Predictive Quantitative StructureâProperty Relationship Model for the

Article pubs.acs.org/IECR

Predictive Quantitative Structure−Property Relationship Model for the Estimation of Ionic Liquid Viscosity Seyyed Alireza Mirkhani and Farhad Gharagheizi* Department of Chemical Engineering, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran S Supporting Information *

ABSTRACT: In this study attention was focused on the development of a predictive model for the viscosity of ionic liquids. A large data set of 435 experimental viscosity data points for 293 ionic liquids incorporating 146 cations and 36 anions was applied for the model derivation. A quantitative structure−property relationship (QSPR) approach was employed to develop a linear model. In this study the effects of both anions and cations were considered in the derivation of the model. Genetic function approximation is applied for the model’s parameter selection (molecular descriptors) and developing a linear QSPR model. Consequently, a simple linear predictive model was obtained with satisfactory results quantified by the following statistical parameters: absolute average deviations (AAD) of the predicted properties from existing experimental values by the GFA linear equation, 8.77%; squared correlation coefficient, 0.8096; and root mean square, 0.232 cP.

1. INTRODUCTION Ionic liquids (ILs) as a new generation of ionic conductive material has become the center of attention in both academia and industrial applications owing to their unique properties. In general, ionic liquid refers to the class of salts, fluid at ambient temperatures with insignificant vapor pressure, completely composed of ions.1,2 Their saltlike nature with fluidity at ambient temperature makes them promising options for superseding the convenient solvents. Surprisingly, their physical, chemical, and biological characteristics could be tuned by the proper anion/cation ratio. However, this is not a simple task owing to the tremendous possible numbers of ILs.3 Therefore, it is essential to propose a predictive computational tool capable of tailoring new ILs with desired properties. In this communication, the attention was focused on deriving a predictive model for IL viscosity. Viscosity is the internal friction or resistance to flow caused by intermolecular interactions and is therefore very important in all physical processes that involve fluid movement or components dissolved in fluids. Therefore, any chemical or pharmaceutical indsutries that deal with the transfer of the fluids or energy require knowledge of the viscosity of pure compounds or their mixtures. Viscosity is the most important physical property when considering any scale-up of ionic liquid applications.4 Viscosity determines the kinetic regimes of organic reactions for solvents design purposes. In addition, viscosity is very important as a physical property in the application of ILs as raw materials as, for example, lubricants or mechanical dampers.5 Viscosity is a difficult property to predict and flexible predictive models will require further experimental data in order to obtain a better understanding of this property. There are several predictive model proposed for the ionic liquid viscosity. Abbott6 introduced a theoretical model for the prediction of viscosity by modifying the ″hole theory″ originally proposed by Fürth.7,8 In his paper, 11 ionic liquids mainly based on © 2012 American Chemical Society

imidazolium at three different temperatures (T = 298, 303, and 364 K) were investigated. Despite an interesting theoretical interpretation of ionic liquid viscosity, the model failed to predict viscosities with acceptable accuracy and not merits for practical applications. (ARD = 122%) Matsuda et al.9 proposed a quantitative structure−property relationship (QSPR) method for the prediction of viscosity. They developed a polynomial expansion model10−12 that consists of the term for temperature, cation, the side alkyl chain attached to cation, and the other side chain except for the anion and alkyl chain. They derived their model based on 300 experimental viscosity data points belong to the alkylamine, pyrrole, piperidine, pyridine, and imidazole families within the range of 263−353 K. Their model made inferior predictions for the pyridine cation and EtOSO3, and the value of R2 was 0.8971. As mentioned earlier, their model is based on the limited number of anion and cation groups, so a viscosity prediction of the ionic liquids when either their anion or cation parts are not present in the data set should be done with caution. Besides, relating the viscosity which has the intermolecular origin merely to the graph structure of the molecules is disputable. In addition, for new anions or cations introduced to the data set, all calculations should be repeated to find the proper correlation coefficients. Another QSPR model was proposed by Bini et al.13 to predict ionic liquid viscosity. The viscosity data for 33 ILs based on imidazolium, pyridinium, piperidinium, and morpholinium cations, bearing linear alkyl or oxyalkyl chains at two different temperature (T = 293 and 353 K) are studied. After omitting all data points pertaining to nitrile-functionalized ILs as outliers, they proposed a four-parameter model for the prediction of viscosity values at the mentioned temperatures with the R2 Received: Revised: Accepted: Published: 2470

November 10, 2011 December 22, 2011 January 10, 2012 January 10, 2012 dx.doi.org/10.1021/ie2025823 | Ind. Eng.Chem. Res. 2012, 51, 2470−2477

Industrial & Engineering Chemistry Research

Article

is the most critical step of QSPR modeling. The favored feature of these models is their capability to give a rational determination of the properties of unknown compounds without the need to synthesize and test them. The QSPR model, on one hand, should be able to properly correlate the desired physical property and, on other hand, should have an ability to predict the desired property for the compounds which are not present in the model. In this study the major aim is to develop a universal and comprehensive model to predict viscosity with a wide diverse number of ILs from different classes.

values of 0.8755 and 0.9460, respectively. According to their results, the model could not satisfactorily predict results for low-viscosity areas. Besides, the absence of other ionic liquid families in addition to the very limited temperature range, drastically confined the predictive capability of their derived model. Gardas and Coutinho14 applied the Orrick−Erbar-type group contribution method to develop a predictive model for viscosity. They investigated a large compilation of 498 experimental data points of 29 ILs based on imidazolium, pyridinium, and pyrrolidinium in the range of 293−393 K and viscosities of 4−21000 cP. Their model predicts the viscosity of ILs with the acceptable average error of 7.7%. However, their proposed model contains the density terms, which should be estimated prior to the calculation. On the other hand, merely three classes of ionic liquid were investigated in their work. As indicated in previous studies, the cation and anion structure have profound effect on the viscosity. So, the prediction capability of a model merely limited to three ionic liquid classes and any extrapolation for ionic liquid belonging to absent classes of ILs could result in erroneous results. In their later publication15 they proposed a new correlation based on the Vogel−Tammann−Fulcher equation without a density term. However, the new model suffers from a lack of extrapolation due to the limited number of investigated ionic liquid classes. Ghatee et al.16,17 retain the form of a well-known power law equation of viscosity and proposed three-parameter model with a two-component-dependent and characteristic exponent parameter. They derived the model parameters for 49 ILs based on 403 experimental data values. The major deficiency of their model is that its parameters are solely derived from statistical and regression calculations. In other word, for ILs not present in their study, experimental data are needed to calculate the model parameters. Han et al.18 proposed a QSPR model for prediction of the viscosity of imidazolium based ionic liquids. Their investigated database consists of 255 ILs (comprising 79 cations and 71 anions), with a total of 1731 data entries. They split their database into four subsets and derived the correlation for each one: [BF4]−, [Tf2N]−, [C4mim]+, and [C2mim]+. There are several drawbacks associated with their model. First, the derived model is temperature independent which confines its application to predict viscosity merely at 298.15 K. Second, their attention was focused on a specific class of imidazolium based ionic liquids; however, they did not propose a universal correlation for all ILs present in their study. In this communication a QSPR method was applied to develop a linear model for viscosity prediction. QSPRs become at the center of attention for the correlation and prediction of physical, chemical, and biological properties owing to their high predictive capability and because mere molecular structures serve as model inputs.19−26 The objective of the QSPR is to unveil the contribution of microscopic properties encoded in molecular structure to macroscopic properties with the aid of ″descriptors″. The molecular descriptor is the final result of a logical and mathematical procedure which transforms chemical information encoded within a symbolic representation of a molecule into a useful number or the result of some standardized experiment.27 After the calculation of molecular descriptors, one should select the least number of descriptors, adequately fit for the predictive model. Statistical and regression analysis provide powerful tools to comb the pool of descriptors and return the best ones for the model. This step

2. METHODOLOGY 2.1. Data Preparation. A total of 435 experimental data points of 293 diverse ionic liquids based on sulfonium, ammonium, pyridinium, 1,3-dialkyl imidazolium, trialkyl imidazolium, phosphonium, pyrrolidinium, double imidazolium, 1-alkyl imidazolium, piperidinium, pyrroline, oxazolidinium, amino acids, guanidinium, morpholinium, isoquinolinium and tetra-alkyl imidazolium are collected from literature.28−98 The collected experimental data cover a wide range of viscosities (5.7−2824 cP) and temperatures (253−373 K). The list of present ionic liquids families with their frequencies in our study are displayed in Table S1 in the Supporting Information. In this study, 146 cations and 39 anions with diverse structures are applied for model development. Extensive tables of anions and cations with their abbreviation and structures are available as Tables S2 and S3 in the Supporting Information. 2.2. Descriptors Calculation. In this step, the whole pool of anion and cation in SMILE (simplified molecular input line entry specification) format was submitted to Dragon software for the sake of descriptor calculations. Treating the anions and cations separately instead of in combination results in major calculation time reduction. However, it disregards anion/cation interaction effects.99 About 2000 descriptors from 15 diverse classes of descriptors were calculated by the Dragon software. These 15 classes of descriptors are constitutional descriptors, topological indices, walk and path counts, connectivity indices, information indices, 2D autocorrelations, burden Eigen values, edge-adjacency indices, functional group counts, atom-centered fragments, molecular properties, topological charge indices, Eigen valuebased indices, 2D binary fingerprint, and 2D frequency fingerprint. Before the descriptors were introduced for model generation, those descriptors which could not be calculated for anion and cation were completely omitted. Next, any one of two descriptors with a pair correlation above 0.93 was randomly eliminated. 3. GENETIC FUNCTION APPROXIMATION (GFA) GFA, as a genetic based variable selection approach, involves the combination of the multivariate adaptive regression splines (MARS)100 algorithm with a genetic algorithm101 to evolve a series of equations instead of one that best fit the training set data. The approach was originally proposed by the pioneering work of Rogers and Hopfinger.102 The GFA approach works by generating the initial population of equations by a random selection of descriptors. The goodness of each progeny equation is assessed by Friedman’s lack of fit (LOF) score which is described by the following formula: 2471

dx.doi.org/10.1021/ie2025823 | Ind. Eng.Chem. Res. 2012, 51, 2470−2477


LOF (model) =

1 N

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EEig02x is the second eigenvalue of the “edge adjacency” matrix weighted by edge degrees. It somehow demonstrates the molecular interaction between adjacent bonds in a molecule. C038 is atom-centered fragments: Al−C(X)−Al where Al refers to aliphatic groups and X,  represent any heteroatom (O, N, S, P, Se and halogens) and double bond, respectively. C008 is atom-centered fragments: CHR2X where X and R represent any heteroatom (O, N, S, P, Se and halogens) and any group linked through carbon, respectively. nNq represents the number of quaternary N that exist in the molecular structure of cation. The statistical parameters for the obtained linear model are presented below eq 2, where ntraining and ntest are the numbers of compounds available in the training set and test set, respectively, and R2 is the squared correlation coefficients of the model. SDE is standard deviation error comparing model results with the experimental logarithm of liquid viscosity values.

LSE (model) (c + 1 + (d × p)) N

(

1−

2

)

(1)

In this LOF function, c is the number of nonconstant basis functions, N is the number of samples in the data set, d is a smoothing factor to be set by the user, p is the total number of parameters in the model, and LSE is the least-squares error of the model. Employment of LOF leads to the models with better prediction without overfitting. The superior models in terms of fitness were selected as the “parents” and new generations of equations were evolved by the “crossover” operation. In the crossover operation, each parent is split randomly in two parts from the crossing point, and the first substring of the first parent combines with the second substring of the second parent to create two new children. This process continues until no significant fitness improvement of the model is observed in the population. For a population of 300 models, 3000 to 10000 genetic operations are usually sufficient to achieve convergence.

5. VALIDATION Validation process is the critical step for the assessment of the model stability and prediction capability. If the developed model stands up to the validation scrutiny, it could be safely employed to estimate the particular properties. The various validation techniques applied in this study are described as follows: 5.1. F-Test. F or the F-ratio is defined as the ratio between the model summation of squares (MSS) and the residual summation of squares (RSS):103

4. RESULT AND DISCUSSION The final QSPR model contains seven descriptors, and model parameters are derived by GFA:

log(ηL ) = intercept + log(ηL )anion + log (ηL )cation − 0.146T intercept = 5.79187

F=

log(ηL )anion = 0.56506 × ATS1v − 0.24393 × EEig02x − 0.88012 × C‐038 log(ηL )cation = 0.2442 × ATS6m + 0.3117 × nNq + 0.51475 × C‐008 R2 = 0.8096;

F = 206.51; 2

Q = 0.8007;

(2)

n test = 87; SDE = 10.01; Q boot 2 = 0.7951;

a = − 0.007;

K x = 0.2375,

ΔK = 0.058;

ΔQ = 0;

Q ext 2 = 0.8502

K xy = 0.2952;

Rp = 0.195;

RN = 0

In eq 2 T is an absolute temperature and ATS1v and ATS6m are determined as follows:

1 ATSdw = 2

n

2

Q Loo = 1 −

n

∑ ∑ wiwjδij (dij; k) i=1 j=1

(4)

Where dfM and dfE denote the degree of freedom of the obtained model and of the overall error, respectively. It is a comparison between the model explained variance and the residual variance. It should be noted that high values of the Fratio test indicate the reliability of models. The F-value calculated for this study is 206.51. 5.2. LOO (Leave One Out) Validation Technique. Leave-one-out is based on splitting of the sample data into two different subsets: one serves as the training set and the other as a validation set. The modified training set was generated by deleting one object from the original data set. For each reduced data set, the model is calculated, and responses for the deleted object were calculated from the model. The associated parameter obtained from this technique is called QLoo2 and is calculated as follows:21−26,104,105

R adj2 = 0.8057;

ntraining = 348;

MSS/dfM RSS/dfE

∑in= 1 (yi − yiĉ )2 ∑in= 1 (yi − y ̅ )2

(5)

where yi is the logarithm of liquid viscosity for ith compound, y ̅ is mean value of logarithm of liquid viscosity for all of the investigated compounds, and ŷic is response of ith object predicted by the obtained model ignoring the value of the related object (ith experimental logarithm of liquid viscosity). If the absolute difference of this value and calculated R2 is small, the reliability of the model would be validated. The evaluated leave-one-out cross validation parameter of the obtained linear model is 0.8007. 5.3. Adjusted R-Squared (Radj2). In a multiple linear regression model, Radj2 measures the proportion of the variation

(3)

This the general definition of Broto−Moreau autocorrelation descriptors: d refers topological lag length and w is the weight which could be m (relative atomic mass), p (polarizability), e (Sanderson electronegativity), and v (van der Waals volume). δij = 1 if the ijth entry in the topological level matrix is = d, and δij = 0 otherwise. Topological level matrix describes the topological distances between atomic pairs in the H-depleted molecular graph. They revealed the distribution of the considered property along the topological structure. 2472



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training set constitutes some duplicated objects, and the evaluation set contains the left-out objects. The model is calculated on the training set, and responses are predicted on the evaluation set. All the squared differences between the true response and the predicted response of the objects of the evaluation set are collected in PRESS which is defined as follows:

in the dependent variable accounted for by the explanatory variables. Radj2 is generally considered to be a more accurate goodness-of-fit measure than R square.

⎛n−1⎞ R adj2 = 1 − (1 − R2)⎜ ⎟ ⎝ n − p′ ⎠

(6)

where n and p′ are the numbers of experimental values and the model parameters, respectively. The less difference there is between this value and the R2 parameter, the more validity of the model would be expected. The evaluated adjusted-R2 parameter of the obtained linear model is 0.8775. 5.4. RQK Validation Technique. Todeschini et al.106 proposed 4 RQK constraints which must be completely satisfied to ensure the model prediction capability and verify that the model is not a chance correlation:20−26,104,105,107 1. ΔK = KXY − KX > 0 (quick rule) 2. ΔQ = QLoo2 − QASYM2 > 0 (asymptotic Q2 rule) 3. RP > 0 (redundancy RP rule) 4. RN > 0 (overfitting RN rule) Where KXY and KX are calculated following the equation:

K=

∑j |(λ j/ ∑j λ j − (1/p))| 2(p − 1)/p

PRESS =

Q k 2 = a + brk(y , yk̃ )

where λ, n, and p values are respectively the Eigen-values obtained from the correlation matrix of the data set X (n, P), the number of experimental data, and model parameters. KXY and KX are calculated using set of the selected variables and the selected variables in addition to the glass transition values, respectively. The statistical parameters QASYM2 and RP are defined as follows:

p+

R =

⎛

p ⎞⎞ ⎟⎟⎟ ⎝ p − 1 ⎠⎠ ⎛

∏ ⎜⎜1 − Mj⎜ j=1 ⎝

(8)

Mj > 0

0 ≤ RP ≤ 1

and

(9)

−

p N

R =

∑in=test1 (yi /̂ i − yi )2 Q ext = 1 − n ∑i =test1 (yi − ytraining )2 ̅

∑ Mj

2

j=1

(10)

where Mj is defined as

R jy

1 Mj = − R p +

(13)

Where Qk2k is the explained variance of the model obtained using the same predictors but the kth y-scrambled vector; rk is the correlation between the true response vector and the kth yscrambled vector. The numerical value of the intercept a is a criteria to assess if the model is a chance correlation or not. The numerical values close to zero verify that the model is not a chance correlation. On other hand, the large values cast doubt on the validity of the model and interpret the model as an unstable, chance correlation. The y-scrambling should be repeated hundreds of times (in this work 300 times). The value of intercept a has been calculated as 0.061 for the developed linear model. 5.7. External Validation Technique. The xternal validation technique is conducted by testing additional compounds for the validation set in order to assess the prediction capability of the model. The Qext2 is demonstrated as follows:108

and P

(12)

where ŷi/i denotes the response of the ith predicted logarithm of liquid viscosity value using the obtained model ignoring the use of ith experimental logarithm of liquid viscosity. The bootstrapping was repeated 5000 times. Consequently, the value Qboot2 parameter of the obtained model has been evaluated to be 0.7951. 5.6. Y-Scrambling Validation Technique. The objective of this approach is to verify the model is not a chance correlation. For this purpose, all responses variable are shuffled randomly without any changes in the predictors set. If the prediction power of the model in terms of R2 or Q2 does not change significantly, then the validity of the model is disputable. The y-scrambling parameter is the intercept of the following equation:

(7)

⎛ n ⎞ Q ASYM 2 = 1 − (1 − R2)⎜ ⎟ ⎝ n − p′ ⎠

∑ (yi − yi /̂ i )2 i=1

j = 1, ..., p

0≤K≤1

and

n

1 1 − ≤ Mj ≤ 1 − p p

(14)

where yt̅ raining is the average value of the logarithm of liquid viscosity of the compounds present in the training set, ŷi/i is response of ith object predicted by the obtained model ignoring the value of the related object (ith experimental logarithm of liquid viscosity). The less difference there is between this value and the R2 parameter, the more validity of the model would be expected. The evaluated Qext2 parameter of the obtained linear model is 0.8449. Ultimately, all the validation techniques demonstrate the final model as a valid, stable, nonchance correlation with high predictive power. Table S4 in the Supporting Information presents the prediction error for studied ionic liquids. The complete list of studied ionic liquids and associated experimental and predicted

(11)

−

and p and p are the number of cases in which Mj has the positive and negative values, respectively. The calculated values of the RQK test are presented as follows: ΔK = 0.058, ΔQ = 0, RP = 0.195, and RN = 0. These values which are greater or equal to zero indicate not only the validity of the model, but also approval for nonchance correlation. 5.5. Bootstrap Validation Technique. In bootstrap methodology, the original size of data set (n) is retained for the training set, by selecting the objects with repetition. The 2473



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viscosity values are available as tables in the Supporting information. The overall ARD% is 8.77 for all ILs, and the maximum deviation is less than 30%. From these, 36.32% of estimated viscosities show the deviation of 0−5%, 26.2% within 5.1−10%, 20% within 10.1−15%, 9.65% within 15.1−20%, and only 7.83% have an error higher than 20%. The maximum calculated absolute deviation from experimental values is 30% for [N6666][ (Me3CCO)-CH-(CO(CF2)2CF3)](tetra-hexyl ammonium 2,2-dimethyl-6,6,7,7,8,8,8-heptafluoro-3,5-octanedionate).The source of error for the experimental viscosity values of the ionic liquids might lie in their contamination with water, halides, or other organic solvents which drastically affects their physical properties. For instance, increasing Cl− concentration from 0.01 to 0.5 m as the contamination in [C4mim][BF4] increases the viscosity from 154 to 201 cP.40 As mentioned earlier, the anion and cation structures profoundly affect the viscosity of ionic liquids. For this purpose, two subsets of the most frequent cation ([C4mim]+) and anion [NTf2]− are selected for further investigation. One of the advantages of the proposed model is studying the anion/cation effect through their contribution terms in the viscosity model. For ionic liquids sharing the [C4mim]+ cation (the most frequent anion), the viscosities of the ILs behave in the following order: [dca]− < [CF3BF3]− < [C2F5BF3]− < [NTf2]− < [TfO]− < [NfO]− < [MeSO4]− < [BF4]− < [PF6]−. The viscosity of ionic liquids appeared to be governed essentially by van der Waals volume and H-Bonding. An increase in the viscosity of the various anion/cation combinations was attributed to an increase in van der Waals forces over hydrogen bonding.31In addition, an increased symmetry of inorganic cations like [BF4]− and [PF6]− compared to that of organic ones may contribute to easier interaction with cations resulting in increased viscosity. From [TfO]− to [NfO]−, the van der Waals attractions are superior over the H-bonding results in decreased and better charger delocalization.31 No trend between anion mass and its contribution was observed in this study. The minimum viscosity is found for [dca]− which combines minimal anion mass with moderate basicity. For 1,3-dialkyl imidazolium-based ILs, alkyl chain lengthening results in higher viscosities owing to increased van der Waals interactions.31 To study the effect of alkyl chain on viscosity, the estimated viscosities of [Cnmim]+(1-alkyl 3methyl imidazolium) with [BF4]−,[PF6]− and [NTf2]− are depicted in Figure 1.The results indicate that the viscosity increases with the alkyl chain of the imidazolium cation which is consistent with the findings of Gardes and Coutinho.14 According to Table S1 in the Supporting Information, the poorest results are obtained for 1-alkyl imidazolium-based ionic liquids with ARD = 14.68%. The small number of data points, in addition to experimental error due to either experimental approach or contamination, might account for this deviation. Employing larger data sets for 1,3-dialkyl imidazolium, ammonium, and sulfonium with, respectively, 168, 87, and 53 data entries, results in an acceptable prediction with an ARD = 8.38% even for the broad diversity of anions/cations. This indicates that the derived model is capable of predicting viscosity with acceptable accuracy for other IL families if larger data sets are submitted to the model. Figure 2 depicts the estimated viscosity logarithm values versus the experimental ones. According to the figure, our model gives an acceptable prediction in the range of the 0.5−

Figure 1. Effect of chain length (n) on the viscosity of several ionic liquids containing [Cnmim]+.

Figure 2. Estimated viscosity values from eq 2 versus experimental values.

2.5 viscosity logarithm. However, larger deviations are observed for high viscous ILs (>2.5). Figure 3 displays the absolute relative deviation defined as follows:

ARD % = 100 ×

log(ηexpt ) − log(ηpredict ) log(ηexpt )

(15)

As indicated in this Figure 3, the associated estimation error for the majority of data points (62.7%) lies in the 0−10% range which is an acceptable accuracy for large and diverse sets of ILs.

6. CONCLUSIONS It is here shown that QSPR method was successfully applied to derive a 7-parameter model for the estimation of ionic liquid viscosity. This model permits the viscosity estimation of 17 diverse ionic liquid classes containing 146 cations and 36 anions in a wide range of temperatures, 253−373 K, and viscosities, 5.7−28.24 cP. For a database consisting of 435 data points for 293 ILs, the absolute relative deviation observed was 8.77%. 2474



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(10) Yamamoto, H. Structure properties relationship of ionic liquid. J. Comput. Aided Chem. 2006, 7, 18. (11) Matsuda, H.; Yamamoto, H.; Kurihara, K.; Tochigi, K. Prediction of the ionic conductivity and viscosity of ionic liquids by QSPR using descriptors of group contribution type. J. Comput. Aided Chem. 2007, 8, 114. (12) Tochigi, K.; Yamamoto, H. Estimation of ionic conductivity and viscosity of ionic liquids using a QSPR model. J. Phys. Chem. C 2007, 111, 15989. (13) Bini, R.; Malvaldi, M.; Pitner, W. R.; Chiappe, C. QSPR correlation for conductivities and viscosities of low-temperature melting ionic liquids. J. Phys. Org. Chem. 2008, 21, 622. (14) Gardas, R. L.; Coutinho, J. A. P. A group contribution method for viscosity estimation of ionic liquids. Fluid Phase Equilib. 2008, 266, 195. (15) Gardas, R. L.; Coutinho, J. A. P. Group contribution methods for the prediction of thermophysical and transport properties of ionic liquids. AlChE J. 2009, 55, 1274. (16) Ghatee, M. H.; Zare, M.; Zolghadr, A. R.; Moosavi, F. Temperature dependence of viscosity and relation with the surface tension of ionic liquids. Fluid Phase Equilib. 2010, 291, 188. (17) Ghatee, M. H.; Zare, M. Power-law behavior in the viscosity of ionic liquids: Existing a similarity in the power law and a new proposed viscosity equation. Fluid Phase Equilib. 2011, 311, 76. (18) Han, C.; Yu, G.; Wen, L.; Zhao, D.; Asumana, C.; Chen, X. Data and QSPR study for viscosity of imidazolium-based ionic liquids. Fluid Phase Equilib. 2011, 300, 95. (19) Gharagheizi, F. QSPR studies for solubility parameter by means of genetic algorithm-based multivariate linear regression and generalized regression neural network. QSAR Comb. Sci. 2008, 27, 165. (20) Gharagheizi, F. A QSPR model for estimation of lower flammability limit temperature of pure compounds based on molecular structure. J. Hazard. Mater. 2009, 169, 217. (21) Gharagheizi, F.; Eslamimanesh, A.; Mohammadi, A. H.; Richon, D. QSPR approach for determination of parachor of non-electrolyte organic compounds. Chem. Eng. Sci. 2011, 66, 2959. (22) Gharagheizi, F.; Eslamimanesh, A.; Tirandazi, B.; Mohammadi, A. H.; Richon, D. Handling a very large data set for determination of surface tension of chemical compounds using quantitative structure− property relationship strategy. Chem. Eng. Sci. 2011, 66, 4991. (23) Gharagheizi, F.; Gohar, M. R. S.; Vayeghan, M. G. A quantitative structure−property relationship for determination of enthalpy of fusion of pure compounds. J. Therm. Anal. Calorim. 2011, 1. (24) Gharagheizi, F.; Sattari, M. Prediction of the θ(UCST) of polymer solutions: A quantitative structure−property relationship study. Ind. Eng. Chem. Res. 2009, 48, 9054. (25) Gharagheizi, F.; Tirandazi, B.; Barzin, R. Estimation of aniline point temperature of pure hydrocarbons: A quantitative structure− property relationship approach. Ind. Eng. Chem. Res. 2009, 48, 1678. (26) Mirkhani, S. A.; Gharagheizi, F.; Sattari, M. A QSPR model for prediction of diffusion coefficient of non-electrolyte organic compounds in air at ambient condition. Chemosphere, 2011, doi: 10.1016/j.chemosphere.2011.11.021. (27) Todeschini, R.; Consonni, V. Handbook of Molecular Descriptors. Wiley-VCH: Weinheim, Chichester, 2000; p xxi. (28) Ohno, H. Ion conductive characteristics of ionic liquids prepared by neutralization of alkylimidazoles. Solid State Ionics 2002, 154−155, 303. (29) Pernak, J.; Goc, I.; Mirska, I. Anti-microbial activities of protic ionic liquids with lactate anion. Green Chem. 2004, 6, 323. (30) Sheldon, R. Catalytic reactions in ionic liquids. Chem. Commun. 2001, 2399. (31) Bonhôte, P.; Dias, A.-P.; Papageorgiou, N.; Kalyanasundaram, K.; Grätzel, M. Hydrophobic, highly conductive ambient-temperature molten salts. Inorg. Chem. 1996, 35, 1168. (32) Berthod, A.; Ruizangel, M.; Cardabroch, S. Ionic liquids in separation techniques. J. Chromatogr. A 2008, 1184, 6.

Figure 3. Relative deviation of predicted viscosity values versus experimental ones.

The validity of the proposed model was verified using several validation techniques. The final model is stable and capable of predicting the viscosities of new ionic liquids in a wide range of temperatures.

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ASSOCIATED CONTENT

S Supporting Information *

Table S1 (the list of studied ionic liquids and their associated family), Table S2 (the structure and abbreviation of anions), Table S3 (the structure and abbreviation of cations), and Table S4 (predicted viscosity values of studied ionic liquids allocated with the source of the data. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: + 98 (21) 88 48 10 87. E-mail: [email protected].

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