Solvation Structure and Dynamics of Alkali Metal Halides in an Ionic Liquid from Classical Molecular Dynamics Simulations.

The structure and dynamics of the solvation of several alkali metal halides in an ionic liquid (IL), 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([BMIm][OTf]), were investigated by classical molecular dynamics simulations. Various properties such as density, radial distribution functions, coordination numbers, spatial distribution functions, mean-square displacements, self-diffusion coefficients, and velocity-velocity autocorrelation functions were calculated to understand the solvation environment of alkali metal halide salts in IL at various salt concentrations. We observe that the halide anions are coordinated in two different ways with [BMIm]+ in all of the mixtures. However, the alkali metal cations interact more with the anion of the ionic liquid as we go from fluorides to iodides. When a common anion was used for the salt and the ionic liquid, we observe significant coordination of Na+ with the anion of the ionic liquid in two different ways, which was not observed in the case of lithium salt. We also find that the Li+ and Na+ ions are involved in the formation of a aggregate-like, stable kinetic entity with anions in their first solvation shells. These aggregate-like entities were seen to be relatively stable, and we noted a rattling motion of salt ions inside them.

Introduction

Room-temperature ionic liquids (RTILs) have a melting point usually below 100 °C and consist of an organic cation and an inorganic anion.[1,2] The ILs are thermally and electrochemically stable, inflammable, capable of dissolving many organic and inorganic salts, and have a low vapor pressure as well as viscosity. Due to high ionic conductivity, they have gathered much attention in the field of electrochemistry as well.[3,4] These also become highly attractive alternative candidates for replacing traditional organic solvents in various applications in industries.[2,5−9] The applications of ionic liquids are also found in fields of cutting-edge research like drug delivery; when ILs interact with drug moieties and proteins, ions present in the vicinity of the biomolecules often play an important role in determining the nature of the entire system.[10−12,34,35] The mixtures of ILs with alkali metal salts have been used in several potential applications. Due to the capability of the ILs to process metals, the area of ionometallurgy is attractive especially because of the redox properties[13] of salts dissolved in them. The process of metal extraction from aqueous solutions using ILs having different positive and negative ions has been reported earlier.[14,15] Other methods involve solvents generally made up of a combination of hydrogen donors and quaternary ammonium salts, known as deep eutectic solvents, used for metal extraction from complicated matrices and metal salts.[16−20] For the separation processes of metal ions, a considerable range of ILs are used.[14] ILs produce solutions that are entirely different from those prepared from aqueous or organic solvents[21] and facilitate the extraction of charged species. Another advantage is the applicability of ion exchange mechanisms to transfer ions,[22] which makes the extraction process more easier.

Many research groups around the world have examined the extraction of metals using ionic liquids and the transport of metals in ionic liquid solvents. The anions in the ionic liquid affect the solubility of most of the metal salts. A study proved that imidazolium-based ILs containing nonafluorobutanesulfonate ([NfO]−) showed excellent capability of metal extraction from an aqueous solution.[14] ILs based on imidazolium cations are better for solvation than their ammonium, pyridinium, and phosphonium counterparts for extraction of metals.[22] The metal salts were found to be sparingly soluble in imidazolium-based ionic liquids without a common anion.[23] Pereiro et al. reported that lithium bis(trifluoromethane)sulfonimide (LiNTf2) salt was more soluble than NaNTf2 in 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [C2C1Im][NTf2].[24] However, these solutions are prone to form [Li(NTf2)2]− anionic clusters, as reported by Lassègues et al.[25] and also supported by Umebayashi et al.,[26] who observed the solvation of the lithium salt in two different ionic liquids, [Emim][NTf2] and N-butyl-N-methyl pyrrolidinium bis(trifluoromethylsulfonyl)imide, [BMPy][NTf2]. Méndez-Morales et al.[27] studied the solvation structure of alkaline salts mixed with imidazolium-based ILs with common anions using molecular dynamics simulations. They observed the formation of stable clusters of the alkaline metal cations (M+) with IL anions. They found a linearly increasing trend in the density of all mixtures of the IL and salt. The same group also studied the solvation of lithium salts in protic ILs with a common anion using molecular dynamics[28] and reported the solvation structure of Li+ cations in the hydrogen-bonded and amphiphilically nanostructured environment. Kuzmina et al.[29] performed the experimental study to find the solubility of alkali metal halides (MXs) in an IL, 1-butyl-3-methylimidazolium trifluoromethanesulfonate ([BMIm][OTf]). They also investigated the effects of common anions on the solubilities of salts in the IL. The difference in the solubility of salts with a common anion compared to halide salts is found to be meager. They provided the schematic representation of the solvation of salt within the IL “cage”; however, the study could not provide the detailed atomistic-level interactions between the solute and solvent. Recently, a study has been reported on the behavior of mono-, di-, and trivalent metal cations relevant to electrodeposition in IL mixtures.[30] Several studies have been reported in the literature for the solvation of divalent and trivalent cations in the bulk and at interfaces. The ionic liquid–metal salt mixtures were also used for the electrochemical applications. The solvated higher-valence salts like Mg or Al in IL solutions may facilitate the development of more efficient energy storage systems.[31] Gómez-González et al. reported the structure and spectral properties of protic and aprotic ILs with magnesium and calcium salts.[32] A molecular dynamics study of mixtures of IL and magnesium tetrafluroborate confined between two parallel graphene plates was also reported.[33]

The dynamics of the ions of metal salts in an ionic liquid environment has not been explored by the scientific community in detail. The knowledge of the solvation characteristics of these salts in IL may prove to be useful information while employing ionic liquids for extraction of metals from their ores. Thus, to get a better understanding of the solvation structure of MX (M = metal cation and X = halide) in the IL, we investigated the mixture of [BMIm][OTf] with various halide salts with the help of classical molecular dynamics (MD) simulations. In this study, we calculated structural properties such as radial distribution functions (RDFs), spatial distribution functions (SDFs), and coordination numbers and dynamical properties such as mean-square displacements (MSDs) and velocity–velocity autocorrelation functions. Here, we investigated the solvation of ions, atomistic details of the interactions, possible rattling motion of ions, and formation of cagelike structures, which can affect the diffusivity of constituent ionic entities (Figure and Table ).

Figure 1

(a) Structure of a single [BMIm][OTf] ion pair with atom labels and (b) complete simulation box with metal ions in ball representations.

Table 1

Initial Configurations of Different Systemsa

number of IL ion pairs	number of MX ion pairs	mol %
201
200	1
190	10	5
180	20	10
170	30	15
160	40	20
150	50	25
100	100	50

These configurations were applied for all of the different M+ and X–.

Results and Discussion

We systematically studied the pure IL and its mixture with alkali halides (MXs) employing classical molecular dynamics simulations; M = lithium, sodium, potassium, rubidium, and cesium cations and X = fluoride, chloride, bromide, and iodide anions. We compared the densities obtained through our MD simulations with experimental values available in the literature to validate the force fields employed. The estimated density of pure IL (1302 kg m–3) shows an excellent agreement with the experimental density (1304 kg m–3). We present the densities of all simulated MX + IL mixtures in Figure a. Cations like Rb+ and Cs+ are heavier than [BMIm]+. When salts containing these are taken at higher concentrations, the overall mass of the system increases, which in turn leads to increase in density. This effect is observed in the figure, for 25 and 50% mole fractions of the salt. For lighter M+-containing systems, the density decreases with the increasing concentration. For lithium and sodium salts with a common anion, we found a linearly increasing trend of density (Figure b) with the increase of salt concentration due to the smaller size and higher charge densities of both Li+ and Na+ than [BMIm]+. The same trend was also reported by Méndez-Morales et al.[28] in their study of solvation of the lithium salt in a protic ionic liquid with a common anion.

Figure 2

Simulated densities of [BMIm][OTf] mixed with (a) different concentrations of LiCl (black circle), NaCl (red square), KCl (green diamond), RbCl (blue triangle), and CsCl (magenta triangle) and (b) Li[OTf] (violet circle) and Na[OTf] (green square). Moreover, experimental density (black triangle) and simulated density (red triangle) of pure IL are also included.

Structure and Dynamics of Pure Ionic Liquid

We calculated the radial distribution functions[34] (RDFs) of various pairs taking the last trajectories obtained from the NVE simulation to know the microstructure of the pure IL. RDF gives the probability of finding an atom/molecule around a reference atom/molecule. We calculated the following RDFs: cation–anion (Figure a), cation–cation, and anion–anion taking the center of mass of each (Figure S1), between the hydrogen atoms on the ring of [BMIm]+ and the oxygen atom of [OTf]− (Figure b). In the case of cation–anion RDF, the peak height is greater compared to that in cation–cation and anion–anion RDFs. In the case of atom–atom RDFs, we observe that the oxygen atom of [OTf]− interacts more strongly with H3 as compared to H1 and H2 of [BMIm]+ due to two electronegative nitrogen atoms attached to C3. These atoms pull electron density toward them, making C3, and consequently H3, more electron-deficient, resulting in oxygen attraction. As evident from Figure , the first peaks for cation–cation, cation–anion, and anion–anion appear at 8, 5.1, and 8.9 Å, respectively. [BMIm]+ is surrounded by [OTf]− in its first solvation shell and a second layer of [BMIm]+ in the second solvation shell and vice versa. We observe splitting of peak in anion–anion RDF due to sequential ordering induced by cation–anion pairs, similar to the observation by Morrow et al.[35] We calculated average coordination numbers by integrating the radial distribution function ranging from zero to the distance of first minimum of corresponding RDF. We observe that the average numbers of [OTf]− and [BMIm]+ around [BMIm]+ are ∼7.12 and ∼21.90, respectively. Similarly, one [OTf]− is surrounded by around 7 [BMIm]+ in the first solvation shell and 17 [OTf]− in the second solvation shell. To get a three-dimensional picture of this scenario, we analyzed the spatial distribution functions (SDFs) with isosurface density value (number of atoms/nm3) 10 using the TRAVIS[36] software package. We can see from Figure c,d that the anions are more distributed around the [BMIm]+ and the cations are distributed around oxygen atoms of [OTf]−.

Figure 3

Radial distribution of (a) [BMIm]+ around OTf and (b) oxygen atom of [OTf]− around the H1, H2, and H3 atoms of [BMIm]+. Spatial distributions of (c) [BMIm]+ (blue) around [OTf]− and (d) [OTf]− (red) around [BMIm]+.

To study the dynamics of cations and anions of pure IL, we illustrated the mean-square displacement (MSD) of [BMIm]+ and [OTf]− (Figure ), which is defined aswhere the location of the center of mass of ion i at time t is given by r⃗(t); the sum extends over all of the species, and the brackets indicate the ensemble average. The MSD of the cation is more than that of the anion, which can be attributed to the lighter mass of the cations. We calculated self-diffusion coefficients of the cation and anion using the Einstein relation[37]The diffusive regime exists where the ratio(β) of the log MSD and log t plot is equal to 1. This was calculated using the following equation, and the results are presented in Figure b,c.We fitted the MSD between 20 and 46 ns (identified as the diffusive regime) to calculate the diffusion coefficients. The values of diffusion coefficient of [BMIm]+ and [OTf]− are 4.3 × 10–12 and 2.5 × 10–12 m2 s–1, respectively. The diffusion coefficient obtained for [BMIm]+ is in the same range as reported by Morrow and Maginn[35] for the IL, [BMIm][PF6], using the CHARMM force field. Another report in the literature by Tsuzuki et al. provided the experimental diffusion coefficients of [BMIm]+ and [OTf]− to be 10 × 10–11 and 9.0 × 10–11, respectively, at a temperature of 353 K, while molecular dynamics simulations at the same temperature reported 5.9 × 10–12 and 4.8 × 10–12 for [BMIm]+ and [OTf]−,[38] respectively.

Figure 4

(a) MSD vs time plot of the cation and anion of pure IL. (b) Logarithmic plot of MSD vs time. (c) β vs time plot.

Structure and Dynamics of Mixtures of Ionic Liquid and Alkali Metal Salts at Different Concentrations

We present the snapshots of the solvation shell of lithium, sodium, potassium, rubidium, and cesium cations in the mixtures of single ion pair of metal chlorides (MCl) with the IL to understand the structural characteristics (Figure S2). We find that all M+ are surrounded by nearly 4 [OTf]− and coordinate through nearly 7 oxygen atoms. On analysis of RDFs of [OTf]− around M+ (Li, Na, K, Rb, and Cs) (Figure S3), we observe that the first peak heights of the RDFs of [OTf]− around M+ decrease when the size of M+ increases, in all of the mixtures. We know that a higher charge density facilitates the coordination with anions. The first solvation shell regions appear at farther distances when we move from Na to Cs due to increasing size of M+. However, as the size of X– increases, we observe that the interactions between M+ and [OTf]− also grow stronger. This can point to a decreasing interaction between the M+ and X–, leading to solvation of the cation by ionic liquid anions. This observation is in accordance with an experimental study of solubility of MX in [BMIm][OTf] conducted by Kuzmina et al.,[29] wherein they reported an increasing trend of solubilities with an increase in the size of X–, based on the calculation of thermodynamic parameters such as ΔH, ΔS, and ΔG. Looking at the distribution of [BMIm]+ around X–, we observe a peak splitting within the first solvation shell of X– (Figure ) in all of the mixtures. This splitting is indicative of two different types of binding of [BMIm]+ with X–. The first peak is more intense than the second peak, and it represents the interaction between X– and the H3 atom of the [BMIm]+. The second peak represents the interaction between MX and H1, H2 atoms of [BMIm]+. Coordination numbers corresponding to the RDFs point out that M+ is surrounded by 4–5 [OTf]−. The number of [BMIm]+ surrounding X– is seen to be in the range of 3–7. For different concentrations of alkali metal chlorides (MCl) in IL (Figure ), Li+ shows much stronger attractions to [OTf]− than the rest in all mixtures. This shows that Li+ is more solvated by [OTf]− and hence is more soluble in solutions.[29] However, Cs+ is observed to be less solvated than its counterparts and is also least soluble. We also see a very tiny shoulder around first peak of RDF in the case of Na+, which vanishes at higher concentrations of salt. This shoulder is also indicative of two different types of binding of the Na+ with [OTf]−, which is not observed at higher concentrations of salt. In the right-hand-side column of Figure , we observe two peaks in the first solvation shell of Cl–, which represent two types of binding environments of Cl– with [BMIm]+. The first type of binding occurs at a closer distance and is stronger, so this is between Cl– and H3 atoms of [BMIm]+. The second type is the coordination between Cl– and the other hydrogen atoms of [BMIm]+. These peak heights decrease at higher concentrations of salt, which implies a decrease in the Cl––[BMIm]+ interactions. The second peak nearly vanishes at higher concentrations. For a clearer picture of the structural environment of the solvation shell of M+ and Cl–, we calculated coordination numbers (Figure S4). The relative numbers of [OTf]− around M+ and [BMIm]+ around Cl– decrease when we go toward a higher percentage of salt because of the more significant number of salt molecules. From these results, we can say that M+ is surrounded by Cl– and [OTf]− in their first solvation shell and further surrounded by [BMIm]+ in the second solvation shell. Cl– is surrounded by the first layer of M+, the second layer of [BMIm]+, and the third layer of Cl– and [OTf]−.

Figure 5

RDFs of [BMIm]+ around X–, (a) F––[BMIm]+, (b) Cl––[BMIm]+, (c) Br––[BMIm]+, and (d) I––[BMIm]+ where the colors violet, red, orange, green, and blue represent the mixture of LiX, NaX, KX, RbX, and CsX (X = halide anion) with the ionic liquid.

Figure 6

RDFs of M+–[OTf]− and X––[BMIm]+ in (a, b) 10% (c, d) 25% and (e, f) 50% concentration of salt in IL. Black, red, green, blue, and magenta represent the mixture of LiCl, NaCl, KCl, RbCl, and CsCl in IL, respectively.

To know how M+ moves through its solvation shells, we calculated the mean-square displacements of the single ionic species of salts (Figure S5). We find that Na+ covers very less displacement in a mixture of its fluoride or chloride with the IL. The contrary is observed when its bromide or iodide is used due to the larger sizes of Br– and I–. We show log–log plot of MSD and β values in Figures S6 and S7, respectively. Since the simulation time required for these systems to reach a proper diffusive regime (β = 1) is quite long, we calculated self-diffusion coefficients from the MSDs, where the values of β are in the range of 0.8–1 (corresponding to the simulation time of 4–20 ns) (Figure ). For anions, F– and I–, K+ shows the largest self-diffusion coefficient among the cations. The larger cations Cs+ and Rb+ show faster diffusion for Cl– and Br– as counter ions, respectively. Na+ is involved in relatively slower motion when the anions are smaller (F– or Cl–) but moves substantially faster for Br– or I–. Hence, it can be seen that the choice of X– also plays a role in determining the diffusion characteristics of M+.

Figure 7

Self-diffusion coefficients for M+ and X– in mixtures of single ion pair of MX in IL.

For a better understanding, we also calculated velocity autocorrelation functions of all single ionic species of MCl. Velocity autocorrelation provides essential information about single-particle dynamics; the profile of the curve that resembles that of a damped oscillator points to the fact that there are strong interactions that act on the ions. The ions that try to stabilize between attractive and repulsive forces are also involved in diffusive motion. This diffusion forms one of the primary reasons for the dampening of oscillatory characteristics. The first zero of this curve provides the first collision time, the average time a particle takes to collide with another particle. A longer collision time is indicative of slower transport dynamics of the ion due to the mass of the ion and its charge density. Normalized velocity autocorrelation functions, C(t), for the M+ and Cl– are represented in Figure and were calculated using the following equationwhere the velocity of the center-of-mass of the ions at time t is represented by v⃗(t) and the brackets indicate the ensemble average. The insets in Figure indicate the estimation of the corresponding collision time. The scaled inset shows the time at which the curves meet the x-axis. We observe that the oscillatory behavior completely vanishes for the mixtures of RbCl and CsCl due to their large size. This relatively faster damping is indicative of weaker interactions acting on these larger cations. Collision times increase as we move from Li+ to Cs+ due to combined effects of the decreasing interaction between M+ and [OTf]− and increase in the size of the cations. A slight decrease in collision time occurs for the larger M+, as the concentration of salt increases. However, the changes in collision time with respect to the changes in the concentration of salt are negligible, and the concentration of salt does not have a huge impact on these values. Li+ and Na+ are found to have a stronger interaction with [OTf]− at a shorter distance. The number of collisions increases, and oscillatory behavior is seen up to nearly 0.6 and 0.3 ps for Li+ and Na+, respectively. These collision times imply a rattling motion of ions in the mixture. Table summarizes the collision times for alkali metal chlorides at different concentrations. For more clarity, we look at the MSD of M+ and Cl– with respect to change in concentration (Figure S8). We also included the MSD for [BMIm]+ and [OTf]− (Figure S9). We see that the MSD of Rb+ is more in the mixtures of 10 and 25% of salt concentration. All M+, in general, traversed much lesser (0.4–0.5 nm) at higher concentrations (50%) of salt, and this is due to the high viscosity of the high-concentration solution. We calculated the self-diffusion coefficients (Figure ) of ions of salt by fitting our MSDs in the range of 5–20 ns for M+ and X– and 10–40 ns for [BMIm]+ and [OTf]−, where values of β were close to unity. We observe a lowering of diffusion coefficients of M+ when we go for a higher concentration of salt due to increased viscosity. We find the same order of self-diffusion coefficients for M+ in the mixtures of 10 and 25% salt with IL: Li+ ≤ Na+ < K+ < Cs+ < Rb+. This can be explained on the basis of the size of M+; since Li+ and Na+ have smaller sizes and higher charge densities, they can solvate more number of anions and become more structured and less diffusive. Moreover, we find very similar diffusion coefficients for all M+ in the mixture of 50% salt with the IL.

Figure 8

Normalized velocity autocorrelation functions of single M+ (1st column) and Cl– (2nd column), where black, red, green, blue, and magenta represent the mixtures of LiCl, NaCl, KCl, RbCl, and CsCl in IL. First, second, and third rows represent the 10, 25, and 50% of salt in IL, respectively.

Table 2

Collision Times (×10–2 ps) of Alkali Metal Chlorides in Mixtures

	LiCl		NaCl		KCl		RbCl		CsCl
%salt	Li+	Cl–	Na+	Cl–	K+	Cl–	Rb+	Cl–	Cs+	Cl–
10.0	1.83	8.01	4.31	8.36	6.86	7.31	12.21	7.58	18.30	7.32
25.0	1.86	7.30	4.35	6.76	6.68	6.42	11.86	6.35	16.68	6.59
50.0	1.98	6.63	4.48	5.94	6.70	6.10	11.57	6.12	16.20	6.48

Figure 9

Diffusion coefficients of M+ and Cl– in different mixtures with IL.

Mixtures of Lithium and Sodium Salts with Ionic Liquid with a Common Anion

RDF peak heights in Figure show that Li+ is much more interactive toward the anion of IL as compared to Na+. There is a double peak within the distance of first solvation shell of Na+ in the mixture of Na[OTf] in IL. Here, the first peak is more intense when the concentration of salt is 5–15%, after which the second peak becomes more intense. This result reveals that the strong coordination of Na+ with the anion of IL is found to be at lower distances till 15% of salt concentration and at higher distances after that. The first and second peaks were found to be at 0.37 and 0.41 nm, respectively. We also included the RDFs of [BMIm]+ and M+ around M+ (Figure S10). Li+ and Na+ show much stronger coordination with the [OTf]− than with other two species. We did not find any significant changes in the structure of the IL. We estimated the coordination numbers of different species around Li+ (Figure S13a) and Na+ (Figure S13b). We also include the number of surrounding [OTf]− around [BMIm]+ of IL anions in the same graph. We found an increasing trend in the number of [OTf]− around Li+ and Na+ with an increase in the concentration of salt. We also found that the number of M+ around itself was increasing from lower to a higher concentration of salt. We observed that nearly 4 [OTf]− were found in their first coordination shells. From these results, we can predict that the Li+ and Na+ are surrounded by a first layer of [OTf]−, the second layer of itself in their first solvation shell, and a third layer of [BMIm]+ in the second solvation shell.

Figure 10

Radial distribution functions of (a) [OTf]− around Li+ and (b) [OTf]− around Na+. The insets show magnified images of the peaks.

We also investigated the concentration dependence of normalized velocity autocorrelation functions of Li+ and Na+ in the mixture of Li[OTf] and Na[OTf] in IL and is presented in Figure S12. We have included estimated collision times for Li+ and Na+ in Table . A clear oscillatory behavior is seen for Na+, and these oscillations are nearly damped out after 1.0 ps. This behavior indicated the rattling motion of Na+ in the “cage” of its nearest neighbors, which is in agreement with previous studies of Li+ and Na+.[27,39] Li+ has random collisions but has a strong correlation up to nearly 1.0 ps because it has stronger interaction with the IL anions in comparison to Na+. We observe an increasing trend in the mean collision time of sodium (except for 5 and 25% of salt), supportive of the fact that the interaction between Na+ and [OTf]− decreases between 10 and 20% of salt concentration; we also suggest this type of behavior from our structural analysis. The dynamics of Li+ and Na+ in their solvation shell is faster at lower salt concentrations. For more details on the single-particle dynamics, we analyzed the MSDs of Li+ and Na+ (Figure S13) for all of the systems. From this, we observed that Li+ and Na+ are displaced more at lower concentrations and much lesser at higher concentrations of salt. We included their log–log plots (Figure S14) and β values (Figure S15) of their corresponding MSDs. To calculate the self-diffusion coefficients included in Tables and 5, we fitted our MSDs in the ranges of 10–25 ns for M+, 10–35 ns for [BMIm]+, and 10–30 ns for [OTf]−, where the values of β are close to unity.

Table 3

Collision Times (×10–2 ps) of Li+ and Na+ in the Mixtures of Li[OTf] and Na[OTf] in IL

%salt	Li+ in Li[OTf] + IL	Na+ in Na[OTf] + IL
5.0	1.83	4.35
10.0	1.86	4.30
15.0	1.88	4.31
20.0	1.86	4.34
25.0	1.85	4.28

Table 4

Self-Diffusion Coefficients (×10–12 m2 s–1) of Different Ionic Species in the Mixture of Li[OTf] in IL

%salt	DLi+	D[Bmim]+	DOTf–
5.0	1.4(±0.6)	7.3(±0.4)	3.6(±0.3)
10.0	0.8(±0.2)	3.4(±0.5)	1.3(±0.0)
15.0	0.6(±0.5)	3.3(±0.9)	1.1(±0.0)
20.0	0.7(±0.3)	2.6(±0.4)	1.0(±0.2)
25.0	1.1(±0.3)	2.6(±0.0)	1.4(±0.2)

Table 5

Self-Diffusion Coefficients (×10–12 m2 s–1) of Different Ionic Species in the Mixture of Na[OTf] in IL

%salt	DLi+	D[Bmim]+	DOTf–
5.0	1.9(±0.5)	5.7(±0.0)	3.2(±0.3)
10.0	1.1(±0.3)	4.5(±0.0)	1.9(±0.1)
15.0	0.4(±0.1)	3.3(±0.1)	1.5(±0.1)
20.0	0.7(±0.2)	3.9(±0.4)	1.2(±0.3)
25.0	0.5(±0.1)	2.5(±0.4)	0.7(±0.3)

From all of these results, we conclude that Li+ and Na+ form a stable kinetic entity ([M(OTf)], where n is the number of surrounding [OTf]− around M+, M = Li, Na) with strong aggregations with [OTf]− in their first solvation shell, which has a longer lifetime, with a rattling motion in its solvation shell. This was also reported by Méndez-Morales et al.,[27] for Li+ and Na+ in a mixture of lithium/sodium salts with different ILs. Moreover, these formations are supported by thermodynamic parameters as well. A metathesis reaction of MCl with [BMIm][OTf] to form M[OTf] and [BMIm]Cl is reported in the literature to have a negative reaction enthalpy, especially when M = Li or Na, making this a thermodynamically favorable process,[29] and lithium salts are more solvable than the larger M+.

Computational Methods

All classical MD simulations were performed using the GROMACS 5.0.4[40,41] package. Bonded and nonbonded parameters for cations and anions of the pure ionic liquid were generated using generalized amber force fields (GAFF)[42] and are presented in the Supporting Information document. Lennard-Jones parameters for alkali metals and anions were taken from reported data by Chen et al. for Na+, K+, Cs+, and Cl–.[43] To find the stable ground-state structures of a single cation and anion of the pure ionic liquid, geometry optimizations were done with the help of Gaussian 09[44] using density functional theory at the B3LYP/6-311+G(2d,p) level.[45,46] Optimized ground-state structures of the cation and anion of pure IL are given in Figure a with atom labels noted using visual molecular dynamics (VMD) software.[47] Alkali metal cations and anions were modeled as a single site of charges +1 and −1, respectively. Generation of partial charges was done by Antechamber.[48] Atomic partial charges in the force field parameters of the cation and anion of pure IL were adjusted by a scaling factor of 0.8 to enhance the dynamics, which will give a very good agreement with experimental results. Initial structures for molecular dynamics simulations were set up using Packmol,[49] and the number of chemical entities used in each system is described in Table . A snapshot of the [BMIm]+ as well as [OTf]− ions and the initial configuration of a system of pure ionic liquid are given in Figure a,b, respectively.

MD simulations of pure IL and its mixture with different MXs were performed at a temperature of 298.15 K and pressure of 1 atm. The particle-mesh Ewald (PME) method with a 0.1 nm grid searching and cubic interpolation of order 4 was used for treating long-range electrostatic interactions. Both Coulombic and van der Waals interactions were treated with a cutoff of 1.2 nm. Initial configurations were relaxed using the steepest descent algorithm[50] for 105 steps. An annealing process of 2 ns was used for stepwise heating and cooling to ensure thorough mixing of the system components. All systems of pure IL, as well as its mixtures of salts, were equilibrated in an isobaric–isothermal ensemble (NPT) for 10 ns followed by a simulation time of 10 ns within a canonical ensemble (NVT). Equilibrium densities of the systems were calculated after the NPT simulations, and these values were used to obtain the length of simulation boxes for subsequent simulations. Finally, a simulation of 50 ns was performed within the microcanonical ensemble (NVE). The mixtures of single ion pair of MX with IL were simulated for 100 ns in the NVE ensemble. A time step of 2 fs was used in all of the simulations. Temperature and pressure were controlled by the V-rescale thermostat[51] and Berendsen barostat[52] algorithms with coupling constants of 0.1 and 2.0 ps, respectively. We applied periodic boundary conditions in all directions so that our system behaves like an infinite system. Equations of motion were integrated with the help of the Verlet algorithm.[53] The LINCS algorithm[54] was used to constrain the bonds with hydrogen atoms. All coordinates were saved at every 2 ps, and the trajectories obtained from the NVE simulation were used for the analysis of various properties.

Conclusions

We performed MD simulations of pure ionic liquid [BMIm][OTf], its mixtures with different MXs and the mixtures containing a common anion. We analyzed the structural and dynamical properties of the systems at T = 298.15 K and P = 1 atm. We calculated the density of the pure IL that showed an excellent agreement. We also calculated densities for all other systems. The analysis of the RDFs of the mixtures shows that the interactions between M+ and [OTf]− decrease from Li+ to Cs+, and stronger interactions between M+ and [OTf]− are found in the mixtures of MI with IL. X– was found to be coordinated in two different ways with the [BMIm]+ in all mixtures. We observed that Na+ is coordinated at two different binding sites of [OTf]− in the case of the same anion, and the structure of IL remained nearly the same upon addition of salt. M+ cations are surrounded by nearly 4 [OTf]− in their first solvation shell in the mixture of a single ion pair of MX in the IL and nearly 2 [OTf]− in the mixtures of different concentrations of MX in the IL. In mixtures with a common anion, i.e., M[OTf] in [BMIm][OTf], we find that Li+ and Na+ are surrounded by the first layer of [OTf]−. By the study of velocity autocorrelation functions, we observe that the Li+ shows a rattling motion in the mixtures of different concentrations of LiCl in IL. We observed that Li+ and Na+ form stable kinetic entities (Na[(OTf)]) with strong aggregation with [OTf]−. They are also found to possess a rattling motion in IL mixtures with a common anion. Calculated self-diffusion coefficients predict that the mobility of all of the ionic species decreases with increasing salt concentration in mixtures of MX and IL with a common anion, pointing to the formation of the stable clusters.