New Experimental Density Data and Soft-SAFT Models of

Article pubs.acs.org/JPCB

New Experimental Density Data and Soft-SAFT Models of Alkylimidazolium ([CnC1im]+) Chloride (Cl−), Methylsulfate ([MeSO4]−), and Dimethylphosphate ([Me2PO4]−) Based Ionic Liquids N. Mac Dowell,*,† F. Llovell,‡ N. Sun,§,∥ J. P. Hallett,⊥ A. George,§,∥ P. A. Hunt,# T. Welton,# B. A. Simmons,§,∥ and L. F. Vega‡,▽ †

Centre for Environmental Policy, Imperial College London, London SW7 1NA, United Kingdom MATGAS Research Center, Campus de la UAB, Bellaterra, Barcelona 08193, Spain § Joint BioEnergy Institute, Physical Biosciences Division, Lawrence Berkeley National Laboratory, Emeryville, California 94608, United States ∥ Biomass Science and Conversion Technology Department, Sandia National Laboratories, Livermore, California 94550, United States ⊥ Department of Chemical Engineering and #Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom ▽ Carburos Metálicos/Air Products Group, C/Aragón, 300, 08009 Barcelona, Spain ‡

ABSTRACT: Ionic liquids have been shown to have application in several areas of importance in the context of sustainable industrial activity. One application of particular interest is the ability of certain ionic liquids to dissolve biomass. This clearly marks them as useful materials with application within biorefineries. In this contribution, we present new coarse-grained soft-SAFT models and experimental density data of chloride (Cl−), methylsulfate ([MeSO4]−), and dimethylphosphate ([Me2PO4]−) based ionic liquids which are relevant for biomass deconstruction processes. Model parameters were obtained by fitting to pure component temperature density data, and the models were subsequently tested by assessing their ability to accurately calculate viscosity and interfacial surface tension. We also developed models of mixtures of the ionic liquids with water and shortchain linear alcohols. We decomposed the contributions to the excess Gibbs energy of mixing to chemical and structural contributions, and used this to provide some insight into the driving forces for solubility of molecular species in these ionic liquids.

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INTRODUCTION The sustainable production of biomass-derived fuels and chemicals via enzymatic routes requires deconstruction of the cell wall, to allow greater enzyme availability to the biomass holocellulose. Efficacious cell wall deconstruction methods generally entails removal of the lignin and decrystallization of the cellulose in the plant. Importantly, this must be achieved without the production of inhibitory compounds that hamper the downstream fermentation process. Additionally, an effective pretreatment method should enhance enzyme kinetics. Many deconstruction processes that can, to varying degrees, improve both the enzymatic hydrolysis rate and the final glucose yield have been proposed. All are subject to their own benefits and drawbacks, such that a commercially viable pretreatment process for future lignocellulosic biorefineries remains to be devised. Different pretreatment methods affect lignin, cellulose crystallinity, accessibility, and hydrolysis kinetics in different ways. Dilute acid,1 liquid hot water,2 and steam explosion do © 2014 American Chemical Society

not remove lignin or decrystallize cellulose but do alter the lignin structure, increasing the cellulose surface area available to enzymes. In addition, these methods remove hemicellulose from the biomass, removing a valuable source of pentose carbohydrates. Ammonia fiber expansion is very effective at decrystallizing cellulose, removing lignin, and increasing hydrolysis rates and yields in herbaceous biomass. However, this technique is less effective for woody biomass, or feedstocks with higher lignin content. Ammonia recycled percolation decrystallizes cellulose, increases accessible surface area, and removes lignin; however, it is subject to high energy costs and low solids loadings. Finally, alkali treatments are efficient delignification processes, with low inhibitor formation, but require expensive catalysis.3 Received: February 14, 2014 Revised: April 23, 2014 Published: May 19, 2014 6206

dx.doi.org/10.1021/jp501619y | J. Phys. Chem. B 2014, 118, 6206−6221

The Journal of Physical Chemistry B

Article

Ionic liquids (ILs), as a class of biomass solvents for biofuel production, have received attention in the past decade and have shown promising performance on all the pretreatment metrics described above.4 Unfortunately, many ILs for which data are available are not themselves suitable for biomass processing owing to their poor chemical stability; many of them, such as hexafluorophosphate ([PF6]−) and tetrafluoroborate ([BF4]−) based ILs, are hydrolytically unstable or corrosive, or both.5 This presents a complex engineering challenge in the development of a process centered on these fluids. However, other ILs such as 1-alkyl-3-methylimidazolium based ILs with chloride (Cl−), methylsulfate ([MeSO4]−), or dimethylphosphate ([Me2PO4]−) anions are considered to be promising ILs for biomass deconstruction.6 These ILs dissolve cellulose, and, upon precipitation with water, an amorphous solid with reduced crystallinity (arising from a reduced lignin/hemicellulose content) is produced, improving the surface accessibility for enzymatic attack. Importantly, these ILs do not degrade into dangerous products such as hydrofluoric acid. Coupled with a nonvolatile nature and tunable physical properties, their chemical stability makes these ILs suitable for use in these industrial processes.7,8 Thus, a biomass process option that involves IL solvents holds promise and a systems engineering based approach aimed at optimizing the energy efficiency and integration of unit operations will provide an important framework for further examination of the relative benefits of these new solvents. However, when compared with traditional process engineering using molecular fluids, ILs based process engineering is still very much in its infancy. One important limiting factor is the limited availability of thermophysical property data for ionic liquids. Another important consideration is the lack of experience in using ILs as working fluids in real processes. Thus, reliable methods for the prediction of thermophysical properties relevant to process engineering are required. One such method is the statistical associating fluid theory (SAFT)9,10 equation of state. The soft-SAFT11 variant in particular has previously been successfully applied to ILs.12−18 In this contribution, we present new experimental data for the C2, C4, C6, and C8 alkyl-methyl-imidazolium chloride, methylsulfate, and dimethylphosphate ILs. We then develop new soft-SAFT models for each of these ionic liquid families. Where data are available, we extend the modeling to binary mixtures of these ILs with H2O and short-chain alcohols. The remainder of this paper is structured as follows; in the next section, we present the experimental methodology, followed by a brief description of the theory used and the models we have proposed. We then present comparisons for the aforementioned ILs, between experimental data of their thermophysical properties (density, surface tension, viscosity, and phase behavior in solution) and the soft-SAFT models developed here.

Figure 1. Illustration of the structures of the ILs used in this study.

platinum thermometers together with Peltier elements, which have a temperature uncertainty of ± 0.01 °C and a range of 20−90 °C. Before each measurement, the accuracy is checked with both air and ultrapure water at 40 and 60 °C, respectively. ILs not liquid at room temperature were heated in a vaccum oven above their melting point and then loaded into a preheated cell. Supercooling was observed for some ILs ([C2mim]Cl and [C4mim]Cl) when they stay in liquid form after the temperature dropped below their melting points. For each ionic liquid, the analysis was performed in duplicate and the standard deviation is within 0.02%. The experimental data obtained in this work are presented in Tables 1−3 for the chloride, methylsulfate, and dimethylphosphate anions, respectively. These data were subsequently used to develop new softSAFT models. This procedure is discussed in the Theory Section.

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THEORY SECTION The statistical associating fluid theory (SAFT)9,10 is a successful approach where the total Helmholtz free energy of a given system is partitioned into different contributions to account for the various interactions of the compound. This equation of state is based on Wertheim’s TPT1 theory,19−22 and, since its publication, several versions have been developed.11,23−26 In this work, we use the soft-SAFT variant,11 which has been successfully applied to describe the thermodynamic behavior of ILs and their mixtures with gases, alcohols, and water.12−18 In this Article, only a high level description of the theory is presented. Further details can be found in previous publications.11,27 For a system of associating chain molecules, the soft-SAFT equation is presented as a = a ideal + a ref + achain + aassoc

(1)

ideal

where a corresponds to the ideal Helmholtz free energy of the mixture, and aref, achain, and aassoc are residual contributions to the free energy due to monomer−monomer repulsive and attractive (dispersion) interactions, to the formation of chains, and to site−site intermolecular association, respectively. Further terms explicitly describing the contribution to the free energy associated with polar28 or electrolyte29 interactions may also be added. However, to be effective, this requires accurate partitioning of the free energy, and often requires extra experimental data concerning dipole/quadrupole moments or dielectric constants. These data are often not available and can be difficult to measure. Therefore, we do not include these terms at this stage, instead aiming to describe the properties and phase behavior of ILs using the conventional SAFT approach. The reference term in the soft-SAFT equation of state (EoS) accounts for both repulsive and attractive van der Waals interactions among the monomers following a Lennard−Jones (LJ) intermolecular potential.11 The LJ monomer is charac-

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EXPERIMENTAL SECTION Materials. [Cnmim]Cl, [Cnmim][MeSO4], [C nmim][Me2PO4] (n = 2, 4, 6, 8) were purchased from IoLiTec Inc. (Tuscaloosa, AL). The structure of these ILs is presented in Figure 1. Their purity is reported as being above 98%, and they are used as received. Density Measurement and Results. IL densities were measured using an Anton Paar DMA 4100 digital densimeter with an accuracy of ±0.0001 g/cm3. The temperature in the oscillating U-tube cell was measured with two integrated Pt 100 6207



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Table 1. Experimental Densities Obtained for the Chloride (Cl−) IL Family T/K

ρ[C2mim] (mol·dm−3)




293.16 298.14 303.14 308.14 313.14 318.14 323.14 328.14 333.14 338.14 343.14 348.14 353.14 358.14 363.14

solid solid solid solid solid solid solid solid 7.6651 7.6463 7.6275 7.6088 7.5897 7.5709 7.5529

solid solid 6.1837 6.1676 6.1510 6.1350 6.1190 6.1029 6.0869 6.0714 6.0554 6.0400 6.0245 6.0090 5.9936

5.1485 5.1347 5.1204 5.1066 5.0922 5.0784 5.0646 5.0508 5.0370 5.0232 5.0094 4.9956 4.9817 4.9684 4.9546

4.3871 4.3749 4.3624 4.3498 4.3372 4.3251 4.3125 4.3004 4.2878 4.2757 4.2640 4.2519 4.2397 4.2276 4.2159

Table 2. Experimental Densities Obtained for the Methylsulfate ([Me2SO4]−) IL Family T/K





293.16 298.14 303.14 308.14 313.14 318.14 323.14 328.14 333.14 338.14 343.14 348.14 353.14 358.14

5.7937 5.7782 5.7626 5.7471 5.7318 5.7162 5.7011 5.6858 5.6707 5.6556 5.6405 5.6257 5.6108 5.5959

4.8426 4.8290 4.8158 4.8027 4.7893 4.7761 4.7631 4.7499 4.7369 4.7240 4.7112 4.6984 4.6856 4.6728

4.1741 4.1626 4.1507 4.1390 4.1273 4.1156 4.1040 4.0924 4.0809 4.0694 4.0579 4.0468 4.0353 4.0241

3.6758 3.6650 3.6542 3.6438 3.6330 3.6222 3.6116 3.6010 3.5905 3.5799 3.5693 3.5588 3.5485 3.5381

Table 3. Experimental Densities Obtained for the Dimethylphosphate ([Me2PO4]−) IL Family T/K





293.16 298.14 303.14 308.14 313.14 318.14 323.14 328.14 333.14 338.14 343.14 348.14 353.14 358.14 363.14

5.1628 5.1484 5.1340 5.1196 5.1052 5.0908 5.0764 5.0624 5.0481 5.0341 5.0201 5.0066 4.9926 4.9786 4.9651

4.3680 4.3552 4.3423 4.3294 4.3166 4.3037 4.2908 4.2782 4.2655 4.2530 4.2405 4.2280 4.2155 4.2031 4.1908

3.8298 3.8182 3.8067 3.7953 3.7840 3.7727 3.7611 3.7498 3.7385 3.7272 3.7163 3.7050 3.6940 3.6827 3.6718

3.3884 3.3778 3.3675 3.3568 3.3469 3.3366 3.3263 3.3163 3.3060 3.2960 3.2860 3.2760 3.2660 3.2560 3.2460

terized by the segment diameter σii and the dispersive energy between segments, εii/kB. This term is computed using the equation of Johnson et al.,30 fitted to molecular simulation data of the LJ monomer in a wide range of temperature and pressure.11 The chain and association terms come directly from Wertheim’s theory and are formally identical in the different versions of SAFT:

n

achain = ρkBT ∑ xi(1 − mi) ln giiLJ(σii) i=1

n ⎡ Mi ⎛ Xa , i ⎞ M⎤ aassoc = ρkBT ∑ xi⎢ ∑ ⎜ln Xa , i − ⎟ + i⎥ ⎝ ⎢ 2 ⎠ 2 ⎥⎦ i=1 ⎣ a=1

6208

(2)

(3)



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where ρ is the molecular density, kB is the Boltzmann constant, T is the absolute temperature, mi is the number of monomer segments forming the chain, xi is the molar fraction of component i, and gLJ ii is the radial distribution function of a LJ monomer fluid. Johnson’s equation for LJ chains,31 fitted to simulation data, is used to evaluate gLJ ii . Xa,i corresponds to the fraction of molecules of component i not bonded at sites of type a, and Mi is the number of association sites of type a on component i. The associating term is solved numerically using the procedure proposed by Tan et al.32 For mixtures, it is necessary to calculate the values of the unlike-interaction parameters. The reference term does not explicitly have an expression for mixtures, and hence, the van der Waals one-fluid theory is applied to obtain an adequate equation. The values of the effective soft-SAFT parameters σij and εij are determined using the modified Lorentz−Berthelot (LB) combining rules: σii + σjj σij = ηij (4) 2

εij = ξij εiiεjj

As in previous contributions,16,36 we treat it as a temperatureindependent parameter, fitted to real surface tension data. Assuming a planar interface and neglecting the density dependence of the influence parameter, it is possible to solve the density profile along the interface. The interfacial tension is a macroscopic consequence of the density profile across the phase boundary, and it is obtained from:

=

⎛ (K HB)1/3 + (K HB)1/3 ⎞3 ii jj ⎟ ⎟ 2 ⎝ ⎠

HB HB HB εabHB, ij = kab , ij εab , iiεab , jj

ΔHB ab,ij

ηo = 40.785

(6) (7)

a=

∫

n

∑∑ i=1 j=1

⎤ 1 cij∇ρi ∇ρj ⎥d3r ⎥⎦ 2

(9)

(10)

M wT Fc , 2/3 vc Ω*(T *)

(11)

where Mw is the molecular weight, vc is the critical volume, and Ω* is the reduced collision integral as a function of a dimensionless temperature T* = 1.2593Tr, with Tr being the reduced temperature with respect to the critical temperature of the compound (T/Tc).42 Fc is an empirical correcting factor that includes information about the nonsphericity of the molecule through the acentric factor, ω, the polarity through the dipole moment, μ, and the hydrogen bonding, using an empirical parameter, κ. In summary, the calculation of the dilute gas term requires the evaluation of the critical parameters, the acentric factor, and the dipole moment of the molecule. In the case of ionic liquids (and heavy molecular fluids), there is a significant degree of uncertainty associated with these data. Furthermore, it is necessary to add an empirical parameter κ in associating systems. This parameter is usually fitted to dilute-gas viscosity data,41 which is not available for ionic liquids. We have evaluated the effect of the dilute gas term on the total value of the viscosity of the fluid. We have performed a preliminary calculation for [C8mim]Cl at atmospheric pressure in the temperature range 298−363 K. The critical parameters and the acentric factor of [C8mim]Cl have been taken from the work of Valderrama and Robles,43 who determined those properties using an extended group contribution method based on the concepts of Lydersen44 and of Joback and Reid.45 The dipole moment has been approximated using the value for [C2mim]Cl proposed in the work of Izgorodina et al.46 Due to the lack of dilute-gas experimental data, the value of κ has been taken from the value of water proposed in the original work of Chung et al.41 The purpose of this calculation is not to have an exact accurate value but to see its order of magnitude compared to the total viscosity of the system. These preliminary calculations have shown that the influence of the dilute-gas term in the range of interest is negligible, contributing less than 0.01% to the total viscosity at the highest temperature with the

where and are two adjustable parameters for the associating volume and energy, respectively. The association HB HB parameters describing the mixture, εab,ij /kB and Kab,ij are calculated in the same way as the dispersion parameters, using the mean arithmetic of the radius of the associating site rc for Kab,ij and the geometric average for εHB ab,ij/kB, following the work of Fu and Sandler.33 The use of binary parameters will depend on the complexity of the system. They will be used only if parameters predicted from the LB averages are insufficiently accurate. The interfacial tension has been computed using the density gradient theory (DGT) of van der Waals.34 Following the approach of Cahn and Hilliard,35 the Helmholtz free energy density is expanded in a Taylor series around a0, the free energy density term of the homogeneous fluid at the local density, and truncated after the second order term: n

i=1

The dilute gas term, η0 is calculated using the model proposed by Chung et al.41 and is based on a modification of the Chapman−Enskog kinetic theory of gases

kHB ab,ij

⎡ ⎢a (ρ ) + ⎢⎣ 0

∑ ρi μ0i + p0 ]dz

η = η0 + Δη

(5)

HB ⎜ Δab , ij ⎜

∫−∞

[a0(ρ) −

where μ0i and p0 are the equilibrium chemical potential and pressure, respectively, and z is the direction perpendicular to the interface. Further details on the DGT implementation on SAFT-type equations can be found in the literature.36−38 The viscosity, η, has been evaluated applying the free-volume theory.39,40 This approach divides the contribution to the viscosity in two terms: a diluted gas term and a dense liquid term,

where ηij and ξij are the adjustable unlike binary parameters for the segment diameter and dispersive energy, respectively. In addition, the chain length m of a mixture is obtained by a linear compositional mixing rule. Finally, the mixture HB association parameters εHB ab,ij/kB and Kab,ij are also calculated using the LB combining rules using the mean arithmetic of the radius of the associating site rc for KHB ab,ij and the geometric average for εHB ab,ij/kB: HB Kab , ij

n

−∞

γ=2

(8)

where the integration is performed in the entire system volume. ∇ρx represents the local gradient in density of a given component x, while cij represents the direct correlation function, which is unknown for an inhomogeneous fluid. In DGT, it is often treated phenomenologically as an adjustable parameter, commonly referred to as the “influence” parameter. 6209



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The Soft-SAFT Models for the ILs Studied in This Work. To date, there has been an extensive body of work applying various versions of SAFT52−55 and other modeling approaches to ILs based fluids. These other approaches have ranged from cubic equations-of-state56,57 to lattice models such as NRTL,58,59 UNIQUAC60,61 or from group contribution based methods62,63 to quantum mechanics based models.64,65 These various approaches have been extensively discussed in a recent review paper.66 However, it is important to recall that SAFT-type models are inherently coarse-grained models.67 Thus, to apply a SAFT based equation of state to a given compound, it is first necessary to propose a model containing an appropriate level of physical detail defined herein as an acceptable compromise between computational efficiency and the level of physical fidelity required to obtain reliable descriptions of the thermophysical properties of a given fluid and its mixtures. ILs are known to be highly structured fluids, and this structuring is mediated by the inclusion of association sites on the model. It has been observed in previous work50,51,68 that this is of particular importance when considering mixtures. In the case of ILs, there remains significant debate surrounding the fluid structure and the anion−cation solvation interactions. Thus, based in previous work12,13 and given the level of approximation of the model used here, we elect to use a simple model of the fluid, where the anion and cation are considered as single entity with specific strong, anisotropic interactions. This kind of model has been successfully applied to a range of ILs in previous contributions.12−18 We would emphasize that this is a convention we have adopted in this work to simplify our models; we are not asserting that ILs are always paired in a real fluid. The accuracy of the model for the properties studied here is assessed by the comparison with the experimental data. Based on this simplification, it remains to decide the number of association sites (or regions of short-ranged, anisotropic attractive interactions between two ILs) for each compound. This will depend on the charge and polarity distribution of the molecule. To make this choice, we have evaluated the density charge distribution of the three different anions of this work by using the conductor-like screening model for realistic solvation tool, abbreviated as COSMO-RS.69 COSMO-RS is a theory based on quantum calculations, which describes the interactions in a fluid as local contact interactions of molecular surfaces. Those interaction energies are quantified by the values of the two screening charge densities, σ and σ′, which form a molecular contact. In COSMO-RS, the charge density is measured as the response of an electric conductor to the charge density of the molecule and, therefore, a measure for the polarity of the different molecular regions.70 The quantum chemical COSMO calculations were performed on the density functional theory (DFT) level, utilizing the BP functional with RI (resolution of identity) approximation and a triple-ζ valence polarized basis set (TZVP). All structures were fully optimized. The quantum chemical calculations are performed only once for each molecule. The results of the COSMO calculation are stored in the so-called COSMO files, which are collected in a database. All calculations were performed with the TURBOMOLE program package.71 For more detail concerning the use of COSMO-RS for the calculation of physical properties of ionic liquids, the reader is referred to the work of Diedenhofen and Klamt.72 According to the COSMO calculations, the chloride anion presents a narrow σ distribution of the negative charge; based

remainder arising from the dense liquid term. This is due to the very high viscosities of ionic liquids, which mainly depend on the dense-state term. Consequently, to simplify the problem, we have omitted this term. The dense-state term is represented by 3/2 ⎤ ⎡ ⎛ 103M w αρ103M w + P /ρ ⎞ ⎥ ⎢ ⎟ Δη = ρLv E exp B⎜ ⎢ ⎝ 3RT RT ⎠ ⎥⎦ ⎣

(12)

Equation 12 relates the molecular structure with a representation of the free-volume fraction and this fraction with the intermolecular energy controlling the potential field in which the molecular diffusion takes place;39,40 R is the universal constant, while the pressure P and the density ρ are calculated from soft-SAFT. The model includes three adjustable parameters: Lv is a length parameter related to the structure of the molecules and the characteristic relaxation time, α is the proportionality between the energy barrier and the density, and B corresponds to the free-volume overlap. These parameters are fitted to experimental viscosity data. More details concerning the implementation of this approach with softSAFT can be found in some of our recent publications.47,48 Parameter Estimation Procedure. Appropriate values for the soft-SAFT parameters are estimated by optimizing the theoretical description of the experimental data. Typically, vapor−liquid equilibrium data are used for this purpose, but as ILs for all intents and purposes do not exhibit a vapor phase, pure component parameters are obtained from single-phase liquid density data at atmospheric pressure. All of the parameter estimation performed in this work is carried out by the minimization of a relative least-squares objective function constructed from the appropriate sum of individual residuals: 1 min FObj = θ Nx

⎡ x Exp(T ) − x Calc(T ; θ ) ⎤2 j j j j ⎥ ∑ ⎢⎢ Exp ⎥⎦ x T ( ) j j j=1 ⎣ Nx

(13)

where θ is the vector of parameters θ = (m, σii, εii, εHB ab,ii, Kab,ii) and Nx is the number of experimental data points of a given property x. The superscripts Exp and Calc denote the experimental data points and calculated values, respectively. A least-squares function is chosen, as it is continuous and mathematically well-behaved, and is one of the most widely used in the estimation of equation of state parameters. The performance of our models in reproducing a given property x is reported using an overall percentage average absolute deviation (%AAD): %AADx =

100 NP

NP

∑ i=1

xiExp(Ti ) − xiCalc(Ti ; θ ) xiExp(Ti )

(14)

The problems associated with parameter degeneracy in SAFT-type approaches are well recognized.49−51 To address this challenge, in addition to fitting the soft-SAFT parameters liquid density data, we subsequently test the adequacy of the models by investigating their ability to evaluate other important properties such as interfacial surface tension and viscosity, as well as the ability to provide a satisfactory performance in mixture calculations. This is considered a more rational means of obtaining reliable parameter sets than simply selecting the parameter set which corresponds to a mathematical minimum. 6210



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Table 4. Soft-SAFT Parameters Characterizing the Pure ILs for the [CnC1im]Cl Familya [CnC1im]Cl n n n n

= = = =

2 4 6 8

m

σii (Å)

εii/kB (K)

εHB aa,ii/kB (K)

Kaa,ii (Å3)

%AAD

3.717 4.650 5.605 6.580

3.795 3.795 3.795 3.795

485.0 454.2 439.0 431.0

2200 2200 2200 2200

2250 2250 2250 2250

0.0107 0.0543 0.0882 0.0763

The number of segments, m, the diameter of the spherical core, σii, the depth, εii/kB of the dispersive interaction, the depth, εHB aa,ii/kB, of the associating site−site interaction, and the bonding volume, Kaa,ii. a

on this and also on the previous work of similar ILs,12,17 we have decided to model this ionic liquid with only one association site used to mediate the IL−IL interactions. For the case of the methylsulfate anion, [MeSO4]− anion, the breadth of the peaks on in the positive sigma region is wider; as the cation is the same, this suggests the possibility that this would correspond to two specific association sites. Therefore, we have decided to model this ionic liquid using two association sites, representing two possible types of association interaction between the cation−anion of different molecules, depending on how they approach each other. This decision is also in accordance with a study published by Gjikaj and co-workers, where the cation−anion interactions on [C1mim][MeSO4] and [C4mim][MeSO4] were characterized by X-ray analysis, Raman spectroscopy, and NMR.73 The authors identified two to three cation−anion possible hydrogen bonds. As our purpose is to have the simplest possible model and always use the same number of association sites for all the members of the same family, we have kept our choice to two association sites. Finally, in the case of the dimethylphosphate anion, [Me2PO4]−, there are two overlapping peaks located at a σ value of approximately 2 but also a wide polarity distribution of the anion up to a slightly positive charge (negative σ value), similarly to the case of the [MeSO4]− anion. As the cation is the same, and following the previous argument, we have chosen to model this ionic liquid with three sites, two of one type and one of another type. Again, this is consistent with the work of Indarto and Palgunadi, who studied the [C1mim][M2PO4] cation−anion interactions by ab initio calculations,74 and found three possible hydrogen-bonding interactions. It is also consistent with previous modeling work of ILs with a similar ILs, the [Cnmim][Tf2N] family.14,16 Regarding the calculation for binary mixtures with water and short-chain alcohols, a molecular model for these solvents is also required. The model for water is taken from previous work.75 Water is considered a single spherical LJ monomer (m = 1) with four association sites, two sites of type e corresponding to the lone pairs of electrons, and two of type H corresponding to the hydrogen atoms (only e−H bonding is allowed), to preserve the tetrahedral character of the molecular geometry of the compound. In addition, alcohols are modeled as homonuclear chainlike molecules where the hydroxyl group is mimicked by two square-well sites embedded off-center in one of the LJ segments. One site is of type e corresponding to the lone pairs of electrons, and the other site is of type H corresponding to the hydrogen atom of the hydroxyl group (again, only e−H bonding is allowed). This model has been previously tested with soft-SAFT and found to provide good agreement to describe the behavior of alcohols and their mixtures with alkanes,76 carbon dioxide77 and water.78 Although the models for the ILs could seem too simple to reliably reproduce the behavior of multicomponent mixtures,

we hypothesize that our proposed association schemes will be sufficient to describe the main physical features of the compounds which we are studying here. Hence, we start with the goal of keeping the model as simple as possible to facilitate its further application in process modeling and simulation. Additional refinements will be included, if necessary, in future work.

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ILS WITH A CHLORIDE ANION [CnC1im]Cl with n = 2, 4, 6, and 8. Using the new experimental data presented in Table 1, we have fitted the softSAFT parameters to find an appropriate set of values for each compound using the one-site association scheme described in previous section. It is known that the optimization of five parameters to a limited amount of experimental data can give rise to potentially severe parameter degeneracy. This is particularly significant for the case of ILs, where single-phase density data are used for parameter optimization, instead of the classical two-phase vapor−liquid equilibrium data, commonly used for most fluids which exhibit a vapor phase. Hence, several assumptions based on physical arguments, previous experience, and the transferability of the soft-SAFT parameters for similar compounds are applied here, to reduce the dimensionality of the problem. First, a constraint is imposed on the site−site association energy and the site−site association bonding-volume. It is assumed that the associating interactions are independent of the alkyl-chain length of the cation, and are assumed to be constant for all the members of the same family. We have made this assumption in several previous papers, and this has been shown to be a robust approximation.12−17 Further, we have previously observed that the site−site bonding volume and site−site association energy are highly correlated parameters. Thus, we assign a fixed value of 22503 to the bonding volume. This value has been shown to be appropriate for a number of other imidazolium based ILs with a range of anions such as [BF4]−,12 [PF6]−,12,17 and [Tf2N]−.13,16 Hence, the parametrization is reduced to four variables in the first instance. With these assumptions, we have performed the parameter estimation for [C2mim]Cl, [C4mim]Cl, [C6mim]Cl, and [C8mim]Cl. An average association energy value of εHB aa,ii/kB = 2000 K was found to be appropriate for all the compounds. From these calculations, it was possible to identify the chain length, m, and the dispersive energy, εii/kB, which were observed to exert a strong influence on the final results, while the segment diameter, σii, was observed to vary only slightly with increasing alkyl chain length. Hence, a third restriction was assumed and the segment diameter was fixed to a constant average, leaving only m and εii/kB free. This last hypothesis assumes that the volume change of the ionic liquid with increasing alkyl chain length is effectively mediated via manipulation of the chain length parameter m. If one considers 6211



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that the difference between the compounds is related to the addition of an integer number of CH2 groups to one particular atom of the imidazolium ring of the cation, the assumption appears to be reasonable. The final set of soft-SAFT parameters are presented in Table 4 with the associated temperature-density calculations shown in Figure 2.

Figure 3. Interfacial tension−temperature plot for (a) [C4C1im]Cl, (b) [C6C1im]Cl, and (c) [C8C1im]Cl. Symbols are experimental data,79 and continuous curves are the soft-SAFT calculations.

Table 5. Influence Parameter, cij, used to Calculate the Interfacial Surface Tension of [CnC1im]Cl (n = 4, 6, 8)

Figure 2. Temperature−density plots for (a) [C2C1im]Cl, (b) [C4C1im]Cl, (c) [C6C1im]Cl, and (d) [C8C1im]Cl. Symbols represent the new experimental data presented in Table 1, and continuous curves the soft-SAFT calculations.

cij × 1019 (J·m/mol5)

%AAD

n=4 n=6 n=8

8.06 9.44 7.50

0.29 0.54 0.23

experimental data is found, with an overall average of %AAD = 0.35%. The slope of the surface tension, mostly determined by the dispersive energy soft-SAFT parameter, is accurately reproduced in all cases, with some slight deviations at the lowest temperatures for [C4mim]Cl. Similarly, the viscosity of [C8mim]Cl, [C4mim]Cl, [C6mim]Cl, and [C8mim]Cl at atmospheric pressure is calculated by means of the free-volume theory. The parameters α, B, and Lv are adjusted to the available viscosity data80−82 (see Table 6), and the description

As can be observed from Table 4, the final model gives an excellent description of the available data with an overall relative error of 0.057%. As expected, the chain length parameter m increases with the molecular weight of the compound. However, it is interesting to note that the dispersive energy parameter decreases with the increase of the molecular weight, contrary to previously reported results for other anions.12,13,16 The very high value for [C2mim]Cl is a consequence of the high density of this ionic liquid (more than 7 mol·dm−3). This indicates a compact structure, probably caused by the small size of the anion combined with the short-alkyl chain in the imidazolium cation. Finally, we note that it is possible to correlate the soft-SAFT parameters with the molecular weight of the ILs by using simple linear correlations: m = 0.0340MWIL + 1.2823 (15)

Table 6. Parameters used to Calculate the Viscosity for [C8C1im]Cl: α, B, and Lv [CnC1im]Cl n n n n

= = = =

2 4 6 8

α (J·m3/mol·kg)

B

Lv (Å)

.

66.72 132.00 188.00 254.50

0.07866 0.03965 0.02126 0.01404

0.01192 0.0009737 0.005725 0.008849

3.28 6.87 9.03 14.75

obtained is represented in Figure 4. Again, the shape of the viscosity curve is reliably reproduced, with an overall %AAD = 8.48%. Noting that the data span 4 orders of magnitude, it is remarkable to note the adequacy of the description obtained using such simple models. Binary Mixtures. Once a final set of parameters for the pure ILs had been obtained, we further evaluated the adequacy of our model with the calculation of the thermophysical properties of some binary mixtures, with particular attention on the interactions with water and alcohols. Recent biomass deconstruction options have begun using water as a cosolvent to break up ionic liquid self-association and to temper overtreatment of biomass.83 The precise effect of water on the IL structure and chemical properties is an issue of longstanding debate,84 as IL−water mixtures are popular solvents for many biological applications. In addition to water, IL mixtures with short chain alcohols present similar opportunities to disrupt hydrogen bonding networks; methanol and ethanol

and mεii /kB = 12.334MWIL − 22.781

[CnC1im]Cl

(16)

where eq 15 is dimensionless and eq 16 has units of K. As discussed in the section wherein the parameter estimation procedure is described, we now test the above-described models by evaluating their ability to describe the interfacial tension and viscosity. In addition to being important thermophysical properties from an engineering perspective, they also provide a stern test of our proposed models. For the case of the interfacial tension, some data have been found for three compounds: [C4mim]Cl, [C6mim]Cl, and [C8mim]Cl.79 These are used to fit the influence parameter cij for each compound using the soft-SAFT pure component parameters presented in Table 4. The results of these calculations are presented in Figure 3, and the influence parameters are provided in Table 5. In all cases, excellent agreement with the 6212



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Figure 5. Isobaric temperature−composition projections for binary mixtures of (a) [C4C1im]Cl + H2O and (b) [C4C1im]Cl + EtOH at 0.1 MPa. Symbols are experimental data,86 and curves are the softSAFT calculations.

for each mixture, whose values are presented in Table 7. It is interesting to note that the ξ values for water and ethanol Table 7. Unlike Interaction Dispersion Energy Parameters Used to Calculate the Vapor−Liquid Equilibrium for the [CnC1im]Cl Mixtures Figure 4. Viscosity−temperature plot for [CnC1Im]Cl. Symbols are experimental data,80−82 and continuous curves are the soft-SAFT calculations. In panel (a), the square symbols (□) represent the data for [C2C1Im]Cl and the diamonds (◇) represent the data for [C4C1Im]Cl. Similarly, in panel (b), the square symbols (□) represent the data for [C6C1Im]Cl and the diamonds (◇) represent the data for [C8C1Im]Cl.

[CnC1im]Cl + j

ηij

ξij

%AAD

n = 4, j = H2O n = 8, j = H2O n = 4, j = C2H5OH

1.0 1.0 1.0

1.320 1.320 1.305

2.37 0.47 1.01

mixtures are greater than unity and very close to each other. That means that the dispersive interactions between the ionic liquid with water and ethanol are underpredicted by the Lorentz−Berthelot combining rule, indicating a stronger interaction. Then, the value obtained for water has been transferred to predict the density of aqueous [C8C1im]Cl. Four isothermal projections between 298.15 and 343.15 K are shown in Figure 6. Here, the agreement between the experimental data82 and the soft-SAFT calculation is excellent along the whole composition diagram.

are also potential wash solvents for ILs based cellulose processing applications.83 Thus, we examine mixtures of H2O, CH3OH, and C2H5OH with the ILs presented in this paper. The soft-SAFT models for these fluids are obtained from previous contributions.75,85 For this purpose, we went on to study isobaric mixtures of [C4C1Im]Cl + C2H5OH and [C4C1Im]Cl + H2O and isothermal mixtures of [C8C1Im]Cl + H2O. The choice of these mixtures was based on the availability of experimental data.82,86 A key issue when modeling these mixtures consists of considering the effects of self- and cross-association between water or alcohols and the ILs. In this regard, particular care has been taken in proposing a reasonable set of interactions for each mixture. For the chloride family of ILs, we remind the reader that the anion−cation pair is modeled via one associating site A. The dual positive−negative nature of this site allows a possible crossed-interaction either with the oxygen atoms (sites e) or with the hydrogen atoms (sites H) of water and alcohols. Hence, Ae and AH interactions are allowed and assumed to be equal and constant. The cross-association values are obtained from eqs 6 and 7 without any adjustment (i.e., HB ΔHB ab,ij and kab,ij are equal to 1), to keep the model as predictive as possible. The same assumptions were successfully applied to describe the interactions between water and [PF6]− imidazolium based ILs in a previous paper.17 First, the phase equilibrium of [C4C1C1im]Cl with water and ethanol at atmospheric conditions was studied and is plotted in Figure 5. An excellent description of the equilibrium was reached by only fitting the unlike dispersive energy interaction parameter ξ

■

ILS WITH A METHYLSULFATE ANION [CnC1im][MeSO4] with n = 2, 4, 6, and 8. In this section, we present the results of the modeling of the alkylimidazolium [MeSO4]− based ILs. Using the data presented in Table 2, the procedure presented in the subsection entitled “Parameter Estimation Procedure”, and the two-site model suggested in the subsection entitled “The Soft-SAFT Models for the ILs Studied in This Work”, we have derived a new set of parameters for each ionic liquid. As in the previous case, a number of assumptions are made in order to reduce the parameter degeneracy and concurrently make the parametrization as transferable as possible. Hence, we have again assumed constant values for the association parameters for the entire [MeSO4]− family, fixing the volume of association to 2250 3. For the energy of association, a value of 4000K was found to give good accuracy for all compounds. Further, quite distinct to what was observed for the chloride anion, we observed that the final value of the dispersive energy, εii/kB was negligibly sensitive to the alkyl chain length. Hence, we have kept this value constant at 400K. This reduces the dimensionality of the optimization problem to two: we only need to determine the 6213



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Figure 6. Isothermal density−composition projections for binary mixtures of [C8C1im]Cl + H2O at (a) T = 298.15 K, (b) T = 313.15 K, (c) T = 328.15 K, and (d) T = 343.15 K.

Table 8. Soft-SAFT Parameters Characterizing the Pure ILs for the [CnC1im][MeSO4] Familya [CnC1im]+[MeSO4]− n n n n n

= = = = =

1 2 4 6 8

m

σii (Å)

εii/kB (K)

εHB aa,ii/kB (K)

KeH,ii (Å3)

%AAD

5.085 5.390 6.010 6.650 7.250

3.650 3.698 3.786 3.846 3.900

400 400 400 400 400

4000 4000 4000 4000 4000

2250 2250 2250 2250 2250

0.6200b 0.1320 0.3185 0.0979 0.0571

The number of segments, m, the diameter of the spherical core, σii, the depth, εii/kB of the dispersive interaction, the depth, εHB aa,ii/kB, of the associating site−site interaction, and the bonding volume, Kaa,ii. bThe density of [C1C1im][MeSO4] was calculated using the parameters obtained from eqs 17 and 18. a

size parameters m and σii. This hypothesis had already been successfully applied with soft-SAFT for the modeling of the [Tf2N]− anion with the pyridinium cation.15 The final set of soft-SAFT parameters for the [CnC1im][MeSO4] are presented in Table 8. As can be observed from Figure 7, the final models give an excellent description of the available data with an overall relative error of 0.04%. Assuming that εii/kB, εHB eH,ii/kB, and KeH,ii are constant and transferable within this family of compounds, the remaining parameters m and σii could again be correlated with the molecular weight of the ILs: m = 0.02221MWIL + 0.4604

(17)

and mσii3 = 1.874MWIL − 142.9

Figure 7. Temperature−density plots for (a) [C1C1im][MeSO4], (b) [C2C1im][MeSO4], (c) [C4C1im][MeSO4], (d) [C6C1im][MeSO4], and (e) [C8C1im][MeSO4]. Symbols represent the experimental data, and continuous curves the soft-SAFT calculations. Black squares represent the data obtained in this work, and red circles represent literature data.87,88

(18)

where eq 17 is dimensionless and eq 18 has units of Å3. Using the available data, we have also calculated the temperature− density diagram of [C1C1im][MeSO4]. We test here the transferability of our approach by using the correlations presented in eqs 17 and 18 to predict the soft-SAFT parameters for [C1C1im][MeSO4]. We have then predicted the density of this compound with an accuracy within 0.62% when compared to experimental data.87,88 Considering the fact that there are two sets of data from different sources for [C1C1im][MeSO4],

the accuracy of the prediction is of the same order than that of the fitted compounds. In addition to the pure-component density data presented in Table 2, literature data for [C1C1im][MeSO4] and [C4mim][MeSO4] were also available for interfacial surface tension, γ, 6214



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and viscosity, η.88−90 These data were again used to test the pure component models as for the chloride based ILs. We have first calculated the interfacial tension of the [MeSO4]− ionic liquids, by using the optimized soft-SAFT molecular parameters and fitting the cij parameter to the available data. These calculations are presented in Figure 8, and

The results of these calculations are presented in Figure 9, and the relevant parameters are presented in Table 10.

Figure 9. Viscosity−temperature plots for (a) [C1C1im][MeSO4] and (b) [C4C1im][MeSO4]. Continuous curves represent the soft-SAFT calculations, and symbols the experimental data.89,95

Table 10. Parameters Used to Calculate the Viscosity for the [CnC1im][MeSO4] Compounds: α, B, and Lv

Figure 8. Interfacial tension−temperature plots for (a) [C1C1im][MeSO4] and (b) [C4C1im][MeSO4]. Continuous curves represent the soft-SAFT calculations, and symbols the experimental data. In the case of [C4C1im][MeSO4], square symbols represent the data of Pereiro et al.90 while the data of Fernandez et al.89 are represented by open circles. The distinct difference in behavior of these data as a function of temperature is clearly visible here.

Table 9. Parameters Used to Calculate the Interfacial Surface Tension for the [CnC1Im][MeSO4] Compounds: cij cij × 1018 (J·m/mol5)

%AAD

n=1 n=4

1.098 1.111

0.79 2.74

α (J·m3/mol·kg)

B

Lv (Å)

%AAD

n=1 n=4

213.3 314.5

0.004166 0.004166

0.07158 0.07158

3.40 2.55

Binary Mixtures of [C4C1im][MeSO4]. In this subsection, we have studied binary mixtures of [C4C1im][MeSO4] using the same procedure described for the case of the chloride anion. Mixture data for the [C4C1im][MeSO4] IL with water and ethanol at atmospheric pressure have been found in the literature,91 and these data have been used to validate our model. The phase equilibria of these mixtures at atmospheric pressure are presented in Figure 10.

the final value of the order parameter, cij, is presented in Table 9. Our models provide a reliable description of the interfacial tension of these ionic liquids, using a very similar value for cij, in both cases, with an average error of 1.77%.

[CnC1im][MeSO4]

[CnC1im][MeSO4]

For [C1C1im][MeSO4], the slope of the curve calculated is in very good agreement with the available experimental data.89 There is, however, some deviation between the model for [C4C1im][MeSO4] and the experimental data at low temperatures. However, it is important to note that there were two different sets of experimental data available for this compound.89,90 These data sets exhibited significantly different temperature dependence. We observe that our proposed model provides a reliable description of the experimental data presented by Fernandez et al.89 while the data presented by Pereiro et al.90 are less well described. Concerning the viscosity, the experimental data are used to fit the three viscosity parameters α, B, and Lv. Keeping in mind the search for transferable paramaterizations, we use the same value of B and Lv for both compounds. The difference between the two compounds is related to the length of the alkyl chain and the α parameter can account for this difference. We obtain a good description of the viscosity of both ILs, with an average %AAD of 2.97%. While this does not appear overly impressive, it is worth noting that this measure of error corresponds to an average deviation of less than 1.2 mPa·s from the available data.

Figure 10. Isobaric temperature−composition projection of binary mixtures of (a) [C4C1im][MeSO4] + H2O and (b) C2H5OH at P = 0.1 MPa. Continuous curves represent the soft-SAFT calculation, while symbols represent the data of Calvar et al.91

For the [MeSO4]− ILs family, two association sites, one positive A and one negative B, were used to build the molecular model. Here, it is assumed that the positive site A will crossinteract with the negative sites of water and ethanol (representing the electron pair on the oxygen atom of those molecules). On the other hand, the negative site B will interact with the positive sites of water and ethanol (representing the 6215



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hydrogen bonding. This evidence further justifies our choice of a three-site model for this family; a three-site association scheme has increased possibilities of self-association over and above a one- or two-site model. As previously, the data in Table 3 were used to obtain softSAFT models of the C2, C4, C6, and C8 compounds. The previous ideas to reduce the dimensionality of the optimization problem are used again here: the association parameters are kept constant for the whole family of compounds, fixing a value 3 of KHB ab,ij to 2250 for the bonding volume and 3500 K for the association energy, εHB ab,ii/kB. The first evaluation revealed a behavior similar to that observed for the chloride family, although here the dispersive energy values are significantly lower. We then decided to follow the same approach described for the chloride family and have kept the segment diameter constant for all fluids. Hence, the only two variable parameters were the chain length and the dispersive energy. The final set of soft-SAFT parameters for these fluids are reported in Table 12, with the correlated temperature−density phase diagrams presented in Figure 11. The proposed models provide an excellent description of the experimental temperature−density data with an overall %AAD of 0.055%. Once again, it was possible to obtain linear correlations between the optimized m and εii/kB soft-SAFT parameters and the molecular weight of the ILs:

hydrogen atoms of water and the hydrogen atom of the hydroxyl group in ethanol). Ae and BH interactions are allowed and assumed to be equal and constant. AH and Be interactions are set to zero. The phase behavior of the two mixtures is remarkably different. The ethanol mixture exhibits similar behavior to that observed in the case of the chloride anion; an increase of the equilibrium temperature as the concentration of ionic liquid increases. This is intuitively expected behavior, and is modeled by fitting the dispersive energy binary interaction parameter ξ. We note that we obtain a value greater than unity, indicating relatively strong interspecies interactions, although in this case the deviation from the classical LB rule is not so important compared to the values obtained with the chloride based IL family. However, the aqueous [C4C1im][MeSO4] mixture exhibits a rather unusual solubility behavior; with the equilibrium temperature remaining approximately constant along the composition diagram where experimental data are available (up to 55% in mole fraction −95% in weight fraction of ionic liquid). This behavior is a result of the solvation of the [MeSO4]− anion by H2O molecules. This solvation interaction is extremely strong, such that the solvated H2O is for all intents and purposes reacted with the [MeSO4]− anion. In our experimental work, we have observed a reaction between [MeSO4]− and H2O to give [HSO4]− and MeOH. This is distinct to what we are observing here, but it does provide evidence for this strong interaction between [MeSO4]− and H2O. However, the remainder of the H2O is, in effect, prevented from interacting with the IL, essentially acting as a pure fluid. This means that the boiling point of the mixture will not change from that of pure water until we begin to actually dehydrate the IL, at which point the boiling point of the mixture would begin to increase, in line with more usual mixture behavior. Developing a physically rationalized model represented a significant challenge for the simple model suggested in this work. We propose that the average unlike association between water and the IL is near zero with the structure of the fluid playing a more important role. We have thus refitted the unlike segment diameter parameter η and the cross-association bonding volume, significantly reducing these values in order to reproduce this behavior. The unlike dispersive energy parameter has been transferred from the value obtained with ethanol. The final binary parameters and values are reported in Table 11.

m = 0.02817MWIL − 2.025

and mεii /kB = 10.669MWIL − 645.93

ηij

ξij

ΔHB ab,ij

%AAD

H2O C2H5OH

0.8 1.0

1.1 1.1

0.485 1.000

0.39 0.08

(20)

where eq 19 is dimensionless and eq 20 has units of K. These correlations were then used to obtain the soft-SAFT parameters of the [C1C1im][Me2PO4] and predict the temperature− density behavior of this compound. Again, we are pleased to note that this approach gives us an accurate prediction with a deviation between the experimental95,96 and predicted values of 0.66%. In fact, as it can be observed in Figure 11, the predicted curve falls in between the two sources of literature data for this compound. As previously, we evaluate our final set of parameters based on their ability to correlate not only the pure component density but also the interfacial tension. Fortuitously, some data were available for the first member of the series, [C1C1im][Me2PO4],95 whose density had already been predicted, representing a good challenge to our simple model. The results of the interfacial tension calculations are presented in Figure 12, with the relevant influence parameter value shown in Table 13. It is interesting to note that, at lower temperatures where association-type interactions dominate, the interfacial tension is higher, and as the temperature increases, the surface tension decreases. This phenomenon is typical of other molecular fluids, but the curvature exhibited by these data is not. This could be a result of reordering of the surface layer of the fluid with increasing temperature. It is interesting to note that the data presented in Figure 8 for the interfacial tension of [C1C1im][MeSO4] do not exhibit this unusual curvature. [C1C1im][MeSO4] also has a significantly higher value of γ of approximately 60 mN·m−1 compared to approximately 47 mN· m−1 at a temperature of 300 K for [C1C1im][Me2PO4]. This difference in interfacial tension is clearly driven by the bulkier [Me2PO4]− anion. This information has clear process engineer-

Table 11. Unlike Interaction Parameters Used to Calculate the Vapor−Liquid Equilibrium for the [C4C1im][MeSO4] Mixtures mixture

(19)

■

ILS WITH A DIMETHYLPHOSPHATE ANION [CnC1im][Me2PO4] with n = 2, 4, 6, and 8. Finally, we present the results of a study of ILs with a [Me2PO4]− anion and alkylimidazolium cations. ILs based on the dimethylphosphate anion tend to be highly basic, and have been used in cellulose dissolution92 and biomass pretreatment93 applications. ILs based on highly basic anions often show appreciable selfassociation behavior,94 presumably due to cation−anion 6216



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Table 12. Soft-SAFT Parameters Characterizing [CnC1im][Me2PO4]a [CnC1im][Me2PO4] n n n n n

= = = = =

1 2 4 6 8

m

σii (Å)

εii/kB (K)

εHB ab,ii/kB (K)

Kab,ii (Å3)

%AAD

4.2338 4.6170 5.4460 6.2040 7.0000

4.0530 4.0530 4.0530 4.0530 4.0530

407.0 405.0 401.0 398.0 396.0

3500 3500 3500 3500 3500

2250 2250 2250 2250 2250

0.663b 0.061 0.045 0.041 0.039

The number of segments, m, the diameter of the spherical core, σii, the depth, εii/kB, of the dispersive interaction, the depth, εHB ab,ii/kB, of the associating site−site interaction, and the bonding volume, Kab,ii. bThe density of [C1C1im]+ [Me2PO4]− was calculated using the parameters obtained from eqs 19 and 20. a

literature.97 These mixtures represent a stern test of our proposed model, as the molecular parameters of the pure ionic liquid had already been transferred from other compounds and predicted from the correlations of eqs 19 and 20. The description of the cross-interactions is analogous to the [MeSO4]− case. [C1C1im][Me2PO4] has been modeled using three association sites, one positive A and two negative B. Hence, it is assumed that the positive site A will cross-interact with the negative sites of water and ethanol, while the two negative B sites will interact with the positive sites of water and ethanol. Once again, only positive−negative site−site interactions are allowed and assumed to be equal and constant, setting the rest to zero. The matrix of association interactions built here follows the same pattern as the one successfully used in previous work for the study of the [Tf2N]− imidazolium based ILs with water and alcohols.16 In Figure 13, the isothermal vapor−liquid equilibrium of mixtures of [C1C1im][Me2PO4] with H2O, CH3OH, and

Figure 11. Temperature−density plots for (a) [C1C1im][Me2PO4], (b) [C2C1im][Me2PO4], (c) [C4C1im][Me2PO4], (d) [C6C1im][Me2PO4], and (e) [C8C1im][Me2PO4]. Continuous black curves represent the soft-SAFT calculations, black squares are the experimental data obtained in this work, and red circles are literature data.95,96

Figure 13. Isothermal pressure−composition projections for binary mixtures of [C1C1im][Me2PO4] and (a) H2O, (b) C2H5OH, and (c) CH3OH at T = 353.15 K. Continuous curves represent the soft-SAFT calculations, and symbols represent the data of Kato and Gmehling.97

Figure 12. Interfacial tension−temperature plots for [C1C1im][Me2PO4]. Continuous curves represent the soft-SAFT calculations, while symbols represent the data of Wang et al.95

C2H5OH at a constant temperature of 353.15 K are presented, with the unlike interaction parameters provided in Table 14. In all cases, the unlike dispersive energy interaction parameter, ξij, was fitted, with values higher than unity. This pattern has been

Table 13. Influence Parameter cij Used to Calculate the Interfacial Surface Tension for [C1C1Im][Me2PO4] [CnC1Im][Me2PO4]

cij × 1018 (J·m/mol5)

%AAD

n=1

1.083

2.575

Table 14. Unlike Interaction Parameters Used to Calculate the Vapor Liquid Equilibrium for the [CnC1im][Me2PO4] Mixtures

ing implications, as materials with lower surface tensions typically exhibit improved mass transfer properties. Binary Mixtures. The ability of the new model to reproduce the solubility behavior of the [Cnmim][Me2PO4] ILs in water and alcohols is finally tested here. In this case, some experimental data for mixtures of [C1C1im][Me2PO4] with water, methanol, and ethanol have been found in the 6217

[C1C1im][Me2PO4] + j

ηij

ξij

%AAD

j = H2O j = CH3OH j = C2H5OH

0.95 0.98 1.00

1.45 1.38 1.23

0.003 0.001 0.011



Article

observed for the three different anions evaluated in this work. Moreover, a slight modification of the unlike segment diameter interaction parameter, ηij, has been applied to the case of water and methanol, to reach quantitative agreement with the experimental data. If not, the system was predicting a false liquid−liquid immiscibility region at very low ionic liquid concentrations. In any case, we note that the simple models we have proposed, with the appropriate and justified corrections, are sufficient to provide an excellent description of the available experimental data,97 with an absolute average deviation from the experimental error of 0.005 MPa. It is particularly encouraging to note that both points of inflection in the isothermal projections for the H2O and C2H5OH mixtures are captured by this model. In addition to the solubility of the molecular fluids in the ILs, we are interested in understanding the driving force behind the mixing. Partitioning the excess Gibbs free energy contributions into chemical (broadly represented by enthalpy) and structural (broadly represented by entropy) effects offers unique insight into the molecular-scale behavior of mixtures of ILs and molecular solvents. The unusual behavior of ionic liquid mixtures with dissolved salts was recently highlighted;98 the contrast with molecular solvent−ionic liquid mixtures highlights differences in ion−ion interactions, which are purely Coulombic (and lead to ideal-type solution structures98,99), and ion−dipole interactions, which can be heavily influenced by hydrogen bonding interactions, leading to preferential solvation effects and clustering. These types of solution behaviors can be distinguished by using energetic approaches such as in the models presented here. The energy contributions to the excess Gibbs free energy of mixing for mixtures of [C1C1im][Me2PO4] with water are presented in Figure 14 and show very unusual behavior, as

until reaching a minimum at approximately xH2O = 0.33 (2 anions per water). We speculate that this could represent a minimum entropy where each water molecule is hydrogen bonding to two different anions in a “bridged″ structure, with the two “free” partially negative oxygen atoms on the [Me2PO4]− anion complexed to the same hydrogen atom on water (and a separate anion on the other side). TΔSmix next gradually increases, becoming positive at around xH2O = 0.67 (2 water molecules per anion). We speculate that this structure would be caused by two water molecules hydrogen bonding to the two “free” oxygen atoms on the [Me2PO4]− anion. TΔSmix continues increasing before reaching a maximum at approximately xH2O = 0.9, before decreasing. This likely represents the onset of bulk water behavior. The mixtures of [C1C1im][Me2PO4] with methanol and ethanol are presented in Figures 15 and 16. In both figures, it

Figure 15. Decomposition of the excess Gibbs free energy of mixing for the [C1C1im][Me2PO4] + CH3OH mixture. The Gibbs free energy of the mixture, ΔGmix, is given by the black dashed curve, the structural or entropic contribution, TΔSmix, is illustrated by the blue dash-dot curve, and finally the chemical or enthalpic contribution, ΔHmix, is given by the continuous red curve

can be seen that the excess entropy change on mixing is negative across the entire composition space, with a minimum at approximately xROH = 0.67. As was the case for the water

Figure 14. Decomposition of the excess Gibbs free energy of mixing for the [C1C1im][Me2PO4] + H2O mixture. The Gibbs free energy of the mixture, ΔGmix, is given by the black dashed curve, the structural or entropic contribution, TΔSmix, is illustrated by the blue dash-dot curve, and finally the chemical or enthalpic contribution, ΔHmix, is given by the continuous red curve

might be expected when highly associating fluids are mixed. The excess entropy change on mixing undergoes a rapid change across the full range of water composition, and its behavior tends to control ΔGmix. At low water concentrations, TΔSmix is negative (as is ΔHmix), resulting in a synergistic lowering of ΔGmix. This can be explained by the hydrogen bonding of water to the IL anions contributing to an enhancement in the degree of structure of the fluid mixture. TΔSmix gradually decreases

Figure 16. Decomposition of the excess Gibbs free energy of mixing for the [C1C1im][Me2PO4] + C2H5OH mixture. The Gibbs free energy of the mixture, ΔGmix, is given by the black dashed curve, the structural or entropic contribution, TΔSmix, is illustrated by the blue dash-dot curve, and finally the chemical or enthalpic contribution, ΔHmix, is given by the continuous red curve 6218



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mixture with the anion [Me2PO4]−, this likely represents the augmentation of the IL structure, with the most structure occurring where two alcohols can each hydrogen bond to one of the “free” oxygen atoms on the [Me2PO4]− anion. The persistently negative TΔSmix is in contrast to the water systems, and is likely a consequence of the alcohols’ inability to fully dissociate the IL in solution. It is interesting to consider the relative changes in the unlike interactions between [C1C1im][Me2PO4] and H2O, CH3OH, and C2H5OH. Each of these solute compounds are strongly associating fluids in their own right. Typically, when one considers mixtures of strongly associating molecular species, it is almost invariably the strong, anisotropic interactions between the functional groups on the different molecules which dominate the mixing behavior. However, this does not appear to be the case in the mixtures of [C1C1im][Me2PO4] and H2O, CH3OH, and C2H5OH. Considering the parameter trend presented in Table 14, one can observe that the unlike interactions are strongest between H2O and [C1C1im][Me 2 PO 4 ] with ε H 2 O,IL /k B = 559.09 K decreasing to εC2H5OH,IL/kB = 380.38 K with the addition of two alkyl groups. Similarly, the effective diameter of the mixture increases from σH2O,IL = 3.423 to σC2H5OH,IL = 3.844. This will obviously be partially owing to the fact that σC2H5OH is somewhat greater than σH2O. However, we propose that what we are seeing is actually a restructuring of the fluid. Initially, when we are considering the dissolution of H2O, one can envisage a scenario where the H2O molecule is positioned in the electron dense region near the cation head. There is an obvious attraction between the electrons on the nitrogen atoms in the imidazole ring of the ionic liquid and the hydrogen atoms on the H2O. This would allow the H2O to integrate with the structure of the ionic liquid, incurring an entropic penalty, which is offset by the enthalpic gain. However, the addition of the alkyl groups to the solute molecule, that is, changing from H2O to C2H5OH, would make positioning the solute in the electron dense region near the cation head highly enthalpically unfavorable. Thus, the solute is repositioned closer to the alkyl chain on the cation tail. This leads to the suggestion that enthalpic effects are important when one is attempting to solublize relatively small and/or strongly associating compounds in ILs, while entropic or excluded volume effects become more important when one is trying to dissolve less polar compounds in ILs. This conclusion is similar to that of Deschamps et al.100 and Blanchard et al.101

thermodynamic properties for other ILs with longer alkyl-chain lengths. The ability to accurately predict properties such as density, surface tension, and viscosity is key in performing an assessment of ILs for process engineering applications. For example, these properties in particular are of key importance in calculating mass transfer coefficients.102,103 Further, as the Chilton-Colburn analogy104 is typically used in obtaining heat transfer coefficients, these properties are therefore vital for the development of detailed process engineering models of ionic liquids based separation processes. The overall aim of this work is to implement these thermophysical property models within a process modeling and simulation environment similarly to our previous work.105−108 Thus, it is gratifying to find that the simple models which we have proposed are suitable for use in this way. Further, as the models appear to be robust over a wide range of thermodynamic states, we propose that they are adequate for process design and optimization activities as well.

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CONCLUDING REMARKS We have presented new experimental data and soft-SAFT models of a range of ILs with application to the deconstruction of biomass in the context of biorefinery processes. The proposed models are based on a coarse-grained approach with assumptions based on quantum calculations and molecular simulations, where the main physical features of the compounds are considered in the simplest possible way. As a result, accurate descriptions of density, viscosity, and surface tension of both pure ILs and their mixtures with associating fluids have been achieved. We suggest that these simple models are appropriate for engineering studies, where correlation and prediction of the fluids’ thermophysical properties are required. The apparent change in relative contribution of enthalpy and entropy to the mixing behavior identified in the section describing the properties of binary mixtures of [Me2PO4]− is a particularly interesting aspect of the work performed to date.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/ 2007-2013) under CO2QUEST Grant Agreement number 309102. F.L. acknowledges a TALENT fellowship from the Catalan Government. This work has been financed by the Spanish government, Ministerio de Economia y Competitividad, under Project CENIT SOST-CO2 CEN2008-01027 (a CENIT project belonging to the Ingenio 2010 program, CDTI), by Carburos Metálicos, Air Products Group, with additional support from the Generalitat of Catalonia, AGAUR under Grant SGR2009-666 also being gratefully acknowledged, and the Natural Environment Research Council (NERC) of the UK (Grant Number: NE/H01392X/1), and was part of work of the DOE Joint BioEnergy Institute (http://www.jbei.org) supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, through Contract DE-AC02-05CH11231 between Lawrence Berkeley National Laboratory and the U.S. Department of Energy.

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DISCUSSION First of all, the high degree of transferability of the parameters involved in the molecular models developed is noteworthy. For a given anion, we have been able to obtain more than adequate results using the same parameter values for the association energy as well as the bonding volume. Moreover, additional constraints related to the dispersive energy and the segment diameter have also been successfully applied here, reducing the dimensionality of the system to two fitting variables, which can be easily correlated with the molecular weight of the IL. This is both physically intuitive and very convenient in light of the paucity of data generally available for ILs. The predictive power of the approach has been tested with success for a few compounds ([C1C1im][MeSO4] and [C1C1im][Me2PO4]), and it is expected to provide a good description of the 6219



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Finally, additional support from the ERC is gratefully acknowledged.

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