Chemical Physics 371 (2010) 55–59
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Using Monte Carlo simulation to compute osmotic coefficients of aqueous solutions of ionic liquids Z. Karimzadeh a,*, S.A.A. Hosseini b, F. Deyhimi a a b
Department of Chemistry, Shahid Beheshti University, Evin-Tehran 1983963113, Iran Faculty of Engineering, Tarbiat Moalem University, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 13 September 2009 In final form 3 April 2010 Available online 8 April 2010 Keywords: Monte Carlo simulation Ionic liquid Osmotic coefficient Unrestricted primitive model
a b s t r a c t We perform, for the first time to our knowledge, Monte Carlo simulation to compute osmotic coefficient of ionic liquid aqueous solutions. The ionic liquids chosen are 1-ethyl-3-methylimidazolium bromide [Emim][Br], 1-methyl-3-methylimidazolium chloride [Mmim][Cl], 1-methyl-3-methylimidazolium bromide [Mmim][Br], 1-methyl-3-methylimidazolium iodide [Mmim][I] and 1-methyl-3-methylimidazolium hexafluorophosphate [Mmim][PF6]. Simulations are carried out in the NVT ensemble at 298.15 K. The Unrestricted Primitive Model (UPM) of electrolyte is used as microscopic model in simulation process. Accuracy of simulation to predict osmotic coefficients is verified by a direct comparison of simulation results with experimental data. Computed osmotic coefficients are in good agreement with available experimental values. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Room temperature ionic liquids (RTILs) are defining as a class of substances constituted by ions, with melting points below 373 K. A negligible vapor pressure, wide temperature liquid range, and possibility to change their structure for given application, are particularly among the remarkable characteristics of these substances [1]. Effectively, because of their chemical and physical properties, they are considered as a green alternative to the conventional organic solvents. This replacement would lead to the reduction in the emission of volatile organic compounds to the atmosphere, which currently is a major source of pollution [2]. Due to their enormous potential in the industrial applicability in green engineering, they are the subject of many experimental and computational researches over the last decade. However, much more research has to be done to fully exploit the various properties of this class of marvelous substances. Among the several alternatives, which prevent the use of volatile organic compounds (VOCs), combination the RTILs and water, may also be considered as environmental interest [3]. Similarly, processes that involve homogeneous mixtures of water and a VOCs solvent might be improved by substitution of the VOCs solvent with hydrophilic RTILs. Water even in small amount can dramatically change the physical properties of RTILs. Thus, combination of water and RTILs would be an attractive alternative to prevent the use of some VOCs. In this context, the values * Corresponding author. E-mail addresses:
[email protected],
[email protected] (Z. Karimzadeh),
[email protected] (S.A.A. Hosseini),
[email protected] (F. Deyhimi). 0301-0104/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2010.04.002
of osmotic coefficient of aqueous RTILs solutions are necessary to design properties of binary mixtures of water and RTILs in many of industrial processes. A review of literature shows that there are insufficient physicochemical properties data available for aqueous solutions of RTILs. Mokhtarane et al. [1] determined the density and viscosity values of two pyridinium-based ionic liquids, [BuPy][BF4] [OcPy][BF4], and their binaries. Heat capacities and excess enthalpies were determined for three different binary water + Imidazoliumbased RTILs by Ficke et al. [4]. The RTILs, investigated by these authors were [Emim][OTf], [Emim][TFA] and [Emim][EtSO4]. Experimental liquid–liquid equilibrium in the binary system [Bmim][PF6] + water was also investigated by Domanska et al. [5]. Fang and coworkers [6] calculated the molar enthalpies of solution of [C6mim][Cl]. The thermal conductivities of water + RTILs were determined, over the temperature range from 293 K to 353 K, at atmospheric pressure by Ge and coworkers [7]. Wang et al. [8] presented densities, conductivities, and polarity indexes of pyrene for aqueous solutions of a series of RTILs [Cnmim][Br] (n = 4, 6, 8, 10, 12) and [C4mim][BF4] at 298.15 K. Rodrıguez and Brennecke [9] reported accurate data at atmospheric pressure for the density and viscosity of mixtures of water and three different RTILs: [Emim][EtSO4], [Emim][Tfa] and [Emim][Otf] from 278.15 K to 348.15 K. Viscosities and densities were determined by Gomez and coworkers [10] over the whole composition range for water + [C6mim][Cl] and water + [C8mim][Cl] at different temperatures and 0.1 MPa of pressure. Anthony et al. [11] considered vapor–liquid equilibrium, liquid–liquid equilibrium phase behavior and associated thermodynamic properties of water with three ionic liquids [C8mim][PF6], [Bmim][PF6] and [C8mim][BF4]. The density, refractive index,
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viscosity, specific conductance and surface tension of systems involving imidazolium-based ionic liquids and water were measured over the whole concentration range by Liu et al. [12]. Osmotic coefficient measurements were carried out by Gardas et al. [13] for aqueous solutions of [Bmim][Cl] and [Emim][Br]. Measurements of osmotic coefficients of [Bmim][Cl] and [Hmim][Cl] with ethanol and [Emim][EtSO4] and [Empy][EtSO4] with water at 313.15 K and 333.15 K, were reported by Calvar et al. [14]. Gonzalez and coworkers [15], reported osmotic coefficients of [Bmim][Cl], [Hmim][Cl], [Mmim][MeSO4] and [Bmim][MeSO4] with water at 313.15 K and 333.15 K. Shekaari and Mousavi [16,17] calculated osmotic coefficients, mean activity coefficients, vapor pressure, and excess gibbs free energies of aqueous solutions of [PMIm][Br], [PnMIm][Br], [BMIm][BF4], [EMIm][ES], [BMIm][MS] and [HMIm][Br] at temperature ranges 298.15–328.15 K. Shekaari and Zafarani-Moattar [18] considered [Bmim][Br], [Bmim][PF6] and [BmimBF4] in water and acetonitrile to calculate the osmotic coefficients. Horn and coworkers investigated the double-layer and solvation forces of ethylammonium nitrate and water [19]. Some authors also investigated computationally RTILs solutions. In this category, computational researches contain: Shi and Maginn [20] studied the absorption of water in the RTILs [Hmim][Tf2N] using MC simulation. Ion pair formation in [Bmim][I] and water was considered by Katoh et al. [21]. Moreno and coworkers [22] investigated the interaction of water with the RTILs [Bmim][BF4] by MD simulations of the RTILs and its mixtures with water from zero up to 0.5 mol fraction of water. Markusson et al. [23] predicted the macroscopic properties of protic ionic liquids, based on alkylamines by ab initio method. Quantum chemical calculations were also carried out by Wang et al. [24] to investigate the interaction between water molecules and RTILs based on the imidazolium cation. Freire et al. [25] predicted LLE and VLE of water and ionic liquids binary systems by COSMO-RS method. Sieffert and Wipff [26] studied the aqueous interface of the hydrophobic [BMI][Tf2N] by MD simulation. Molecular simulation study of aqueous [Mmim][Cl] and [Mmim][PF6] to calculate excess volumes and the enthalpies of mixing was carried out by Hanke and Lynden-Bell [27]. Lynden-Bell and coworkers [28] determined the excess chemical potentials of water dissolved in the [Mmim][Cl] by MD simulation. Thermodynamic and transport properties of [Emim][EtSO4] and its mixtures with water was investigated by Kelkar et al. [29]. Shah and Maginn computed the Henry’s constants of water in the [Bmim][PF6] [30]. Solvation of diatomic and benzenelike solute in [Emim][PF6] and [Emim][Cl] was studied by Shim et al. [31,32]. Bhargava and Klein investigated aqueous solutions of imidazolium ionic liquids by MD simulation to study the structural analysis [33]. Finally, some researchers used electrolyte models to study RTILs. Some of this models are: NRTL, modified NRTL (MNRTL), mean spherical approximation NRTL (MSA-NRTL), non random factor (NRF), extended Wilson models [16,19], Pitzer-ion interaction [13], modified NRTL (MNRTL) [17] and Restricted Primitive Model (RPM) [34]. In this context, objective of our work is to perform MC simulations to study systems containing imidazolium type RTILs + water, using Unrestricted Primitive Model of electrolyte [35–38]. To this aim, for the first time, imidazolium type aqueous ionic liquids are simulated to predict the osmotic coefficients. Finally, the simulation process is validated by the direct comparison of the simulated results to those reported experimentally.
2. Modeling The simulations are carried out on the NVT ensemble using the Monte Carlo (MC) technique and Metropolis algorithm [39]. A FOR-
TRAN code is developed for use on a PC (with Windows Operation) system. In a PC Pentium 4 system, the estimated time for each run (including 10 million configurations) is about 15 min. First simulation of RTILs by RPM was performed to consider influence of ion size asymmetry on the properties of ionic liquid [34]. According to the RPM, the ions were assumed to have equal size. In this work, the Unrestricted Primitive Model (UPM) of electrolyte is used as microscopic model [35–38]. According to the UPM, the pair potential (uij) is a combination of the extremely short-ranged hard sphere potential and the extremely long-ranged Columbic potential,
uij ðrÞ ¼ þ1;
r rij
¼ qi qj =em r;
ð1Þ
r > rij
where rij = 1/2(ri + rj) is the combined hard sphere diameter of the pair of interesting ions, qi = zie and qj = zje are the charges of the ions, zi and zj are the valence numbers, e is the electronic unit charge and em is the uniform dielectric constant (relative permittivity) of the homogeneous solvent medium embedding the charges, r is the center-to-center interionic separation. The ions are of different sizes and the values of the anion and cation diameters are depicted in Table 1. A total number of 108 cations and anions are simulated in a cubic simulation box with standard periodic boundary conditions. Initial configurations are generated according to the FCC lattice. The maximum size of the displacement change is adjusted to achieve an acceptance ratio of 40–50%. Finally, well-equilibrated systems (generally reached after 5 million configurations) are used as starting configurations for the final computational runs. Theses consist of five million configurations. Long-ranged electrostatic interactions are handled by the Ewald summation method [43], with the permittivity of the surrounding medium set equal to that of water. The convergence parameter, a = 5/L, is chosen 2.5 similar to the ionic systems. A spherical cutoff distance kc roughly grater than 10p/L is necessary to compute the reciprocal space sum, a number of 337 reciprocal vectors are used in the calculation of that sum. Statistical errors for quantities calculated from MC simulations are estimated by the method of block averages [43]. The statistical error for the average of configuration is reported. The osmotic coefficient can be obtained using the Virial equation [44] as follows:
u ¼ 1 þ ð1=3ÞhUi=NkB T þ contact;
ð2Þ
contact ¼ f2g=½ðrþ =r Þ3 þ 1gfðrþ =r Þ3 g þþ ðrþ Þ þ 2ðrþ =r Þ3 g þ ðrþ Þ þ g ðr Þg;
ð3Þ
where hUi is the average configurational energy, kB is the Boltzmann constant, T is the temperature in Kelvin scale and N is the total number of ions. In Eq. (3), the contact values g++(r+), g(r), and g+(r+) can be obtained by the calculated radial distribution functions. The packing fraction (g) is:
Table 1 Ion diameter used in this work. Ion
Dimeter (Å)
Ref.
Cl Br I PF6 Emim Mmim
3.62 3.90 4.32 3.20 8.79 7.27
[40] [40] [40] [41] [42] [42]
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Z. Karimzadeh et al. / Chemical Physics 371 (2010) 55–59 Table 2 Acronyms used for the RTILs.
Table 3 Comparison of computed osmotic coefficient with experimental results of aqueous [Emim][Br] solutions at 298.15 K.
Name
Acronym
1-Methyl-3-methylimidazolium iodide 1-Methyl-3-methylimidazolium bromide 1-Methyl-3-methylimidazolium chloride 1-Methyl-3-methylimidazolium hexafluorophosphate 1-Ethyl-3-methylimidazolium bromide
[Mmim][I] [Mmim][Br] [Mmim][Cl] [Mmim][PF6] [Emim][Br]
g ¼ g0 =2ðc3 þ 1Þ
ð4Þ
here, c = r+/r and also
g0 ¼ ðp=6Þqr3 ;
M (mol L1)
hUib (NkT)
Usim (MM)
Uexp (MM)a
0.0875 0.1337 0.1807 0.2273 0.2729 0.3231 0.3703 0.4161
0.25335 ± 0.002 0.28919 ± 0.001 0.31694 ± 0.004 0.33942 ± 0.003 0.35819 ± 0.001 0.37566 ± 0.003 0.39053 ± 0.002 0.40354 ± 0.001
0.9155 0.9036 0.8944 0.8869 0.8806 0.8748 0.8698 0.8655
0.9235 0.9169 0.9133 0.9113 0.9103 0.9096 0.9087 0.9069
a
Uexp (MM) are obtained using density values [9] and Uexp (LR) [13].
b
Standard deviations of block averages are reported.
ð5Þ
where q is the total number density of ions in solution. Acronyms used for the RTILs are provided as Table 2. 0.98
3. Results and discussion 0.93
A validation of molecular models and force fields generally involves a comparison of simulated with experimental data. To this aim the simulation process ability is validated by comparison of the simulated results, for aqueous solution [Emim][Br] at 298.15 K to those reported experimentally. In authors’ knowledge, there are few works, which consider simulation of water and RTILs mixture. Furthermore, there is no direct comparison with experimental values to calculate excess quantity of aqueous solutions of RTILs [27,28]. They found only qualitative agreement between simulation and experimental values. So, in order to make a quantitative comparison between simulated and experimental results [13], we choose aqueous solutions of [Emim][Br] due to reported experimental values of osmotic coefficients and densities. Since the Virial equation i.e. Eq. (2), yields values of osmotic coefficients on the molar concentrations basis (referred to as the McMillan–Mayer (MM) scale), and experimental values of the osmotic coefficient are reported on the molal concentration basis (referred to as the Lewis–Randall (LR) scale), then following equation is used to convert MM scale to LR scale [45].
uMM ¼ uLR
xw m V wM
;
ð6Þ
where xw the molecular weight of solvent, m is the molality (mol kg1) and M is the molar concentration (mol L1). V w , partial molal volume of the solvent, is given by:
Vw ¼
m @ qs ln ; xs V V 1000 qs ln @m
xw
ð7Þ
where xs is the molecular weight of the ionic liquid, V is the total volume of solution and qsln is the mass density (g cm3) of solution. The total volume of the solution V can be obtained in terms of the qsln as
V¼
mxs þ 1000
qs ln
:
ð8Þ
By polynomial interpolation from the experimental density data of ionic liquid solutions, the derivative, oqsln/om, can be obtained. The computed osmotic coefficients and experimental results [13] of aqueous solutions of [Emim][Br] are depicted in Table 3. Comparison of the simulated results for aqueous solution of [Emim][Br] at 298.15 K is shown in Fig. 1. As sketched in figure, a reasonable agreement is obtained between the computed and
Φ(MM)
3.1. Validation of the MC simulations
0.88
Exp 0.83
Sim
0.78 0
0.1
0.2
M(mol
0.3
0.4
L-1 )
Fig. 1. Comparison of osmotic coefficient values for an aqueous [Emim][Br] solution at 298.15 K and various concentrations as obtained from MC simulation and experiment [13].
experimental values in this concentration range. Especially in concentration ranges below 0.3 M, the osmotic coefficients are predicted with error less than 3%. 3.2. Results In subsequent simulations we investigate four other systems. Aqueous solutions of [Mmim][Cl], [Mmim][Br], [Mmim][I] and [Mmim][PF6] are considered at 298.15 K. Simulated results to compute osmotic coefficients, are shown in Table 4. Fig. 2 shows variation of computed osmotic coefficients with RTILs concentration for all considered systems. Analysis indicates that in all RTILs, osmotic coefficient decreases with increasing concentration in studied concentration range. A similar trend is observed for the internal energy which is not presented here. It is interesting that all five RTILs investigated here, which contain different anions i.e. [Cl], [Br], [I] and [PF6] exhibit this behavior. Results show that the thermodynamic properties i.e. osmotic coefficient and internal energy for a series of RTILs with the same cation seem to increase with the effective anion size. These trends are similar to those observed by Gardas et al. for osmotic coefficients [46]. Centered-mass radial distribution functions (RDF) are reported only for aqueous solutions of [Emim][Br] at 298.15 K. Other RTILs solutions are qualitatively similar; so they are not shown here. The main changes with composition in cation–anion RDF of aqueous [Emim][Br] solution at 298.15 K are shown in Fig. 3. As can be seen, the first peak is higher for solution with more RTILs. Moreover, formation of the next solvation shells can be observed by increase of concentration from 0.7 M to higher concentrations.
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Table 4 Predicted osmotic coefficient results of aqueous [Mmim][Cl], [Mmim][Br], [Mmim]I] and [Mmim][PF6] solutions at 298.15 K, as obtained from MC simulation. M (mol L1)
[Mmim][Cl]
[Mmim][Br]
a
0.0500 0.1000 0.2500 0.3075 0.3908 0.4640 0.6143 0.7603 0.9205 1.2267 a
a
[Mmim][I] a
[Mmim][PF6]
hUi /NkT
Usim (MM)
hUi /NkT
Usim (MM)
hUi /NkT
Usim (MM)
hUia/NkT
Usim (MM)
0.2669 ± 0.002 0.2957 ± 0.003 0.3662 ± 0.002 0.3879 ± 0.001 0.4150 ± 0.004 0.4360 ± 0.002 0.4711 ± 0.002 0.4990 ± 0.001 0.5255 ± 0.002 0.5672 ± 0.003
0.9110 0.9014 0.8779 0.8707 0.8617 0.8547 0.8430 0.8337 0.8248 0.8109
0.2712 ± 0.003 0.2977 ± 0.002 0.3636 ± 0.003 0.3841 ± 0.001 0.4112 ± 0.001 0.4306 ± 0.003 0.4653 ± 0.002 0.4937 ± 0.001 0.5192 ± 0.002 0.5610 ± 0.004
0.9099 0.9010 0.8788 0.8720 0.8629 0.8565 0.8449 0.8354 0.8269 0.8130
0.3636 ± 0.004 0.2977 ± 0.002 0.2712 ± 0.001 0.3780 ± 0.002 0.4044 ± 0.003 0.4242 ± 0.004 0.4580 ± 0.001 0.4849 ± 0.003 0.5104 ± 0.002 0.5508 ± 0.003
0.8788 0.9010 0.9099 0.8740 0.8652 0.8586 0.8474 0.8384 0.8299 0.8164
0.2693 ± 0.002 0.2998 ± 0.004 0.3872 ± 0.001 0.3939 ± 0.003 0.4224 ± 0.002 0.4436 ± 0.001 0.4796 ± 0.002 0.5086 ± 0.003 0.5351 ± 0.002 0.5792 ± 0.001
0.9102 0.9004 0.8761 0.8687 0.8592 0.8521 0.8401 0.8305 0.8216 0.8069
Standard deviations of block averages are reported.
0.88
5
0.87
4
0.86
3
[Mmim][I]
[Mmim][Cl]
g(r±)
Φsim (MM)
[Mmim][Br]
0.85
[Mmim][PF6]
2
0.84
1
0.83
[Mmim][I] [Mmim][Br]
0.82
[Mmim][Cl] [Mmim][PF6]
0.81 0.1
0.3
0 0
1.5
3
4.5
6
r/σ-
0.5
0.7
0.9
1.1
Fig. 4. Radial distribution functions of cation–anion for the binary systems, [Mmim][Cl] + water, [Mmim][I] + water, [Mmim][Br] + water, [Mmim][PF6], as obtained from MC simulation at 298.15 K and 1.5 M.
M(mol L-1 ) Fig. 2. Values of osmotic coefficient as a function of concentration, at 298.15 K, for the binary systems, [Mmim][Cl] + water, [Mmim][I] + water, [Mmim][Br] + water, [Mmim][PF6], as obtained from MC simulation.
6 1.22M
4.5
0.92M
g(r±)
0.76M
The results of this study show that in low concentration ranges where the main forces are the long range i.e. electrostatic forces the UPM model of electrolyte is an applicable model to predict osmotic coefficients of imidazolium-based ionic liquids, with short chain length. This model can save a significant amount of computer time as it avoids a large fraction of the most time consuming step, namely the evaluation of short range interactions. Though simulation by this model need to less time and cost, but at higher concentration, which the short range forces are becoming important, this model is not sufficient and short range interactions have to be included.
3 0.61M
4. Summary
0.46M
For the first time, simulations are performed to calculate osmotic coefficient of ionic liquid aqueous solutions. Binary mixture i.e. [Mmim][X] + water, X = Cl, Br, I, PF6 and [Emim][Br] + water are studied. Predicted model to calculate the osmotic coefficient of RTILs, is expressed by the UPM model of electrolyte and MC simulation. The osmotic coefficients are computed for all systems at 298.15 K. Simulation results show reasonable agreement between computed and experimental data. The paper presents the possibility of using UPM model of electrolyte in MC simulation to calculate the osmotic coefficient of short chain length imidazolium RTILs. The most important result is that in low concentration ranges, which the main forces are the long range interactions, the UPM model of electrolyte is an applicable model to compute osmotic coefficients of short chain length imidazolium-based ionic liquid. However, at higher concentrations, which the short range forces
1.5
0 1
1.8
2.6
3.4
r(σ-) Fig. 3. Radial distribution functions of cation–anion for an aqueous [Emim][Br] solution at 298.15 K and various concentrations as obtained from MC simulation.
Fig. 4 shows the changes in cation–anion RDFs for solutions of [Mmim][PF6], [Mmim][Cl], [Mmim][Br] and [Mmim][I] at 298.15 K and 1.5 M. The main point is that the first peaks are sharper for RTILs with bigger anion.
Z. Karimzadeh et al. / Chemical Physics 371 (2010) 55–59
are more active, this model is not sufficient and short range forces have to be exerted.
[19] [20] [21] [22]
Acknowledgments [23]
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