Ionic liquids are an intriguing class of molten salts, which are composed of molecular ions the asymmetry of which results in packing frustration leading to their melting points below 100 • C. At molecular level, ionic liquids are characterized by a delicate balance of Coulombic, dispersion, hydrogen bonding, and π-π interactions giving rise to properties such as negligible vapor pressure and solvation of polar and non-polar solutes. A natural way of manipulating these interactions to obtain ionic liquids with improved properties is by changing the cation, anion or both. Due to the diversity of available ions, such approach has been the primary focus to design ionic liquids with desired properties resulting in a large number of ionic liquids synthesized till date. As an illustration, the ILThermo Database maintained by the National Institute for Standard and Technology contains physicochemical properties of 1400 unique ionic liquids. In lieu of synthesizing new ionic moieties, mixing of two ionic liquids is probably the simplest and cost-effective strategy to generate new ionic liquids in which molecular-level interactions governing macroscopic properties are modified. [1][2][3][4][5][6][7][8] Considering that the mole fractions of the constituent ionic liquids can be varied almost continuously, the approach holds great promise to produce a large number of ionic liquids increasing the probability of discovering ionic liquids with desired properties. However, due to the combinatorics, the number of potential ionic liquid becomes too large to be studied rapidly either experimentally or with molecular simulations. To navigate a large chemical space comprised of potentially 10 18 ionic liquids, 9 it is imperative that a first-pass, rapid, robust, easy-to-use screen based entirely on the properties of pure ionic liquid be developed to differentiate ideal vs. non-ideal ionic liquid mixtures.
While results from several studies indicate that thermodynamic properties such as enthalpy and chemical potential, or volumetric properties such as excess molar volumes obey ideal mixing law, there exist ionic liquid mixtures exhibiting non-ideal behavior. The ideal behavior is generally explained in terms of the similarity between interactions in the mixture 3 Page 3 of 25
The Journal of Physical Chemistry and pure ionic liquids. On the other hand, changes in one or more molecular level interactions with respect to those present in pure ionic liquids have been invoked to rationalize the non-ideal behavior. The origin of such non-ideality has been suggested to be rooted in the differences in the anion size/ionic liquid molar volumes and the hydrogen bond ability (β) of anions. For example, binary ionic liquid mixtures containing anions with a very substantial difference in β parameter have been reported to yield non-ideal behavior in terms of excess molar volumes, viscosity, conductivity, and glass transition temperature experiments. 1,2,10 Our work and that of others have also shown that when binary ionic liquid mixtures with a common cation and two anions with a large difference in the hydrogen bond ability are formed, the molecular arrangement of anions around the cation in the mixture can markedly differ from those in the pure ionic liquids. 11 We have also demonstrated that the presence of "non-native" arrangements of anions exert a profound influence on the physical dissolution mechanism of CO 2 at molecular level. 12 Despite the significance of molar volumes and hydrogen bond ability of the anions in predicting the non-ideal behavior in ionic liquid mixtures, it is surprising that a systematic investigation evaluating the influence of these markers has been absent in the literature.
In the present work, we resort to molecular dynamics simulations to assess the ability of these two descriptors in providing clues to the non-ideality in binary ionic liquid mixtures.
We report a comparison of molecular arrangements for a total of sixteen binary ionic liquid
The intra-and inter-molecular interactions were modeled using an all-atom force field developed by Canongia Lopes-Pádua 13,14 (CL&P) for all the molecules except [Me 2 PO 4 ] -anion, the parameters of which were taken from OPLS-AA force field 15 which has been shown to work well when combined with CL&P parameters. [16][17][18] The force field has the following functional form:
where k r,ij , k θ,ijk , k m,ijkl represent the force constants for bond stretching, angle bending, torsion (both proper and improper), respectively, σ and denote the size and energy parameter of the 6-12 Lennard-Jones (LJ) potential and q indicate partial charges. As proposed for the force field model, the unlike interactions were computed by the geometric-mean combining rule and 1-4 nonbonded interactions were reduced by a factor of 2 for both LJ and electrostatic interactions. The total charge on the cation and anion is ± 1. It is worth mentioning that not using either polarizable force field or scaled non-integer charges may be justified as polarizability has minor effect on the local structural properties. 19 Molecular dynamics (MD) simulations were carried out at a temperature and pressure of 353 K and 1 bar using GROMACS 5.1.5 package. 20,21 Along with pure ionic liquid systems, simulations for a total of five intermediate molar ratios The Journal of Physical Chemistry pairs was used for all the ionic liquid compositions, except for 10:90 and 90:10 compositions, for which 250 ion pairs were simulated. The simulations were performed in two steps. First, random initial configurations were generated using PACKMOL. 22 These initial configurations were then subjected to a steepest descent minimization followed by a 2 ns annealing scheme, where the temperature was increased from 353 K to 553 K and then lowered to the desired temperature of 353 K iteratively. Each ionic liquid system was then simulated in canonical (NVT) ensemble for a duration of 10 ns, followed by isothermal-isobaric (NPT) equilibration run of 20 ns. In second step, the last configuration obtained from the NPT equilibration run was used as the initial configuration. This configuration was subjected to the same annealing scheme followed by 10 ns of NVT, and 25 ns of NPT equilibration and subsequent NPT production run of 40 ns. The trajectories obtained from the last 20 ns of the production run, with coordinates were saved every 0.4 ps, were used for the analyses.
During the production run, Nosé-Hoover thermostat and Parrinello-Rahman barostat with a coupling time constant of 0.4 ps and 2.0 ps were used to maintain the temperature and pressure. Particle Mesh Ewald (PME) method was used to handle electrostatic interactions while analytical tail corrections were applied for nonbonded LJ interactions, each with a potential cutoff of 16 Å. Since all the fast vibrating modes comprising hydrogen atoms were constraint, the simulations were integrated with a time step of 2 fs. The analysis of the trajectories was performed using TRAVIS package. 23
The systems studied here allowed us to change the values of ∆V (difference in molar vol- Freire and co-workers. 26 Same inferences can also be made using the β parameter values taken from the works of Welton and co-workers 27 (see Supporting Information). The molar volumes were predicted from molecular dynamics simulations. Based on these values, we generated Figure 1 displaying (∆V ) and (∆β) of the anions for all the ionic liquid mixtures. Non-native structures as a surrogate for non-ideality
In this article, we adopt the differences in the molecular arrangement of anions around the cation between those encountered in a binary ionic liquid mixture and constituent ionic liquids as markers for non-ideality. The choice of this metric is partly due to the difficulty in predicting excess thermodynamic properties for ionic liquid mixtures, such as excess molar volumes and excess enthalpies, which are traditionally invoked to classify ideal vs. non-ideal solutions. The excess quantities tend to be rather small and are sensitive to the selection of a force field model, while the microstructure is more robust. As an evidence, the radial (∆β ∼ 0.55 and ∆V ∼ 218.7 cm 3 /mol -the highest differences encountered in this work).
The general features of SDFs for pure ionic liquid systems share similarities: (i) both anions interact with the cation via acidic ring-hydrogen atoms (H2, H4, and H5 -refer to Figure 1 for the nomenclature); (ii) even though both anions are found in the plane between the two imidazolium rings, the SDFs above and below the plane for the anion with stronger hydrogen bonding interaction are not as extended as those of the weakly coordinating anion.
The difference in the spatial extent of the anions enables neighboring cations to participate in π-π interactions in the presence of a strongly coordinating anion, while a weakly coordinating anion itself establishes anion-π interactions thereby mediating the interactions of two neighboring cations; (iii) The coordination of the anion at the CN3 position (3-methyl position identified in Figure 1) is possible with a strongly coordinating anion; however, the site becomes inaccessible to weakly coordinating anion as shown here and by us and others for different ionic liquid systems. 11,18,28 Next, we consider five intermediate mole fractions (0.1, 0.25, 0.5, 0.75, 0.9) for every binary ionic liquid mixture and analyze how the anions distribute around the cation and compare these distributions to those observed for pure ionic liquids. x [TFA] 1-x system may be a reason that the ionic conductivity of mixtures with x = 0.1 and x = 0.25 are higher than those for the pure ionic liquid counterparts, while thermophysical properties such as excess molar volumes and self-diffusion coefficients can be approximated with ideal mixing rule. 10 When the strongly coordinating anion is [Me 2 PO 4 ] -, the loss in the interaction of [TFA] -and the H2 site occurs only at the [Me 2 PO 4 ] -mole fraction of 0.9. The composition of any of the mixtures does not perturb the cation-cation interactions observed in the corresponding pure ionic liquids.
Overall, the four ionic liquid mixtures (∆V max ∼ 30 cm 3 /mol and ∆β max ∼ 0.36) exemplify ideal mixing behavior.
To identify the threshold for ∆β, we turn our attention to two systems with similar ∆V example, the elimination of the in-plane density of TFA occurs at the Cl -mole fraction of 0.5; however the hydrogen bonding interactions are preserved at the H4 and H5 sites. Thus, it appears that increasing the difference between the molar volumes of ionic liquids begins to manifest in the development of non-native molecular structures, especially for the weakly coordinating anion at increasingly lower concentrations of the anions with stronger hydrogen bonding ability. Collectively, the results for these five systems demonstrate that the critical value for ∆V for separating ideal vs. non-ideal mixing for ionic liquid mixtures is located within 50-70 cm 3 /mol range for a given ∆β value. As a conservative estimate, we establish this limit to be 60 cm 3 /mol. The non-native structures, presented in Figure S9, for [C 4 mim]
35 and ∆V ∼ 168.4 cm 3 /mol) confirms that a difference in molar volumes greater than 60 cm 3 /mol will produce non-ideal behavior.
Non-native structures are produced in ionic liquid mixtures when the limit for ∆V or The general applicability of Figure 1 for predicting non-ideal behavior can be further demonstrated using a contrived example of the ionic liquid mixtures containing a common anion
] -(∆V ∼ 100 cm 3 /mol) at 298.15 K. The binary mixtures have been recently reported to exhibit non-ideal behavior reflected in terms of dielectric constants; for few mixture compositions, the dielectric constant was almost a factor of two higher than those for the pure ionic liquids. 33 Although the molecular-level explanation of the non-ideal behavior is completely different from that used to identify non-native struc- observed to be much more pronounced that those for the third ionic liquid mixture. 34 This observation correlates very well with the guidance provided from Figure 1 as the ∆V values are ∼ 141 cm 3 /mol, 106 cm 3 /mol, and 35 cm 3 /mol, respectively, based on the densities of the ionic liquids reported at 323 K (∆β ∼ 0 for all the ionic liquids). 35
Molecular dynamics simulations were conducted for a total of sixteen ionic liquid mixtures comprising of the cation [C 4 mim] + and a combination of anions enabling us to vary the enthalpic and entropic contributions through the difference in the hydrogen bonding ability of the anions and ionic liquid molar volumes, respectively. Distributions of anions around the cation and their deviation from those in the pure ionic liquids making up a given mixture were employed to quantify the non-ideality of the mixture. A considerable imbalance in the enthalpic and entropic effects reflected in terms large differences in molar volumes and hydrogen bonding ability of anions (∆V > 60 cm 3 /mol and ∆β > 0.4) translated into anion distributions that differed markedly from those in the corresponding pure ionic liquids.
Specifically, the anion with weaker hydrogen bonding ability lost its favorable interaction with the ring hydrogen atoms, resulting in its occupying positions above and below the plane of the imidazolium ring. The rearrangement induced a disruption in the π-π stacking of the two neighboring cations, leading to the observation of structures non-native to those in the parent ionic liquids. We also illustrated that non-native structures could arise in ionic liquid mixtures even when a large difference exists in only one of the descriptors. On the other hand,