Dielectric behavior of Water in [bmim] [Tf 2 N] room-temperature Ionic Liquid, molecular dynamic study

In this work we present the dielectric behavior of water with a novel flexible model that improved all three sites water models Different concentrations of the ionic liquid 1- butyl-3-methylimidazolium [bmim] bis(trifluoromethanesulfonyl)imide [Tf 2 N] with water was investigated. The study was performed by molecular dynamics simulations using three water models, being two non-polarizable 3-site SPC/E and SPC/e, and a novel flexible 3-site FAB/epsilon model. Systematic thermodynamics, dynamical and dielectric properties were investigated, such as density, diffusion coefficient, heat of vaporization Delta-Hvap, and surface tension at 300 K and 1 bar. We extrapolated the experimental molar fraction of the mixtures and a pattern change for all properties was observed, evidencing the phase separation previously reported by experimental data. The results also display the dielectric effect of the system on the calculated properties.


Introduction
Ionic Liquids (ILs) have been investigated widely in the last years, with applications being reported since the early 20th century. For instance, ILs were applied to cellulose dissolution in 1930s, when a pattent described the use of a molten pyridinium salt for this purpose. 1 Ionic liquids have great capacity to dissolve an extensive group of polar and non-polar compounds,making them a desirable solvent for many applications, such as catalysis, 2-4 extraction, 5,6 self-assembly, 7-12 electrochemical 13-15 and biochemical processes. [16][17][18] The search for new anions for organic polymer electrolytes raised the concept of a "plasticizing anion", i.e., an anion with delocalized charge and multiple conformations which differ in energy only slightly. One example of this is the anion bis (trifluoromethanelsulphonyl) imide [CF 3 SO 2 -N-SO 2 CF 3 ] + , also known as [Tf 2 N] − . It was shown that this anion, together with imidazolium cations such as [bmim][Tf 2 N], forms an IL with a melting point around 288 K, ionic conductivity comparable to that of good organic electrolyte solutions 1 and no decomposition or significant vapour pressure up to 550-650K. 19 It is well known that the water content can disrupt and strongly affect the ionic liquids properties . 21,22 For instance water has an important role in the dissolution of cellulose in ILs, revealing the importance of hydrogen bonds making and disrupting environment. Recently, McDaniel and Verma studied the miscibility of ILs in water and showed the dependence of the dielectric medium based on ion type and cation/anion combination . 23  In the present work we employ this model to study a water/IL mixture by the first time.
In the literature there are several force fields for [bmim][Tf 2 N], which have been established by the reproduction of some experimental property, such as density, X-ray structure factors, self-diffusion coefficients from NMR and heats of vaporization from vapor pressure measurements. 34 The first force fields were obtained from ab initio 36 methods and compared with the reproduction of the liquid density. Currently there are more experimental data and therefore conditions to improve the IL force field. 34 The remaining of the paper goes as follows. In section 2 we introduce the models. Section 3 shows the simulation details. The results are analysed in Section 4. Conclusions are presented in section 5.

Computational Details and Models
Force Fields  Table 1 shows the force field parameters for the three models.
where α and β refers to atomic sites, r is the distance between the sites α and β, q α and q β accounts to the electric charges for the sites α and β, respectively; 0 is the vacuum permittivity, αβ is the LJ energy scale and σ αβ is the repulsive diameter for an α − β pair.
The cross interactions between different atoms are obtained using the Lorentz-Berthelot mixing rules, The FAB/ model includes two harmonic potential,that improve the calculation of experimental properties, 35 one at the OH bond and another at the angle formed by the three atoms of a water molecule, as shown in the Equations 3 and 4: where r is the bond distance and θ is the bond angle. The subscript 0 denotes their equilibrium values, while k r and k θ are the corresponding spring constants. The water static dielectric constant, , is a collective property of an ensemble of water dipoles, which can be calculated from the equilibrium total dipole moment fluctuations, . The calculations of the dielectric constant was obtained by (equation 5) 40 of the total dipole moment M, where k B is the Boltzmann constant, T is the absolute temperature and V is the volume.
The surface tension was obtained in a NVT simulation where a rectangular cell was used, with L x =L y =7.9 nm and L z = 3L x to avoid finite effects, 41 containing 5324 molecules.
Periodic boundary conditions were applied in all directions.
The average components of the pressure tensor were obtained for 30 ns after an equilibration period of 5 ns. The densities of the two phases were extracted from the statistical averages of the liquid and vapor limits of the density profiles. 43 The corresponding surface tension γ on the planar interface was calculated from the mechanical definition of γ . 43 where L z is the length of the simulation cell in the longest direction and P αα are the diagonal components of the pressure tensor. The factor 0.5 outside the squared brackets takes into account the two symmetrical interfaces in the system. Figure 2 shows the density of the IL-water system at different mole fraction of water X H2O .

Results
Although the calculated density of the pure IL is underestimated in 2.68%, indicating that the force field for the IL can be improved, the behavior of the density using the three different force fields for water has a systematic decreasing. The inset (A) of the Figure 2 shows the equilibrated configuration at the fraction of X H2O =0.95, where a non-homogeneous mixture is evidenced, suggested previously by Rollet et al. 25 The density of the IL-water system (figure 2) with respect to an increment of X H2O decreases by 40% until reaching a composition of pure water; the density obtained with the FAB/ model shows lower values than those obtained when using the non-polarizable models, within the region from X H2O =0.2 to X H2O =0.8. This is due to the contracting ability of the OH bond in the water molecule, as will be analyzed and discussed in the average structure of the water molecules in the system IL-water in this work. Figure 3A exhibits the results of the dielectric constant of the IL-water system for the three models studied. The difference between the water models is closer to the pure water, where the dielectric derived models present a better agreement to the experimental data.
Following the previous trend, the IL force field understimate the dielectric constant of the neat IL. The dielectric constant of the system can be reduced up to 60%, when compared to pure water, even with a small amount of the IL. However, the system has a monotonic behavior for molar fractions of water lower than 80%. Figure 3A shows the dielectric constant of the IL in the system. Analizing the dielectric constant of water in the solution, Figure 3B, it can be seen that the three water models show an identical description of this property. However, the FAB/ model has the advantage of giving more information on the structural behavior of figures6, 7 and 8. Figure 4 shows the behavior of the anion, cation and both in the IL-water system. The anion remains within a constant range, even when the amount of water in the system increases and the cation presents variations within a percentage of 20% with respect to the absence of water. Thus the cation with this model has more reactivity than the anion.
The static dielectric constant, ε, of a polar liquid is related to the thermal equilibrium fluctuations of the polarization at zero field. 46 Polarization fluctuations are long-range and vary with the shape of the dielectric body. ε, on the other hand, is an intrinsic response coefficient independent of geometry. This led Kirkwood to postulate that it should be possible to express ε in terms of a short-range orientational correlation function. 47 The values of the polarization of simulation is presented in the figure 5. We introduce the polarisation factor G K (equation 7), 49 in order to check if the force field changes its polarisation; the G K factor measures the equilibrium fluctuations of the collective dipole moment of the system and is related to the orientational correlation function.. The calculus of the polarization is consistent for the three water models, including the polarizable FAB/ε model, which implies that the system is consistently reproduced by these water models, and that water also governs the polarization of the system. By having a small amount of water in the system, it becomes more polarized and this causes its dielectric properties to increase, even when the system is not miscible.
The result is consistent with the three water models, Figure 5, which indicates that a water model that does not reproduce the dielectric constant well, will not reproduce this behaivor, as shown in the work of Schröder et al 50 N is the total number of molecules, M is the total sum of dipoles µ i in the system (including the dipole of initial molecule ). Local orientational correlations are averaged out by thermal motion after the first few coordination shells.
Even though the result of the dielectric constant and the polarization of water in the system with IL is consistent, the use of the new force field generates structural information on the behavior of water through the dipole moment, as seen in the figure 6. The average dipole moment of water, when increase its quantity with respect to IL, show water changes structurally with an angle less than isolated water, when it is closer to the IL. And by not being in contact with IL, it again deploys to a state of bulk.  The analysis of the enthalpy of the liquid phase ( Figure 9A), as we increase the amount of water in the solution, shows a decrease that stabilizes within a composition between 0.5 to 0.64 of the fraction of water. Outside that range there is a linear increase in the enthalpy.
The Hvap of the system( Figure 9B) has a linear behavior outside the range of 0.5 to 6.4 of the fraction of water. Since the force field of IL underestimates the value of Hvap of pure IL, the value calculated with the FAB water model might seem wrong, but having a calculation of pure water closer to experimental allows us to infer that the work must focus on a better force field of the IL , in order to have a better description of this property. The self-diffusion coefficients of water is show in Figure 10. When the water mol fraction is 0.2 in the solution, we have a description close to the experimental value of the diffusion, which describes the three water models, where the combination of IL-FAB/ describes this behavior closer to the experiment. Then there is a decrease indicated by the three systems until the system reach the value that every water model reproduce at 1 bar and 298K. Taking into account that IL is somewhat hygroscopic and not very miscible in water, the value it contains is 1.3 25 percent by mass, at the pressure and temperature conditions used.  The self-diffusion coefficients of cation and anion is described by the Figure 11. Although the diffusion is almost equal for both according to the reported experimental value, 25 the calculated values that were obteined with the FBA/ model are closer to the experimental values. Self-diffusion coefficient result is interesting, since IL is expected to be a little hygroscopic, so that water increases the dissociation rate of the ion pair and consequently causes a higher diffusion increase mainly from the anion, due to its size. When the amount of water is high, the diffusion of both is greater by a factor 1.3 than when there is less amount of water. These calculations show that increasing the water in the system does not produce a significant increased dissociation of the anion-cation pair, that is, it appears that water interacts rather weakly with the ion pair. Heinz et al ? discuss how the water content depends on the interaction with the anion. The hydrophobicity of anions [NTf 2 ] prevents the water from dissociating ion pairs and incorporates more between the IL.
The surface tension of the system when the water is increased is show in the Figure 12.
Although the SPC/E model diverges from the experimental value by almost 12% at 300K and 1 bar, there is a similar behaivor since we started adding water to pure IL, until the increase reaches a mole fraction of 0.9 water. With a small amount of water, ( χ H 2 0 = 0.12), the system decreases in value by almost 50%, which may be attributable to the fact that the IL force field does not describe this property well. From χ H 2 0 = 0.32 to χ H 2 0 = 0.8 we notice a similar behavior of the system, with small additions of water the system increases its value widely. Water SPC/ε Water SPC/E Water FAB/ε Exp Figure 12: The surface tension of the system with respect to the fraction of water in the solution IL-water. Black triangles are the experimental data, 25 red circles are the result using the SPC/ model, green box are the result using the SPC/E model and the blue dimonds are the result using FAB/ model, all calculated in this work.

Conclusions
The novel flexible water FAB gives a novel information on how water is structured in these systems and how its dipole moment changes, this helps to understand water with IL that does not solubilize, giving a guideline to improve IL. The three water models used in this work together with IL reproduce the experimental properties of the system from a small amount of water to pure water. The fact that the FAB/ model can change its structure within the simulation, generating a type of polarization, allows us to have a descriptive aspect of how the water molecule behaves through increasing its presence in the system, giving an The dielectric behavior of water within IL, as we increase its content, is reflected in the dipole moment, which indicates how the charges are located with respect to the atoms that form the molecule, and this is generated by the average structure defined by the O-H bond and angle, so the polarization of the water increases as its angle and O-H bond decrease.