Vapor–Liquid Coexistence and Critical Behavior of Ionic Liquids via

LETTER pubs.acs.org/JPCL

Vapor
Liquid Coexistence and Critical Behavior of Ionic Liquids via Molecular Simulations Neeraj Rai and Edward J. Maginn* Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556, United States

bS Supporting Information ABSTRACT: Vapor
liquid coexistence curves and critical points are of great practical and fundamental importance. Our understanding of these phenomena is well-developed for most fluids but is severely lacking for ionic liquids, a class of salts that are liquid near ambient temperatures. Thermal stability limitations virtually eliminate direct experimental determination of these properties. In this Letter, we report the first vapor
liquid phase diagrams and critical points for ionic liquids obtained in silico with an atomistic force field. We show that within a homologous series of imidazolium-based ionic liquids, the critical temperature, critical density, critical pressure, boiling point, and enthalpy of vaporization all decrease with increasing length of the cation alkyl chain, while the saturation pressure increases with chain length. These trends are opposite to what is observed for alkanes and other nonionic polar compounds such as alcohols. In the vapor phase, we find that ions are distributed across clusters of different sizes with neutral ion pairs being the predominant aggregation state. SECTION: Statistical Mechanics, Thermodynamics, Medium Effects

S

ome salts, known as ionic liquids (ILs), are liquid near ambient conditions. This is in stark contrast with table salt, which remains crystalline up to about 800 °C. ILs have attracted much commercial and scientific attention due to their many favorable properties.1 ILs were considered to be nonvolatile liquids until recently when it was shown that certain aprotic ILs could be distilled without degradation.2,3 ILs are now known to have extremely low but nonzero vapor pressures.4 These and subsequent works5
7 have highlighted the importance of understanding the vapor
liquid equilibria (VLE) of IL systems. From a practical standpoint, VLE governs the performance of ILs when they are used as low-volatility solvents, lubricants, coatings, and separating agents. From a fundamental standpoint, VLE gives important information on the nature of intermolecular interactions present in the liquid and vapor phases. The conditions at the vapor
liquid critical point play a central role in the development of equations of state and corresponding states theories, which provide a unified framework for understanding thermodynamic properties of fluids.8
10 Hence, knowledge of critical points and VLE properties are key to advancing the application of ILs as well as achieving a fundamental understanding of these complex fluids. Not surprisingly, there has been much interest in this area in recent years. Unfortunately, thermal stability limitations prevent direct experimental determination of all but the exceptionally low pressure regions of IL vapor
liquid coexistence curves (VLCCs), leading some to state that the determination of these properties is “forbidden territory”.11 Most ILs will decompose before reaching r 2011 American Chemical Society

their critical point, but hypothetical critical points are still essential for the development of liquid-state theories of ILs. This led several groups to resort to empirical or semitheoretic means for estimating critical points of ILs,2,12,13 but results have been conflicting. Rebelo et al.2 and Weiss et al.12 employed the Guggenheim and E€otvos empirical relations, while Valderrama and Robles13 developed a group contribution method to estimate critical properties. In a recent report, Martin-Betancourt et al.14 employed a grossly simplified model of ionic liquids consisting of charged spheres and cylinders to compute critical points. Even with such a simple model, the authors could not compute VLCCs beyond a hypothetical chain length of 3.5 alkyl groups due to sampling difficulties.14 The above approaches not only predict widely varying critical temperatures (differing by up to 1000 K), but they also are inconsistent in the way critical properties depend on cation size. Moreover, none of these methods provide a complete set of vapor
liquid coexistence properties nor do they give molecular-level insight into the energetic factors that govern VLE of ILs. The aggregation state of ions in the vapor phase has also been debated extensively.11,15 Early on, it was speculated that the vapor phase consisted of individual ions.3 Depending on the analytical and/or theoretical technique employed, recent work has suggested that the vapor consists of neutral ion pairs,5,15
17 Received: April 18, 2011 Accepted: May 24, 2011 Published: May 24, 2011 1439

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Figure 1. Molecular structure of the ionic liquids under study.

neutral clusters of several ion pairs,18 or isolated ions.11,18 There have also been conflicting experimental reports of the way in which properties such as vapor pressure and enthalpy of vaporization vary with factors such as the size of the cation. Much of this experimental uncertainty is due to the fact that pressures are very low and/or temperatures are high, making measurements extremely difficult to conduct. Even trace impurities can cause large differences in measured properties. For this reason, it is advantageous to use molecular-based models to predict the VLE of ILs. Such models, which utilize atomistic potential functions, have been shown to reproduce condensedphase thermodynamic and transport properties of ionic liquids with a high degree of fidelity,19 but up until now, there have been no reports of calculated IL VLE or critical points. The most direct simulation method for studying VLE is Gibbs ensemble Monte Carlo (GEMC).20 The main drawback of GEMC is its reliance on particle exchanges between the vapor and the liquid phases to equilibrate the chemical potential (Figure S1, Supporting Information).21,22 Configurational bias Monte Carlo22 and other enhanced sampling techniques for ionic systems23 circumvent this problem and have enabled GEMC to be used to study systems such as long-chain alkanes21 and simple alkali halides.23 However, simulations of VLE of ILs have been intractable due to their long-range Coulombic interactions and complex molecular structure. Here, we report the results of GEMC simulations that predict the vapor
liquid phase behavior of a homologous series of four 1-alkyl-3-methylimidazolium tetrafluoroborate ([Cnmim][BF4]) ILs, with alkyl chain lengths of n = 1, 2, 4, and 6 (Figure 1). The simulations were made possible through the application of advanced techniques including configurational bias sampling methods,22,24,25 parallel computing strategies, and enhanced biasing schemes specifically designed for ionic systems23 (see the simulation details section in the Supporting Information). Because the accuracy of computed thermodynamic properties depends on the quality of the intermolecular potential used in the simulations, we chose a potential that yields excellent thermodynamic and transport properties of the condensed phase (Zhong, X. J. et al. unpublished results). This force field models the aromatic ring explicitly, while CHx groups in the alkyl side chain are modeled as united atoms. Additionally, it uses a scaled charge of 0.8|e| for the cation and anion (Zhong, X. J. et al. unpublished results). For computational efficiency, the aromatic ring and bonds were modeled as rigid as the flexibility of these degrees of freedom have a negligible effect on VLCCs.26 The computed VLCCs and critical points are shown in Figure 2A. Compared to nonionic compounds such as alkanes,21 the VLCCs have a high degree of asymmetry with a very steep vapor branch. Similar asymmetry is observed for alkali halides,23

Figure 2. Vapor
liquid equilibria of [Cnmim][BF4]. (A) VLCCs, (B) Clausius
Clapeyron plots, and (C) temperature dependence of ΔHvap. The black circles, cyan squares, orange diamonds, and magenta triangles represent GEMC simulation data for [C1mim], [C2mim], [C4mim], and [C6mim], respectively, while filled symbols show the corresponding critical points. (A) The filled green square, red diamond, and blue triangles show critical points obtained with a group contribution method13 for [C2mim], [C4mim], and [C6mim], respectively. The brown dashed and blue dashed
dotted lines show the critical temperature of [C4mim] using Guggenheim and E€otvos empirical relations, respectively.2 The solid black, dotted cyan, dashed orange, and dashed
dotted magenta lines represent regression fit (B) and a thirddegree polynomial fit (C) for [C1mim], [C2mim], [C4mim], and [C6mim], respectively. Error bars are smaller than the symbol size. All numerical data with uncertainties are provided in Supporting Information Tables S1
S4.

but their critical temperatures are approximately 2000 K higher than our predictions for ILs (Table 1).23 The high precision of our calculations allows us to quantify the effect of a single methylene group (CH2) on the critical properties. For these ILs, we find that the critical temperature (Tc) and critical density (Fc) decrease with increasing alkyl chain length (Table 1). The decrease in Tc is about 65 K in going from C2 to C6, that is, a 1440

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Table 1. Computed Thermophysical Properties of [Cnmim][BF4] Ionic Liquidsa

a

Cn

Tc (K)

Fc (g/cm3)

Pc (kPa)

Zc

Tb (K)

ΔHvap Tb (kJ/mol)

ΔSvap Tb (J/mol.K)

C1

13172

0.2192

4927

0.0381

10522

71.85

68.27

C2

12833

0.2072

4376

0.0391

10352

70.24

67.86

C4

12523

0.1812

3907

0.0471

10253

66.23

64.65

C6

12184

0.1604

3126

0.0491

10192

62.54

62.57

The subscripts are uncertainties in the last digit.

“methylene increment” of approximately
16 K. For comparison, the corresponding methylene increment is about þ50 and þ25 K for alkanes and alcohols, respectively.27 This shows that the methylene increment for Tc changes sign when going from nonpolar fluids to ILs. These results are remarkable because any “group additivity” method based on knowledge gained from VLE of traditional fluids will fail for ILs. Not surprisingly, the group contribution method developed by Valderrama et al.13 predicts an increase in Tc with increasing alkyl chain length. Additionally, their predicted critical temperatures are ∼500 K lower than our results13 and are comparable to that of water (Tc = 647 K),27 which has much weaker intermolecular interactions than ILs. In contrast, a primitive model of an IL consisting of a charged spherocylinder yields a Tc that is nearly 500 K higher than our estimate for [C2mim][BF4].14 Moreover, the primitive model predicts a methylene increment of nearly
250 K, which is unphysically large. This suggests that idealized models and group contribution methods have serious limitations in obtaining quantitative predictions for ILs due to their inability to adequately represent the detailed structure and interactions present in these systems. It is unclear whether a negative methylene increment for Tc will hold as the length of the cation alkyl chain increases beyond C6. When the chain length becomes very long (for example, greater than C10), it may be that the Coulombic screening due to the alkyl chain becomes saturated while at the same time the van der Waals interactions due the increasing chain length continue to increase the cohesive energy. Thus, it is conceivable that this trend of decreasing critical temperature with increasing chain length may reverse for certain values of n in [Cnmim]. Rebelo et al.2 extrapolated low-temperature experimental surface tension and density data to estimate the critical temperature of [C4mim][BF4]. Using the E€otvos model, they obtained an estimate of Tc = 1240 K, while the Guggenheim model gave an estimate of Tc = 1158 K. Both estimates are in good agreement with our GEMC simulations (Tc = 1252 K). There is a good physical reason for this agreement. These models employed lowtemperature surface tension and density data for the predictions,2 thus effectively capturing underlying intermolecular interactions of the liquid state. The force field used in the present work models liquid-state thermodynamic and transport properties very well (Zhong, X. J. et al. unpublished results). Therefore, it is not too surprising that the two approaches give similar critical temperatures. Perhaps the most remarkable finding is that one can make extrapolations over such a large temperature range and still achieve reasonable estimates of the critical temperature. Consistent with critical property trends, increasing cation alkyl chain length increases the vapor pressure (Psat) (Figure 2B), thus lowering the normal boiling point (Tb) (Table 1). We believe that increasing the “nonpolar” content of the cation weakens the Coulombic interaction between ions, resulting in increased volatility. With knowledge of the critical temperature and subcritical

Figure 3. Spatial distribution function of the BF4 ion around the C2mim cation at T = 1000 K in the first solvation shell (r e 7.97 Å). (A) 20% most likely positions in the vapor phase and (B) 20% most likely positions in the liquid phase.

saturation pressure, one can easily determine the critical pressure (Pc). In the case of ILs, we find that Pc decreases with increasing alkyl chain length (Table 1), while the critical compressibility factor, Zc, ranges from 0.038 for [C1mim] to 0.049 for [C6mim]. The predicted compressibility factors are an order of magnitude smaller than those of simple fluids,10 suggesting highly nonideal behavior of the vapor phase. Although Zc for [Cnmim][BF4] ionic liquids is much smaller than nonassociating fluids, it is larger than the critical compressibility factor of the restricted primitive model (Zc = 0.024).28 The temperature dependence of the enthalpy of vaporization (ΔHvap) is shown in Figure 2C. In contrast to low-temperature experimental5,29 and simulation data for the model employed in the present work (Zhong, X. J. et al. unpublished results), we find that at high temperatures, ΔHvap decreases with increasing size of the cation (Table 1). It is not clear from our work if the trend reversal is due to significant aggregation in the vapor phase or due to the pronounced effect of the alkyl chain on the cohesive energy of the condensed phase upon increasing temperature. The enthalpy of vaporization at the normal boiling point, ΔHvap Tb , ranges from 68 to 72 kJ/mol, which is about twice the value for a hydrogen-bonding liquid such as ethanol (38 kJ/mol)27 but much lower than the energy required to completely dissociate two ions (∼250
300 kJ/mol).16 This suggests that the vapor phase exists as either ion pairs or larger aggregates, not as isolated ions. To further explore association in the vapor phase, we computed the probability distribution for the localization of [BF4] ions around a [C2mim] cation at T = 1000 K (Figure 3A). In the vapor phase, the [BF4] ions tend to localize exclusively around the acidic C2 position (Figure 1) of the cation and form ion pairs (Figure 3A). In contrast, in the liquid phase, the [BF4] anions surround the cation (Figure 3B), localizing near the C2, C4, and C5 positions (Figure 1). Another quantity closely related to ΔHvap is the entropy of vaporization at the boiling point, ΔSvap Tb , known as Trouton’s constant. For [Cnmim][BF4], it is approximately 65 J/(mol K). 1441

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ion pairs are the dominant species in the vapor phase, a substantial fraction of ions is present in larger aggregates, and this fraction increases as the temperature and pressure increase. This could be an explanation for the discrepancies observed between different experimental techniques, although we emphasize that these clusters appear at high temperatures and densities. At low temperatures where the vapor density is small, single ion pairs will be the overwhelmingly dominant species. This work shows that it is feasible to determine VLCCs and vapor
liquid critical points for ILs by employing Monte Carlo simulations with realistic intermolecular potentials. The VLE of this family of imidazolium-based ILs differs from that of conventional molecular fluids in several important ways. First, the shape of the VLCCs is highly asymmetrical. Second, the vapor pressure increases and the critical temperature and density decrease as the size of the cation increases. Third, the Trouton’s constant is smaller than that of conventional fluids, consistent with the finding that the vapor state consists of a significant fraction of aggregated ion pairs. We find that the Guggenheim and E€otvos equations, which utilize extrapolated surface tension and density data, provide estimates of the critical points consistent with our simulations. Future work needs to focus on other classes of ILs to see if the results of the present study can be generalized.

’ ASSOCIATED CONTENT Figure 4. (A) Temperature dependence of fraction of total clusters that are of a given size or aggregation number (fNaggr) and (B) temperature dependence of the fraction of ions present in a cluster of given size (fion) for [C2mim][BF4]. The cyan, magenta, and orange colors represent T = 900, 1000, and 1100 K, respectively. Insets show selected snapshots of clusters (A) Naggr = 6 and 12 and (B) Naggr = 2 and 18. The white, black, blue, orange, and yellow colors represent hydrogen, carbon, nitrogen, boron, and fluorine atoms, respectively.

This is smaller than that of nonpolar (∼ 85 J/mol K) and polar compounds (∼105 J/mol K).10 This can in part be explained by the significant aggregation of ions that occurs in the saturated vapor phase (see discussion below), which lowers the vapor phase entropy relative to typical fluids where the vapor phase consists mainly of isolated molecules. Other associating fluids such as acetic acid also have smaller Trouton’s constants.30 To address the issue of the aggregation state of ions in the vapor phase, we performed a cluster analysis of the saturated vapor. Two ions were considered to be part of a cluster if their center of mass separation was less than 10.5 Å, a criterion determined from an ion pair simulation at T = 1100 K. As the aggregation states are similar for different cations used in the present work, we focus only on [C2mim][BF4] in the following discussion. Figure 4A shows the distribution of cluster sizes (or aggregation number, Naggr) as a function of temperature, while Figure 4B shows the temperature dependence of the fraction of ions that are in a cluster of a given size, Naggr. Even at T = 1100 K, less than 0.2% of ions are isolated, while the vast majority of the clusters are neutral. For all three temperatures, single ion pairs account for more than 60% of the total clusters, but less than 50% of the ions are in single ion pair clusters (Figure 4B). The number of single ion pairs decreases with increasing temperature, whereas the number of larger clusters increases with temperature. At T = 1100 K, more than 25% of the ions are in clusters with Naggr g 8, while only about 15% of the ions are in such aggregates at T = 900 K. Even though individual

bS

Supporting Information. Simulation details, a schematic representation of ion pair exchange between liquid and vapor phases, and numerical data for liquid and vapor densities, vapor pressures, and enthalpies of vaporization with their standard deviations for [C1mim][BF4], [C2mim][BF4], [C4mim][BF4], and [C6mim][BF4]. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank Dr. Jindal Shah for helpful discussions, Prof. Zhiping Liu for providing us force field parameters before publication, Dr. Kristina Furse for visualization support, and Dr. Sai Jayaraman for help with statistical analysis. Computational resources were provided by the Notre Dame Center for Research Computing. This material is based upon work supported by the Air Force Office of Scientific Research under AFOSR Award Number FA9550-10-1-0244. ’ REFERENCES (1) Plechkova, N. V., Rogers, R. D., Seddon, K. R., Eds. Ionic Liquids: From Knowledge to Application; American Chemical Society: Washington DC, 2010. (2) Rebelo, L. P. N.; Lopes, J. N. C.; Esperanca, J. M. S. S.; Filipe, E. On the Critical Temperature, Normal Boiling Point, and Vapor
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