Molecular dynamics simulation of lithium fluoride in aqueous solutions at different temperatures 300 K – 360 K

. Lithium metal is one of the most promising anodes for rechargeable batteries due to its large capacity, but its performance is plagued by high chemical reactivity, forming an unstable Li–electrolyte interface. Lithium fluoride has been recently touted as a promising material to improve this interface. Computer simulation of lithium in fluoride aqueous solution has an important tool in understanding the structural and dynamical characteristics of ionic complexes. In this investigation, the structural and dynamical properties of supersatured LiF systems have been studied by molecular dynamics simulations at different temperatures range from 300 K up to 360 K using SPC/E water model and the ions which are modeled as charged Lennard-Jones particles. The cartesian positions of each atom of lithium chloride aqueous solution are recorded at every time step of the trajectory. Therefore, the analysis of data requires to calculate the radial distribution functions (RDF) describing the structural and dynamical properties of the water and Li + and F - ions, such as the coordination numbers, interparticle distances, self-diffusion coefficients and dielectric constants at various temperatures.


Introduction
Lithium fluoride possesses some unique properties, including high mechanical strength [1], low solubility [2], a wide electrochemical stability window (0 to 6.4 V vs. Li) [3,4], and low calculated barriers to Li diffusion [5], which suggests that LiF may enable homogeneous Li+ flux and suppress dendrites. Consequently, the prevalence of fluoride combined with its attractive properties has led to the suggestion that LiF is a particularly beneficial phase for Solid Electrolyte Interphases [6,7]. Molecular dynamics (MD) have been established as a powerful and valuable method to investigate the molecular structure of liquids. However, computer simulation of fluorinated salts has an important tool in understanding the dynamics of condensed phases at the molecular level. The development of the fluorine chemical industry is increasing and there is an increasing demand for fluorite. In fact, the hydration properties of fluorinated compounds are relevant to many natural processes and industrial applications [8][9][10][11][12].
The hydration numbers of Li + were considered to be dependent on salt concentrations, with higher salt concentrations resulting in lower hydration numbers. Many structural studies of solutions of alkali metal salts are devoted to hydrated complexes of lithium ions. A large number of works have been undertaken to identify the structure forming and structure breaking properties of ions [13,14].
The dynamical properties of the alkali fluoride aqueous solutions are of great interest for the knowledge and better understanding of the physico-chemical processes governing industrial, environmental and energetic processes. The analysis of literature of lithium fluoride in aqueous solutions shows a deficiency of data at various temperatures.
The outline of this paper is the following. The simulation details of the MD simulations are given in section 2. The computed structural properties, selfdiffusion coefficients and dielectric constants are determined in section 3. The conclusion and final remarks are presented in section 4.

Simulation details
Equilibrium molecular dynamics (MD) simulations of lithium in fluoride aqueous solution have been investigated using the GROMACS package [15]. The density of the system is adjusted to reflect the composition of the specific solution being simulated. Coulombic interactions were evaluated with the smooth PME method [16]. NPT simulations were fixed at 1 bar with Parrinello-Rahman pressure coupling [17]. The MD calculation is executed for 3 000 000 steps using 0.1 fs for one time step. In all simulations, we used the simple three-site extended single point charge (SPC/E) model [18] for the water molecules because of its performance combined with a reasonable description of structure and dynamic properties, which is known to also give an appropriate description of several solution properties. The ion-ion and the ionwater interactions are represented by a combination of Coulombic and LJ potentials [19]. The potential can be written in general as: Where q i is the charge of the ith atom (or ion). The Lennard-Jones parameters σ ij and ε ij are obtained by using the combination rules σ ij = (σ i + σ j ) 2 ⁄ and ε ij = √ ε i ε j . The values of the potential parameters q i , σ ij and ε ij for water, Li + and Fions are summarized in Table 1. During dynamic simulations, the OPLS-AA force-field [20] was employed to describe the interatomic potentials of the ions and water components. The simulations were performed at various temperatures. The temperature is controlled by a Nosé-Hoover thermostat [21,22]. The lithium and fluoride ions were added to a cubic (40 × 40 × 40) Å3 simulation box with 2165 water molecules.
The structure of the liquid was characterized by calculating the pair distribution functions (RDFs) of different pairs and the radial coordination numbers. The radial coordination numbers n ij (r)of different ions are obtained by integrating the radial distribution function, an estimate of the number of water molecules surrounding the M+ particle between 0 and the distance r min .
Where ( ) is pair distribution function for the i-j pair,  to the minimum of the first peak in the RDF The most common quantity to describe the dynamical behavior of a aqueous system is its self-diffusion coefficient . The translational self-diffusion coefficient can be obtained from the long-time limit of the Mean Square Displacement (MSD) by the Einstein relation: Where r(t) is the position vector of the centre of mass of the molecule (or ion) at time t.
The dielectric constant of non-polarizable fluids was computed from fluctuations [23] of the total dipole moment M = ∑  i N i=1 in the simulation volume by  = 4 3k B T⟨V⟩ (⟨M 2 ⟩ − ⟨M⟩ 2 ) + 1 (4) Where k B is the Boltzmann constant and  i is the individual dipole moment vector of the molecule. The angled brackets denote the ensemble average.

Thermodynamical and structural properties
The effect of temperature is a fundamental element in the structural study of aqueous electrolytic solutions. The computed densities, total energy and structural properties of aqueous LiF solutions at different temperatures are presented in Table 2. The calculated density of aqueous lithium fluoride solutions is a decreasing linear function of temperature.
The hydration structural properties for each aqueous ion (Li + and F -) are computed from canonical NVT ensemble molecular dynamics simulations. It is convenient to study the local structure of an electrolyte solution by means of ion-ion, ion-water, and waterwater pair correlation or the radial distribution functions. The RDFs for the case of saturated aqueous LiF electrolytes having a molality m = 0.1 mol.Kg -1 at different temperatures from 300 K to 360 K are presented in Figs. 1-3. The bibliographic study revealed that the effect of temperature has been less often reported for the aqueous LiF system. Increasing temperature for the cases of Li + -Ow, Li + -Hw, F − -Ow, F − -Hw, Ow-Ow and Ow-Hw RDFs (Figs. 1-a, 1-b, 2-a, 2-b, 3-a and 3-b) causes to decrease in the height of the first peak. This is due to increment of kinetic energies of water molecules and ions. But for the Li-F radial distribution function it inversely causes to increase. The first peak of gLi−Ow(r) was at 0.203 nm and the second shell at around 0.433 nm respectively. The magnitude and position of the first peak in Li + -Ow radial distribution functions agree closely with the previous computer simulations [24][25][26].
The structural around the fluoride anion can be evaluated by the gF−Ow(r) and gF−Hw(r). Figs. 2-a and 2-b show that the gF−Hw(r) presented two peaks at 0.162 nm and 0.307 nm, respectively. The gF-Ow(r) also presented two peaks, the first peak lay between those of gF-Hw(r) at a distance of 0.261 nm, which indicates that water molecules in the first shell were oriented in such a way that only one hydrogen atom pointed toward the fluoride anion.
The coordination numbers of Li + and Fions decrease significantly with increasing temperature, witch proves the rupture of pairing ions and the increase of separated ones.  The gLi-F(r) curve shows a pronounced two peaks, the first sharp peaks at 0.195 nm correspond to the presence of contact ion pairs (CIP) and the second peaks at 0.387 nm show the presence of solvent-shared ion pair (SIP). The CIP peaks are also higher with increasing of temperature and the number of water separated ion pairs is found to be less significant for this saturated solutions. A generally good concordance is obtained by comparing these simulation results with those reported in the literature by Fennell and all [27].
The noticeable effects of the increase of the temperature are a decrease of the first and second peaks maximum of Oxygen -Oxygen RDFs. In Fig 4-a we report the gOw-Ow(r) of LiF(aq) at various temperatures and saturated molality m = 0.1 mol/Kg. They are representative of the effects of the temperature on the structure of water. The position of the second peak of gOw−Ow(r) moves from 3.29 -5.66 Å to 3.56 -5.84 Å, which indicates a strong distortion of the Oxygen-Oxygen structure in LiF(aq) system when the temperature is increased . Fig 4-b showed the effect of temperature on the hydrogen bond network. According to this figure, when the temperature of the solution increases, the value of the first peak of RDFs decreases. This could be explained by thermal agitation which makes the water molecules faster and subsequently the breaking of the hydrogen bond. These observations on the effect of temperature are in agreement with those of literature [28,29].

Dynamical properties
The new values obtained from the simulation for the dielectric constant and self-diffusion coefficients of water, Li + and Fat different temperatures and saturated molality m = 0.1 mol.kg -1 are listed in Table  3. As presented in this table, although there are some exceptions for the ion species, the values of the selfdiffusion coefficients increase with increasing temperature. This behavior is more pronounced for the water molecules and less for the ions. This may be related to the strong effect of the columbic forces which are more effective on the ion species. Another interesting result is that the dielectric constant decrease with decreasing temperature.
We notice that our value of the simulated dielectric constant using SPC/E is relatively small compared to that found experimentally for pure water (ε = 78.5). However, our results are in good agreement with other studies [30][31][32].

Conclusion
The computer simulations are able to give quantitative information on the dynamics of aqueous electrolytes. We have investigated the structural and dynamical properties of lithium fluoride salt solution at various temperatures ranging from 300 to 360 K by using a SPC/E water model in combination with the OPLS-AA force-field to describe the ion-ion, ion-water and waterwater interactions in solution. The results may therefore be used with some confidence in predicting coordination numbers and ion-water geometries for those systems.
The reliability of these force-field parameters has been validated here by comparison of our results with those available in the literature from of molecular simulations and spectroscopic experimental techniques. The hydration structure and dynamical properties of LiF aqueous system are so influenced by the temperature and chemical nature of counterion.
We found that the dielectric constant values decreases as the temperature increases. This is due to increment of kinetic energies of water molecules and ions.