A GEP based model for prediction of densities of ionic liquids

    A GEP based model for prediction of densities of ionic liquids Adel Najafi-Marghmaleki, Afshin Tatar, Ali Barati-Harooni, Amir H Mohammadi PII: DOI: Reference:

S0167-7322(16)32971-3 doi:10.1016/j.molliq.2016.11.072 MOLLIQ 6619

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

1 October 2016 14 November 2016 15 November 2016

Please cite this article as: Adel Najafi-Marghmaleki, Afshin Tatar, Ali Barati-Harooni, Amir H Mohammadi, A GEP based model for prediction of densities of ionic liquids, Journal of Molecular Liquids (2016), doi:10.1016/j.molliq.2016.11.072

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A GEP based Model for Prediction of Densities of Ionic Liquids

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Adel Najafi-Marghmaleki,a Afshin Tatar,b Ali Barati-Harooni,a1 Amir H Mohammadic,d,e 2 a

Young Researchers and Elite Club, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran Young Researchers and Elite Club, North Tehran Branch, Islamic Azad University, Tehran, Iran c Discipline of Chemical Engineering, School of Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban 4041, South Africa d Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France e Département de Génie des Mines, de la Métallurgie et des Matériaux, Faculté des Sciences et de Génie, Université Laval, Québec, QC G1V 0A6, Canada

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Abstract - One of the most important properties of ionic liquids (ILs) is their densities.

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Accurate knowledge of this property is required in engineering and scientific purposes including equipment design, liquid metering calculations, and other applications. As a result, it is important to develop accurate and effective models for prediction of this property. The present work aims to develop a model based on Gene Expression Programming (GEP) technique for prediction of experimental density values of 146 different ionic liquids at different temperatures. A databank containing 602 data gathered from the literature was utilized to develop the model. The input parameters of the model are temperature, molecular weight of IL, normal boiling point temperature of IL, critical pressure of IL, critical volume of IL, and acentric factor of IL. The outcomes of this work indicate that the developed model is capable of estimating target density data with an acceptable accuracy. The effectiveness and accuracy of the model was checked by utilizing different statistical and graphical techniques. Moreover, results of the proposed model are compared with predictions of literature correlations and it is shown that the GEP model is effectively superior to other correlations and exhibits higher accuracy and reliability.

Keywords: Ionic liquid (IL); Density; Gene expression programming (GEP); Model; Data

Corresponding author: 1 Email Address: [email protected] (A. Barati-Harooni) 2

Email Address: [email protected] and [email protected] (A. H. Mohammadi)

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Introduction

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Ionic Liquid (IL) refers to a liquid, which is composed of organic cations and organic or inorganic anions, which remains in liquid phase below 100 oC [1, 2]. It is possible to achieve

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different required and useful features of ILs by performing synthesis processes on them and

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altering the length and branching of their cationic and anionic parts. This is the reason for existence of a vast number of these compounds with various characteristics and different

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applications. In addition, they are famous as “design solvents” [3-6]. ILs have special

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characteristics such as, non-flammability, non-volatility, excellent solubility capability in polar and nonpolar compounds, notable electrical and ionic conductivity, etc. [4, 5, 7-20]. Researchers

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investigated and reported various applications of ILs. One of the most useful applications of

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these compounds is their usage as solvent in many scientific and industrial fields [3, 5-8, 12, 16,

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20]. However, in order to use these substances in various applications it is needed to achieve clear and detail information about their physical and chemical properties. Although various investigations and experimental measurements were conducted on the characteristics of ILs in both mixture and pure condition, gaining more information about the physicochemical properties of them seems necessary because of the increase in their applications. Liquid density is one of the mostly measured properties of ILs [21, 22]. This property is needed in different design processes and in liquid metering calculations [21, 23]. It could be measured precisely by utilizing appropriate devices such as a pycnometer [24]. However, accurate experimental determination of this property at different temperature and pressure conditions is usually time-consuming, difficult, and costly [25, 26]. Moreover, sometimes it is not possible to conduct experimental tests. This is where using accurate and reliable models and correlations to predict the required properties of ILs such as density could be of great importance to decrease the laboratory

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ACCEPTED MANUSCRIPT investment. Intelligent models are one of the powerful estimation techniques, which can be applied in prediction of ILs physical properties and their mixture [27-29]. Recently, the use of

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these techniques for effective prediction of properties of ILs attracted the attention of many

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scientists and researchers. For example, Valderrama et al. [30] used Artificial Neural Networks (ANNs) to predict the viscosity of pure ionic liquid. Taskinen and Yliruusi [31] analyzed and

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presented a complete list of characteristics of ILs using ANN approaches. In addition, ANN was

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utilized to predict mixture properties (vapor-liquid equilibrium, activity coefficients, PVT properties) [32, 33]. The purpose of present work is to develop an accurate model based on gene

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expression programming (GEP) model for prediction of density of a number of ionic liquids at various temperatures. Moreover, results of the implemented model were put into comparison

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with the literature correlations for prediction of density of ionic liquids. The obtained results

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show the accuracy and superiority of GEP model over other correlations.

Data gathering

The precision and reliability of a model is greatly affected by the existence of dependable and accurate experimental data [27, 34, 35]. In addition, selection of proper parameters the output parameter depends on which is also important. In present study, a number of 602 data points of density for 146 ionic liquids were collected from literature [36-67]. The name of ionic liquids and their physical properties are listed in Table 1. Moreover the experimental density data and the corresponding references are provided as supplementary material. Table 2 shows the statistical details of utilized data. Figure 1 shows the frequency plots for gathered data points. The data bank includes temperature (K), molecular weight (Mw) of IL (g/mol), boiling temperature (Tb) of IL (K), critical temperature (Tc) of IL (K), critical pressure (Pc) of IL (Pa),

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ACCEPTED MANUSCRIPT critical volume (Vc) of IL (cm3/mol), critical compressibility factor (Zc) of IL, acentric factor (w)

Overview of Gene Expression Programming (GEP)

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of IL, and density of IL (ρ).

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Genetic Algorithm (GA) is a well-known optimization algorithm, which is frequently

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utilized for solving complex and nonlinear regression problems in different fields of science such as chemical and petroleum engineering. The operation of GA is based on Darwinian theory of

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survival of the fittest [68]. From structure and performance point of view, GA is similar to human brain. GA simultaneously updates the population of solutions by creating new

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populations through selecting the better members (solutions) from old populations during the

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optimization process. GA modeling differs from numerical modeling in a manner that in GA

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allocation and tuning of parameters is genotype while numerical modeling utilizes phenotype allocation of parameters [69]. This algorithm was updated and modified over the time and a new version of this algorithm called genetic programming (GP) was introduced. This new algorithm is accurate and effective in handling nonlinear regression problems [70, 71]. Later, Ferreira [72] introduced the most recent evolutionary soft computing technique, which is known as Gene Expression Programming (GEP). While the GA utilizes encoded numbers as solutions for a problem, GP benefits from parse trees to achieve the solution of the problem under consideration [73]. Hence, in the GP approach the individuals of populations, which are random solutions for the problem are symbolic expression trees (ETs) [74]. In GEP technique, these candidate solutions are linear chromosomes, which will be translated into appropriate ET forms during the progress of modeling process. In GEP technique, three basic sections exists in genes of chromosomes, which are called functions, terminals (variables) and constants [75]. In general,

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ACCEPTED MANUSCRIPT GEP utilizes two main operating parts named ETs and chromosomes to handle the modeling problem. To more efficient explanation of the performance of GEP method, Figure 2 is In this figure w, v and j denote the terminals and -, +, and / are symbols

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represented.

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representing the functions. This figure is a schematic structure of a chromosome, which is involves two genes which Karva language is usually utilized to express them. GEP algorithm

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benefits from basic operators including selection, replacement, cross-over and mutation to

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enhance the accuracy of solutions [76]. The selection operator chooses better solutions by utilizing the principle of survival of the fittest considering the cost values of solutions [77]. The

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mutation operator eliminates the risk of fast converging of model at the initial steps of modeling procedure [78]. The cross-over operator combines the genetic information of the survived

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solutions by altering the genetic structure of them and to create better solutions [79]. The role of replacement operator is to update and modify the population by replacing the inaccurate

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solutions with more accurate and suitable ones. These operators are used continuously to generate new population of better solutions until converging to an optimum and reliable solution for the problem in hand. During the implementation of GEP model for prediction of density of various ILs, the collected data was categorized into two subsets of train and test data sets on a random basis. The train data were used to construct the primary structure of model and train it appropriately (fitting the GEP model). The purpose of using test data set is to seek the capability of trained GEP model in estimation of unseen data (external evaluation of GEP model). Hence, the division of data points was performed by allocating 80% of data points to training phase of GEP model and the rest 20% of data points to testing process of the model. A cost function was used as an indication for achieving to the optimum solution for estimation of density data by GEP model. The applied cost function is the mean square error (MSE) between the estimated

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Model Development

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solution.

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As it was noted earlier, the precision and effectiveness of GEP model relies on several

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factors. Hence, in order to construct a dependable and accurate model great attempt has been put forward to run different models according to trial and error approach. Through these trial and

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error runs for development of the GEP model for prediction of density data, it was noticed that increasing the number of genes for a solution increases the depth of ETs and as a result brings

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complexities in solution domain of problem and derived function and increase in run time of the

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model. Hence, in the present study, three genes were considered and the MSE as a cost function ), and power (ab) were used for

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as well as operators and functions of *, +, -, /, sqrt (

implementing the GEP model. The input parameters were temperature, molecular weight of IL, normal boiling point temperature of IL, critical pressure of IL, critical volume of IL, and acentric factor of IL. It should be noted that the constants were furthermore optimized using the hybrid PSO-Genetic (HPSOG) algorithm. The proposed optimum correlation, which was attained by applying optimized GEP model for estimation of density of various ILs is as follows:

  A  B C A

(1)

3Mw   5.837703 VC 

(2)

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T  e  ) 1.92067 26.60977 1 C  673.6503PC (2T b  Mw  803.7) B  (2.586557 

(3) (4)

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Evaluation of GEP model

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This section focuses on graphical and statistical validation of the proposed GEP model in

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estimation of experimental density data. In addition, within this section, the outcomes of

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optimized GEP model were put into comparison with literature correlations. The mathematical formulation of these correlations is provided in Table 3. In the case of graphical evaluation, first,

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a comparison was conducted between the target and estimated values by plotting the cross plot of

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estimated values against the experimental data as it is depicted in Figure . This figure indicates that the data points are excellently accumulated around the 45o line (Y=X line), which means that

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there is an appropriate accordance between predicted and target data. Moreover, the cross plot of

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actual density data and results of different correlations are depicted in Figure . It is clear from this figure that outcomes of these correlations exhibit lower R2 values in comparison with

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optimized GEP model and as a result show more deflections from 45o line, which indicates the precision of optimized GEP model over other correlations. Comparing the predictions of different correlations, the LGM [80] correlation provides the most accurate estimations and the BH [81] correlation exhibits the most inaccurate predictions. To prove this claim about the precision of the optimized GEP model, the relative deviations of model results were plotted against actual values as it is illustrated in Figure . Based on this figure, there is a tight cloud of data points near the zero deviation line, which confirms the appropriate agreement between experimental values and model predictions. This figure also indicates that many of data points fall in the region bordered by lines with relative deviations of  5%. Another point in this figure is that the maximum relative deviation of predictions of developed model is no more than 11%. The relative deviation plot of other correlations is shown in Figure . It is evident from this figure

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ACCEPTED MANUSCRIPT that these correlations exhibit higher relative deviations for estimation of density data. This means that the optimized GEP model is capable of predicting the target data precisely with lower

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relative deviations in comparison with other correlations. To provide a more clear view about the

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accuracy and reliability of implemented model the actual and predicted density values were plotted simultaneously versus the sequence of data point as it is indicated in Figure . This figure

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also proves the precision of developed model in a way that the outcomes of optimized GEP

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model properly tracks the trend of experimental data as it is clear from the well coverage between target and predicted density values. The generalization ability of the model and

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prediction of trend and behavior of target value against changes of input parameters is another point, which must be taken into consideration when developing a model. To this end, the trends

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of target data and outcomes of the optimized GEP model and the literature correlations versus temperature were compared for several numbers of data points as it is indicated in Figure . This

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figure shows that the developed model is able to effectively reproduce the effect of different temperatures on the density value because of reasonable overlap and consistency between trends of target and estimated data. This figure shows poor performance of other correlations for trend estimation of density values versus changes in temperature as it is evident from deviations of estimations of these correlations from actual values. In the next step, the statistical evaluation and comparison of model predictions and literature correlations was also conducted by utilizing four statistical parameters namely correlation factor (R2), Average Absolute Relative Deviation (AARD%), Standard Deviation (STD), and Root Mean Squared Error (RMSE) (Equations (5)(8)). The formulation of these parameters is as below:

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 ( i 1

(5) Pr ed

(i )  Exp )

2

N

 (

RMSE  ( i 1

Pr ed

(i )  Exp (i )) 2 ) 0.5

N

N

(Pr ed (i)  Exp (i)) 2

i 1

N

) 0.5

(7)

(8)

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STD   (

(6)

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100 N (Pr ed (i)  Exp (i))  N i 1 Exp (i)

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% AARD 

(i )  Exp (i )) 2

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i 1 N

Pr ed

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R2  1

 (

Table 4 summarizes the calculated values of statistical parameters for GEP model and

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literature correlations. This table reveals that the developed optimized GEP model exhibits

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higher R2 and lower RMSE, STD and AARD% values in comparison with other correlations,

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which means that the GEP model is more accurate and reliable than other correlations and is able to predict the whole set of data points with acceptable accuracy. In addition, Figure shows the visual comparison of different predictors with each other regarding the R2 and RMSE values.

Conclusions In the present work, a GEP model was proposed to estimate the density of 146 different ionic liquids at different temperatures. A databank including 602 data points were gathered to develop the model. Temperature, molecular weight of IL, normal boiling point temperature of IL, critical pressure of IL, critical volume of IL, and acentric factor of IL are considered as input parameters of the model. Different statistical and graphical approaches were used to validate its accuracy and reliability. Moreover, its results were put into comparison with different literature

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ACCEPTED MANUSCRIPT correlations for estimation of density of ILs. Results show that the model is precise and dependable for prediction of target density data. Moreover, the proposed optimized GEP model

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provides accurate estimations compared to other literature correlations. Results of this work

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could be used in areas were rapid and accurate estimation of IL density is required.

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13

ACCEPTED MANUSCRIPT

AC CE P

TE

D

MA

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SC

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PT

[65] J. Troncoso, C.A. Cerdeiriña, Y.A. Sanmamed, L. Romaní, L.P.N. Rebelo, Thermodynamic properties of imidazolium-based ionic liquids: densities, heat capacities, and enthalpies of fusion of [bmim][PF6] and [bmim][NTf2], Journal of Chemical & Engineering Data, 51 (2006) 1856-1859. [66] J. Valderrama, P. Robles, Critical properties, normal boiling temperatures, and acentric factors of fifty ionic liquids, Industrial & Engineering Chemistry Research, 46 (2007) 1338-1344. [67] J.O. Valderrama, W.W. Sanga, J.A. Lazzús, Critical properties, normal boiling temperature, and acentric factor of another 200 ionic liquids, Industrial & Engineering Chemistry Research, 47 (2008) 1318-1330. [68] C. Romero, J. Carter, Using genetic algorithms for reservoir characterisation, Journal of Petroleum Science and engineering, 31 (2001) 113-123. [69] Y. Xue, L. Cheng, J. Mou, W. Zhao, A new fracture prediction method by combining genetic algorithm with neural network in low-permeability reservoirs, Journal of Petroleum Science and Engineering, 121 (2014) 159-166. [70] A.H. Alavi, A.H. Gandomi, H.C. Nejad, A. Mollahasani, A. Rashed, Design equations for prediction of pressuremeter soil deformation moduli utilizing expression programming systems, Neural Computing and Applications, 23 (2013) 1771-1786. [71] H.M. Azamathulla, A.A. Ghani, Genetic programming to predict river pipeline scour, Journal of Pipeline Systems Engineering and Practice, 1 (2010) 127-132. [72] C. Ferreira, U. Gepsoft, What is Gene Expression Programming, 2008. [73] H. Kaydani, A. Mohebbi, M. Eftekhari, Permeability estimation in heterogeneous oil reservoirs by multi-gene genetic programming algorithm, Journal of Petroleum Science and Engineering, 123 (2014) 201-206. [74] F. Gharagheizi, P. Ilani-Kashkouli, N. Farahani, A.H. Mohammadi, Gene expression programming strategy for estimation of flash point temperature of non-electrolyte organic compounds, Fluid Phase Equilibria, 329 (2012) 7177. [75] L. Teodorescu, D. Sherwood, High energy physics event selection with gene expression programming, Computer Physics Communications, 178 (2008) 409-419. [76] H. Kaydani, M. Najafzadeh, A. Hajizadeh, A new correlation for calculating carbon dioxide minimum miscibility pressure based on multi-gene genetic programming, Journal of Natural Gas Science and Engineering, 21 (2014) 625-630. [77] C. Cranganu, E. Bautu, Using gene expression programming to estimate sonic log distributions based on the natural gamma ray and deep resistivity logs: a case study from the Anadarko Basin, Oklahoma, Journal of Petroleum Science and Engineering, 70 (2010) 243-255. [78] K.C. Seavey, A.T. Jones, A.K. Kordon, G.F. Smits, Hybrid genetic programming− first-principles approach to process and product modeling, Industrial & Engineering Chemistry Research, 49 (2010) 2273-2285. [79] A.H. Gandomi, A.H. Alavi, M.G. Sahab, New formulation for compressive strength of CFRP confined concrete cylinders using linear genetic programming, Materials and Structures, 43 (2010) 963-983. [80] J.O. Valderrama, K. Zarricueta, A simple and generalized model for predicting the density of ionic liquids, Fluid Phase Equilibria, 275 (2009) 145-151. [81] V.L. Bhirud, Saturated liquid densities of normal fluids, AIChE Journal, 24 (1978) 1127-1131. [82] L.C. Yen, S. Woods, A generalized equation for computer calculation of liquid densities, AIChE Journal, 12 (1966) 95-99. [83] H.G. Rackett, Equation of state for saturated liquids, Journal of Chemical and Engineering Data, 15 (1970) 514517. [84] R. Gunn, T. Yamada, A corresponding states correlation of saturated liquid volumes, AIChE Journal, 17 (1971) 1341-1345. [85] T. Yamada, R.D. Gunn, Saturated liquid molar volumes. Rackett equation, Journal of Chemical and Engineering Data, 18 (1973) 234-236. [86] R.C. Reid, J.M. Prausnitz, B.E. Poling, The properties of gases and liquids, DOI (1987). [87] R.W. Hankinson, G.H. Thomson, A new correlation for saturated densities of liquids and their mixtures, AIChE Journal, 25 (1979) 653-663. [88] J.O. Valderrama, B.F. Abu-Sharkh, Generalized rackett-type correlations to predict the density of saturated liquids and petroleum fractions, Fluid phase equilibria, 51 (1989) 87-100. [89] A. Mchaweh, A. Alsaygh, K. Nasrifar, M. Moshfeghian, A simplified method for calculating saturated liquid densities, Fluid phase equilibria, 224 (2004) 157-167.

14

ACCEPTED MANUSCRIPT Table 1: The names and physical properties of ILs utilized in the present work (The values were taken from Valderrama and Robles [66] and from Valderrama et al. [67]).

[dmim]

[BF4]

310.2

632.5

784.6

PT

Vc Pc(Pa) (cm3/mol)

1 C14H27N2BF4

997.7

2 C7H13N2BF4

[prmim]

[BF4]

212.0

472.3

619.7

21.9

597.9

0.2537

0.8485

3 C9H17N2BF4

[bdmim]

[BF4]

240.1

523.1

671.0

18.9

710.5

0.2413

0.9476

4 C6H11N2OBF4

[mommim]

[BF4]

214.0

471.9

623.7

23.3

556.4

0.2505

0.8296

5 C7H13N2OBF4

[moemim]

[BF4]

228.0

494.8

647.0

21.7

613.5

0.2471

0.8692

6 C9H17N2O2BF4

[moeoemim] [BF4]

272.1

562.9

720.2

18.8

743.3

0.2331

0.9644

7 C7H10BF4N

[N-epy]

[BF4]

195.0

411.2

549.9

23.5

533.9

0.2747

0.7495

8 C15H34N3BF4

[C15guan]

[BF4]

343.3

620.3

755.9

12.2

1146.7

0.2225

1.1454

9 C27H58N3BF4

[C27guan]

[BF4]

511.6

894.8

1100.3

8.2

1832.0

0.1640

0.7076

10 C9H13N3F6S2O4

[prmim]

[bti]

405.3

839.6

1259.3

30.0

933.0

0.2670

0.2575

11 C11H17N3F6S2O4

[pmim]

[bti]

433.4

885.3

1281.1

25.6

1047.2

0.2521

0.3444

12 C13H21N3F6S2O4

[hpmim]

[bti]

461.5

931.1

1305.0

22.3

1161.5

0.2392

0.4349

13 C15H25N3F6S2O4

[nmim]

[bti]

489.5

976.8

1331.2

19.8

1275.7

0.2277

0.5276

14 C16H27N3F6S2O4

[decmim]

[bti]

503.5

999.7

1345.1

18.7

1332.8

0.2225

0.5741

Tc(K)

MA

D

14.5

RI

Tb(K)

SC

Mw

NU

Abbreviation

TE

Formula

AC CE P

N

Zc

w

0.2214

1.0818

15 C11H17N3F6S2O4

[beim]

[bti]

433.4

885.3

1281.1

25.6

1047.2

0.2521

0.3444

16 C13H21N3F6S2O4

[dbim]

[bti]

461.5

931.1

1305.0

22.3

1161.5

0.2392

0.4349

17 C10H15N3F6S2O4

[E1.3M4I]

[bti]

419.4

867.4

1269.7

27.5

988.6

0.2572

0.3226

18 C10H15F6N3O4S2

[dmprim]

[bti]

419.4

867.4

1269.7

27.5

988.6

0.2572

0.3226

19 C9H13N3F6S2O5

[eomim]

[bti]

421.3

862.0

1285.2

29.1

948.6

0.2579

0.2695

20 C8H16N2F6S2O4

[tmpa]

[bti]

382.4

692.6

1023.4

28.0

898.4

0.2953

0.2900

21 C22H44N2F6S2O4

[tpa]

[bti]

578.7 1012.9

1267.0

12.8

1697.9

0.2060

0.8923

22 C26H52N2F6S2O4

[tha]

[bti]

634.8 1104.4

1353.0

11.0

1926.4

0.1885

0.9857

23 C30H60N2F6S2O4

[thpa]

[bti]

690.9 1195.9

1449.6

9.7

2154.8

0.1726

0.9913

24 C34H68N2F6S2O4

[toa]

[bti]

747.1 1287.4

1559.2

8.6

2383.2

0.1579

0.8960

25 C42H84N2F6S2O4

[tda]

[bti]

859.3 1470.5

1831.8

7.0

2840.1

0.1310

0.4734

26 C7H14N2F6S2O5

[N111C2O]

[bti]

384.3

692.1

1035.7

29.5

856.9

0.2933

0.2599

27 C9H18N2F6S2O4

[N1123]

[bti]

396.4

715.4

1038.7

25.9

955.5

0.2863

0.3334

28 C9H18N2F6S2O4

[N1114]

[bti]

396.4

715.4

1038.7

25.9

955.5

0.2863

0.3334

29 C10H20N2F6S2O4

[BNM2E]

[bti]

410.4

738.3

1054.3

24.1

1012.6

0.2779

0.3777

30 C11H22N2F6S2O4

[N1134]

[bti]

424.4

761.2

1070.1

22.5

1069.7

0.2701

0.4228

31 C11H22N2F6S2O4

[N6111]

[bti]

424.4

761.2

1070.1

22.5

1069.7

0.2701

0.4228

15

[N7111]

[bti]

438.5

784.1

1086.1

21.1

1126.8

0.2627

0.4685

33 C13H26N2F6S2O4

[N8111]

[bti]

452.5

807.0

1102.5

19.8

1183.9

0.2558

0.5146

34 C14H28N2F6S2O4

[N6222]

[bti]

466.5

829.8

1119.2

18.7

1241.0

0.2492

0.5608

35 C15H30N2F6S2O4

[N7222]

[bti]

480.5

852.7

1136.3

17.7

1298.1

0.2430

0.6068

36 C16H32N2F6S2O4

[N8222]

[bti]

494.6

875.6

1153.7

16.8

1355.3

0.2371

0.6523

37 C17H34N2F6S2O4

[N723'3']

[bti]

508.6

897.6

1176.6

16.1

1408.9

0.2324

0.6653

38 C20H40F6N2O4S2

[N6444]

[bti]

550.7

967.1

1227.4

13.9

1583.7

0.2156

0.8216

39 C21H42F6N2O4S2

[N7444]

[bti]

564.7

990.0

1247.0

13.3

1640.8

0.2108

0.8585

40 C22H44F6N2O4S2

[N8444]

[bti]

578.7 1012.9

1267.0

12.8

1697.9

0.2060

0.8923

41 C15H30F6N2O4S2

[N1444]

[bti]

480.5

852.7

1136.3

17.7

1298.1

0.2430

0.6068

42 C9H10F6N2O4S2

[N-epy]

[bti]

388.3

778.4

1207.9

32.7

869.0

0.2834

0.1671

43 C11H14N2F6S2O4

[N-bupy]

[bti]

416.4

824.2

1229.1

27.7

983.3

0.2666

0.2505

44 C11H14N2F6S2O4

[pmpy]

[bti]

416.4

829.1

1228.9

27.5

981.7

0.2645

0.2723

45 C12H16N2F6S2O4

[bmpy]

[bti]

46 C5H9NF6S3O4

[S111]

[bti]

47 C8H15NF6S3O4

[S222]

[bti]

48 C14H27NF6S3O4

[S444]

[bti]

49 C10H16N2F6S2O4

[MP3]

50 C11H18N2F6S2O4

[MP4]

51 C10H18N2F6S2O4

[prmpyr]

52 C11H20F6N2O4S2

MA

NU

SC

RI

32 C12H24N2F6S2O4

PT

ACCEPTED MANUSCRIPT

852.0

1240.5

25.5

1038.8

0.2571

0.3160

357.3

729.0

1156.5

27.3

875.3

0.2481

0.0384

399.4

797.6

1189.9

21.9

1046.6

0.2317

0.1603

483.6

934.9

1269.2

15.6

1389.3

0.2052

0.4263

[bti]

407.4

810.0

1196.5

27.1

960.7

0.2615

0.2793

[bti]

421.4

832.9

1208.8

25.1

1017.8

0.2545

0.3229

[bti]

408.4

810.4

1196.9

26.7

969.8

0.2607

0.2754

[mbpyr]

[bti]

422.4

833.3

1209.2

24.8

1026.9

0.2537

0.3191

53 C17H34N4F6S2O4

[C15guan]

[bti]

536.6

987.5

1271.0

15.6

1481.8

0.2184

0.7803

54 C29H58N4F6S2O4

[C27guan]

[bti]

704.9 1262.0

1529.0

9.8

2167.1

0.1676

1.0120

55 C10H11N3F10S2O4 [emim]

[BEI]

491.3

853.1

1231.4

21.9

1045.4

0.2238

0.2895

56 C8H15N2Cl

[bmim]

[Cl]

174.7

558.0

789.0

27.8

568.8

0.2415

0.4914

[hmim]

[Cl]

202.7

603.8

829.2

23.5

683.0

0.2328

0.5725

58 C12H23ClN2

[moim]

[Cl]

230.8

649.6

869.4

20.3

797.2

0.2241

0.6566

59 C9H17N2O2Cl

[moeemim]

[Cl]

220.7

625.8

863.6

24.8

657.1

0.2273

0.5707

60 C27H58N3Cl

[C27guan]

[Cl]

460.2

957.6

1158.9

9.2

1745.7

0.1665

0.9692

61 C35H74N3Cl

[C35guan]

[Cl]

572.5 1140.7

1411.1

7.4

2202.6

0.1385

0.5680

62 C8H11N5

[emim]

[dca]

177.2

737.2

999.0

29.1

597.8

0.2095

0.7661

63 C10H15N5

[bmim]

[dca]

205.3

783.0

1035.8

24.4

712.0

0.2017

0.8419

64 C10H18N4

[mppyr]

[dca]

194.3

730.9

968.8

22.9

691.7

0.1966

0.7920

65 C11H20N4

[mbpyr]

[dca]

208.3

753.8

988.3

21.3

748.8

0.1938

0.8316

66 C13H24N4

[mhpyr]

[dca]

236.4

799.6

1028.0

18.6

863.0

0.1880

0.9087

67 C11H21N2PF6

[hpmim]

[PF6]

326.3

623.2

787.8

14.7

933.8

0.2101

0.9055

TE

AC CE P

57 C10H19N2Cl

D

430.4

16

[nmim]

[PF6]

354.3

669.0

834.1

13.4

1048.1

0.2028

0.9680

69 C14H27N2PF6

[oprim]

[PF6]

368.3

691.9

857.6

12.8

1105.2

0.1991

0.9937

70 C9H17F6N2P

[bdmim]

[PF6]

298.2

582.4

746.3

16.2

818.0

0.2142

0.8526

71 C9H17F6N2P

[mpim]

[PF6]

298.2

577.5

742.1

16.3

819.6

0.2171

0.8316

72 C6H11N2OPF6

[mommim]

[PF6]

272.1

531.2

701.2

19.3

663.9

0.2201

0.7277

73 C7H13N2OPF6

[eommim]

[PF6]

286.2

554.1

723.7

18.2

721.0

0.2177

0.7697

74 C9H17N2O2PF6

[moeemim]

[PF6]

330.2

622.3

795.3

16.1

850.8

0.2069

0.8676

75 C9H14NPF6

[N-bupy]

[PF6]

281.2

516.3

674.4

17.3

755.6

0.2325

0.7381

76 C9H11F6N3O3S

[emim]

[tsac]

355.3

764.4

1069.9

25.2

833.5

0.2359

0.4981

77 C8H14F6N2O3S

[TMEA]

[tsac]

332.3

617.4

854.1

23.3

798.8

0.2622

0.5261

78 C9H14F6N2O3S

[TMAIA]

[tsac]

344.3

637.0

875.2

22.5

842.3

0.2609

0.5479

79 C9H16F6N2O3S

[TMPA]

[tsac]

346.3

640.3

873.7

21.7

855.9

0.2560

0.5705

80 C9H16F6N2O3S

[TMiPA]

[tsac]

346.3

639.9

876.1

21.9

854.2

0.2569

0.5540

81 C11H20F6N2O3S

[TEA]

[tsac]

82 C9H14F6N2O3S

[P11]

[tsac]

83 C6H12N2O4S

[dmim]

[MSO4]

84 C9H18N2O4S

[bmim]

[MSO4]

85 C8H16N2O5S

[dmim]

86 C9H15NO5S

[py]

87 C20H37O3PS

[tibmp]

MA

NU

SC

RI

68 C13H25N2PF6

PT

ACCEPTED MANUSCRIPT

686.1

913.2

19.1

970.2

0.2443

0.6596

344.3

712.4

999.5

24.2

813.1

0.2371

0.4676

208.2

666.9

1040.0

52.9

545.6

0.3339

0.3086

250.3

735.6

1081.6

36.1

716.9

0.2878

0.4111

[MOESO4] 252.3

735.1

1094.4

38.9

675.4

0.2887

0.3855

[EOESO4] 248.3

696.1

1065.4

41.6

658.8

0.3097

0.2980

[pTSO3]

388.6

874.8

1176.4

18.2

1249.9

0.2321

0.5628

AC CE P

TE

D

374.4

88 C7H15N2O4P

[dmim]

[DMPO4]

222.2

623.0

880.4

28.6

598.4

0.2342

0.5065

89 C12H21N2F3SO3

[dbim]

[TfO]

330.4

776.4

1072.0

23.2

922.0

0.2396

0.5325

90 C12H13N2F3SO4

[mpmi]

[TfO]

338.3

830.4

1184.7

28.0

827.7

0.2353

0.4481

91 C21H44NF3SO3

[N8444]

[TfO]

447.7

858.2

1066.7

12.6

1458.4

0.2072

0.9461

92 C11H16N2F6SO3

[bmim]

[HFPS]

370.3

747.6

1032.1

21.3

912.6

0.2266

0.4933

93 C12H16N2F8SO4

[bmim]

[FS]

436.3

788.2

1061.3

17.9

1012.9

0.2056

0.5488

94 C12H16N2F8SO4

[bmim]

[TPES]

436.3

788.2

1061.3

17.9

1012.9

0.2056

0.5488

95 C11H16N2F6SO4

[bmim]

[TTES]

386.3

770.0

1058.3

20.9

928.2

0.2205

0.5085

96 C12H15F9N2O6S3

[bmim]

[TMEM]

550.4 1034.4

1571.4

24.0

1213.6

0.2233

0.1322

97 C12H15F9N2O6S3

[dmpim]

[TMEM]

550.4 1039.3

1568.6

23.9

1212.0

0.2222

0.1526

98 C8H15N2I

[bmim]

[I]

266.1

613.7

871.2

28.6

607.5

0.2402

0.4835

99 C12H15N2F9SO3

[bmim]

[NfO]

438.3

762.3

1028.8

17.3

1004.8

0.2030

0.5151

100 C9H10F3NO2

[N-epy]

[ta]

221.2

535.1

739.9

24.2

586.5

0.2311

0.5483

101 C10H17N2F6S2O4

[bmpyr]

[bti]

422.4

833.3

1209.2

24.8

1026.9

0.2537

0.3191

102 C8H15N2BF4

[bmim]

[BF4]

226.0

484.6

632.3

20.4

672.0

0.2602

0.8490

103 C6H11N2BF4

[emim]

[BF4]

198.0

438.9

585.3

23.6

557.8

0.2699

0.7684

17

[hmim]

[BF4]

254.1

530.4

679.1

17.9

786.2

0.2495

0.9260

105 C10H16NBF4

[mbupy]

[BF4]

237.0

484.8

625.8

18.9

703.7

0.2556

0.8924

106 C9H14NBF4

[N-bupy]

[BF4]

223.0

456.9

597.6

20.3

648.1

0.2652

0.8307

107 C12H23N2BF4

[omim]

[BF4]

282.1

576.1

726.1

16.0

900.4

0.2388

0.9954

108 C11H17N3F6S2O4

[beim]

[bti]

433.4

874.7

1275.9

25.6

1064.2

0.2570

0.3094

109 C10H15N3F6S2O4

[bmim]

[bti]

419.4

851.8

1265.0

27.6

1007.1

0.2644

0.2658

110 C9H13N3F6S2O4

[deim]

[bti]

405.3

829.0

1254.7

29.9

950.0

0.2725

0.2233

111 C9H16N3F6S2O4

[dmeim]

[bti]

405.3

833.9

1254.1

29.7

948.4

0.2703

0.2448

112 C7H9N3F6S2O4

[dmim]

[bti]

377.3

783.2

1235.7

35.8

835.8

0.2910

0.1419

113 C9H13N3F6S2O4

[edmim]

[bti]

405.3

833.9

1254.1

29.7

948.4

0.2703

0.2448

114 C9H13N3F6S2O4

[eDmim]

[bti]

405.3

833.9

1254.1

29.7

948.4

0.2703

0.2448

115 C8H11N3F6S2O4

[emim]

[bti]

391.3

806.1

1244.9

32.6

892.9

0.2813

0.1819

116 C12H19N3F6S2O4

[hmim]

[bti]

447.4

897.6

1287.3

23.9

1121.3

0.2500

0.3540

117 C1oH15N3F6S2O4

[i-bmim]

[bti]

118 C1oH15N3F6S2O4

[mdeim]

[bti]

119 C8H14N3F6S2O4

[meim]

[bti]

120 C9H13N3F6S2O4

[moemim]

[bti]

121 C14H23N3F6S2O4

[omim]

122 C8H8N3F9S2O4

[tfemim]

123 C12H23N2Cl

[omim]

MA

NU

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104 C10H19N2BF4

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ACCEPTED MANUSCRIPT

851.4

1270.4

27.8

1005.4

0.2650

0.2502

419.4

856.8

1264.7

27.4

1005.5

0.2624

0.2877

391.3

806.1

1244.9

32.6

892.9

0.2813

0.1819

421.3

851.4

1280.6

29.0

965.6

0.2632

0.2352

[bti]

475.5

943.4

1311.9

21.0

1235.6

0.2374

0.4453

[bti]

445.3

800.7

1205.3

26.6

942.3

0.2505

0.2004

[Cl]

230.8

638.9

860.1

20.3

814.2

0.2310

0.6190

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TE

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419.4

124 C8H16N2SO4

[emim]

[SE]

236.3

702.1

1061.1

40.4

676.8

0.3099

0.3368

125 C3H9NO3

[OHea]

[f]

104.2

491.2

683.2

52.6

285.2

0.2641

0.8848

126 C12H15N2F7O2

[bmim]

[hb]

352.3

644.9

836.7

15.6

894.0

0.2009

0.7248

127 C12H15N2F7O2

[emim]

[hb]

324.2

599.2

793.9

17.4

779.8

0.2058

0.6393

128 C10H20N2SO3

[beim]

[MsO]

248.3

725.4

1062.7

33.5

775.4

0.2942

0.3987

129 C7H14N2SO3

[emim]

[MsO]

206.3

656.8

1019.5

48.0

604.0

0.3423

0.2931

130 C13H17N2F9SO3

[beim]

[NfO]

452.3

774.6

1038.5

16.4

1078.9

0.2047

0.5257

131 C12H15N2F9SO3

[emim]

[NfO]

439.3

752.4

1012.1

16.7

1031.5

0.2050

0.5172

132 C8H15N3O2

[bmim]

[NO3]

201.2

684.3

946.3

27.3

662.9

0.2299

0.6039

133 C8H15N2PF6

[bmim]

[PF6]

284.2

544.0

708.9

17.3

779.5

0.2283

0.7552

134 C6H11N2PF6

[emim]

[PF6]

256.1

498.2

663.5

19.5

665.3

0.2351

0.6706

135 C10H19N2F6P

[hmim]

[PF6]

312.2

589.7

754.3

15.5

893.7

0.2206

0.8353

136 C12H23N2PF6

[omim]

[PF6]

340.3

635.5

800.1

14.0

1007.9

0.2127

0.9069

137 C11H17N2F3O2

[beim]

[ta]

266.3

631.4

838.0

19.5

781.7

0.2193

0.6935

138 C10H15N2F3O2

[bmim]

[ta]

252.2

608.6

817.2

20.9

724.6

0.2229

0.6510

139 C9H13N2F3O2

[deim]

[ta]

238.2

585.7

796.5

22.4

667.5

0.2263

0.6085

18

[emim]

[ta]

224.2

562.8

775.7

24.2

610.4

0.2294

0.5664

141 C10H17N2F3SO3

[beim]

[TfO]

302.3

720.0

1032.1

27.0

824.8

0.2595

0.4093

142 C9H15N2F3SO3

[bmim]

[TfO]

288.3

697.1

1016.3

29.4

767.6

0.2674

0.3678

143 C8H13N2F3SO3

[deim]

[TfO]

274.3

674.2

1000.7

32.3

710.5

0.2760

0.3277

144 C18H31N2F3SO3

[doeim]

[TfO]

414.5

903.0

1168.6

16.1

1281.6

0.2120

0.7583

145 C8H13N2F3SO3

[edmim]

[TfO]

274.3

679.2

1001.9

32.0

709.0

0.2726

0.3500

146 C7H11N2F3SO3

[emim]

[TfO]

260.2

651.4

985.2

35.8

653.4

0.2855

0.2891

AC CE P

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140 C8H11N2F3O2

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ACCEPTED MANUSCRIPT

19

ACCEPTED MANUSCRIPT Table 2: The statistical parameters of the input and output data. Average 310.8 347.5 717.5 991.3 22.2 935.3 0.2419 0.5861 1.289

PT

Maximum 358 859.3 1470.5 1831.8 52.9 2840.1 0.3423 1.1454 1.66

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Minimum 278 104.2 411.2 549.9 7 285.2 0.131 0.0384 0.9

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Status Input #1 Input #2 Input #3 Input #4 Input #5 Input #6 Input #7 Input #8 Output

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Parameter T (K) Mw (g/mol) Tb (K) Tc (K) Pc (Pa) Vc (cm3/mol) Zc w ρ (g /cm3)

20

Standard Deviation 18.34 104.27 161.37 255.18 7.139 262.11 0.0276 0.2591 0.1427

ACCEPTED MANUSCRIPT

Table 3 Literature correlations for prediction of densities of ILs. Ref.

Equation



i 3

4



  C 1   k i (1 T r ) 

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[82]

i 1   k 1  17.4425  214.578ZC +989.625ZC2  1522.06ZC3

ZC < 0.26: k 2 =  3.28257+13.6377ZC +107.4844ZC2  384.211ZC3

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Yen andWoods (YW)

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Model

Zc > 0.26: k 2 = 60.2091  402.063ZC +501.0ZC2 +641.0ZC3 2

[83]

  C Z

 (1T r ) 7 C

Gunn and Yamada (GY)

[84]

V0 PC Mw ; V0  V 1 (1  V 2 ) RTC (0.292  0.0967 )

PT ED



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Racket (RA)

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k 3  0 ; k 4  0.93  k 2

0.2 < Tr < 0.8: V1 = 0.33593  0.33953Tr +1.51941Tr2  2.02512Tr3 +1.11422Tr4 0.8 < Tr < 1.0: V1 = 1.0+1.3(1  Tr ) 0.5 log(1  Tr )  0.50879(1  Tr )  0.91534(1  Tr ) 2

Reid et al. (RR)

[85]

AC

Yamada and Gunn (YG)

CE

Tr > 0.2: V2 = 0.29607  0.09045Tr  0.04842Tr2

[86]

  C (0.29056  0.08775 ) 

[81]

1



  C 1  0.85(1 T r )  (1.6916  0.984 )(1 T r ) 3  

ln

Bhirud (BH)

2

 (1T r ) 7

PC

 RT



 lnV 0   lnV 1

ln V0 = 1.39644  24.076Tr +102.615Tr2  255.719Tr3 +355.805Tr4  256.671Tr5 +75.1088Tr6 ln V1 = 13.4412  135.7437Tr +533.380Tr2  1091.453Tr3 +1231.43Tr4  728.227Tr5 +176.737Tr6

21

ACCEPTED MANUSCRIPT

Hankinson and Thomson (HT)

[87]

C V 0 (1  V 1 )

PT



1

2

4

V0 = 1  1.5281(1  Tr ) 3 +1.4390(1  Tr ) 3  0.8144(1  Tr )+0.19045(1  Tr ) 3

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V1 = (  0.296123+0.386914Tr  0.0427258Tr2  0.0480645Tr3 )/(Tr  1.00001)

[88]

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Valderrama and Abu-Sharkh (VSD)

[88]

Mw  0.0039 0.2987 1.033    (0.01256  0.9533 ) (  )V C  V C  Mw VC 

PC Mw  PCV C1.0135   0.3445  RTC  RTC 

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Valderrama and Abu-Sharkh (VSY)

1

 (T )

2    1 (1T r ) 7   2  7  1 (1Tbr ) 

2

4

[89]

PT ED

  C (1+1.169 3 +1.818 3  2.658 +2.161 3 )

Mchaweh et al. (MH)

  1

[80]

AC

Valderrama and Zarricueta (LGM)

CE



Tr ; m  0.48+1.574  0.176 2 2 (1  m (1  T r ))

A 2 A ln B (T T b )  B 7 B (TC T b )

A  a b

Mw c d ; B=( + )VC VC V C Mw

a  0.3411, b  2.0443, c  0.5386, d  0.0393,   1.0476

22

2

 1 T r  7 ;  (T )     1 T br 

ACCEPTED MANUSCRIPT Table 4: Comparison between the statistical parameters of various correlations.

D TE AC CE P 23

STD 0.081 0.127 0.123 0.068 0.056 0.139 0.066 0.071 0.055 0.048 0.034 0.0261 0.0266 0.0262

PT

AARD 7.71 8.98 9.00 5.12 4.32 11.49 4.92 5.38 5.01 7.22 2.63 1.82 1.72 1.80

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[82] [83] [84] [85] [86] [81] [87] [88] [88] [89] [80]

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R2 0.6819 0.434 0.1911 0.6783 0.7732 0.1808 0.6999 0.6904 0.7735 0.8448 0.9345 0.9511 0.9531 0.9513

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Correlation YW RA GY YG PR BH HT VSD VSY MH GLM Train data Optimized GEP Test data Total data

RMSE 0.129 0.156 0.161 0.086 0.070 0.191 0.082 0.088 0.078 0.110 0.043 0.0317 0.0306 0.0315

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ACCEPTED MANUSCRIPT

Figure 1: The frequency of utilized data in this study.

24

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ACCEPTED MANUSCRIPT

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Figure 2: The structure of a chromosome including two genes and its related mathematical expression.

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ACCEPTED MANUSCRIPT

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Figure 3: Predictions of GEP model against experimental density data.

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(b)

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(a)

(c)

(d)

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(f)

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(e)

(g)

(h)

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(j)

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(i)

(k) Figure 4: Predicted values of density data against experimental values for literature correlations: (a) YW [82], (b) RA [83], (c) GY [84], (d) YG [85], (e) PR [86], (f) BH [81], (g) HT [87], (h) VSD [88], (i) VSY [88], (j) MH [89] ,and (k) LGM [80]

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Figure 5: Relative deviation plot of predictions of GEP model.

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(b)

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(a)

(c)

(d)

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(f)

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(e)

(g)

(h)

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(j)

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(i)

(k) Figure 6: Relative deviation of outcomes of various correlations versus target density data: (a) YW [82], (b) RA [83], (c) GY [84], (d) YG [85], (e) PR [86], (f) BH [81], (g) HT [87], (h) VSD [88], (i) VSY [88], (j) MH [89] ,and (k) LGM [80]

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ACCEPTED MANUSCRIPT

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Figure 7: Simultaneous plot of outcomes of GEP model and target data against index of data.

34

(a)

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(b)

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ACCEPTED MANUSCRIPT

AC CE P

(c) Figure 8: Comparison between predictions of various models and correlations against temperature: (a) C20H40F6N2O4S2 ([N6444][bti]), (b) C8H15N2PF6 ([bmim][PF6]), (c) C11H20F6N2O4S2 ([mbpyr][bti])

36

(a)

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ACCEPTED MANUSCRIPT

(b) Figure 9: Comparison between HPSOGA GEP and GEP regarding (a) R2 and (b) RMSE values.

37

(a)

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(b) Figure 10: Comparison of different density predictors regarding (a) R2 and (b) RMSE values.

38

ACCEPTED MANUSCRIPT

We have developed a GEP model for prediction of density values of 146 different ionic

RI



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Research Highlights

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liquids.

The input parameters of the model are temperature, Mw, Tb, Pc, Vc, and w of IL.



The developed model is capable of estimating target density data with an acceptable

NU



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accuracy.

The accuracy of the model is checked using statistical and graphical techniques.



The proposed model is effectively superior to other methods and exhibit higher accuracy

AC CE P

and reliability.

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

39