic properties, the descriptors used in these models need to be calculated by complicate software, which will lead to the inconvenience of model application. Therefore, the convenient and successful application of QSPR models for predicting the properties of density, viscosity and thermal conductivity is of great value for the design, development and application of ILs.
The focus of this work is to establish QSPR models for predicting the density, viscosity and thermal conductivity properties of ILs under variable temperature and pressure. There are four main works in this paper: (1) the f-T-P model of ILs under variable temperature and pressure was established; (2) the cationic, anionic and ILs descriptors were calculated to build the QSPR model; (3) three QSPR models were established for three properties of ILs at variable temperatures and pressures; (4) f-T-P model parameters of 16329 ILs were predicted by the QSPR models.