Prediction of Thermophysical Properties for Binary Mixtures of

Article pubs.acs.org/IECR

Prediction of Thermophysical Properties for Binary Mixtures of Common Ionic Liquids with Water or Alcohol at Several Temperatures and Atmospheric Pressure by Means of Artificial Neural Network Karim Golzar,† Sepideh Amjad-Iranagh,‡ and Hamid Modarress*,† †

Department of Chemical Engineering, Amirkabir University of Technology, No. 424, Hafez Street, Tehran, Iran Department of Chemistry, Amirkabir University of Technology, No. 424, Hafez Street, Tehran, Iran

‡

S Supporting Information *

ABSTRACT: In this work, thermophysical properties such as density, dynamic viscosity, excess molar volume, refractive index and speed of sound of binary mixtures of common ionic liquids (ILs) with water or alcohol are predicted by the artificial neural network (ANN) technique. In each ANN proposed models, the density and dynamic viscosity of pure components IL, water or alcohol (including methanol, ethanol, 1-propanol and 2-propanol) and pure IL and the temperature as well as mole fractions of water or alcohol of studied binary mixtures were given as the inputs and the desired properties were predicted as the outputs. The obtained results revealed that the selected input parameters were appropriate and the high statistical quality represented by various criteria and the low prediction errors indicated that the presented models can accurately predict the properties of IL + water/alcohol binary mixtures.

1. INTRODUCTION Room temperature ionic liquids (RTILs) are molten salts that are composed of an organic cation and an organic or inorganic anion with melting point below 100 °C. A wide range of cation and anion families that both determine the properties of an IL have been used to synthesize RTILs. To obtain the RTIL solvents with customizable physical, chemical or biological activities, appropriate cations and anions must be used in their syntheses. ILs are nonvolatile with negligible vapor pressure and are considered as environmentally favorable materials.1−12 Considering their especial characteristics, ILs are distinguished from classical solvents and offer new opportunities for their usage as a new class of solvents, namely green solvents, for application in various chemical reactions involving gaseous reactants, for example, hydrogenation, hydroformylation, and oxidation processes. On the other hand, some processes, for instance, the electrochemical reduction of aluminum from alumina, can be conducted only in molten salts and are impossible in aqueous solutions. But, until recently, before recognizing the properties of ILs, the use of molten salts were considered to be confined to high-temperature applications.12−14 ILs are known as attractive electrochemical solvents,15−18 because they have many adaptable properties common to ILs, like wide electrochemical window, high ionic conductivity, wide temperature range for liquid phase, high thermal stability, negligible vapor pressure, high solvation capability and rather high viscosity.18,19 In some practical applications, such as electric double layer capacitors,19,20 lithium ion batteries18,21,22 and dye-sensitized solar cells,23,24 the bis(trifluoromethylsulfonyl)imide (Tf2N−) anion-based ILs have more operation in compared with other ILs. To provide vast opportunities for the optimization of properties toward lower © 2014 American Chemical Society

viscosity, higher molar conductivity, and higher electrochemical stability for synthesized ILs, the Tf2N− anion was composed with different cations, such as imidazolium, pyridinium, pyrrolidinium, piperidinium and quaternary ammonium derivatives.18 With such novel properties and interesting industrial applications, thermophysical properties of ILs such as density, dynamic viscosity, excess molar volume, refractive index, speed of sound, melting temperature, gas solubility, surface tension, conductivity and critical temperature are very demanding, especially for any industrial design and laboratory applications. For example, Shannon and Bara25 characterized the density, viscosity and CO2 solubility of a series of 1-n-alkylimidazoles with chain lengths ranging from methyl (C1) to tetradecyl (C14). Then they used experimental measurement of density and viscosity to develop empirical models for these thermophysical properties of ILs with respect to temperature and the contribution of the n-alkyl chain. Also, they indicated that the CO2 solubility in 1-n-alkylimidazoles at ambient temperature (25 °C) and low pressures (3−7 atm) is less than most common organic solvents. Liu et al.26 investigated effects of dispersed ILs on chemical absorption of CO2 in alkanolamine aqueous solution. Pratap Singh and Kumar Singh27 measured the ultrasonic velocity, density, viscosity and surface tension of ILs 1-butyl-3-methyl imidazolium hexafluorophosphate, 1-butyl-3-methyl imidazoliumoctyl sulfate and 1-ethyl-3methyl imidazolium methanesulfonate at temperature range of 303 to 333 K. Ferreira et al.28 reported the density, viscosity Received: Revised: Accepted: Published: 7247

February 20, 2014 April 7, 2014 April 9, 2014 April 9, 2014 dx.doi.org/10.1021/ie5007432 | Ind. Eng. Chem. Res. 2014, 53, 7247−7262

Industrial & Engineering Chemistry Research

Article

0.1 MPa of pressure. Emilio J. Gónzalez et al.36 measured dynamic viscosities, densities, and speeds of sound of 1-ethyl-3methylimidazolium ethyl sulfate with methanol, 1-propanol and 2-propanol at T = 298.15, 313.15 and 328.15 K and refractive indices at T = 298.15 K and at atmospheric pressure over the whole composition range. Practical measurement of thermophysical properties of ILs are costly, difficult and time-consuming and is not possible to be carried out at all required temperatures and pressures. Therefore, in recent years, reliable computational prediction methods such as genetic function approximation (GFA), artificial neural network (ANN), adaptive-neuro-fuzzy-interference system (ANFIS) and radial basis function (RBF) have attracted great attention.42−52 For example, Torrecilla et al.43 used a multilayer perceptron neural network model for the estimation of the water content present in the following ILs: 1butyl-3-methylimidazolium tetrafluoroborate, 1-butyl-3-methylimidazolium methylsulfate, 1,3-dimethylimidazolium methylsulfate and 1-ethyl-3- methylimidazolium ethylsulfate. They applied the density and viscosity values of ILs as inputs of their presented neural network model and then compared their estimated results with the experimental measurements of the water content, which were carried out by the Karl Fischer technique, and the difference between the real and estimated values was less than 0.05 and 3.1% in the verification and validation processes of their results. Shojaee et al.44 proposed a new correlation with both correlative and extrapolative capabilities for thermal conductivity of 21 different pure ILs and the obtained optimum values for their fitting parameters by a genetic algorithm. Their calculated average absolute relative deviation percent (AARD%) during the training stage was 5.22%, whereas for testing stage, it was 10.76%. Matsuda et al.45 developed prediction models for ionic conductivity and viscosity of ILs by using quantitative structure property relationships (QSPR) coupled with the descriptors of group contribution type. For this purpose, they presented the polynomial expansion model based on the type of cation, length of side chain and type of anion to the expression of IL properties. Lashkarbolooki et al.46 used the optimized network configuration consisting of one hidden layer with 16 neurons (4:16:1) and tansig and purelin transfer functions for the hidden and output layers to predict the binary heat capacity of ILs. Their results, which were obtained from the training and testing stages of their presented model, showed that the proposed network was able to predict accurately the binary heat capacity of ILs binary mixtures with AARD% of 1.60% and the relation coefficient (R2) of 0.9975. Han et al.47 and Chen et al.49 presented some different QSPR models for predicting the viscosity of pure imidazolium-based ILs with R2 > 0.93 and R2 = 0.99, respectively. Hezave et al.48 used a feed-forward multilayer perceptron neural network model to predict the electrical conductivity of the ternary mixtures of 1-butyl-3-methylimidazolium hexafluorophosphate ([C4mim][PF6]) + water + ethanol and [C4mim][PF6] + water + acetone in the temperature range of 288.15 to 308.15 K. They investigated the effect of transfer functions, number of hidden layers, hidden neurons and the training algorithm on the accuracy of the results. Safamirzaei and Modarress53 modeled Henry’s law constants of CO2, CO, Ar, O2, N2, CH4 and C2H6 in [C4mim][PF6]. They employed the gas molecular weight, gas acentric factor, ω (sphericity of gas molecule), reduced temperature and absolute pressure as network inputs. Golzar et al.54 presented GFA and ANN models to predict the density,

and surface tension of trihexyltetradecylphosphonium tris(pentafluoroethyl)trifluorophosphate at temperature ranges of 293.15 to 343.15 K, 283.10 to 363.17 K and 298.51 to 343.29 K, respectively. Domańska et al.29 determined the density and viscosity of the binary mixtures containing the IL N-octylisoquinolinium bisimide and a series of 1-alcohol at five temperatures (298.15, 308.15, 318.15, 328.15 and 338.15 K) and ambient pressure. Paul and Panda30 evaluated the physicochemical properties of the 1-butyl-3-methylimidazolium methanesulfonate in combination with water by density, viscosity, surface tension, conductance, cyclic voltammetry, absorption and emission spectroscopic measurements. Troncoso et al.31 reported the experimental densities, isobaric heat capacities, and enthalpies of fusion for one sample of 1-butyl-3methylimidazolium hexafluorophosphate and two samples of 1butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide. Nieto de Castro et al.32 investigated the binary diffusion, electrical conductivity, heat capacity, surface tension, viscosity and thermal conductivity of 1-n-butyl-3-methyl-imidazolium bis(trifluoromethanesulfonyl)imide, 1-n-butyl-3-methyl-imidazolium dicyanamide, 1-ethyl-3-methyl-imidazolium ethylsulfate and methyltrialkylammonium dicyanamide. Diogo et al.33 measured the density and viscosity of 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide, 1-ethyl-3-methylimidazolium ethyl sulfate and 1-ethyl-3-methylpyridinium ethyl sulfate by means of an Anton Paar U-tube density meter and vibrating wire viscometer, respectively. Tariq et al.34 measured the dynamic viscosities of several members of the 1-alkyl-3methylimidazolium bis(trifluoromethylsulfonyl)amide [Cnmim][Tf2N], ILs family, with the cation alkyl side-chain length varying from 2 to 14 carbon atoms in a temperature range of 278.15 to 393.15 K by using two different apparatuses (Stabinger and the rolling ball viscometers). Recent studies have presented that ILs can replace organic solvents in extractive distillation of the (water + alcohol) system by means of VLE experiments4−8 and among others, 1ethyl-3-methylimidazolium acetate [C2mim][OAc] and 1-ethyl3-methyl-imidazolium dicyanamide [C2mim][DCA] are able to improve the relative volatilities of this system. Process design for this application requires the knowledge of densities, dynamic viscosities and surface tensions with either temperature and/or concentration dependence. For this purpose, some researchers presented their experimental results of some thermophysical properties of IL+water/alcohol binary mixtures. 14,35−39 For example, Quijada-Maldonado et al.40 presented the experimental densities and dynamic viscosities of binary and ternary mixtures of water and/or 1-ethyl-3methylimidazolium based ILs with the anions acetate and dicyanamide in a wide temperature range (298.15 to 343.15 K) and atmospheric pressure. Rilo et al.41 presented the experimental data of the surface tension and density in binary mixtures of the 1-alkyl-3-methyl imidazolium tetrafluoroborate with water and ethanol at 25 °C and atmospheric pressure. Suojiang Zhang et al.42 presented the experimental data of densities and viscosities for 1-ethyl-3-methylimidazolium tetrafluoroborate + water binary systems over the entire range of their compositions at several temperatures and also they measured the excess molar volumes and viscosity deviations of studied binary systems and fitted to the Redlich−Kister equation. Elena Gómez et al.35 determined the dynamic viscosities and densities over the whole composition range for water + [C6mim][Cl] and water + [C8mim][Cl] at T = 298.15, 313.15, 328.15 and 343.15 K and 7248

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Table 1. Density and Viscosity of Pure Water, Studied Alcohols and Ionic Liquids no.

IUPAC name

abbreviation name

global formula

density (g·cm−3)

viscosity (mPa·s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1-ethyl-3-methylimidazolium ethylsulfate 1-ethyl-3-methylimidazolium acetate 1-ethyl-3-methyl-imidazolium dicyanamide 1-ethyl-3-methylimidalozium tetrafluoroborate 1-butyl-3-methylimidazolium chloride 1-hexyl-3-methylimidazolium chloride 1-methyl-3-octylimidazolium chloride 1-ethyl 3-methylpyridinium ethylsulfate 1-ethyl-3-methylimi-dazolium trifluoromethanesulfonate 1-ethyl-3-methylimidazolium trifluoroacetate 1-butyl-3-methylimidazolium methylsulfate water methanol ethanol 1-propanol 2-propanol

[Emim][EtSO4] [Emim][OAc] [Emim][DCA] [Emim][BF4] [C4mim][Cl] [C6mim][Cl] [C8mim][Cl] [Empy][EtSO4] [Emim][OTf] [Emim][TFA] [Bmim][MeSO4]

C8H16N2O4S C8H14N2O2 C8H11N5 C6H11BF4N2 C8H15CIN2 C10H19CIN2 C12H23CIN2 C10H17NO4S C7H11F3N2O3S C8H11N5F3N2O2 C9H18N2O4S H2O CH4O C2H4O C3H8O C3H8O

1.240 1.098 1.102 1.340 1.024 1.040 1.009 1.222 1.384 1.291 1.213 0.997 0.786 0.785 0.800 0.781

101.420 132.910 14.900 45.290 19486.000 18089.000 20883.000 161.400 41.000 32.000 182.300 0.890 0.546 1.087 2.017 2.082

separate collected data of the experimental measurements for these properties (density, dynamic viscosity, excess molar volume, refractive index and speed of sound) were used to construct the ANN models, and the best models of ANN that can predict desired properties of ILs + water/alcohol binary mixtures with the lowest error were found. It is indicated that by applying these models, it is possible to estimate the desired properties of binary mixtures with an acceptable accurately.

surface tension and viscosity of pure quaternary ammoniumbased ILs ([N222(n)]Tf2N with n = 5, 6, 8, 10 and 12). They used the critical temperature and water content of studied ILs as well as operation temperature as the input parameters and obtained results with R2 > 0.999, 0.993 and 0.998 for density, surface tension and viscosity in testing sets, respectively. The computational prediction methods including GFA, ANN, ANFIS and RBF were not only applied to predict some desired properties of ILs but they were also used for predicting other important properties.55−69 For example, by using the artificial neural network (ANN) technique, Mohanty55 estimated the vapor liquid solubility of binary mixtures with an average absolute deviation of 3% for liquid phase and less than 0.02% for vapor phase mole fractions. Nguyen et al.56 applied ANN with 8:6:7:4 network as the optimum architecture to estimate vapor−liquid equilibrium (VLE) data and bubble point for ternary systems with the lowest possible error. Ahmadi57 proposed a model based on ANN to predict asphaltene precipitation in the oil reservoir. Nasouri et al.58 employed the ANN technique to model the average diameter of electrospun polyacrylonitrile (PAN) nanofibers and showed that the technique had high prediction ability. Safamirzaei and Modarress70 investigated the solubility of hydrogen in heavy n-alkanes (C10H22, C16H34, C28H58, C36H74 and C46H94) within the temperature range of 283−448 K and pressure range of 1.15−15.97 MPa by applying the ANN technique. The large number of works done by utilizing artificial intelligence techniques show that this technique can be used in various fields of science for prediction the desired properties.55−60,71,72 In this work, to predict some thermophysical properties of binary mixtures of ILs + water/alcohol (such as methanol, ethanol, 1-prapanol and 2-propanol) including density, dynamic viscosity, excess molar volume, refractive index and speed of sound, a powerful artificial intelligence technique (ANN) was applied. For this purpose, the density and dynamic viscosity of pure water/alcohol and pure IL and operation temperature as well as mole fractions of water/alcohol of studied binary mixtures of ILs with water or alcohol were given as the input parameters and above-mentioned properties were calculated as the outputs of the prediction procedure. It must be mentioned that all of the ILs that were considered in this study were miscible in all proportions in water and the alcohols. Five

2. METHODOLOGY 2.1. Data Set Used. The data set in this investigation consisted of the experimental results of density (884 samples), dynamic viscosity (496 samples), excess molar volume (656 samples), refractive index (85 samples) and speed of sound (105 samples) for binary mixtures of some common ILs (11 different ILs) that are presented in Table 1 and water or alcohol such as methanol, ethanol, 1-propanol and 2-propanol in the operation temperature range of 278.15 to 348.15 K.11,12,14,35−39,42,51,68 These properties for ILs were selected because in several chemical engineering particular operations such as distillation, extraction, absorption, adsorption and extractive fermentation, knowledge of density, viscosity, etc. is highly relevant. Therefore, presenting accurate predicting models for necessary thermophysical properties is a justifiable task. Figure 1a−e depicts the distribution range of desired properties versus the number of compounds in the each range of experimentally measured properties. As it is shown in this figure, most of the studied components have the density, dynamic viscosity, excess molar volume, refractive index and speed of sound values, respectively, in the ranges of 0.98−1.21 g·cm−3, 0−5 mPa·s, −0.01−0 cm3·mol−1, 1.45−1.49 and 1550− 1600 m·s−1. The highest and lowest values of these properties as well as six selected input parameters used in this study with their symbols are presented in Table 2. It must be mentioned that 70% and 15% of the data were, respectively, used to train and validate each network and the residual data, which were not used in the training and validation but were used for testing. 2.1. Artificial Neural Network (ANN). ANN is a mathematical and numerical method; its original idea was inspired by biological neural nets. Each kind of data, which, in some cases, the relations between them are very complicated, can be modeled via ANN.53,57,70−84 By using appropriate experimental data, which can be obtained from the literature, 7249



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Figure 1.

architecture and setting. One of the most difficult tasks in studying ANN is finding an appropriate architecture. This task is performed via trial and error and the number of middle layers and neuron presented in each layer are being identified. Appropriate designation of initial amounts of weights and biases is very effective on the performance of network and the time of calculation. But there is not a reasonable law and process to identify suitable architecture. The only step that is very time-consuming is the trial and error.53,70,76−82 Figure 2 shows a network for predicting refractive index of studied IL+water/alcohol binary mixtures that contains 6 inputs and 4 neurons in the hidden layer. Each neuron has inputs, bias, weight, summation function, transfer function and output. At first, each input (p) will be multiplied by its weight (w),

most physicochemical properties can be calculated by means of ANN. ANN is an especially efficient algorithm that, by learning the relationships between input and output vectors, approximates any thermophysical properties by utilizing a nonlinear model. To apply the technique, a three-layer feed-forward neural network utilizing the back-propagation algorithm is employed. Usually, a back-propagation network consists of two essential layers: input layer and output layer. Each layer is composed of some neurons, and each neuron is a simple microprocessing unit that receives and combines signals from many neurons located in the previous and next layers. The number of neurons presented in the input and output layer depends on the number of variables.53,76,77,79,81−83 The performance of ANN is generally based on parameters of 7250



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Table 2. Variation Ranges of Inputs and Output of Presented ANN Models set

parameters

symbol

variation range

inputs

density of pure water or alcohol, g·cm−3 viscosity of pure water or alcohol, mPa·s density of pure ionic liquid, g·cm−3 viscosity of pure ionic liquid, mPa·s operation temperature, K mole fraction of water or alcohol, mol/mol density of mixture, g·cm−3 viscosity of mixture, mPa·s excess molar volume, cm3·mol−1 refractive index speed of sound, m·s−1

ρW/A ηW/A ρIL ηIL T x ρmix ηmix VE n u

0.785−0.997 0.546−2.017 0.781−1.384 2.082−20883.000 278.150−348.150 0.000−1.000 0.74453−1.400 52 0.369−51.500 −1.175−0.404 1.326−1.506 1006.000−1679.000

outputs

Figure 2.

After calculating the summation function for output layer by eq 3,

weighted input is composed and the summation function (∑) is computed from weighted inputs of all neurons of the hidden layer that exist in the network. Then this value sums with bias of current neuron and lead to activate the neuron. This activation signal (n) is passed on to the transfer function (f) to calculate the output (a). The behavior of a back-propagation network is mainly determined by the transfer functions of its neurons. Weight and bias are two adjustable parameters in a neuron.53,82 According to what was mentioned before, each input vector is presented to the input layer of the network and by using the following equation: n jh =

∑ wijpi

+ bj

i

nko =

2 −1 1 + exp( −2n jh)

(3)

by using the linear transfer function (purelin), the final output is calculated by eq 4: ako = f2 (nko) = nko

(4)

In eqs 1−4, wij and wjk are the connection weights between the hidden unit and other units.ahj ,nhj ,pi and bj are, respectively, the output of hidden layer and input of next layer, summation function, input and bias of hidden layer of network. aok,nok, and bk are, respectively, final output, summation function and bias of output layer. In this study, MATLAB Neural Network Toolbox has been used for modeling the operation.85 MATLAB Neural Network Toolbox has different algorithms to perform the network training phases using the back-propagation method. MATLAB Neural Network Toolbox receives entire experimental data as the input and divides them randomly into three parts (train, validation and test). Most of the data is devoted to the training part. After determining the effective parameters of ANN such as the number of middle layers, the number of neurons of each layer, transfer function, the number of epoch, etc. by user and determining randomly the amounts for weight and bias by software (usually the software set these parameters on zero as

(1)

the summation function is calculated from inputs, along with their weights and biases. The output of each neuron is obtained by applying the nonlinear transfer function, which is presented as a jh = f1 (n jh) =

∑ wjkajh + b k

(2)

Several linear and nonlinear transfer function are available in ANN and in this work, the tansig (symmetric sigmoid transfer function) and the purelin (linear transfer function) was used as transfer functions in, respectively, the hidden and output layers. 7251



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into three separate sets including training set, validation set and testing set by applying the random number generation tool box (r and tool) of MATLAB software. According to the other studies,53,56,60,82 70%, 15% and 15% of all data were, respectively, allocated to training, validation and testing sets. Then, by means of the trial−error method, the effective parameters of the network, which consisted of weight, bias, number of hidden layers, number of neurons in each layer, transfer function, learning algorithm, etc. were changed until the most accurate architecture was found. The best architecture of networks obtained for density, dynamic viscosity, excess molar volume, refractive index and speed of sound properties had, respectively, four, seven, eight, six and eight neurons in their single hidden layer (6:4:1 network for density prediction, 6:7:1 network for dynamic viscosity prediction, 6:8:1 network for excess molar volume, 6:6:1 network for refractive index and 6:8:1 network for speed of sound, see Figure 2). In each of the five networks, tansig and purelin transfer functions were used, respectively, for the hidden and output layers. The chosen learning algorithm for these models was trainlm (Levenberg− Marquardt back-propagation) and the other parameters were set as defaults. Both transfer functions and learning algorithm are available in MATLAB Neural Network Toolbox of R2011a (Mathworks Inc.).85 Figure 3a−e and five tables in the Supporting Information present, respectively, the values of the predicted density, dynamic viscosity, excess molar volume, refractive index and speed of sound obtained by ANN models versus the experimental values. As it is obvious from this figure, the aggregation of all points (red circles, blue squares and turquoise triangles are, respectively, presented the predicted values of training set, validation set and testing set) is more intense in the vicinity of the bisection, so, as a result, this would illustrate the accuracy of the models in predicting the five thermophysical properties. In Table 4, the optimum values of weights and biases related to the presented ANN models for predicting desired thermophysical properties of studied binary mixtures of IL + water/alcohol are listed. The best architecture network of the density ANN model is 6:4:1 and this model has 33 adjustable parameters. Similarly, the numbers of adjusted parameters for dynamic viscosity, excess molar volume, refractive index and speed of sound prediction ANN models are 57, 64, 49 and 65, because the best architecture networks for these properties are 6:7:1, 6:8:1, 6:6:1 and 6:8:1, respectively. Therefore, the application of proposed models (weights and biases, Table 4) based on the ANN technique for predicting the abovementioned properties for binary mixtures of IL + water/ alcohol are not limited only to these studied system, but by using the required parameters (ρW/A, ηW/A, ρIL, ηIL, T and x), the models can be applied to produce the same thermophysical properties for other IL + water/alcohol systems. In addition, the error of these models is lower than that for other presented models in previous studies. For example, Quijada-Maldonado et al.40 using a three-adjustable parameter model to model their experimental density results with AAD% > 0.21, while the corresponding error of this study is less than 0.0076 (see Table 5). 3.2. Applicability Domain. Applicability domain (AD) should be applied to ensure that a domain is defined as broadly as possible for the desired property prediction.71,87 ANN models should be applied to predict properties of a system within the domain by interpolation rather than extrapolation,

the initial guess), the process of training is performed with the train parts of data. For decreasing the time of learning process and to ensure that the influence of input variables in the course of model building is not biased by the magnitude of their native values, or their range of variations, the data normalization is necessary before starting the training process.78,80,82,84 In the normalization technique, a linear transformation is applied. The most commonly linear normalization is as follows:86 x − xmin x′i = α i +β xmax − xmin (5) where x′i is the normalized value, xi is the original data, xmax and xmin are the maximum and minimum values, respectively, α and β are the positive constants allowing to fix the limits of the interval for the normalized values. In this study, α and β are set as 0.8 and 0.1, respectively, so the normalized input/output variables are in the range of 0.1 to 0.9. Training is automatically completed when generalization stops improving, as indicated by an increase in the mean square error of the validation samples.60 In the process of training, one problem may occur called “over fitting”; this means that the network has memorized the training examples, but it has not learned to generalize to the new situations.60 To solve this problem, by using the data related to the validation part, the weights and biases of the train phase are evaluated and continued so that the difference between experimental and calculated values becomes trivial. When this stage has been finished, software utilizes the test part data to study the network performance and to monitor the sets.

3. RESULTS AND DISCUSSION Table 3 shows the correlation matrix of the selected parameters for predicting the desired thermophysical properties (ρmix, ηmix, Table 3. Correlation Matrix of the Six Selected Parameters Used in ANN Model for Predicting the Density, Viscosity, Excess Molar Volume, Refractive Index and Speed of Sound for Binary Mixtures of Water/Alcohol and Ionic Liquids ρW/A ηW/A ρIL ηIL T x

ρW/A

ηW/A

ρIL

ηIL

T

x

1.000 −0.377 0.109 0.264 −0.017 0.119

−0.377 1.000 0.013 −0.103 −0.005 −0.037

0.109 0.013 1.000 −0.643 −0.209 0.035

0.264 −0.103 −0.643 1.000 0.119 0.079

−0.017 −0.005 −0.209 0.119 1.000 0.000

0.119 −0.037 0.035 0.079 0.000 1.000

VE, n and u). If one of the selected parameter (ρW/A, ηW/A, ρIL, ηIL, T and x) is highly correlated to the others, it would mean that one of them is redundant and must be removed. If the linear correlation coefficient value of two selected parameters is less than 0.40; the selected parameters would be independent of each other and can be considered as effective suitable parameters for ANN models. By considering Table 3, it can be seen that all linear correlation coefficient are much less than 0.4 and even are almost zero. Therefore, six selected parameters are independent and they are suitable for predicting the desired thermophysical properties of the studied binary mixtures of IL + water/alcohol. 3.1. ANN Models. To investigate the nonlinear interactions between ρW/A, ηW/A, ρIL, ηIL, T and x parameters, five backpropagation artificial neural networks (BP-ANNs) were developed. For this purpose, the original data set was divided 7252



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Figure 3.

which are more precise and reliable.87 In this study, the applicability domain of each five proposed models based on the ANN technique for prediction of density, dynamic viscosity, excess molar volume, refractive index and speed of sound was investigated by means of a simple scattered plot of the leverage versus the standardized residuals (R) or Williams plot. In this approach, the residual is equal to the differences between the observed and predicted values of desired thermophysical properties (ρmix, ηmix, VE, n and u) of binary mixtures and the

leverage or hat indices are calculated based on hat matrix (H) with the following definition:71,87

H = X(XTX)−1XT

(6)

where X is a two-dimensional matrix comprising n samples (rows) and k descriptors (columns). The leverages or hat values (hi) of each case in the descriptor space are the diagonal elements of H. For graphical presentation of AD and outliers, the Williams plots of the models are depicted in Figure 4a−e. 7253



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Table 4. Optimum Weights and Biases for the ANN Models wija layers

1

2

3

4

5

6

7

8

bjb

‑3

ρmix (g·cm ), (6:4:1) input 1 2 3 4 output 1

−0.020 −12.154 0.122 0.116

−0.046 −0.313 0.063 −0.193

0.084 0.681 −0.167 −0.066

0.006 −0.872 −0.001 0.046

7.448

−0.242

8.580

−1.282

−0.010 −0.144 −0.002 0.012

33 −0.390 0.561 1.971 0.717

0.123 10.260 −0.777 0.628

−4.559 ηmix (mPa·s), (6:7:1)

input 1 2 3 4 5 6 7 output 1 input 1 2 3 4 5 6 7 8 output 1 input 1 2 3 4 5 6 output 1 input 1 2 3 4 5 6 7 8 output 1 a

no. of parameters

−0.500 0.326 −1.015 −3.599 −0.396 0.339 0.116

−4.259 0.007 −4.189 0.559 −0.213 0.129 2.804

1.590 −2.448 0.507 1.045 1.383 −1.483 0.774

1.167 2.319 −15.691 −5.025 5.863 −1.100 4.326

4.662

−2.062

−4.672

2.622

0.360 −0.335 0.412 0.400 0.257 −0.294 −1.147

57 0.879 −1.674 0.825 0.890 1.510 −1.307 −2.559

7.302 12.531 VE (cm3·mol−1), (6:8:1) −0.006 0.092 0.252 −0.166 0.116 −0.048 0.022 −0.076

0.761 1.645 −15.927 −0.892 6.640 −1.814 −6.829 1.920

1.445 64

−0.786 −0.518 −6.503 0.744 −1.809 5.736 −1.441 4.040

0.361 0.497 −7.060 −0.793 0.400 −4.935 2.127 8.253

−0.478 1.370 9.734 −2.757 −2.327 0.315 1.946 4.927

−11.738 0.690 7.953 −1.123 −2.772 4.856 1.955 1.109

−1.308 0.390 2.404 −0.891 0.787 1.380 −0.389 −0.458

−10.193

−5.362

0.638

−1.703 1.753 n, (6:6:1)

−8.779

−0.257 −0.072 −0.726 0.774 −0.859 0.479

1.397 −1.331 0.757 −4.765 −1.168 2.292 −3.228

2.469

1.636

−1.430 49

−2.087 −0.341 −0.021 0.389 −2.306 1.810

−0.670 0.295 −2.447 −0.215 −0.399 0.603

−0.161 −1.955 −0.237 0.084 0.287 0.074

−0.436 1.186 1.269 −0.004 0.064 0.465

−0.138

−0.213

0.279

−3.305 0.245 u (m·s−1), (6:8:1)

0.563

2.071 0.454 −2.193 3.617 −1.941 −0.556

−9.815 0.583 3.386 −1.331 2.014 −4.398 2.784 2.152

65

−1.738 0.001 −1.571 1.064 2.051 0.444 −2.327 −4.680

1.804 −0.017 −1.723 −0.563 −0.563 −1.419 1.085 −0.918

−0.168 0.031 0.214 −4.223 −0.393 −2.247 0.195 −0.028

−2.413 0.543 0.130 0.245 1.627 −0.006 −1.266 −2.465

0.033 −0.008 −1.647 0.251 0.744 −0.487 −0.621 −2.799

−1.290 0.287 0.172 −1.989 0.617 −1.126 −0.535 −1.247

−0.073

−2.118

−1.912

−0.030

0.066

0.078

1.110 −0.624 1.565 −1.207 0.288 −1.564 −1.295 0.561 −0.199

1.950

−0.786

Weight matrix. bBias matrix.

dynamic viscosity, excess molar volume, refractive index and speed of sound are, respectively, 884, 496, 656, 85 and 105. The value of p for the models is 6, so the warning leverages of models are, respectively, 0.02, 0.04, 0.03, 0.25 and 0.20. For

A warning leverage (h*), blue vertical line in Figure 4a−e, is generally fixed at 3p/n, where n is number of training samples and p is the number of model variables plus one.71 As mentioned above, in this study, the values of n for density, 7254



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Table 5. Squared Correlation Coefficient (R2), Root-Mean-Squares Error (RMSE), Average Relative Deviation (ARD), Average Absolute Deviation Percent (AAD%) and Statistical Parameters for the ANN Models to Predict Density, Viscosity, Excess Molar Volume, Refractive Index and Speed of Sound for Binary Mixtures of Water/Alcohol and Ionic Liquids sets training set

validation set

total data

parameters 2

R RMSE ARD AAD% R2 RMSE ARD AAD% R2 RMSE ARD AAD% Radj2 F-ratio k k′ n m R2m Q2 F1 Q2 F2 Q2 F3

ρmix (g·cm−3)

ηmix (mPa·s)

VE(cm3·mol−1)

n

u (m·s−1)

0.9939 0.0102 0.0071 0.0076 0.9941 0.0103 0.0068 0.0073 0.9990 0.0000 0.0000 0.0000 0.9980 29 417 0.9904 1.0097 0.0000 0.0000 0.9970 0.9977 0.9972 0.9969

0.9207 2.5056 0.3458 1.3389 0.9572 1.5831 0.2225 1.0898 0.9000 2.3000 0.3000 1.3000 0.9000 1297.8 1.0048 0.9952 −0.1000 −0.1000 0.7000 1.0000 1.0000 1.0000

0.9740 0.0479 0.1500 0.0347 0.9620 0.0537 0.1800 0.0398 1.0000 0.1000 0.2000 0.0000 1.0000 4029.2 0.9611 1.0405 0.0000 0.0000 0.800 0.9975 0.9972 0.9405

0.9996 0.0010 0.0005 0.0007 0.9986 0.0017 0.0008 0.0012 1.0000 0.0000 0.0000 0.0000 1.0000 15 423 1.0002 0.9998 0.0000 0.0000 1.0000 0.9997 0.9988 1.0000

1.0000 0.9980 0.0006 0.7973 1.0000 1.1790 0.0008 0.9830 1.0000 0.0000 0.0000 0.0000 1.0000 657 320 1.0004 0.9996 0.0000 0.0000 1.0000 1.0000 1.0000 1.0000

indicate that no systematic error exists in the development of the five models. Figure 6a−e illustrates the error distribution of the predicted density, dynamic viscosity, excess molar volume, refractive index and speed of sound values. As shown in this figure, the majority of the error values are distributed in the vicinity of zero, which illustrates the accuracy of the ANN models to predict the five desired thermophysical properties of IL + water/alcohol binary mixtures. 3.3. Validation Techniques. The predictability and robustness of the developed models were evaluated using several internal and external procedures. The most commonly used validation techniques for internal validation are crossvalidations (CV), which are classified as the statistical techniques. In these techniques, different proportions of samples are iteratively held-out from the training set used for model development (an optimal parameters’ selection step) and “predicted” again as new values by the developed model in order to verify internal “predictability” by Leave-One-Out (QLOO2) and Bootstrapping (QBoot2) techniques.71,87−89 Initially, the Leave-One-Out cross-validation technique was applied to the five presented models and the value of QLOO2 for predicting the properties density, dynamic viscosity, excess molar volume, refractive index and speed of sound of the IL + water/alcohol binary mixtures were found to be 0.982, 0.962, 0.958, 0.986 and 0.991, respectively. Because the absolute difference of these values and their corresponding calculated squared correlation coefficients (R2, see Table 5) for each six proposed models are small, the reliability of the models was validated. Bootstrap is another validation technique applied in this study. QBoot2 is the key parameter of Bootstrap and defines as the average of the prediction error of sum of squares (PRESSs) calculated in this technique. PRESS is defined as follows:87−89

dynamic viscosity, excess molar volume, refractive index and speed of sound the leverage was taken as 2 and for the density, it was 3. These values were considered as the cutoff values to accept the points that lay respectively with in ±2 and ±3 (two horizontal red lines in Figure 4a−e) of the standard deviations from the mean (to cover 99% normally distributed data). As it is seen in Figure 4a−e, the most influential samples have small residuals, which indicates stabilization of the models and their high precision. For example, the AD of density model (Figure 4a) is located in the region of 0 ≤ h ≤ 0.02 and −3 ≤ R ≤ +3. The majority of data points of the five models (Figure 4a−e) that correspond to the training, validation and testing sets are in this domain and reveal that the model derivation and the resulting predictions for each of the five thermophysical properties have been in the applicability domain and this approves the validity of the models and the obtained results. Some predicted results have standardized residuals in range of AD, but the corresponding leverages of them are higher than h (i.e., h ≥ 0.02 and −3 ≤ R ≤ +3 for density); these points fit the model well and are known as “good high leverage”points . In Williams plot of the ANN model, a point that is located outside of the red lines and has a h greater than 0.02 is known as a “bad high leverage” point and it is an outlier in the model. The obtained results for density that exist in h ≥ 0.02 and R > +3 or R < −3 domains are wrongly predicted, but in this case, they belong to the models AD, being within the cutoff value of hat. This erroneous prediction could probably be attributed to wrong experimental data measurement.71,87 The residual percent values of the predicted properties: density, dynamic viscosity, excess molar volume, refractive index and speed of sound of the binary mixtures (IL + water/ alcohol) that are defined as the percentage differences between the experimental and predicted values are plotted versus the experimental data in Figure 5a−e. The normal distributions of the residual percent values on both sides of the zero line 7255



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Figure 4. n

PRESS =

∑ (yi − yi/̂ i )2 i=1

speed of sound for IL + water/alcohol binary mixtures were 0.978, 0.959, 0.963, 0.983 and 0.988, respectively. In addition, to test the models for chance correlations, the yscrambling validation technique was applied. Chance correlations are able to successfully predict the responses but their parameters are actually of no real significance. Therefore, to eliminate this possibility, y-scrambling technique was advocated. In this method, the connection of the target values (such as density, dynamic viscosity, excess molar volume, refractive index and speed of sound of studied IL + water/alcohol binary

(7)

where ŷi/i denotes the response of the ith predicted values of the desired parameter by using the obtained model but ignoring the ith experimental parameter.87 The bootstrapping has been repeated 200 times for five models. Consequently, the QBoot2 values obtained from ANN models for predicting the density, dynamic viscosity, excess molar volume, refractive index and 7256



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Figure 5.

mixtures) and selected parameters (ρW/A, ηW/A, ρIL, ηIL, T and x) deliberately destroyed by permutation of y data and new prediction models were developed by using the original selected parameter matrix. This y-scrambling is repeated 200 times and the highest calculated R2 value for density, dynamic viscosity, excess molar volume, refractive index and speed of sound was evaluated as 0.103, 0.192, 0.199, 0.121 and 0.118, respectively. In addition, the cRp2 criterion was calculated by applying the following formula:48 c

R p2 = R2 (R2 − R r 2) ≥ 0.5

where R2 is squared correlation coefficient of the original model and Rr2 is the average of the squared correlation coefficient of the randomized models. The values of cRp2 calculated for the proposed ANN models for predicting the density, dynamic viscosity, excess molar volume, refractive index and speed of sound for IL + water/alcohol binary mixtures were 0.771, 0.801, 0.835, 0.749, and 0.784, respectively. The evaluated results by means of y-scrambling indicate that the chance correlation or structural dependence of the training set has ignorable or no significant effect on the presented models.

(8) 7257



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Figure 6.

External validation of the presented models was done by means of the external test set based on four statistical quantities including squared correlation coefficient (R2), root-meansquare error (RMSE), average relative deviation (ARD) and average absolute deviation (AAD%) given by the following formulas:

n

∑i = 1 (yiexp − yical )2

RMSE =

n n

∑i = 1 ARD =

n

R2 = 1 −

∑i = 1 (yiexp − yical )2 n ∑i = 1 (yiexp

2

− y̅ )

(10)

yiexp − yical yiexp

(11)

n n

AAD% =

(9) 7258

∑i = 1 |yiexp − yical | n

× 100

(12)



Article

cal where yexp i , yi , y ̅ and n are the experimental data, calculated data, average calculated values and the number of compounds in the data set, respectively. The obtained results of the abovementioned quantities (R2, RMSE, ARD and AAD%) for density, dynamic viscosity, excess molar volume, refractive index and speed of sound prediction models based on ANN for each three sets (training, validation and testing sets) as well as the total data set are tabulated in Table 5. Considering this table, it can be concluded that the six selected parameters (ρW/A, ηW/A, ρIL, ηIL, T and x) are appropriate for predicting the desired properties and the predicted results by the models are reliable because their correlation and error values are in an acceptable range. As this table indicates, R2 values of predicted by the models are very close to the unity and their corresponding errors are negligible. In Table 5, the obtained value of adjusted R2 for the proposed ANN models for predicting each thermophysical property is presented. The small difference between these values and the R2 parameter represent the validity of the models. In addition, the criteria recommended by Golbraikh and Tropsha90 and Roy91 were also applied for the external validation. These criteria are presented as follows:

0.85 ≤ k ≤ 1.15

(13)

0.85 ≤ k′ ≤ 1.15

(14)

m=

n=

(R2 − R 0 2) R2

R2 − R′0 2

≤ 0.1

R2

R m 2 = R2 × (1 − k=

k′ =

≤ 0.1

|R2 − R 0 2| ) ≥ 0.5

n

Q F12 = 1 −

(15)

(16) (17)

n

∑i = 1 (yical − kyicalc )2 n

(20)

n

R′0 2 = 1 −

∑i = 1 (yiexp − k′yiexp )2 n

∑i = 1 (yiexp − y ̅ exp )2

n

2 ∑i =EXT1 (yiexp − yEXT ̅ )

(23)

[∑i =EXT1 (yiexp − yical ) 2]/nEXT n

2 [∑i =TR1 (yiexp − yTR ̅ ) ]/n TR

(24)

4. CONCLUSIONS In the present study, models have been developed by using nonlinear the artificial neural network (ANN) technique for prediction of the thermophysical properties density, dynamic viscosity, excess molar volume, refractive index and speed of sound for IL + water/alcohol binary mixtures based on the density and dynamic viscosity of pure water/alcohol and pure IL and operation temperature as well as mole fractions of water/alcohol. The obtained results reveal that the selected parameters, as the inputs, are very appropriate for estimation of thermophysical properties of IL + water/alcohol binary mixtures. In addition, the high statistical quality represented by various criteria and the low prediction errors of the presented models indicate that they can accurately predict the density, dynamic viscosity, excess molar volume, refractive index and speed of sound for IL + water/alcohol binary mixtures.

(19)

∑i = 1 (yical − y ̅ cal )2

∑i =EXT1 (yiexp − yical ) 2

cal where yexp i , yi , yT ̅ R, yE̅ XT, nTR and nEXT are, respectively, defined as the experimental data, the calculated value, the average of training set, the average of external prediction set (test set), the number of compounds in the training set and the number of compounds in the external prediction set. However, eq 22 is widely used in validation techniques by different authors and it was also implemented in the software used for QSAR modeling (MOBY DIGS) of Todeschini et al. 94 After the Q 2 F1 formulation, Schüürmann et al.93 proposed an alternative criterion (Q2F2), which differs from Q2F1 because the average value at the denominator is calculated using the prediction data set instead of the training set and at last, as can be seen from eq 23, the suggested validation technique by Consonni et al.94 differs from both Q2F1 and Q2F2 as the denominator is calculated on the training set, and both numerator and denominator are divided by the number of the corresponding elements. The calculated results of Q2F1, Q2F2 and Q2F3 for proposed ANN models are listed in Table 5. Schüürmann et al.93 note a concern about these parameters: QF22 ≤ QF12. The obtained results of these methods reveal that the abovementioned concern was satisfied (for example, to predict the density of studied ILs: QF22 = 0.9972 ≤ QF12 = 0.9977).

∑ yiexp yicalc

R 02 = 1 −

(22)

n

Q F32 = 1 −

(18)

∑ (yiexp )2

n

2 ∑i =EXT1 (yiexp − yTR ̅ ) n

Q F2 2 = 1 −

∑ yiexp yicalc ∑ (yical )2

∑i =EXT1 (yiexp − yical ) 2

(21)

The parameters in the above-mentioned equations (m, n, k and k′) as well as Rm2 values are presented in Table 5. As can be seen in this table, these parameters satisfy the criteria presented by eqs 13−21 and indicate that the presented models are substantially valid and can be used to estimate desired thermophysical properties of studied IL + water/alcohol binary mixtures. In addition, to ensure more validity for the presented ANN models, three validation methods, which were, respectively, developed by Shi et al.92 (Q2F1), Schüürmann et al.93 (Q2F2) and Consonni et al.88 (Q2F3), were employed and they are calculated, respectively, by following equations were applied.

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ASSOCIATED CONTENT

S Supporting Information *

Inputs as well as experimental and calculated data for thermophysical properties presented in five tables, respectively, containing the density, viscosity, excess molar volume, refractive index and speed of sound of ILs + water/alcohol binary mixtures. This material is available free of charge via the Internet at http://pubs.acs.org. 7259



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AUTHOR INFORMATION

Corresponding Author

*H. Modarress. E-mail: [email protected]. Tel.: (+98)2164543176. Fax: (+98)21 66405847. Notes

The authors declare no competing financial interest.

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