Myths and Realities about Existing Methods for Calculating the Melting

Article pubs.acs.org/IECR

Myths and Realities about Existing Methods for Calculating the Melting Temperatures of Ionic Liquids José O. Valderrama* Department of Mechanical Engineering, Faculty of Engineering, University of La Serena, Casilla 554, La SerenaChile Center for Technological Information, Monseñor Subercaseaux 667, La Serena Chile ABSTRACT: The several methods presented in the literature during the past few years to estimate the melting temperatures of ionic liquids and the alleged accuracy of the methods mentioned by several authors are analyzed and discussed in this work. Because of the importance of the melting temperatures for the development and applications of ionic liquids, several models have been proposed in the literature. Methods based on computational chemistry, group contribution, artificial neural networks, and chemical homology are considered in this analysis, and results from the different approaches are discussed. The general conclusion about these advances is that it is a myth that, with the present experimental data and knowledge we have of ionic liquids, we can obtain accurate and generalized correlations and estimation methods for determining the melting temperatures of ionic liquids. Ideas about what is needed and on how to proceed in the future are presented.

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play different roles for different kinds of ILs.6 Glass transition has been widely discussed in the literature, and an excellent review can be found in the book by Schmelzer and Gutzow.7 The authors present a thorough, exhaustive, comprehensive review and evaluation of the major literature about glass formation and glass transition. In the area of ionic liquids a complete description and discussion on the glass transition phenomenon is given by Holbrey and Rogers.8 The complex way in which ILs change from solid to liquid (melting) or from liquid to solid (solidification) has been recognized for years. Wilkes et al.9 wrote, “The melting temperature of many ionic liquids can be problematic, since they are notorious glass-forming materials. It is a common experience to work with a new ionic liquid for weeks or months to find one day that it has crystallized unexpectedly.” More recently, Preiss et al.10 discussed the possibility of finding a universal, simple, physically well-founded method for predicting the melting temperature of organic salts. The authors analyzed several possible sources that may introduce errors in the experimental determination of the melting temperature. Among other sources they discussed contamination of sample during the measurement, formation of liquid-crystalline phases and plastic crystalline phases, disorder and defects in the lattice, existence of polymorphs, pressure variations during measurement, thermal stability of the salts, and equipment calibration. Additionally, Bodo and Migliorati11 indicates that the melting temperature is particularly difficult to measure because, “it is almost impossible to heat the solid cell and to obtain the liquid without introducing substantial overheating due to the high nucleation barriers that have to be overcome”. To the best of the author’s knowledge at present there is no standard procedure for experimentally determining the melting

INTRODUCTION The melting temperature is the most characteristic property that is used for defining the so-called room temperature ionic liquids, usually named simply ionic liquids (ILs). These are substances formed only by ions and having melting temperatures below 100 °C.1 It has been found that the melting temperatures of ILs are in some way related to the structure and composition of ILs.2 Selection of both the cation and anion determines the melting temperature of an IL, but the effects of the anion and cation seem to be complex and unknown. Some general observations, however, have been reported in the literature: (i) an ionic liquid with low symmetry cation will have low melting temperature compared to one with high symmetry; (ii) weak intermolecular interactions and a good distribution of charge in the cation favor low melting temperature of ionic liquids;3 (iii) in a family of ionic liquids, for instance [Xmim][Y], the melting temperature decreases with the length chain of [Xmim], passes through a minimum, and then increases again to become asymptotically constant for large chains.2 The melting temperature is controlled by both single-molecule properties and intermolecular interactions due to packing in the solid state. It finds applications in chemical identification, purification, and calculation of a number of other physicochemical properties such as vapor pressure and aqueous solubility. However, because of the complex influence of energy and entropy factors, melting temperatures of ionic liquids are difficult to predict. Also, the many ionic liquids that have been synthesized up to now, and the very many that are possible to obtain, makes it impossible to elaborate any simplistic generalization about ionic liquid behavior, as is commonly and successfully done with organic molecular substances.4,5 Melting happens when the molecules or ions fall out of their crystal structures and become disordered liquid. This should not be confused with glass transition, which is the change that happens from the solid state to amorphous solid. The melting process of ILs is governed by van der Waals forces and electrostatic interaction forces, and the impacts of the two forces © XXXX American Chemical Society

Received: October 2, 2013 Revised: December 5, 2013 Accepted: December 5, 2013

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dx.doi.org/10.1021/ie403293z | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Table 1. Deviations between Experimental Melting Temperature Data Published by Different Authors for Some Ionic Liquidsa anion

Tm/K

ΔTm

|%ΔTm|

1-butyl-3-methylimidazolium chloride

C8H15N2Cl

[bmim]

[Cl]

1-butyl-3-methylimidazolium hexafluorophosphate

C8H15N2F6P

[bmim]

[PF6]

C14H27N2F4B

[C10mim]

[BF4]

− 24 28 29 − 53 64 65 71 72 − 52 73 − 36 − 4 5 6 11 17 18 − 5 35 − 31 − 21

− 7.6 8.9 9.2 − 25.0 30.2 30.7 33.5 34.0

1-decyl-3-methylimidazolium tetrafluoroborate

314 338 342 343 212 265 276 277 283 284 196 248 269 234 270 252 256 257 258 261 269 270 198 203 233 294 327 238 259

ionic liquid

a

formula

cation

1-ethyl-3,5-dimethylimidazolium bis[(trifluoromethyl) sulfonyl]imide

C9H13N3F6S2O4

[E1M3,5im]

[bti]

1-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

C8H11N3F6S2O4

[emim]

[bti]

1-octyl-3-methylimidazolium hexafluorophosphate

C12H23N2F6P

[omim]

[PF6]

1-tetradecyl-3-methylimidazolium bromide

C18H35N2Br

[C14mim]

[Br]

triethylsulfonium bis[(trifluoromethyl)sulfonyl]imide

C8H15NF6S3O4

[S222]

[bti]

The values are taken from the NIST database.

26.5 37.2 15.4 − 1.6 2.0 2.4 4.4 6.7 7.1 2.5 17.7 10.5 8.8

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some ionic liquids. As observed, differences up to 70 K are found for some ionic liquids, a difference that is not acceptable for producing good and general correlating and predicting models for the melting temperature. It should be mentioned that estimations of the uncertainty values reported in the NIST database12 include several assumptions and must be considered as preliminary values only. In the NIST Web site itself, one can read, “Information provided by the authors in the text of the articles is considered in the uncertainty evaluation process. Numerous issues with regard to synthesis, purification, analysis, and measurement details for these materials often make estimation of uncertainties impossible without numerous assumptions. The listed values of the combined expanded uncertainties should be considered preliminary, and are subject to change as more information becomes available and analysis of the experimental data continues.” The discrepancies among reported values of melting temperatures indicate that data analysis is required before applying any mathematical technique for any type of modeling (correlations, group contributions, and neural networks). In some models such as simple polynomial or similar correlations the inaccuracies are absorbed by the values of the empirical parameters and usually average deviations are low. But that means very little from a practical point of view because it could only indicate that negative and positive deviations, despite their magnitude, cancel each other resulting in average deviations close to zero. In other modeling methods such as an artificial neural network, the use of inaccurate data makes the network unable to find a reasonable

temperatures of ILs that can guarantee reproducibility. It seems that the glass-forming tendency, and therefore the melting temperature, depends on the thermal history of the sample, but there are various other problems that have been well summarized by Holbrey and Rogers.2 All the concepts presented in the preceding section are the main cause of the great differences in melting temperature data reported in the literature for the same ionic liquid, creating a major problem when experimental melting temperature data are needed. Most papers including correlations with the use of literature data do not explain the reasons for choosing one or another value, although the literature sources are provided. Additionally, data compilations and databases are not clear about the accuracy of the reported values, although in some cases uncertainty values are given.12−15 The NIST database,12 for instance, gives a value of 342.1 K with an estimated uncertainty of 1 K for 1-butyl-3-methylimidazolium chloride and also reports a second value of 314.1 K with an estimated uncertainty of 4 K. This means a maximum difference of 28 K between the two values with an alleged uncertainty of maximum 4 K. For 1-butyl3-methylimidazolium tosylate the NIST database gives a value of 340.1 K with an estimated uncertainty of 1 K but it also gives another value of 330.16 K with an estimated uncertainty of 0.4 K. This means a maximum difference of 20 K between the two values with an alleged uncertainty of maximum 1 K. All this is confusing for a user who is just looking for an accurate value to use in design, in modeling, or for developing new estimation methods. Table 1 shows deviations between experimental melting temperature data published by different authors for B



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Table 2. Selected Applications for Correlating and Estimating the Normal Melting Temperature of ILs Showing the Maximum Errors for Each Method authors

type of ILs

method

no. of data

Emax (°C)

Aguirre et al.31

various types of ILs

group contribution

136

80

Bini et al.20

pyridinium bromides

126

27

Carrera and Aires-de-Sousa18 Eike et al.32

pyridinium bromide

neural network model Dragon + ANN

126

70

quaternary ammonium bromides various types of ILs

QSPR

109

72

QSPR

808

68


group contribution group contribution QSPR

799

67

155

50

149

98

QSPR

126

90

Farahani et al.24 Gharagheizi et al.23 Huo et al.21 Katritzky et al.16 Katritzky et al.17

imidazolium and benzimidazolium imidazolium bromides and benzimidazolium bromides pyridinium bromides

López-Martin et al.33 Preiss et al.22

imidazolium

QSPR

84

51


67

90

Preiss et al.10


modified QSPR + COSMO COSMO-RS

520

180

Sun et al.34

imidazolium tetrafluoroborates 1-substituted 4-amino-1,2,4triazolium bromide and nitrate various types of ILs

QSPR

41

43

QSPR

13

25

104

25

190

50

717

38

394

102

Trohalaki et al.35

Valderrama and Rojas36 Valderrama et al.27

imidazolium

Varnek et al.37


Yan et al.38


chemical homology group contribution several machinelearning methods QSPR

comments by authors The proposed model can be used for the prediction of Tm of a wide range of ILs, and for the design of these compounds using computer-aided molecular design (CAMD) methods. This ANN provides a good prediction model of Tm of ionic liquids starting directly from their molecular structure, thus avoiding the use of dedicated molecular descriptors. Regression trees were able to build good predictive models for the melting temperatures of pyridinium bromides from the molecular structure. The results obtained from a QSPR study of quaternary ammonium salts are able to correlate melting temperatures with some success. In addition, analyzing the model with various validation techniques verify the reliability, robustness, and stability of the present model. Presented here is a group contribution approach successfully developed to estimate the normal melting temperatures of ionic liquids. The results show that melting temperatures of ILs determined by the method are accurate and thus the new model can be applied to predict melting temperatures of ILs. The five-parameter correlation equation should be able to predict the melting temperatures of unknown or unavailable compounds of this class. A six-descriptor equation with a reasonably good correlation has been developed for the prediction of the melting temperatures of pyridinium bromides. Computing descriptors for the cation and the anion separately and then combining them in one model gives good predictions of melting temperatures. The quality of our model is comparable to today’s QSPR methods but has a broader basis in fundamental thermodynamics and needs much less specialized descriptors. For a large variety of complex ionic compounds, from acyclic to (homo- or hetero) polycyclic, good results were achieved in developing a simple, yet useful prediction model. The developed QSPR models can give a fair estimate of unknown or unavailable compounds of the same class. Good correlations with the experimental data were found. The correlation coefficients exceed 0.9. The estimation method is considered to give reasonable values of the normal melting temperature. Average deviation for the 190 ionic liquids is 1.5% and average absolute deviation is 11%. However, high and unacceptable deviations are found for some few ionic liquids. For the full set, the accuracy of predictions does not significantly change as a function of the type of descriptors. The overall results show that this method has a good predictive ability.

of ILs and state that, “behind the large number of correlations for the melting properties of the ILs, in particular of their melting points, is the quest for understanding the characteristics that allowed the synthesis of liquid salts”. All this progress is most welcome, and new methods and approaches should be explored in the future. What is questionable, however, is the pretentious generalization of the methods as done by some authors, indicating that the melting temperatures of ionic liquids can be predicted with some defined low accuracy. With our present knowledge about what is really happening during the melting process of ionic liquids, such generalizations cannot be done. In what follows, the main four methods presented in the literature are briefly discussed, their mathematical complexity is analyzed, the accuracy and generalization of the methods are summarized, general conclusions are drawn, and suggestions for future developments are provided.

relation between the variables. In other cases the network memorizes, providing excellent correlation of data but poor predicting capabilities. The presence of outliers in a set of data (an observation point that is distant from other observations) must be clearly determined so that those outliers are not considered in developing a model. Otherwise not only the results may be sometimes erratic but it could lead to wrong conclusions about the accuracy of the model. Data scattering must also be considered to not request the model to give deviations below the inherent deviation of the experimental data used. As discussed in the section Chemical Homology, the homology concept represents a good alternative approach to detect wrong data. Despite all the problems mentioned above, some methods have been proposed in the literature to estimate the melting temperatures of ionic liquids using classical and modern approaches such as group contribution, chemical homology, neural networks, and quantitative structure−property relationship (QSPR) among other methods.16−25 A good review of the different methods available in the literature for estimating several properties of ionic liquids, including melting temperature, has been made by Coutinho et al.26 The authors dedicate an important section of the article to the different attempts presented in the literature to estimate the melting temperatures

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DATA, MODELING, AND CORRELATIONS As indicated in the Introduction , values of the melting temperatures of ionic liquids reported in the literature present great discrepancies, errors that are then propagated to the correlation results. Despite this, some progress has been done and new approaches are frequently published. There are four main methods that have been used for correlating melting temperature data of ionic liquids: chemical homology (ChemH), C



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homologous series, Karapetyants40 used the concept of homologous compounds to determine several properties of solids and liquids in a method he called “comparative calculations”. Chickos and Nichols41 studied the melting behavior of homologous organic series and found that for most series the melting temperature follows a hyperbolic behavior. In a more recent paper Valderrama and Rojas36 applied the concept of homology for the estimation of the normal melting temperatures of ionic liquids using a method based on homologous cations. The authors found that ionic liquid families having the largest amount of melting temperature data were those including the anions hexafluorophosphate and tetrafluoroborate. According to the concept of chemical homology, those compounds that do not follow a common smooth behavior could be in error. This means that for those points the value for [X][PF6] could be wrong, the value for [X][BF4] could be wrong, or both. Figure 1 shows all available data for [X][PF6] and

group contribution methods (GCM), quantitative structure− property relationship (QSPR), and artificial neural network (ANN). Combinations of some of these methods have been also suggested27 and other methods such as ab initio calculations,28 atomistic simulation methods,29 and molecular dynamics simulations30 have been presented. Table 2 presents some examples for each of these methods indicating the number of data treated and showing comments presented by the authors themselves about the method they used. More important is the column Emax (°C) in which the maximum error found by the authors mentioned in the first column, for correlating or predicting the melting temperature, is presented. As seen in Table 2, errors higher than 100 K are found, although reported average deviations are lower than 5% for most cases. In correlating data, besides the relative average deviation and the average absolute deviation, the maximum deviation is a relevant statistical parameter for determining the accuracy and goodness of a model, especially for correlation and prediction purposes.39 Once the limitations and ranges of applicability of a model are well-defined, the model should not give erratic results (unexpected high deviations), especially if average and absolute deviations are low. The prediction of an erratic value will mean that those limitations were not well-defined or that the model is being applied in ranges and situations not considered during the formulation of the model. Therefore, model developers must be clear not only in establishing the limitations of the model but also in stating their conclusions. Some of the comments given in the literature about the goodness of some models are clearly misleading, as shown in Table 2. Authors should not forget that a good model developer should identify and inform in papers and reports the limits of applicability of a proposed model to guide users on its appropriate use. The relative average deviations express the true negative and positive deviations of the calculated values. If this average deviation is zero, it means that deviations compensate each other, but it says nothing about the magnitude of the deviations. This is indicated by the average absolute deviation in which no compensation between negative and positive values occurs. If both deviations are low (close to zero), still they do not say much about the maximum deviation found in the whole set of data. If the global accuracy of a method is going to be reported, the maximum deviation in correlating and predicting the property should also be given. Honestly, no one can guarantee that the model will give a deviation below the average deviation found during correlation and testing. Maximum deviations, at least put a top value of the error which is likely to be found. It should also be mentioned that although these three deviations are the only parameters considered in the analysis presented in this paper, there are other factors that are of importance when assessing estimation methods. These include, for instance, the range of applicability, the simplicity of use, the potential for integration with process simulators and other simulation tools, and the number of fitted parameters included in the model. Chemical Homology. In chemistry, a homologous series is a group of compounds with a similar general formula, having similar physicochemical properties due to the presence of the same functional groups. The n-alkanes and the n-alkanols, for instance, form homologous series. The properties of the compounds of a series present in many cases a regular and smooth change as the molecular size, molecular mass, or other basic properties change. On the basis of this same concept of

Figure 1. Correlation of melting temperature of ionic liquids using homology between two types of ionic liquids: [X][PF6] and [X][BF4]. The data are from the NIST database.12

[X][BF4] having common cation [X]. As observed in Figure 1, there are some data (around 200 K for Tm of [X][PF6]) that do not follow the common behavior of most data. Which data to choose as the correct ones is a matter that has been discussed elsewhere by the authors.36 Chemical homology seems to be a reasonable method for discriminating erroneous data, but it suffers the problem of needing many and accurate enough data for at least one reference fluid so that the method can be of more general application. Valderrama and Rojas36 used [X][PF6] as the reference fluid for estimating the melting temperature of seven other ionic liquids that are homologous in the cation: [X][BF4], [X][Cl], [X][I], [X][TFPB], [X][Br], [X][NO3], and [X][ClO4]. Important to notice in this method is its limitation due to the few data available for homologous ionic liquids. Despite this, it would be interesting to analyze the homology concept using other reference ionic liquids. Group Contribution Methods. In group contribution methods the property of a compound is calculated by summing up the contributions of certain defined groups of atoms, considering at the same time the number frequency of each group occurring in the molecule. Although all these methods have been questioned in the literature,42 they have the advantage of quick estimates without requiring sophisticated computational calculations. D



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Table 3. Different Definitions of Chemical Groups for Estimating Properties of Ionic Liquids Found in the Literature

a

critical propertiesa

viscosityb

heat capacityc

melting temperatured

Without Rings −CH3 −CH2− >CH− >CC−]− =CH2 =CH− =C< −O−, [−O]− >CO −COO− >N−, [>N< ]+ −N= −CN −F, [F−] −Cl, [Cl−] −I, [I−]

Cations 1,3-dimethylimidazolium 1-methylpyridinium 1,1-dimethylpyrrolidinium

Without Rings −CH3 −CH2− >C< −O− >N− −CN −F −Cl −Br

Cations 1,3-dimethylimidazolium 1,2,3-trimethylimidazolium 1-methylpyridinium 1,1-dimethylpyrrolidinium tetramethylammonium tetramethylphosphonium 1,1-dimethylpiperidinium

Anions BF4 PF6 Cl Br CH3SO4 C2H5SO4 N(CN2)2

With Rings −CH2− =CH− >C< =C< >N− [>N< ]+ −N= [>N=]+

Anions PF6 BF4 Tf2N Cl CH3COO MeSO4 EtSO4 CF3SO3

Cations imidazolium pyridinium pyrrolidinium

New Groups −B −P

−CH2 −CH3

Anions PF6 BF4 Tf2N Cl CH3COO MeSO4 EtSO4 CF3SO3 Br CF3COO N(CN)2 C(CN)3 AlCl4 Pf2N Groups −CH2 dimethylamino

With Rings −CH2− =CH− =C> CH− >C< −OH −O− −COO− −NH2 −NH− −F −Cl −Br −I −P −B −S− SO2 With Rings =CH− =C< −NH− >NH− =N− −NH3

Valderrama and Robles.43 bGardas and Coutinho.44 cGe et al.45 dAguirre et al.31 eLuis et al.46 fValderrama and Reátegui.47

Table 4. Some Group Contribution Models for Estimating Tm’s of Ionic Liquids Presented in the Literature authors

parameters and variables

model equations

∑ Nk ΔTmp, k + Z H ∑ NjΔTmp, j

Huo et al.21

group contributions (ΔT), number frequency (N), type of group connections (δ and σ), number of ring groups in the molecule (τ)

Tmp =

Aguirre et al.31

group contributions (ΔT), number frequency (ni), symmetry parameter (σc), cation flexibility (τc)

Tm =

Gharagheizi et al.23

group contributions (Tmai, Tmci), number frequency of functional groups of anions (Nai) and cations (Nci), and intercept Tmo

Tm = Tmo +

AH + BH σ + C Hτ + DHδ ∑ niΔTm, i a + σc + cτc Na

Nc

∑ NaiTmai + ∑ NciTmci i=1

i=1

A + ∑ ηijτi

Valderrama et al.27

group contributions only (τi), number frequency (ηij)

Tmj =

Valderrama et al.27

group contributions (τi), number frequency (ηij), packing density index, Kier connectivity index (λ), van der Waals volume (ψ)

Tmj = (a + bΩj) +

B + α ∑ ηijτi + β ∑ ηijτi 2

∑ ηijτi

Tmj = (a + bΩj + cλi) +

∑ ηijτi

Tmj = (a + bΩj + cλi + dψi ) +

Several authors have applied group contributions for estimating some properties of ILs using different groups for the same molecules. Table 3 presents different definitions of

∑ ηijτi

chemical groups for estimating properties of ionic liquids found in the literature. Table 3 shows that there is no agreement on how to divide the molecules for estimating properties of ILs and also E



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shows the implicit acceptance of the fact that, since we do not know the correct division of groups (if there is any), definitions of groups is more or less an arbitrary matter. Despite the fact that the most appropriate division of groups is unknown, GCM methods seem to be an interesting approach to continue exploring in the future. Chemically based division of groups and also more physically founded model equations for defining the dependence of the melting temperature on the groups are necessary to make some progress using this method. Besides the commonly used contribution values and number frequency of groups employed in most methods for estimating the melting temperature of ionic liquids, the following parameters have been considered by some authors: type of group connections, number of ring groups, symmetry parameters, cation flexibility, packing density index, connectivity indexes, and van der Waals group volume. Table 4 presents some models that have been used for estimating the melting temperature of ionic liquids using group contributions presented in the literature. The type of parameters and variables that have been used are listed in the second column of Table 4 (groups, number frequency of each group, type of group connections, number of ring groups, symmetry parameter, cation flexibility, packing density index, Kier connectivity index, mass connectivity index, van der Waals volume). Quantitative Structure−Property Relationship. The method known as QSPR (quantitative structure−property relationship) is a mathematical model that attempts to relate structure-derived characteristics of a compound (known as descriptors) to its physical, chemical, or physicochemical properties. Therefore, this method has, in theory, predictive capabilities and according to Clark48 has had a long and successful development history. The method can also be used in property estimation in which structural characteristics influence a property of interest, such as the case of the melting temperature. Good descriptions of these methods and their applications are found in Dehmer et al.49 and Yongsheng et al.50 Molecular modeling techniques such as QSPR enable the definition of a large number of descriptors, for characterizing the structure, shape, and binding properties of a molecule or groups forming a molecule (for instance, the anion and cation in an IL). Some descriptors encode physical information useful for property estimation, in particular for the melting temperature. Figure 2 shows a general flow diagram for developing QSPR models. As observed in Figure 2, the development of QSPR requires first the collection of data for the property of interest, the melting temperature in this study, data that must be accurate enough to obtain good results. The model discriminates between one ionic liquid and another by the value of the different molecular characteristics defined through chemical descriptors. Selection of the appropriate descriptors is of paramount importance to obtain good correlating and predicting models. Also, the testing or validation of the models should be done using a set of independent data initially separated from the data used for learning. Table 5 shows different descriptors used in estimating the melting temperatures of ionic liquids through QSPR methods found in the literature, while Table 6 shows selected values of descriptors suggested here for developing models for the melting temperatures of ionic liquids. In Table 6, λ is the mass connectivity index, Rci is the Randic connectivity index, SAtot is the total surface area, Vvdw is the van der Waals group volume, and ρpack is the packing density index. The mass connectivity index was calculated using the definition of

Figure 2. Flow diagram for developing QSPR models.

Valderrama and Rojas,51 and the other descriptors were estimated using the software Dragon6.52 Artificial Neural Networks. Artificial neural networks is a computational model inspired by the behavior of natural neurons. A structure of neurons organized in different layers (known as architecture) receives data of a given property, the melting temperature for instance, and data of some independent variables that are supposedly related to the dependent main variable (molecular mass, connectivity index, density, for instance). The input and output variables are weighed by weights and shifted by a bias factor specific to each neuron. By optimization the network learns the relation between the variables and stores the values of the weights and biases that give the lowest error between calculated and experimental data of the dependent variable. Figure 3 presents a simple diagram of an ANN method that we have used for correlating and predicting several properties of ILs, using Matlab. Figure 3 shows the connections between the different files created for training and testing the ANN. Similar to the QSPR methodology, the application of ANN also requires first the collection of accurate enough data for the property of interest, the melting temperature in this study. Since ANN are used to find the relation between the variable of interest and some other properties, selection of such properties is also of importance to get accurate correlating and predicting models. Testing or validation of the ANN is also recommended. In most applications of ANN to IL property correlation and prediction, it seems that the independent variables so far employed and readily available for ionic liquids are not enough.36 Even in those cases in which group contributions are employed in combination with ANN, results are not accurate enough. The use of some chemical descriptors used in QSPR methods could be a good option for improving predictions using ANN. Figure 4 presents an example of the concepts and methods summarized above: (a) chemical homology from Valderrama and Rojas;36 (b) group contribution from Aguirre et al.;31 (c) F



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Table 5. Different Descriptors Used for Estimating the Melting Temperatures of Ionic Liquids Found in the Literature Katritzky et al.16

Sun et al.34

López-Martin et al.33

f-average complementary information content (order 0)

Onsager−Kirkwood solvation energy

Y index, Balaban index

average nucleophilic reactivity index for an N atom average information content (order 2)

Emin,e−e,C−C, minimum e−e repulsion for a C−C bond

X3A, average connectivity index chi-3 X5sol, solvation connectivity index chi-5 STN, spanning tree number

lowest normal mode vibrational frequency

Emax,R,C−H, maximum resonance energy for a C−H bond qmin,H, minimum partial charge for a H atom

f-relative number of rings

PN, maximum bond order of an N atom

minimum Coulombic interaction for a C−H bond

RNCSQ-C, relative negative charged surface area BCmax,MO, maximum bonding contribution of a molecular orbit of atoms B and C

Valderrama et al.27 Randic connectivity index van der Waals volume of groups packing density index mass connectivity index

SRW05, self-returning walk count of order 5 SRW06, self-returning walk count of order 6 Gm, G total symmetry index weighted by atomic masses PW5, path/walk 5 Randic shape index RNCG, relative negative charge

Table 6. Selected Values of Molecular Descriptors Suggested for Developing Models To Estimate the Melting Temperatures of Ionic Liquids cation

anion

λ

Rci

SAtot

Vvdw

ρpack

[mim] [C2F3mim] [sec-C4mim] [C3mim] [PhCH2CH2mim] [C3C8im] [C9mim] [mim] [i-C3mim] [i-C4mim] [C7mim] [eim] [eim] [emim] [E1M3,5im] [E1M3,5im] [e′mim] [e′mim] [e′mim] [e′mim] [e′mim] [e′mim] [Em2im] [C12mim] [C10mim] [C20mim] [C4CNmim] [bmim] [mmim] [dmprim] [Me5im]

[Br] [TfO] [NfO] [Cl] [PF6] [PF6] [PF6] [Cl] [I] [bti] [bti] [Br] [NO3] [TfO] [bti] [TfO] [Br] [Cl] [BEI] [TfO] [ClO4] [NO3] [ba] [Br] [tos] [Br] [PF6] [I] [tos] [PF6] [bti]

0.931 2.243 3.420 1.397 2.848 2.896 2.753 0.963 1.365 2.675 3.092 1.074 1.219 1.830 2.540 1.991 1.235 1.264 3.249 1.838 1.642 1.380 2.427 2.650 3.669 3.791 2.150 1.497 2.386 2.059 2.720

29.358 67.695 90.243 34.296 72.979 78.873 75.873 24.162 46.223 91.083 100.948 32.502 33.792 57.816 88.374 60.243 37.565 31.201 103.853 57.721 49.067 36.618 53.491 67.660 89.344 91.660 67.227 50.024 62.201 60.448 90.333

153.408 298.397 432.270 226.800 336.443 453.696 427.619 147.048 246.777 426.991 501.465 179.485 212.278 280.698 397.158 306.775 205.562 199.202 433.048 279.177 254.698 238.355 348.526 467.850 566.403 676.464 326.835 268.669 331.713 297.236 423.235

62.858 111.493 161.586 88.054 138.480 173.840 164.248 59.277 97.306 160.728 189.505 72.450 76.392 106.435 151.136 116.028 82.042 78.461 165.521 106.435 94.446 85.984 135.757 177.966 220.958 254.705 126.818 106.898 134.627 116.286 160.728

0.946 0.884 0.893 0.911 0.980 0.917 0.918 0.928 0.929 0.899 0.906 0.939 0.839 0.896 0.908 0.896 0.934 0.920 0.914 0.901 0.872 0.846 0.927 0.911 0.937 0.907 0.922 0.940 0.965 0.927 0.907

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QSRP method from López-Martin et al.;33 (d) ANN from Bini et al.20 As observed in Figure 4, the accuracy of the methods cannot be objectively compared because they were applied to different types of ionic liquids, different data were used, and the assumptions and limitations of each method are also different. However, Figure 4 gives a general picture of the goodness of each method.

THE MYTHS AND THE PROPOSED SOLUTIONS Certainly, the exactness of correlations and accuracy of results where such correlations are used (material and energy balances, process design and simulation) can be as good as the experimental data used in obtaining such correlations. Therefore, we need to have more accurate data on melting temperatures than those discussed before and shown in Table 1 if more accurate models are going to be developed. It is a myth that with G



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ionic liquid research should come up with such standards. Fortunately, some attempts have been made. The IUPAC Project 2002-005-1-100 was motivated because of serious disagreements in the published data for various properties of ionic liquids.53 This study group selected 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide, [C6mim][Tf2N], as a reference ionic liquid and measured several properties following a common standardized procedure. Glasstransition temperature and enthalpy of fusion, among other properties, were studied, but melting temperature was not included. Clearly, this type of detailed analysis cannot be done for the thousands of ILs already synthesized and for the many that will come in the future. The procedure would be lengthy and costly. Even if accurate data were available, none of the alternative procedures discussed above can give a clear answer to the problem of predicting the melting temperatures of ionic liquids in an acceptable way. This view agrees with that of Preiss et al.22 who wrote, “But, even if a pure substance was synthesized, and the melting temperature was unequivocally determined, there might be a multitude of unfavorable factors”, for developing a general model for the prediction of the melting temperature of ionic liquids. I believe that attempts go in the right direction, but with the present information about the structure and the effects of the different cations and anions that can be combined to produce ionic liquids, it is not possible to claim success as many authors do. It is important that in forthcoming publications authors explain clearly the limitations of the proposed methods so that real advancement in the development of more accurate and general models can be obtained. If we believed the good

Figure 3. Flow diagram of the ANN method, showing the connections between the different input, calculating, and output files. The file w_tm is the weight matrix that defines the ANN model.

the present data we can obtain better and generalized correlations and estimation methods for the melting temperatures of ILs, at least in the way done up to now. It is necessary to standardize the determination of the melting temperature so that good experiments guarantee reproducibility, which seems not to be the case at present. Institutions such as IUPAC, the American Chemical Society, or emerging groups on

Figure 4. Prediction and correlation of melting temperature of ionic liquids using the four main methods presented in the literature: (a) Valderrama and Rojas;36 (b) Aguirre et al.;31 (c) López-Martin et al.;33 (d) Bini et al.20 H



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of special importance in machine-learning procedures such as ANN because different data produce different results and each run during training produces a new different model (the weight and bias matrices). Therefore, to guarantee reproducibility, authors of papers must provide the code and the data used for learning and testing the model. This information must be as clear as possible so that any trained reader can reproduce the results that will be otherwise useless. Nowadays, most journals provide the option of including supporting information that is freely available for all users, so there is no reason for not publishing the data and programs used. The development of computer software has tremendously facilitated the application of computer methods and mainly the so-called machine-learning procedures. Nowadays it is very easy to do computational chemistry or artificial intelligence calculations without knowing much about the meaning of those computations. Probably, that is happening with many of the results that we see in the present literature. As Young60 wrote, “As a result, many people don’t understand even the most basic description of how the calculation is done and are therefore successfully doing a lot of work which is, frankly, garbage.” However, good work has also been done and I am convinced that all honest contributions are valuable to add pieces to this interesting puzzle.

conclusions that some authors write about their methods, it would seem that all has been already done and that predicting melting temperatures of ionic liquids is a solved problem. The truth is that we are still far from that. In group contribution methods, definition of new variables that could have influence on the melting temperature must be explored. Additionally, definitions of groups must be refined, although, this process being somewhat arbitrary, the tendency would be to rely more on the results than on the physical meaning of the groups. My impression is that chemical descriptors is the easiest way to go, to find the most appropriate variables that could describe melting temperature variations for different types of ionic liquids. Preliminary calculations using the descriptors presented in Table 6 are encouraging, although the accuracy of experimental data continues to be the main problem for obtaining good models. The studies that use QSPR for estimating the melting temperatures of ionic liquids show that the descriptors used are not able to represent the different phenomena involved in the process of melting and in the definition of a melting temperature. However, there are so many descriptors that most probably the correct ones for representing the melting temperatures of ILs will eventually be found and a more general correlating and predicting method would be possible to obtain. However, one must be careful and thoroughly analyze the meaning of descriptors and models used in computational chemistry.54 With respect to the use of ANN for correlating and predicting melting temperatures of ionic liquids, the most common myth is that the method can be used for any situation if just enough data are available for the variable of interest (for instance, the melting temperature). This is simply not true. For an ANN to be capable of correlating data, it is necessary that a series of requirements are fulfilled for that specific property and for the variables on which such a property depends. For the case of interest here, estimating the melting temperatures of ILs, there is not enough information (for instance, other properties of ILs) to find an appropriate relation between the melting temperature and those other variables. Livingstone et al.55 stated that, “data modeling with neural networks is certainly not an answer to the maiden’s prayer, but neural networks do offer a number of advantages over some of the more traditional methods of data modeling and should be viewed as a useful adjunct to these techniques.” According to our experience, neural networks represent a good correlating and predicting method if handled in a proper way. However, the method is not accurate enough to discriminate data and select wrong data, such as outliers. Molecular descriptors seem to be a good alternative to define the parameters that have the most influence on the melting process and to incorporate them in the mathematical models for GCM or ANN. Our research group in La Serena is exploring the use of some molecular descriptors associated with structural and bonding characteristics of ionic liquids (connectivity indexes, van der Waals volume, and packing density index, among others). The descriptors are being calculated with the use of the software Dragon6 from Talete,52 an Italian company dedicated to scientific software development. We have also used our own definition of molecular parameters such as the mass connectivity index that we have successfully used for correlating other properties of ionic liquids.56−59 A valuable contribution to the development of better methods for estimating the melting temperatures of ionic liquids is the publication of the data used in developing a given model. Although all modeling procedures are data sensitive, this factor is

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CONCLUSIONS It is essential for making progress in this area of melting temperature estimation for ionic liquids to standardize the determination of this property, so good experiments guarantee reproducibility and eliminate the great differences between experimental data sometimes found in the literature. A combination of the different methods nowadays available seems to be the best alternative for formulating models for predicting the melting temperatures of ionic liquids: chemical homology to analyze data, group contribution to include structural factors, QSPR to define appropriate chemical descriptors of groups and bonds, and neural networks to find the best relation between these variables with melting temperature. This means that we need to know better the structure, the relation between groups, and the characteristics of the anion and cation that form the ionic liquid. Since interactions between atoms and groups in an ionic liquids are of physical and chemical nature, probably division of physical and chemical contributions could be for some people a more arbitrary decision than a real fact. However, for correlation and modeling of experimental data this division could be acceptable.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author is grateful for the support of the National Council for Scientific and Technological Research (CONICYT), through the research grant FONDECYT 1120162, of the Direction of Research of the University of La Serena, and of the Center for Technological Information of La Serena, Chile. I



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Myths and Realities about Existing Methods for Calculating the Melting

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