Predicting Infinite-Dilution Activity Coefficients of Organic Solutes in

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Ind. Eng. Chem. Res. 2004, 43, 1039-1048

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SEPARATIONS Predicting Infinite-Dilution Activity Coefficients of Organic Solutes in Ionic Liquids David M. Eike, Joan F. Brennecke, and Edward J. Maginn* Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556

Room-temperature ionic liquids have shown great potential as media for reactions and separations. Information on how solutes interact with these solvents is crucial in assessing their usefulness. Here, the quantitative structure-property relationship (QSPR) method is used to correlate values of infinite-dilution activity coefficients for 38 solutes in three ionic liquids. Constant-temperature and temperature-dependent correlations are created with correlation coefficients ranging from R2 ) 0.90 to R2 ) 0.99. In addition, correlation parameters are analyzed to understand the interactions that affect infinite-dilution activity coefficients. are directly related to γ∞i through the relation

1. Introduction Solvents play a critical role in key chemical operations such as reaction and separation processes. Most organic solvents have relatively high volatilities, which lead them to contribute to air pollution problems. Roomtemperature ionic liquids (ILs), which are salts that melt near room temperature, have been under investigation as compounds that could be used in place of many current solvents. The primary appeal of ILs is based on their unique physical properties, which include the ability to solvate a wide range of materials, high thermal stability, and lack of vapor pressure.1 Although all of these properties show that ILs can serve well as solvents, it is the lack of vapor pressure that is especially appealing as it eliminates volatilization problems. Recent work has shown that ILs function well as solvents for homogeneously catalyzed reactions. They have also found use in other areas, including separations.2-4 For ILs to be used effectively as solvents, it is essential to know how they interact with different solutes. A quantitative measure of this property is given by the activity coefficient, γi, which describes the degree of nonideality for species i in a mixture. The infinitedilution activity coefficient, γ∞i , is especially important because it describes the extreme case in which only solute-solvent interactions contribute to nonideality. In addition to its theoretical importance, γ∞i has practical implications.5 Separation processes for removing dilute impurities, as encountered in many environmental applications, require knowledge of γ∞i for design purposes. Values of γ∞i are also important for evaluating the potential uses of ILs in liquid-liquid extraction and extractive distillation. Moreover, Henry’s law constants * To whom correspondence should be addressed. E-mail: [email protected]. Fax: (574) 631-8366

γ∞i )

Hi Psat i

(1)

where Hi is the Henry’s constant for solute i in the is the vapor pressure of solvent of interest and Psat i solute i at the temperature for which γ∞i is valid. As defined here, the Henry’s law constant has units of pressure and yields the partial pressure of the solute in the vapor phase when multiplied by the liquid-phase mole fraction. In many cases, the Henry’s law constant is more useful than γ∞i , especially when the temperature of the system is above the critical temperature of is not defined. Thus, Henry’s law the solute and Psat i constants find wide use in design calculations for gas separation applications. Because of the importance of γ∞i , a great deal of experimental work has been done measuring this quantity, especially for aqueous systems; several review papers5-7 summarize the different experimental techniques used to measure γ∞i and list data for various solutes in water and conventional organic solvents. Recent experimental measurements involving ILs provide γ∞i values8-12 and Henry’s law constants13,14 for gaseous and liquid solutes in various ILs. In these works, it has been shown that γ∞i can vary by several orders of magnitude depending on the solute, and it can be changed by making relatively small modifications to the cation or anion of the IL. It is this disparity among γ∞i values, along with the “tunability” of ILs, that has spurred interest in these liquids as media for separation processes. Significant work aimed at predicting γ∞i in conventional solvents using little or no experimental data has also been performed. Semitheoretical methods such as the UNIFAC group contribution method and modified

10.1021/ie034152p CCC: $27.50 © 2004 American Chemical Society Published on Web 01/22/2004

1040 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004

regular solution theory methods have been explored as ways to predict γ∞i for a wide range of solute-solvent systems.15 These methods tend to have trouble with systems containing strong hydrogen-bond networks, such as water. Also, one would not anticipate that UNIFAC would work well for ILs given that it was parametrized using only nonionic systems. More recently, the quantitative structure-property relationship (QSPR) method has been used to correlate γ∞i values16-18 and Henry’s constants19 for organic compounds in water. A similar method, the linear solvation energy relationship (LSER) method, has been used to estimate Henry’s law constants of organics in water from the solvatochromic parameters of the solutes.20 This method has also been used to characterize chromatographic retention times of solutes in ILs (which are related to γ∞i ).21-23 The QSPR method has been used to correlate melting points for different IL classes,24-26 but to our knowledge, it has not been applied to the analysis of γ∞i values of solutes in ILs. Analysis of γ∞i values of solutes in ILs has, however, been studied using the COSMORS approach.27 The subject of dilute solutes in ILs has also been studied using classical simulation techniques to determine solute-solvent associations,28 excess chemical potentials,29 and Henry’s constants.30 The goal of this work is to apply the QSPR method to the analysis of γ∞i values for various solutes in ILs. The premise of the QSPR method is that chemical structure completely determines the physical properties of a given compound. If a property of interest, in this case γ∞i , is known for several compounds, it is possible to construct a quantitative relationship between this property and molecular structure, which can then be used to predict this property for many other compounds. As noted above, the QSPR method has been used successfully to correlate γ∞i values for solutes in water and to correlate melting points for ILs. In addition, the QSPR method has been applied to the prediction of retention times for gas chromatography.31 This is important because a popular method for measuring γ∞i for solutes in lowvolatility conventional solvents or in ILs involves passing the solutes through a GC where the stationary phase is the low-volatility conventional solvent or the IL. The rest of the paper is organized as follows: First, a discussion of the methods used to prepare data and create QSPR correlations is given. Following this is a presentation of results, including the important descriptors used and correlations for the ILs. Next, the predictive uses of the correlations are examined, and the physical importance of the descriptors is considered. Finally, conclusions are presented. 2. Methodology The goal of the QSPR method is to create a quantitative relationship between a property of interest and molecular structure and then use this relationship in a predictive capacity. Constructing a QSPR correlation requires a training set of data for which the property of interest is already known so that a relationship between structure and property can be created. One key difficulty in creating this relationship is finding a way to quantify structure. This is accomplished by encoding structural features in descriptors. Numerous descriptors have been proposed to capture the many different aspects of structure. Some of these descriptors are properties themselves that

can be measured, such as octanol-water partition coefficients and dipole moments. However, the vast majority of descriptors are quantities calculated from knowledge of the physical and electronic structure of the molecule. This differs from the LSER approach,21-23 where the descriptors are a small number of experimentally determined quantities. The advantage of the QSPR approach is that a wide range of descriptors can be computed for any compound. Topological descriptors, for example, take as input the molecular formula and connectivity and arrive at a quantitative measure of features such as branching, molecular size, and shape. To quantify more chemically important features, other descriptors are available that encode aspects of the electronic structure of compounds. Another important class of descriptors yields information on the threedimensional structure of the molecule. Many descriptors combine different classes, such as ones that analyze the three-dimensional nature of the charge distribution. For a thorough explanation of molecular descriptors, several good references32,33 are available. To create a QSPR correlation, first, a pool of descriptors is chosen based on the property to be correlated, and descriptors are calculated for each compound in the training set. Because a large number of descriptors can be calculated, methods are needed to select the most important ones, which are those that quantify structural aspects that most affect the property of interest. For this purpose, statistical methods are used to explore the descriptor space and select the most important descriptors. Many of these methods combine the tasks of descriptor selection and correlation development. A QSPR correlation created in this manner gives two major results: (1) The correlation produced should be able to predict the property of interest for compounds outside the training set, especially those structurally similar to training-set compounds. (2) Of the initial descriptor pool, the final descriptors chosen should be most relevant to the system. Therefore, analysis of which structural aspects are encoded by these descriptors provides insight into which features most affect the given property. Data for this study were taken from a series of papers by Heintz et al.8-10 that present values of γ∞i for a set of 38 solutes in the ionic liquids 1-butyl-4-methylpyridinium tetrafluoroborate ([bmpyr][BF4]), 1-methyl-3-ethylimidazolium bis(trifluoromethylsulfonyl)amide ([emim][Tf2N]), and 1,2-dimethyl-3-ethyl-imidazolium bis(trifluoromethylsulfonyl)amide ([emmim][Tf 2N]). Values of γ∞i were measured at four different temperatures, which enabled the authors to determine the partial molar excess enthalpy at infinite-dilution, HE,∞ i , for each solute. In addition, a paper by Krummen et al.11 includes values of γ∞i at several temperatures in [emim][Tf2N] for a number of solutes not included in the above references; these data were used for validation purposes. The training set used for this study consisted of the solutes used by Heintz et al.,8-10 except for a representative sample of seven solutes left out for validation purposes. The solutes used in this study are listed in Table 1, along with experimental and predicted values of ln γ∞i at 298 K for each IL. All solutes (including those used for validation) were prepared by first building the molecules using Cerius2 software.34 Molecularmechanics-based energy minimization methods using the universal force field35 were used to initially optimize geometry. Next, MOPAC36 was used with the PM3

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1041 Table 1. Experimental and Predicted Values of ln γ∞i for the 38 Solute Compounds Used in This Study ln γ∞i at 298 K [bmpyr][BF4]

a

[emim][Tf2N]

[emmim][Tf2N]

solute i

expt8,9

eq 11

expt10

eq 12

expt10

eq 13

hexane heptane octanea nonane decane cyclohexane 2,2,4-trimethylpentane cyclohexene 1-methylcyclohexene styrene R-methylstyrene benzene toluene ethylbenzene o-xylenea m-xylene p-xylene isopropylbenzenea tert-butylbenzene methanol ethanol 1-propanola 1-butanol 1-pentanol 2-propanol tert-butanola sec-butanol tert-pentanol cyclohexanol 1-hexanol acetonitrile acetone ethyl acetatea methyl tert-amyl ether methyl tert-butyl ether dichloromethane trichloromethanea tetrachloromethane

4.1542 4.5390 4.9628 5.3850 5.8406 3.4595 4.6812 2.5802 3.0350 0.6206 0.8286 0.4886 0.9555 1.5686 1.2947 1.4929 1.3962 2.0757 2.4159 0.1823 0.6780 1.0296 1.4255 1.7174 0.9933 1.1184 1.2726 1.3324 1.3863 2.0015 -0.5293 -0.1031 0.9933 2.5104 2.0334 -0.3052 -0.3783 1.2920

4.0070 4.4834 4.9262 5.3557 5.8901 3.7691 4.1269 2.9855 3.4485 0.5430 1.1216 0.4322 1.0502 1.4667 1.6931 1.7380 1.7243 1.6094 1.8206 -0.0055 0.3958 0.8831 1.3012 1.7391 0.6847 0.8350 1.3032 1.4321 1.9535 2.1853 0.1670 -0.2260 0.1555 1.7937 1.3119 0.2397 -0.1397 1.0907

3.2995 3.7448 4.1790 4.6444 5.1648 2.7408 3.6864 2.0844 2.5726 0.5008 0.8587 0.1570 0.5423 1.0543 0.8629 1.0043 0.9858 1.4563 1.6901 0.2311 0.5247 0.8416 1.2060 1.5994 0.7747 0.7419 1.0006 0.8838 1.2384 1.8610 -0.8119 -0.9390 -0.1427 1.3533 0.8879 -0.0998 -0.0608 1.1725

3.2071 3.6774 4.1227 4.5581 5.0716 2.9360 3.3604 2.2395 2.6973 0.2878 0.8299 0.0362 0.6461 1.0688 1.2771 1.3092 1.2984 1.2377 1.4467 -0.1872 0.2000 0.6955 1.1223 1.5639 0.5107 0.6744 1.1040 1.2518 1.7424 2.0117 -0.4295 -0.7954 -0.3562 1.1521 0.6607 -0.1162 -0.2621 1.1515

3.3069 3.7160 4.1239 4.5664 5.0239 2.7973 3.6558 2.1102 2.5878 0.3853 0.6627 0.0862 0.4947 1.0543 0.7839 0.9670 0.9478 1.5019 1.7596 0.5008 0.8329 1.1442 1.4974 1.9081 1.0578 1.0080 1.2669 1.1632 1.5173 2.0412 -0.7787 -0.7529 0.0677 1.5748 1.0886 -0.0672 -0.0672 1.2528

3.2130 3.6644 4.0912 4.5083 5.0021 2.9552 3.3578 2.2815 2.7209 0.2497 0.7703 -0.0075 0.6001 1.0025 1.2303 1.2607 1.2498 1.1620 1.3621 0.1368 0.5090 0.9836 1.3923 1.8155 0.8055 0.9616 1.3761 1.5166 1.9890 2.2449 -0.2876 -0.6402 -0.2228 1.2320 0.7614 -0.0029 -0.1581 1.1854

Compounds left out of training set and later used for validation.

semiempirical Hamiltonian37,38 to further optimize geometry and assign partial charges based on a fit to the electrostatic potential. Higher-level quantum calculations were not deemed necessary for correlative work of this type. Finally, all descriptors available were calculated using the QSAR module available in Cerius2. This module allows for calculation of a large number of descriptors based on the structures described above and provides several statistical methods for selecting and correlating descriptors. Initial data analysis was done for the solutes in the ILs at 298 K. Correlations for ln γ∞i at 298 K were created for each IL using the genetic function approximation (GFA)39 to search descriptor space and select the best descriptors. The GFA works by creating an initial set of random correlations and using evolution operators such as crossover and mutation to “evolve” the correlations. A scoring function that favors correlations using fewer descriptors is used to assess the “fitness” of the correlations and guide the evolution. After a fixed number of cycles, the final set of correlations is expected to be the best possible set. Because the GFA method produces many correlations, the descriptors selected varied between the different correlations and between the different ILs. However, it was desired that a consistent descriptor set be used to create correlations for all three of the ILs considered to facilitate comparison of the correlations. To do this, the top 10 correlations for each IL were analyzed, and the frequency of occurrence of each descriptor was tabu-

lated. Two descriptors appeared in all of the top 10 correlations and were retained. In addition, when two or more descriptors were found to be highly correlated, only one was retained. In this way, the descriptor set was pared down to the four most significant descriptors. This four-descriptor set was able to correlate ln γ∞i at 298 K with a best R2 of 0.975. This compares favorably with the R2 of 0.99 obtained by allowing different descriptors to be used for the different ILs. This drop was deemed acceptable considering the benefits gained by using a small, consistent descriptor set. After a consistent descriptor set able to accurately correlate ln γ∞i at 298 K had been successfully identified, it was desired to capture the effects of temperature on ln γ∞i . This was done by first creating correlations of ln γ∞i with the four descriptors for each IL at each of the four different temperatures used (from 313 to 343 K, in 10 K intervals). Some solutes in the data set were recorded over a higher temperature range (either 333363 K or 323-354 K); these solutes were left out of the correlations and used later for validation. To create a single temperature-dependent correlation for each IL, the coefficients for the individual descriptors were related to temperature using the following equation

Ci(T) ) ai +

bi T

(2)

where Ci is the coefficient for descriptor i and the

1042 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 Table 2. Values of the Four Descriptors Used in the Consistent Descriptor Set solute

[log KOW] [Hbonds]

hexane 3.1088 heptane 3.5650 octane 4.0212 nonane 4.4774 decane 4.9336 cyclohexane 2.7372 2,2,4-trimethylpentane 3.3624 cyclohexene 2.2926 1-methylcyclohexene 2.7390 styrene 2.3817 R-methylstyrene 2.8281 benzene 1.8300 toluene 2.3162 ethylbenzene 2.7724 o-xylene 2.8024 m-xylene 2.8024 p-xylene 2.8024 isopropylbenzene 3.0242 tert-butylbenzene 3.2304 methanol -0.3580 ethanol -0.0092 1-propanol 0.5145 1-butanol 0.9707 1-pentanol 1.4269 2-propanol 0.3683 tert-butanol 0.5733 sec-butanol 0.8920 tert-pentanol 1.0970 cyclohexanol 1.5003 1-hexanol 1.8831 acetonitrile 0.0446 acetone -0.2440 ethyl acetate 0.3699 methyl tert-amyl ether 1.5055 methyl tert-butyl ether 0.9818 dichloromethane 1.0729 trichloromethane 1.6172 tetrachloromethane 3.5846

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

[WNSA1] (Å4) [SaaCH] 4.9742 5.3619 6.2783 7.4038 6.8759 2.2904 7.4771 6.9530 7.3819 30.1325 28.5189 18.9986 20.6011 21.6071 22.0922 21.2273 21.3894 23.6095 23.7949 7.9221 7.6328 9.0168 10.3239 11.3176 9.6142 10.7946 8.9283 10.4451 9.2052 12.1800 12.4816 13.6829 18.3003 12.1236 10.6521 29.1517 44.5706 59.2412

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 10.0288 10.1579 12.0000 10.2616 10.4552 8.3565 8.4491 8.4815 10.5197 10.5520 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

variables ai and bi are the regression variables. This particular functional form was chosen on the basis of the relation between ln γ∞i and T as specified by the Gibbs-Helmholtz equation (see eq 4 below). By using the definition of the coefficients given in eq 2, it is possible to create the following temperaturedependent correlation

( ) ∑( )

ln γ∞j ) ao +

bo T

+

ai +

i

bi T

Xi,j

( )

HE,∞ )R j

∂ ln

∂(1/T)

) R(b0 +

∑i biXi,j)

I ) [(2/N)2δv + 1]/δ

(4)

where R represents the gas constant and all other terms have been previously defined. 3. Results Descriptor Set. As described above, the correlations are composed of the four descriptors most commonly

(5)

where N is the principal quantum number, δv is the number of valence electrons, and δ is the number of σ electrons. δv is given by

δv ) σ + π + n - h

(6)

with σ representing the number of σ electrons, π representing the number of π electrons, n representing the number of lone-pair electrons, and h representing the number of hydrogen atoms bonded to the atom. δ is defined as

δ)σ-h (3)

where ai and bi are the regression variables described above (with a0 and b0 belonging to the constant of regression, or intercept) and Xi,j represents the value of descriptor i for species j. Once such a correlation is created, the Gibbs-Helmholtz equation can be used to calculate predicted values of the partial molar excess enthalpy at infinite dilution, HE,∞ j , as

γ∞j

used. For reference, the values of the four descriptors for all 38 compounds investigated in this study are given in Table 2. The first descriptor, used in all 10 top correlations, was the value of the logarithm of the octanol-water partition coefficient, represented hereafter as [log KOW]. This descriptor was estimated using the atom-based group contribution approach of Ghose et al.40 In this method, the value of the partition coefficient is simply the sum of the contributions due to each atom. Atom classes are defined on the basis of both the type of atom (i.e., H, C, etc.) and the local environment. For example, the hydrogen atoms in dichloromethane are bonded to a carbon with two halogens attached. These hydrogens contribute differently than the hydrogen atom of trichloromethane, which is bonded to a carbon atom with three halogens attached. Another example is that the carbon atoms of cyclohexane contribute differently than the aromatic carbon atoms of benzene. The complete list of atom types, along with their contributions, is given in the aforementioned reference.40 The physical significance of [log KOW] is based on the underlying physical factors that determine it, namely, the polarity and hydrogenbonding ability of a solute. The second descriptor, also used in all 10 top correlations, was the sum of the electrotopological state41 values for carbon atoms bonded to one hydrogen and participating in two aromatic bonds, represented below as [SaaCH]. The electrotopological state, also called the E-state, for an atom is determined by first assigning an intrinsic state I, defined as

(7)

where σ and h retain the above definitions. This definition of I assigns a high intrinsic state value to more electronegative atoms with few bonds (such as a carbonyl oxygen). The next step in determining the E-state value is to assess how neighboring atoms perturb the intrinsic state of the selected atom. The perturbation term of the intrinsic state of atom i due to atom j, ∆Iij, is defined as

∆Iij ) (Ii - Ij)/(dij + 1)2

(8)

where Ii and Ij are the intrinsic states of atoms i and j, respectively, and dij is the number of bonds separating the two atoms. Finally, the E-state value for atom i, Si, is defined as

Si ) Ii +

∑j ∆Iij

(9)

This definition of the E-state describes both the electrostatic and steric nature of the atoms by accounting

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1043

for the valence state and local environment. In this work, only the E-states of the carbon atoms bonded to a hydrogen and participating in two aromatic bonds are considered. The descriptor [SaaCH] is the sum of the E-state values for such carbons, meaning that this descriptor essentially indicates the presence of aromatic rings. Because the training-set data contain only benzenebased aromatics, the values for the [SaaCH] descriptor are similar for all aromatic compounds, although the ability of the E-state descriptors to differentiate between isomers can be seen by comparing the [SaaCH] values for the xylene series. The next descriptor found to be important in several of the 10 top correlations was the number of hydrogenbond donors present for a solute, referred to below as [Hbonds]. In the training set used, only alcohols have a nonzero value for this descriptor, which indicates that the physical importance of this descriptor for our correlation is likely related to the relative strength of hydrogen-bond association in the pure solute (the alcohol) as compared to solute-solvent (alcohol-IL) association. To a degree, hydrogen bonding is encoded in the [log KOW] descriptor given that hydrogen-bonddonating ability is important in solvation with water. However, the correlation between the [log KOW] and [Hbonds] descriptors is low, indicating that the inclusion of [Hbonds] contributes significant information. In addition, it will be shown below that explicit inclusion of this descriptor is necessary to capture the temperature dependence. The final descriptor found with some frequency was the surface-weighted partial negative surface area, [WNSA1]42

SASA [WNSA1] )

∑SAa

-

a-

1000

(10)

In eq 10, SASA stands for the solvent-accessible surface area as traced out by a sphere of radius 1.5 Å, which is meant to approximate the surface accessible to a water molecule. SAa- represents the surface area contribution of each negative atom. The summation includes all atoms with a negative partial charge. Note that [WNSA1] has units of Å4 and quantifies the magnitude of the negatively charged surface area weighted by the total surface area, which means that larger values indicate a larger negatively charged surface. It is physically reasonable to expect surface charge to affect solute-solvent interactions in a highly charged medium such as an IL. 1-Butyl-4-methylpyridinium Tetrafluoroborate Data Set. Using the four-descriptor set, the following correlation was obtained for ln γ∞i at 298 K in the IL [bmpyr][BF4]

ln γ∞i ) 0.908 97 + 1.097 94[log KOW] 0.019 395[Hbonds] 0.063 367[WNSA1] - 0.106 841[SaaCH] (11) The resulting correlation coefficient obtained was R2 ) 0.952. A plot of predicted versus experimental values of ln γ∞i is shown in Figure 1 for data points in the training set and for data points left out of the training set. The consistency of error between compounds both

Figure 1. Predicted vs experimental values of ln γ∞i for solutes in the ionic liquid [bmpyr][BF4] with R2 ) 0.952.

belonging to and left out of the initial training set is a good indicator of the predictive ability of this correlation. Several things can be noted from this correlation. First, the correlation says that an increased value of the partition coefficient, [log KOW], increases the value of ln γ∞i , which indicates decreased solute-solvent interactions. This agrees with the expectation that increasingly apolar compounds should be less soluble in polar ionic liquids. The correlation also indicates that the presence of aromaticity, described by [SaaCH], decreases the value of ln γ∞i , indicating a favorable interaction between aromatic solutes and the ILs. Finally, negative surface charge and hydrogen-bond-donating ability play a role in determining ln γ∞i . Both of these effects can be attributed to the energetic differences between pure solute interactions and solute-solvent interactions. For example, a large negative surface area, as indicated by a large value of [WNSA1], should lead to unfavorable pure solute interactions due to negative surface charges interacting with one another. However, when a solute molecule is taken from the pure solute and placed into the ionic solvent, it finds a more favorable environment. This preference for the solvent environment is reflected in the negative coefficient for the [WNSA1] descriptor, which indicates that a large negative surface area lowers the value of ln γ∞i . Similarly, considering hydrogen-bond-donating ability, it is important to recall that all training-set molecules with hydrogen-bond donors are alcohols, which can form hydrogen-bond networks. Breaking these networks by removing a solute molecule from pure solute is energetically unfavorable. However, the small negative coefficient for the hydrogen-bond descriptor indicates that the solute is able to associate with the solvent more favorably than with itself. More specifically, it likely interacts with the anion more favorably, because the anion acts as a Lewis base.43-45 1-Methyl-3-Ethylimidazolium Bis(trifluoromethylsulfonyl) Amide. For the IL [emim][Tf2N], the correlation obtained for ln γ∞i at 298 K using the fourdescriptor set was

ln γ∞i ) 0.112 755 + 1.071[log KOW] + 0.457 946[Hbonds] 0.047 271[WNSA1] - 0.094 863[SaaCH] (12) The resulting correlation coefficient was R2 ) 0.975. Figure 2 shows a plot of predicted versus experimental

1044 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004

Figure 2. Predicted vs experimental values of ln γ∞i for solutes in the ionic liquid [emim][Tf2N] with R2 ) 0.975.

Figure 3. Predicted vs experimental values of ln γ∞i for solutes in the ionic liquid [emmim][ Tf2N] with R2 ) 0.970.

ln γ∞i values. In Figure 2, data left out of the initial training set include compounds taken from Krumen et al.11 The fact that the correlation reproduces all data points equally well again shows the predictive ability of the correlation. In analyzing the descriptors and their coefficients, it is seen that there are only two major differences between eqs 11 and 12. First, the intercept of the correlation is considerably smaller here. Even though the intercept is not physically meaningful, it does indicate a base value, and its drop shows that solutes should generally have more favorable interactions with [emim][Tf2N] than [bmpyr][BF4]. The other main difference between the two correlations is that, in eq 12, the hydrogen-bond-donor coefficient is positive and fairly large. Using the same argument as before, this indicates that hydrogen-bonding solutes interact more favorably with themselves than with the [Tf2N] anion. This agrees with experimental work that shows that the [Tf2N] anion is a weaker Lewis base than the [BF4] anion.45 A more complete discussion of this effect is given below. The remaining coefficients retain the same signs and essentially the same order of magnitude as in the previous case. 1,2-Methyl-3-Ethylimidazolium Bis(trifluoromethylsulfonyl) Amide. The correlation for ln γ∞i at 298 K in the IL [emmim][Tf2N] is given as

Table 3. Regressions Parametersa for the Temperature-Dependent Descriptor Coefficients Given by Eq 2 along with the Correlation Coefficient for the Regression

ln γ∞i ) 0.245 454 + 1.028 78[log KOW] + 0.627 051[Hbonds] 0.046 383[WNSA1] - 0.104 532[SaaCH] (13) The correlation coefficient is R2 ) 0.970. A comparison of predicted ln γ∞i values against experimental values is shown in Figure 3. Again, compounds from outside the training set are included, and the correlation works equally well for these points. The only major differences between this correlation and that for the [emim] counterpart are that the intercept and the coefficient for the [Hbonds] descriptor are slightly higher. The reason for the change in hydrogen-bond-donor effect is due to the relatively acidic hydrogen on the C2 carbon being replaced with a methyl group. Otherwise, the signs and values for the coefficients remain largely the same. Temperature Dependence of Correlations. The temperature dependence of the above correlations, determined over the range 313-343 K, is shown in Table 3, where the regressions parameters a and b, as defined in eq 2, are listed for all three ILs, along with

IL

a

b (K)

R2

235.5 64.68 226.6

0.9799 0.8290 0.8982

[bmpyr][BF4] [emim][Tf2N] [emmim][Tf2N]

intercept 0.5023 -0.1524 -0.5214

[bmpyr][BF4] [emim][Tf2N] [emmim][Tf2N]

[log KOW] 0.6026 0.3106 0.3053

157.9 235.8 224.2

0.9766 0.9996 0.8909

[bmpyr][BF4] [emim][Tf2N] [emmim][Tf2N]

[Hbonds] -2.662 -2.481 -2.342

855.8 929.0 910.4

0.9998 0.9997 0.9944

[bmpyr][BF4] [emim][Tf2N] [emmim][Tf2N]

[WNSA1] -0.005 748 -0.005 355 -0.002 201

-17.13 -12.56 -13.50

0.9998 0.9958 0.8141

[bmpyr][BF4] [emim][Tf2N] [emmim][Tf2N]

[SaaCH] -0.021 98 0.025 82 0.043 58

-24.84 -36.80 -44.90

0.9861 0.9984 0.9266

a

Parameters are given for each descriptor in each ionic liquid.

the correlation coefficient for the linear regression between the coefficients and 1/T. The table shows that these correlation coefficients are typically around R2 ) 0.9, but can be as low as 0.81. The b parameters indicate the importance of each descriptor in determining the temperature dependence. Judging from this table, the most important descriptor for all ILs is the [Hbonds] descriptor. As hydrogen bonding is known to exhibit a strong temperature dependence, this result is physically expected. The next most important parameter is the value of [log KOW], followed by [SaaCH] and [WNSA1], which are of roughly equal importance. The ability to predict HE,∞ using eq 4 is an indication i of how well the temperature dependence is captured. Figures 4-6 show predicted versus experimental values for all three ILs. The correlations for HE,∞ are of HE,∞ i i less accurate than those for ln γ∞i , as shown by the overall drop in R2 from around 0.97 for ln γ∞i at 298 K to around 0.85 for HE,∞ i . However, the correlations still provide very good agreement with experiment, and some drop is expected given that this is a derivative property. In addition, the value of R2 for HE,∞ jumps to around i

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1045

Figure 4. Predicted vs experimental values of HE,∞ for solutes in i the ionic liquid [bmpyr][BF4] with R2 ) 0.835 (R2 ) 0.923 with extreme outlier removed).

Figure 5. Predicted vs experimental values of HE,∞ for solutes in i the ionic liquid [emim][Tf2N] with R2 ) 0.860 (R2 ) 0.906 with extreme outlier removed).

Figure 7. Values of ln γ∞i vs T -1 for solutes in the ionic liquid [emim][Tf2N]. Points represent experimental data, and lines represent predicted values of ln γ∞i as follows: (b, s) ethyl acetate, ((, - - -) n-propanol, (2, s s s) isopropylbenzene, (1, s ‚ ‚ s ‚ ‚ s ) cyclohexane.

values), which indicates that it is an negative HE,∞ i unusual solute. The predictive abilities of the temperature-dependent correlations can be further analyzed by considering predictions of ln γ∞i for varying temperatures. Figure 7 shows a plot of ln γ∞i versus temperature for solutes left out of the training set for the IL [emim][Tf2N]. The plot shows the excellent agreement that can be obtained for predicting ln γ∞i over a range of temperatures. These predictions are not quite as good, though, as predictions made using the constant-temperature correlations. Typically, the correlation coefficient for predictions based on the temperature-dependent correlations is around 0.96, instead of 0.97 for the temperatureindependent correlations. The experimental and calculated values of ln γ∞i for all of the solutes in all three ILs at temperatures other than 298 K are given in the Supporting Information. Note that the calculated values were obtained from the temperature-dependent correlations. 4. Discussion

Figure 6. Predicted vs experimental values of HE,∞ for solutes in i the ionic liquid [emmim][Tf2N] with R2 ) 0.865 (R2 ) 0.925 with extreme outlier removed).

0.90 if the extreme outlier present for all three correlations, R-methylstyrene, is removed from the data set. There is no immediately apparent reason why the correlations predict HE,∞ so poorly for R-methylstyrene. i It is possible that there are solute-solvent interactions that are not taken into account in the consistent descriptor set. Analysis of the experimental data shows that R-methylstyrene is the only solute with a value of that is both negative and extremely large (one HE,∞ i order of magnitude larger than for other solutes with

Using Correlations for Prediction. The above results show that the QSPR method can be used to correlate ln γ∞i accurately, as well as its temperature dependence, in different ILs using a small, physically meaningful, consistent descriptor set. This is very useful in gaining physical understanding of how structure influences activity. It is also useful in predicting values of ln γ∞i for unknown compounds. This is especially important in the case of solutes that are expensive or hazardous, where experimental determination might be infeasible. As an example of the predictive use of these correlations, we estimate ln γ∞i for several solutes in these ILs at 298 K. To our knowledge, experimental values of ln γ∞i are not available for these solutes. These solutes are listed in Table 4, along with predictions of ln γ∞i obtained using the constant-temperature correlations from eqs 11-13. Many of the solutes are variations on training-set compounds, which allows for an examination of the effects of changing structure. Also, the pair of propane and propylene is an example of predicting how relatively similar solutes interact with different ILs, which could be important for gas separa-

1046 Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 Table 4. Predicted Values of ln γ∞i at 298 K for Selected Compounds ln γ∞i at 298 K solute i

[bmpyr][BF4] [emim][Tf2N] [emmim][Tf2N]

acetic anhydride propenal methoxybenzene chlorobenzene dipropyl ether divinyl ether ethane-1,2-diol 3-methylphenol methylcyclohexane phenol n-propyl acetate propane-1,2-diol propane propylene acrylonitrile

-1.2126 0.1600 0.2241 1.8913 2.3380 -0.0889 -1.0291 0.7614 3.9615 0.0630 0.4393 -0.6706 2.6064 1.8201 0.3310

-1.5190 -0.3431 -0.0880 1.3308 1.6312 -0.5765 -0.6143 0.8829 3.1430 0.2157 -0.0124 -0.2518 1.8175 1.1325 -0.1583

-1.3513 -0.2108 -0.1025 1.2774 1.6957 -0.4357 -0.0927 1.0516 3.1527 0.3899 0.1029 0.2547 1.8797 1.2162 -0.0345

Table 5. Comparison of Predicted and Experimental Henry’s Coefficients for CO2 in Two Ionic Liquids at Different Temperatures T ) 283 K

T ) 298 K

Hpred (bar) Hexpt (bar) Hpred (bar) Hexpt (bar) [emim][Tf2N] [emmim][Tf2N]

17.4 21.4

25.3 28.6

25.6 30.7

35.6 39.6

tions. A good example of predicting ln γ∞i for a hazardous compound is acrylonitrile. According to the table, the indication is that acrylonitrile should be more favorably solvated by the imidazolium ILs than by [bmpyr][BF4]. These predications include compounds that are significantly different from the training-set compounds. For instance, values for two diols are given in Table 4. For these compounds, the value of [Hbonds] is 2, although the training set contains only alcohols with a single hydroxy group. Although the predictions for these compounds do not appear unreasonable, the error is likely to be greater than for compounds that are more similar to the training-set molecules. Although none are shown in the table, this would also be true for polyaromatic compounds or aromatics containing heteroatoms. Another way to test the predictive capability of this method is to use the correlations to predict γ∞i values and convert these to Henry’s law constants using vapor pressure data as specified in eq 1. This was done for CO2 because Henry’s law constant data for this compound in several ILs are known and because CO2 differs dramatically from the training-set compounds. Reported in Table 5 are Henry’s law constants for CO2 in the imidazolium-based ILs predicted using the temperaturedependent correlations for two different temperatures. For comparison, the experimental values are also listed.46 For both ILs, the predicted values agree well with the experimental values, especially considering that Henry’s law constants typically vary by orders of magnitude. In addition, the correct temperature dependence is predicted. Values for the pyridinium IL are not included because experimental data are not available for comparison. Phyiscal Significance of Correlations. The power of this method is that the descriptors have physical significance, and the signs and magnitudes of the associated coefficients indicate the relative importance of the corresponding properties on the solute-solvent interactions for a particular ionic liquid. In the previous discussion, the meaning of the descriptors was ex-

plained, and their effects on ln γ∞i were analyzed for each ionic liquid. Here, we use the constant-temperature correlations (eqs 11-13) to compare the solvation properties of the three ionic liquids. The first feature that is apparent is that the partition coefficient descriptor, [log KOW], is the most important property in determining ln γ∞i for all three ILs. Moreover, the coefficient for this descriptor is essentially the same in eqs 11-13, indicating that [log KOW] is of equal importance for all three ILs. By examining the values of the descriptors in Table 2, it is also clear that γ∞i can be almost completely predicted for saturated nonpolar solutes with this descriptor alone, and that this descriptor is extremely important for all other compounds as well. This is an important finding, as experimental octanol-water partition coefficients are available for a wide range of compounds and thus the relative affinities of many solutes for ionic liquids can be readily estimated. Therefore, to first order, the IL solvents behave like conventional organic solvents, where the degree of hydophobicity is a key predictor for γ∞i . The difference with ILs is that interactions can be further tuned by changing the nature of the cation and anion independently. These effects are captured in the other three descriptors. As discussed earlier, hydrogen bonding between the solute and IL is captured to some extent by [log KOW]. Interestingly, if [Hbonds] is not used, ln γ∞i is accurately correlated for all three ILs at 298 K. There is, however, a complete inability to describe temperature dependence when [Hbonds] is discarded. This is good evidence that the [Hbonds] descriptor is important for capturing subtle energetic interactions due to hydrogen bonds, which show up in the temperature dependence of ln γ∞i . There is experimental evidence that hydrogen bonding with the anion is present in these systems.44 More generally, it appears that Lewis acid-base interactions between the solute and the anion are of primary importance.43 From the correlations, it can be seen that, when the [Tf2N] anion replaces the [BF4] anion, the coefficient for the hydrogen-bond descriptor goes from slightly negatively to largely positive. This suggests that the [BF4] anion is a stronger Lewis base than the [Tf2N] anion. This conclusion is in agreement with solvatochromic probe results,45 but it differs somewhat from the results of FTIR studies with water,44 which show similar interactions between water and both anions. On the other hand, it has recently been shown that ILs containing [BF4] and [PF6] anions readily degrade over relatively short times, even when the samples are kept reasonably dry.47 Hydrolysis would produce fluoride anions, which are expected to be an even stronger Lewis base than either [BF4] or [Tf2N] anions. This might explain why the experimental measurements of ln γ∞i , and thus the correlations, indicate that [BF4] is a stronger hydrogen-bond acceptor than [Tf2N]. This issue cannot be resolved by the type of model used here, which merely correlates experimental data. Nonetheless, the results indicate that hydrogen bonding between solutes and ILs is clearly important. Finally, in considering the [WNSA1] and [SaaCH] descriptors, it is seen that their coefficients show almost no change for the three ILs. As for the partition coefficient descriptor, this indicates that the interactions captured by these descriptors change very little between the three ILs. Because the [WNSA1] descriptor quanti-

Ind. Eng. Chem. Res., Vol. 43, No. 4, 2004 1047

fies negative surface charge characteristics, it is understandable why changing IL structure should not affect the importance of this descriptor. The fact that the solvent is composed of charged species is the essential feature for electrostatic interactions. It is reasonable to expect that the importance of this descriptor will be similar for all ILs. In the case of [SaaCH], which encodes the presence of aromaticity, the relatively constant values of the coefficient for the three different correlations is likely due to the fact that all three IL cations are based on an aromatic ring. It is expected that, if cations were employed that had no aromatic character, the coefficient would likely change, becoming less important. Thus, we believe that the opportunity to tailor ILs with respect to this descriptor is available. Overall, analysis of the descriptors and their coefficients leads to significant insight into the solvating abilities of ILs. A key feature of ILs that makes them so potentially useful is their ability to solvate a wide range of compounds and the possibility of tuning this solvating ability. The above analysis shows that, for all three ILs considered here, the main contribution to solute-solvent interactions is the octanol-water partition coefficient. However, the Lewis basicity of the anion plays an important role in the solvation of hydrogenbond-donating solutes. Also, the presence of aromaticity in the solute is a key feature for the three ILs studied here. 5. Conclusions The results of applying the QSPR method to predicting values of ln γ∞i demonstrate a very good ability to correlate and predict solute-solvent interactions for various solutes in three different IL solvents. Correlations were created for all three ILs using a consistent and physically meaningful descriptor set composed of four descriptors, and temperature dependence can be incorporated into these correlations. Physical analysis of these descriptors shows the relative importance of hydrophobicity, as indicated by the octanol-water partition coefficient, hydrogen bonding, solute aromaticity, and charge distribution on solute-solvent interactions. The physical insights obtained from the analysis provide valuable information for future efforts at tailoring ILs for different solvent applications. The method was also shown to be predictive, thus demonstrating that QSPR is a powerful tool for extending experimental activity coefficient data. Acknowledgment Funding through the National Science Foundation (Grant CTS99-87627) and a fellowship from the Arthur J. Schmitt foundation is gratefully acknowledged. Special thanks are given to Dr. Sudhir Aki for initial discussions on using QSPR for correlating infinitedilution activity coefficients in ionic liquids. Supporting Information Available: Complete listing of experimental and predicted infinite-dilution activity coefficients for each solute at 313-343 K in all three ionic liquids. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Welton, T. Room-temperature ionic liquids. Solvents for synthesis and catalysis. Chem. Rev. 1999, 99, 2071-2083.

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Received for review September 29, 2003 Revised manuscript received December 10, 2003 Accepted December 18, 2003 IE034152P