A Priori Prediction of Dissociation Phenomena and Phase Behaviors

Article pubs.acs.org/IECR

A Priori Prediction of Dissociation Phenomena and Phase Behaviors of Ionic Liquids Bong-Seop Lee and Shiang-Tai Lin* Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617 S Supporting Information *

ABSTRACT: Many unique properties of ionic liquids (ILs) are closely related to the extent of dissociation (α) in solution. However, most of the existing models for ILs assume either full dissociation or full nondissociation regardless of mixture compositions. In this work, the dissociation of ILs (CA = C+ + A−) is described as a chemical reaction. Together with the predictive COSMO-SAC model, the dissociation constant can be determined based on the value of α in the pure state. Our results show that the predicted composition dependence of α is in good agreement with experiment over the entire concentration range. We further examine the prediction of a variety of thermodynamic properties and phase behaviors of IL solutions, covering high (infinite dilution activity coefficient of solvent), medium (vapor−liquid and liquid−liquid), and low (osmotic coefficient and mean ionic activity coefficient) IL concentrations (a total of 9857 data points). Our results show that the composition dependence of IL dissociation has a significant impact on the phase behaviors of IL solutions. The dominating factors for the solution nonideality changes from short-range ion-pair interactions at high IL concentrations to long-range ion−ion interactions at low IL concentrations.

1. INTRODUCTION Ionic liquids (ILs) have attracted much attention1−7 recently because of their unique properties such as nonflammability, negligible vapor pressure, broad liquid-state temperature ranges with a melting point at or below 373.15 K, high thermal and chemical stability, and high ionic conductivity.8 In particular, the properties of mixtures containing ionic liquids often exhibit interesting composition dependence.9 For example, Zarrougui et al.10 observed abrupt increase in viscosity and a maximum conductivity with increasing concentration of PYR14 (IL) in its mixture with methanol. The unusual behavior was explained qualitatively based on the formation of dissociated ions in low IL concentrations and ion pairs at high concentrations. The dissociation of ILs also have a profound impact on toxicity,11 their use in chemical reactions,12 and applications as an active pharmaceutical ingredient (API).13−15 Many experimental efforts (e.g., using NMR,16,17 dielectric relaxation spectroscopy (DRS),18,19 and conductivity measurements20) have been devoted to investigating the extent of dissociation (α) of ILs. In the dilute solution limit, ILs tend to fully dissociate. As the concentration of IL increases, some of the IL starts to associate and form ion pairs. In the limit of neat IL, a significant portion (0.2−0.4) of the IL still exists in the dissociated state.16,21 While many theoretical efforts were made for describing the dissociation phenomena of electrolytes,22−26 there are few theories that can quantify the variation of IL dissociation with concentration. Li et al.27 used a square-well chain fluid with variable range equation of state to correlate the thermodynamic properties (i.e., liquid densities and osmotic coefficients) of aqueous IL solutions, with the association energy between cations and anions treated as fitting parameters. More recently, Yee et al.23 used molecular dynamics simulation to determine the degree of dissociation of 5 ILs in water. They found that the © 2015 American Chemical Society

association constant increases with increasing alkyl chain length on the cation of ILs with the same anion. Despite these works, the modeling of phase behaviors of mixtures containing ILs based on predictive local composition models, such as the UNIFAC model28−30 and COSMO-based models (COSMO-RS31−33 and COSMO-SAC34,35), have been quite successful, especially in describing vapor−liquid and liquid−liquid equilibria. The success of these models is rather surprising because these models take into account only shortrange molecular interactions. The long-range coulomb interactions, which should be important for ions, are not included. Furthermore, these models do not have a clear description on the state of association and dissociation of the IL under different solvent environments. More recently, Lee and Lin combined the Pitzer−Debye−Hü ckel model, which accounts for the long-range electrostatic interactions in electrolyte solutions, with COSMO-SAC and showed that the long-range interactions are important for describing the solution nonideality in diluted IL solutions, while the ion− ion interactions are nearly completely screened at highconcentration IL solutions. They also proposed a semiempirical model for describing the dissociation of IL with concentration.36 In this work, the dissociation of IL when mixed with a nondissociative solvent is modeled as a chemical reaction. The transition of IL in the associated (ion pairs) and dissociated (free ions) states is a result of minimizing the free energy of the mixture. We show that the concentration dependence of the extent of dissociation of IL thus determined is in good Received: Revised: Accepted: Published: 9005

May 12, 2015 August 26, 2015 August 26, 2015 August 26, 2015 DOI: 10.1021/acs.iecr.5b01762 Ind. Eng. Chem. Res. 2015, 54, 9005−9012

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Industrial & Engineering Chemistry Research

by the Pitzer−Debye−Hückel (PDH) model42 and a shortrange term, modeled by the COSMO-SAC model,43 i.e.

agreement with the experiment. Furthermore, the same model can be used for the prediction of thermodynamic properties and phase behaviors of IL solutions over the whole concentration ranges. We show that the proposed method not only captures the proper dissociation behavior of IL but also allows for accurate, a priori prediction of properties of IL mixtures.

ln γi = ln γi*PDH + ln γi COSMO‐SAC

The asterisk in above equation indicate the use of unsymmetric reference states for the activity coefficient: pure liquid for uncharged species, and infinite dilution for charged species. The reference state is where the activity coefficient becomes unity. According to the PDH model, the activity coefficient of a species i in a solvent is42

2. THEORY AND MODEL 2.1. Thermodynamic Background. In this work we consider that an IL molecule may exist either as dissociated ions (C+ and A−) or nondissociated ion pairs (C+A−), as indicated by the reaction Ka

C+ + A− ↔ C+A−

ln γi*PDH = −

(1)

where ai is activity and γ± = (γ+γ−)1/2 = (γCγA)1/2 is the mean ionic activity coefficient. For the cation and anion, the reference state is chosen to be the infinite dilution of these ions in the pure liquid of ion pairs. For the ion pair, the reference state is chosen to pure ion-pair state. In other words, the last term in eq 2 ((γCA/γ2± )) becomes unity for a completely undissociated IL. The mole fractions (xi) are related to that of an undissociated system x0s and x0CA (x0s + x0CA = 1) through the extent of dissociation a as

ρ = R 2e 2Nads/(Ms ϵskT )

xCA =

(3)

0 xCA (1 − α) 0 1 + αxCA

xC = xA =

(4)

ln γi COSMO‐SAC = ln γi res + ln γi comb

0 xCA α 0 1 + αxCA

(5)

(1 − α0)(1 + α0) γCA α02

γ±2

(10)

The combinatorial term considers the nonideality resulting from the repulsive interactions between species, with consideration of size and shape differences between molecules. In the COSMO-SAC model, the Staverman−Guggenheim combinatorial term48 was used

where α is the extent of dissociation. In the limit of pure IL (x0s = 0), association constant Ka becomes K a (T ) =

(9)

where R, the upper limit of distance of closest approach for ionpair formation parameter is taken as R = kra, which is the sum of the radii of each ion (a+ + a−) and kr is assumed to be 2.5 for all solvents.45,46 The ion pair of ILs is considered as a cosolvent as in previous work.36 The solvent properties are averaged from neutral components,36,47 i.e., Ms = ∑j xj/(∑k xk)Mj, εs = ∑j Mjxj/(∑k xkMk)εj, and 1/ds = 1/(∑k xkdk). The COSMO-SAC model describes the activity coefficient due to interactions between molecules in contact, including a combinatorial (comb) and a residual (res) term

xs0 0 1 + αxCA

⎡ 2 zi2 Ix − 2Ix3/2 ⎤ 1000 ⎢ 2zi ⎥ Aϕ ln(1 + ρ Ix ) + Ms 1 + ρ Ix ⎥⎦ ⎣⎢ ρ (8)

where Ms is the molecular weight of solvent, ρ the closest approach parameter, Ix the ionic strength (Ix = 1/2∑i xizi2, where z is the electrovalence), and Aϕ the Debye−Hückel constant (Aϕ = 1/3(2πNads/1000)1/2 (Qe2/εskT)3/2, with ds being the density of solvent, Na Avogadro’s number, Qe the charge of an electron, εs the average dielectric of solvent, and k the Boltzmann constant). In this work, the closest approach parameter in PDH term is obtained from the approximate theory proposed by Pitzer et al.44

The equilibrium constant, Ka, depends only on temperature and can be expressed in terms of mole fractions (xi) and activity coefficient (ri)37 a x γ K a(T ) = CA = CA CA2 aCaA xCxA γ± (2)

xs =

(7)

ln γi comb = ln

(6)

where α0 is the degree of dissociation of the pure IL (i.e., the value of α at x0s = 0). Therefore, the equilibrium constant Ka can be determined using the actual degree of dissociation of IL in the pure liquid state (α0). Recent experimental studies16,21,38−40 show that the value of α0 for several imidazolium-based ILs ([C1MIM][TF2N] to [C8MIM][TF2N]) falls in the range between 0.21 and 0.41. In addition, the degree of association of neat ILs is not sensitive to temperature.38−40 For example the change of α0 of [C2MIM][EtSO4] from 298 to 333 K is less than 0.07.21 Therefore, to the first approximation, we assume α0 to be 0.35 for all ILs at all temperatures in this study. 2.2. Activity Coefficient Model. The activity coefficient of a charged species in a solvent has contributions from long-range coulomb interactions and short-range molecular surface interactions.36,41 In this work, the long-range term is modeled

ϕi xi

+

ϕ θ z qi ln i + li − i 2 ϕi xi

∑ xjlj j

(11)

where ϕi is the normalized volume fraction; θi the normalized surface-area fraction, li = z/2(ri − qi) − (ri − 1)); z = 10 the coordination number; and xj the mole fraction. ri and qi are the normalized volume and surface area parameters, i.e., qi = Ai/q and ri = Vi/r, where Ai is the cavity surface area and Vi is the cavity volume. Both Ai and Vi are obtained from the COSMO calculation, and the values of q and r are 79.532 Å2 and 66.694 Å3, respectively. The residual term accounts for the nonideality due to differences in the attractive interactions. In the COSMO-SAC model, this term is determined from the screening charge on the molecular surface. The distribution of screening charges on the molecular surface can be obtained from the COSMO calculation,49,50 where a molecule is dissolved in a perfect conductor. The electronic features of the molecule can be 9006

DOI: 10.1021/acs.iecr.5b01762 Ind. Eng. Chem. Res. 2015, 54, 9005−9012

Article


solution (CA). The activity coefficient of ion pair and other nondissociable solvents (S) is given as

characterized by the induced screening charges appearing on the cavity surface. To quantify the distribution of the screening charges, the molecular surface is dissected into small segments. Furthermore, the surface of a molecule is classified into three categories: non-hydrogen bonding (nhb) surfaces, hydrogen bonding from OH groups (OH), and any other hydrogen bonding surfaces (OT).51 The probability of finding a surface segment with a screening charge density σm, associated with surface type t (t = nhb, OH, or OT), referred to as the σprofile, is Ait (σmt ) Ai

pit (σm) =

γi = γi*PDHγi COSMO‐SAC with i = CA or S.

3. COMPUTATIONAL DETAILS To obtain the activity coefficient of a molecule with the COSMO-SAC model, the σ-profiles of ionic liquids (cation and anion) are required and are obtained from the quantum mechanical COSMO calculation.49,52 Each anion and cation is considered as individual species in the COSMO calculations. (A list of all the ions considered in this work is given in Table S1 of Supporting Information.) The σ-profiles of the ion pair of ILs are then obtained by adding the σ-profiles of both cation and anion without any additional COSMO calculation. The detailed procedure of obtaining the activity coefficients from the σprofiles can be found elsewhere.53 For each ionic liquid, the equilibrium constant Ka is determined from eq 6 with the assumption of α0 = 0.35. At given temperature and pressure conditions, the equilibrium concentration of free ions and ion pairs is determined from the degree of dissociation α (eqs 3−5) by solving eq 2. In liquid−liquid equilibrium (LLE) calculations, additional constraint of electroneutrality (xC = xA) must be satisfied in each phase. In vapor−liquid equilibrium (VLE) calculations, the IL is assumed nonvolatile and the vapor pressure is calculated as the partial pressure of the solvent

(12)

where Ai is the total surface area of the species i and Ai(σm) = ∑t Ait(σmt) is the surface area of a segment with a screening charge density σm (note that the summation is over all different surface types t with σm). The σ-profile for a mixture is the mole fraction weighted sum of the σ-profiles of all the components, i.e., pst (σmt ) =

∑i xiAi pit (σmt ) ∑i xiAi

(13)

The activity coefficient of component i is determined from the sum of surface segment contributions as ln γi res = ni Σnhb,OH,OT ∑ pit (σmt )[ln ΓSt(σmt ) − ln Γit(σmt )] t σm

(14)

P = xs·γs·Psvap(T )

where Γjt(σmt) is the activity coefficient of a segment of type t and charge density σm in a solution j (j = S for the mixture, and j = i for pure liquid i), and is calculated using the following equation

xso =

(15)

The ΔW measures the energy of interaction between two surface segments51 ΔW (σmt ,

σns)

=

c ES(σmt

+

σns)2

−

chb(σmt ,

σns)(σmt

−

(16)

(17)

with AES (6525.69 [kcal/mol·A /e ]) and BES (1.4859 × 108 [kcal/mol·A4/e2·K2]) being universal constants. The hydrogen bonding interaction parameter is given by ⎧c ⎪ OH−OH ⎪c chb(σmt , σns) = ⎨ OT−OT ⎪c ⎪ OH−OT ⎩0

xs + xC + xCA

(22)

xC + xCA xs + xC + xCA

(23)

The reported experimental data for the mean activity coefficient of ionic liquid are given in a molarity scale, and the mole fraction activity coefficient, r±, needs to be converted into the activity coefficient in molality scale as

The electrostatic interaction parameter, cES, is defined as 4

xs

o xCA =

σns)2

c ES = AES + BES /T 2

(21)

Note that experimental data from VLE and LLE compositions are given by regarding IL as undissociated components with mole fraction of xso for the solvent and xCAo for the IL (xso + xCAo = 1). The composition used in our calculation and experimental data can be converted as follows

ln Γtj(σmt ) = −ln{Σsnhb,OH,OTΣσnpjs (σns) exp[−ΔW (σmt , σns) /kT + ln Γ sj(σns)]}

(20)

2

γ±(m) = 1/(1 + 0.001vmmx Ms)γ±

where mmx is the molarity of the ionic liquid. The osmotic coefficient of the ionic liquid solution, ϕ, can be obtained from the activity coefficient of the solvent

if s = t = OH and σmt · σns < 0 if s = t = OT and σmt · σns < 0 if s = OH, t = OT, and σmt · σns < 0

ϕ=

otherwise

1 ln(xsγs) ln(xs)

(25)

The absolute average relative deviations (ARD) in each property (Xi = P, ri∞, r±2, and ϕ) are used to measure the quality of predictions in this work

(18)

Finally, the activity coefficient of each ions is expressed as γi = γi*PDHγi COSMO‐SAC/γi/CA ∞ ,COSMO‐SAC

(24)

(19)

ARD(%) =

where i = C (cation) or A (anion). This ensures that the activity coefficient of the ions are unity in the limit of pure ion-pair 9007

100% Np

∑ i

Xexp − Xcal Xexp

i

(26)


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4. RESULTS AND DISCUSSION To examine the effects of IL dissociation on the properties and phase behaviors of IL solutions, we present the prediction results from three methods: (1) the ion-pair model (α = 0), where the ILs are considered as ion pairs under all circumstances; (2) the free-ion model (α = 1), where the ILs are considered as dissociated free ions under all conditions; and (3) the dissociation model (α0 = 0.35), where ILs consist of both free ions and ion pairs (eq 1) and the equilibrium composition is determined using the equilibrium constant determined by assuming the extent of dissociation of 0.35 in the pure IL state (eq 6). The performance of the proposed models for different properties of IL solutions is summarized in Table 1.

experiment appears to be worse in the very dilute conditions (x0s → 1); however, experimental data show large uncertainties in this region. Our model predicts that in the limit of infinite dilution, the ILs are fully dissociated (α = 1). The success of the dissociation model (α0 = 0.35) in describing the degree of dissociation on solvent concentration is strong support for its validity. 4.2. Infinite Dilution Activity Coefficient of Nondissociable Solvent in Ionic Liquids. Figure 2 and Table 1 summarize the prediction accuracy for the infinite dilution activity coefficient (IDAC) of the solvent in pure ionic liquid (i.e., xs = 0) from the three methods α = 0, α0 = 0.35, and α = 1. Both the ion-pair model (α = 0) and the dissociation model (α0 = 0.35) provide reasonable prediction for IDAC (see Table S2 for further details). The free-ion model (α = 1) is inaccurate, especially for nonpolar solvents (i.e., alkane, cycloalkane, alkene, and alkylbenzene), for which the values of IDAC are often from 2 to 7 times larger than those for the ion-pair model; however, for polar solvents, such as ketone and alcohol/ water group, the difference is smaller (about 1.5 times larger). The significant deviation of the free-ion model is a result of the overestimation of the solvent activity coefficient from the PDH model.36 The failure of the free-ion model implies that there should be a strong screening effect (as a result of ion-pair formation) for the long-range electrostatic interactions in the pure liquid state of ILs. Therefore, both the ion-pair and dissociation model are capable of describing the IDAC of nondissociable solvents in ILs. 4.3. Vapor−Liquid Equilibrium of Ionic Liquid Solutions. Table 1 summarizes the performance of the three methods in the prediction of vapor pressure of IL solutions (53 binary mixtures from 15 ILs, 16 solvents; a total of 1626 data points). The VLE data covers a wide range of solvent compositions, and the results can be used to examine the performance of different methods in intermediate concentration ranges. In general, the ion-pair model gives the best overall results (ARD 28.89%). The dissociation model shows similar performance with an ARD of 31.46%. The free-ion model shows the worst results (ARD 92.52%), particularly in the case of nonpolar solvent (ARD 225%, see Tables S3 and S4). Interestingly, if one examines the aqueous IL solutions, the performance from the three methods are similar (ARD around 30%), with the free-ion model showing accuracy (29.22%) slightly better than that of the other models.

Table 1. Average Relative Deviations (ARD%) in Different Properties of Ionic Liquids from Different Methods propertya

method

b

free-ion dissociation ion-pair npc

IDAC

VLE

LLE (ILrich)

464.54 224.61 165.79 3553

92.52 31.46 28.89 1626

8.94 3.90 5.11 2275

LLE (solventrich)

OC

MAC

1.18 1.12 1.31 637

37.81 50.72 70.24 1348

50.12 51.63 318.46 484

a

IDAC: infinite dilution activity coefficient of a chemical in pure ionic liquid. VLE: vapor−liquid equilibrium. LLE: liquid−liquid equilibrium. OC: osmotic coefficient. MAC: mean activity coefficient. bFree-ion model: the IL is assumed to be fully dissociated (α = 1). Dissociation model: the IL can stay as dissociated ions and undissociated ion pairs with the equilibrium constant determined from eq 6. Ion-pair model: the IL is assumed to form ion pairs in the liquid state. cnp: number of experimental data points.

4.1. Extent of Dissociation of ILs. The variation of degree of dissociation, α, of [C2MIM][EtSO4] and [C2MIM][OTf] with the concentration of water from experiment and our prediction (the dissociation model) is shown in Figure 1. The predicted composition dependence of α is in good agreement with the general features observed in experiment: the value of α remains roughly constant over a wide range of water concentrations and exhibits a minimum in the dilute IL concentrations. The agreement between the prediction and

Figure 1. Degree of dissociation (α) of [C2MIM][EtSO4] (a) and [C2MIM][OTf] (b) as a function of solvent (water) concentration at 313.15 K. Open squares are experimental data,21 and solid lines are predictions from this work (using the dissociation model, α0 = 0.35). 9008


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Figure 2. Comparison of natural log of infinite dilution activity coefficients of solute in ionic liquid from prediction (Pred) and experiment (Exp): (a) free-ion model (α = 1), (b) dissociation model (α0 = 0.35), and (c) ion-pair model (α = 0).

Figure 3. Comparison of vapor pressure of binary ionic liquid solutions from experiment (open symbols) and predictions (free-ion model, (α = 1, dotted line), dissociation model, (α0 = 0.35, solid line), and ion-pair model, (α = 0, dashed line)): (a) [C2MIM][TF2N] mixed with tetrahydrofuran (red), cyclohexane (purple), and benzene (orange); (b) [C4MIM][BF4] with water (red), methanol (purple), and ethanol (orange).

Figure 4. Liquid−liquid phase equilibium of [C8MIM][PF6]/water (a,b), [C5MIM][PF6]/1-butanol (c), and [C6MIM][PF6]/1-butanol (d) binary mixtures from free-ion model (α = 1, dotted line), dissociation model (α0 = 0.35, solid line), and ion-pair model (α = 0, dashed line). Experiment data are shown as open circles.

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Figure 5. Liquid−liquid phase equilibium of [C2MIM][EtSO4]/2-hexanone (a), [C4MIMI][CNS]/di-n-butylether (b), [C6MIM][CNS]/ cyclohexane (c), and [C4MIM][C8SO4]/decane (d) binary mixtures. The legends are the same as those in Figure 4.

Figure 6. Osmotic coefficient of [C2MIM][EtSO4]/ethanol binary mixture (a) and mean activity coefficient of [C1MIM][MeSO4]/1-propanol binary mixture (b) at 323.15 K. The legends are the same as those in Figure 4.

different dissociation models. The calculation with α0 = 0.35 (dissociation model) shows the best accuracy with the rootmean-square-deviation (rmsd) being 3.9 and 1.1 in IL-rich phase and solvent-rich phase, respectively. It is noteworthy that the calculation with full dissociation (α = 1) in solvent-rich phase shows a good result regardless of solvent. These results imply that ILs in solvent-rich phase are mostly dissociated. This holds true even for low dielectric constant (nonpolar) solvents. In the IL-rich phase, however, the undissociated IL state is more prominent. Figure 4 illustrates the typical LLE of ILs mixed with polar solvents (water and alcohols), whereas Figure 5 shows examples of LLE of ILs with nonpolar solvents. As can be seen, the long-range electrostatic interactions (free-ion model vs ion-pair model) can have a significant impact on the immiscibility gap. However, there does not seem to be a general pattern regarding the mutual solubility and the dielectric

Figure 3 illustrates the vapor pressures for [C2MIM][TF2N] and [C4MIM][BF4] solutions with different solvents. The freeion model (α = 1) shows larger deviations, especially for nonpolar solvents (benzene and cyclohexane). For polar solvents, the performances from the three methods are similar. Note that the prediction accuracies are poor for a few aqueous IL solutions (e.g., the ARD values for [C6MIM][TF2N]/water are greater than 100% from the three methods). The inaccuracy may be a result of possible self-aggregation of IL in aqueous solution (e.g., formation of micelles),54−58 a physical phenomenon not considered in our model. 4.4. Liquid−Liquid Equilibrium of Ionic Liquid Solutions. The LLE phase behaviors for IL-containing solutions are important in extraction and extractive distillation. As reported in Table S5, the LLE in various solvent types such as water, alcohols, ketones, ethers, alkylbenzenes, cycloalkanes, and alkanes (overall, 2912 data points) is investigated with 9010


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constant of the solvent. Furthermore, the consideration of degree of dissociation of ILs seems to result in a much lower upper critical solution temperature (UCST). This explains the fewer calculated data points for the dissociation model in Table 1. 4.5. Osmotic Coefficient and Mean Ionic Activity Coefficient. Tables S6 and S7 compare the predicted results for the osmotic coefficient (OC, ϕ) and mean ionic activity coefficient (MIAC) to experimental data. Such data covers a range of solvent conditions (xs0 > 0.7797), indicating dilute IL solutions. The ion-pair model gives the worst prediction accuracy (ARD 318.46%), while the free-ion model and dissociation model are comparable (ARD about 50%). The poor performance of the ion-pair model can be understood from Figure 6. The ion-pair model, which does not have any free ions in the system, does not reproduce the Debye−Hückel limiting behaviors. Both the free-ion model and the dissociation model allow the IL to behave like free ions and therefore properly reproduce the experimental values of OC and MIAC.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was partially supported by the Ministry of Science and Technology of Taiwan (NSC 101-2628-E-002-014-MY3, MOST 104-2221-E-002-186-MY3) and Ministry of Education of Taiwan (NTU-CDP-104R7876). The computational resources from the National Center for High-Performance Computing of Taiwan and the Computing and Information Networking Center of the National Taiwan University are acknowledged.

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(1) Plechkova, N. V.; Seddon, K. R. Applications of ionic liquids in the chemical industry. Chem. Soc. Rev. 2008, 37, 123−150. (2) Viswanathan, G.; Murugesan, S.; Pushparaj, V.; Nalamasu, O.; Ajayan, P. M.; Linhardt, R. J. Preparation of biopolymer fibers by electrospinning from room temperature ionic liquids. Biomacromolecules 2006, 7, 415−418. (3) Park, S.; Kazlauskas, R. J. Biocatalysis in ionic liquids - advantages beyond green technology. Curr. Opin. Biotechnol. 2003, 14, 432−437. (4) Planeta, J.; Karasek, P.; Roth, M. Distribution of sulfur-containing aromatics between hmim Tf2N and supercritical CO2: a case study for deep desulfurization of oil refinery streams by extraction with ionic liquids. Green Chem. 2006, 8, 70−77. (5) Cole-Hamilton, D. J. Homogeneous catalysis - new approaches to catalyst separation, recovery, and recycling. Science 2003, 299, 1702− 1706. (6) Blanchard, L. A.; Gu, Z. Y.; Brennecke, J. F. High-pressure phase behavior of ionic liquid/CO2 systems. J. Phys. Chem. B 2001, 105, 2437−2444. (7) Ito, Y.; Nohira, T. Non-conventional electrolytes for electrochemical applications. Electrochim. Acta 2000, 45, 2611−2622. (8) Marsh, K. N.; Boxall, J. A.; Lichtenthaler, R. Room temperature ionic liquids and their mixtures - a review. Fluid Phase Equilib. 2004, 219, 93−98. (9) Wang, H.; Wang, J.; Zhang, S.; Pei, Y.; Zhuo, K. Ionic Association of the Ionic Liquids [C4mim][BF4], [C4mim][PF6], and [Cnmim]Br in Molecular Solvents. ChemPhysChem 2009, 10, 2516−2523. (10) Zarrougui, R.; Dhahbi, M.; Lemordant, D. Volumetric and transport properties of N-Butyl-N-methylpyrrolidinium bis(Trifluoromethanesulfonyl)imide−methanol binary mixtures. Ionics 2011, 17, 343−352. (11) Ranke, J.; Stolte, S.; Störmann, R.; Arning, J.; Jastorff, B. Design of Sustainable Chemical ProductsThe Example of Ionic Liquids. Chem. Rev. 2007, 107, 2183−2206. (12) Podgoršek, A.; Salas, G.; Campbell, P. S.; Santini, C. C.; Pádua, A. A. H.; Costa Gomes, M. F.; Fenet, B.; Chauvin, Y. Influence of Ionic Association, Transport Properties, and Solvation on the Catalytic Hydrogenation of 1,3-Cyclohexadiene in Ionic Liquids. J. Phys. Chem. B 2011, 115, 12150−12159. (13) Patel, D. D.; Lee, J.-M. Applications of ionic liquids. Chem. Rec. 2012, 12, 329−355. (14) Heinrich, S. P.; Wermuth, C. G. Handbook of pharmaceutical salts: Properties, selection, and use, 2nd ed.; Verlag Helvetica Chimica ActaWiley-VCH: Weinheim, 2011. (15) Stoimenovski, J.; MacFarlane, D. R. Enhanced membrane transport of pharmaceutically active protic ionic liquids. Chem. Commun. 2011, 47, 11429−11431. (16) Tokuda, H.; Tsuzuki, S.; Susan, M. A. B. H.; Hayamizu, K.; Watanabe, M. How Ionic Are Room-Temperature Ionic Liquids? An Indicator of the Physicochemical Properties. J. Phys. Chem. B 2006, 110, 19593−19600. (17) Kanakubo, M.; Umecky, T.; Aizawa, T.; Kurata, Y. Waterinduced Acceleration of Transport Properties in Hydrophobic 1-Butyl-

5. CONCLUSIONS In this work, we assume that IL molecules can exist as ion pairs or free ions in the liquid state. We examined the prediction of various properties of ILs by assuming that IL always present as free ions (the free-ion model), as ion pairs (ion-pair model), or can transform between the two on chemical equilibrium (dissociation model). The poor performance of the free-ion model for the infinite dilution activity coefficient of nondissociable solvents in ILs indicates a strong screening effect (as a result of ion-pair formation) at high IL concentrations. The success of the ion-pair model at high IL concentrations implies that the COSMO-SAC model, which considers only interactions of molecules in contact, captures the short-range interactions in IL solutions. On the other hand, the poor performance of the ion-pair model for osmotic coefficient suggests the dissociation of the IL to free ions in the dilute IL solutions. The PDH model is necessary for describing the longrange ion−ion and ion−solvent interactions. By allowing the IL to transfer between the two configurations, the dissociation model allows most ILs to stay as ion pairs in high IL concentrations and as free-ions in dilute IL concentrations. Such transition of molecular configuration, together with the proper description of short and long-range interactions by COSMO-SAC and PDH models, provides the best overall prediction accuracy over the whole concentration range. Therefore, the dissociation model is expected to be a reliable tool for a priori prediction method for properties for ILcontaining mixtures as well for the design of new ILs with desired properties.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b01762. Complete list of ionic liquids and detailed information on the performance of the proposed models for different systems (PDF)

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A Priori Prediction of Dissociation Phenomena and Phase Behaviors

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