Correlation between lithium-ion diffusion and coordination environment in solid polymer electrolytes: a molecular dynamics study

Lithium-ion diffusion in solid polymer electrolytes (SPEs) is a pivotal characteristic that significantly influences overall lithium-ion battery performance. This characteristic can be affected by the coordination environment of lithium ions within the polymer matrix. However, the correlation between lithium-ion diffusion and its coordination environment in biopolymer-based SPEs such as carboxymethyl chitosan (CMCS) remains understudied. In this study, we used molecular dynamics (MD) simulations to investigate this correlation. Lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) was used as the lithium salt in the simulated systems. All MD simulations were conducted using the GROMACS package with the general AMBER force field (GAFF). The coordination structures around Li+ were successfully estimated using the radial distribution function obtained from the MD simulations. These results indicate a preference for Li+ coordination with oxygen atoms, both from the CMCS polymer chains (OCMCS) and TFSI− ions (OTFSI-). The coordination number between Li+ and OCMCS decreases as the concentration of LiTFSI increases. The diffusion coefficients of Li+ varied depending on the concentration of LiTFSI and demonstrated a sensitivity to the coordination structure of Li+. A high diffusion coefficient of Li+ ions was observed at low LiTFSI concentrations, where Li+ was primarily coordinated with oxygen atoms from the CMCS polymer chains.


Introduction
Owing to their high energy density, long cycle life, and environmental friendliness, lithium-ion batteries (LIBs) have had a significant influence on the fields of energy storage, powering electric vehicles, and portable electronics [1].One of the key components in LIBs is the electrolyte owing to its critical role in enabling the transport of lithium ions between the anode and cathode.Organic-based liquid electrolytes are widely used in lithium-ion batteries (LIBs) for years.However, conventional liquid electrolytes have limitations.Safety risks associated with flammability, volatility, and leakage have emerged in certain high-energy applications [2,3].Therefore, it is necessary to develop efficient electrolyte systems beyond liquid electrolytes [4].
Solid polymer electrolytes (SPEs) are regarded as viable substitutes for liquid electrolytes because of their stability, safety, and potential to enhance battery efficiency.SPEs have intrinsic benefits including non-flammability, non-leakage, and enhanced stability [5].These characteristics render them a highly appealing choice for the development of advanced lithium-ion batteries.Furthermore, the adoption of SPEs has the potential to facilitate the advancement of battery designs that are thinner and more flexible [6], thereby broadening their range of potential uses in diverse applications.Poly(ethylene oxide) (PEO), poly(acrylonitrile) (PAN), poly(ethylene carbonate) (PEC), and poly(vinylidene fluoride) (PVdF) are some examples of the most commonly used SPE materials.Extensive research has been conducted to improve the ionic conductivity of SPE and their compatibility with electrodes.In addition to these SPE materials, there is growing interest in the development of biomaterial-based SPEs [7].Materials such as cellulose, chitosan, and its derivatives, including carboxymethyl chitosan (CMCS), have attracted considerable interest because of their sustainable nature and environmentally favorable attributes [8].In particular, CMCS has been reported to have notable ionic conductivity and the capacity to stabilize lithium anodes during plating-stripping procedures [9].
The diffusion of lithium ions within SPEs directly affects the performance of LIBs, such as the rate capability and overall efficiency [10].The coordination environment of lithium ions within the electrolyte is known to influence the diffusion behavior [11,12].Understanding this relationship is vital for tailoring the SPEs to optimize their performance.The correlation between lithium-ion diffusion and its coordination environment can be theoretically studied using molecular dynamics (MD) simulations.While significant research has investigated the lithium-ion diffusion behavior in various solid electrolyte materials [13,14], knowledge regarding this correlation within CMCS-based SPE systems is still limited.In this study, MD simulations were employed to investigate the correlation between lithium-ion diffusion and the coordination environment within the CMCS-based SPEs.Lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) was used as the lithium salt in the simulations.

Computational methods
The CMCS/LiTFSI SPE systems are represented by 50 CMCS chains with various numbers of LiTFSI ion pairs in a cubic cell.Each CMCS chain contained 20 monomers, with a carboxymethylation degree of 0.8.Three simulated systems were constructed, with each system containing a different LiTFSI weight percentage of 10, 15, and 20.The number of LiTFSI ion pairs in the systems were 80, 128, and 182 ion pairs for the CMCS/LiTFSI-10, 15, and 20%, respectively.A charge scaling of 0.75|e| was employed for the charges of Li + and TFSI -ions to account for ionic polarization [15][16][17].Packmol program was used to generate random coordinates for the CMCS chains, Li + ions, and TFSI − ions [18].Interactions at the molecular level were described using the general amber force field (GAFF) [19].All minimization procedures, system equilibrations, and molecular dynamics simulations were performed using the GROMACS software package (version 2020.4)[20] with periodic boundary conditions.A series of energy minimization, compression/decompression, annealing/cooling at isothermal-isobaric (NPT) ensemble and canonical (NVT) ensemble with total duration of 82 ns was applied to the systems to achieve a more representative structures [15].Energy minimization was performed using the steepest descent algorithm, and the equation of motion was integrated using the leapfrog algorithm.The simulation temperature was maintained by velocity rescaling with stochastic terms (v-rescale), while constant pressure was maintained by Berendsen coupling.The particle mesh Ewald (PME) summation was used to calculate long-range interactions.LINCS algorithm was used to constrain all the hydrogen bonds.Finally, a 40 ns production run was performed under NPT conditions at 298 K and 1 bar.The trajectories were visualized using the VMD 1.9.3 package [21].

Results and discussion
The simulation boxes containing the CMCS polymer, Li + ions, and TFSI -ions that were subjected to energy minimization and system equilibration processes (compression-decompression and annealingcooling) are shown in Figures 1a, 1b, and 1c for CMCS/LiTFSI-10, 15, and 20%, respectively.In the figure, the CMCS polymer chains are represented by line structures, TFSI -ions by bond structures, and Li + ions by van der Waals structures.It can be observed that as the LiTFSI content increased, the particle density of Li + and TFSI -also increased noticeably.MD production run was performed after equilibration.The simulated structures were validated using the calculated system densities (Figure 1d), which were within the SPE density range.It was found that the system density increased with increasing LiTFSI content, which is consistent with previous reports [14,22].The calculated densities of CMCS/LiTFSI-10, 15, and 20% were 1.435, 1.463, and 1.487 g cm -3 , respectively.Figures 1e and 1f show the mean square displacement (MSD) of the Li + and TFSI -ions in the simulated systems, respectively.The slopes of the MSD curves were used to evaluate the diffusion coefficients of Li + and TFSI -ions in each simulated system.The calculated values of the diffusion coefficients, obtained from the slopes of MSD curves, are presented in Figures 2a and 2b.The diffusion coefficients of Li + (  + ) and TFSI -(  − ) ions in the simulated CMCS/LiTFSI systems are shown in Figures 2a and 2b, respectively.Both diffusion coefficients decreased as the LiTFSI content increased.The   + values in the CMCS/LiTFSI-10, 15, and 20% were 9.03 x 10 -10 , 5.95 x 10 -10 , and 4.38 x 10 -10 cm 2 /s, respectively.Meanwhile, the   − values were also decreasing with the increase of LiTFSI content, i.e., 1.60 x 10 -9 , 1.36 x 10 -9 , and 1.11 x 10 -9 cm 2 /s for the CMCS/LiTFSI-10, 15, and 20%, respectively.One of the factors affecting lithium-ion diffusion is the strength of the interparticle interactions, that is, the interactions between Li + and TFSI -ions and between Li + and CMCS polymer chains.The interaction between Li + and TFSI -ions is reported to be stronger than that between Li + and CMCS polymer chains [9].Li + ions surrounded by CMCS polymer chains have higher mobility than the Li + ions which are surrounded by TFSI -ions.Therefore, the decrease in lithium-ion mobility is not only influenced by the strength of the interaction between particles, but also by its coordination environment.The lithium-ion coordination in all simulated CMCS/LiTFSI systems was analyzed using the radial distribution function (RDF).An example of the Li + -O RDF curve for the CMCS/LiTFSI-10% system is presented in Figure 2c.The first coordination peak between Li + ions and oxygen atoms in the TFSI -ions (Li + -OTFSI-) occurs at 0.216 nm.Meanwhile, the first coordination peak between Li + ions and oxygen atoms in the CMCS polymer chains (Li + -OCMCS) occurs at 0.22 nm.The Li-O coordination radius of around 0.2 nm is similar to the literatures [14,23].The coordination radius of Li + -OCMCS is larger than Li + -OTFSI-due to its weaker intermolecular interactions and the large steric hindrance of the CMCS polymer chains.The coordination number between Li + with the oxygen atoms in the CMCS/LiTFSI systems was also analyzed, and the curve for the CMCS/LiTFSI-10% system is presented in Figure 2d.It can be seen that the coordination number of Li + -OCMCS is generally larger than Li + -OTFSI-, owing to the many oxygen atoms contained in each CMCS chain.The coordination numbers of Li + -OTFSI, Li + -OCMCS, and Li + -OTotal for all simulated systems are summarized in Figure 2e.As the LiTFSI content increased, the Li + -OTFSI-coordination number also increased.The values of the Li + -OTFSI coordination numbers in CMCS/LiTFSI-10, 15, and 20% were 1.39, 1.58, and 1.92, respectively.The Li + -OTFSI coordination numbers in the simulated CMCS/LiTFSI systems were similar to those in PEC/LiTFSI electrolytes at moderate LiTFSI content [20].Consequently, with the increasing LiTFSI content from 10% to 20%, the Li + -OCMCS coordination number decreased from 4.32 to 3.36, with an intermediate value of 4.07 at 15% LiTFSI content.Meanwhile, there was no significant change in the total Li + -O coordination number.These tendencies of coordination numbers between lithium ions with the oxygen atoms in polymer chains and TFSI -anions were similar to the reported solvation structure in the PEC/LiTFSI SPE system [14].
Snapshots of typical lithium-ion coordination environments at 0, 20, and 40 ns for CMCS/LiTFSI-10 and 20% are presented in Figure 3.In the CMCS/LiTFSI-10% system (Figure 3a), the Li + ions were mostly far apart from each other.Each Li + ion was coordinated to one TFSI -ion and one or two CMCS chains.Meanwhile, in the CMCS/LiTFSI-20% system, two closely spaced lithium ions are commonly observed.The ions were surrounded by two TFSI -ions and one or two CMCS chains.However, the TFSI -ions and CMCS chains in this system can be coordinated to more than one lithium ion.

Conclusions
To evaluate the correlation between lithium-ion diffusion and its coordination environment, molecular dynamics simulations were successfully performed on CMCS-based SPE systems with LiTFSI concentrations of 10, 15, and 20%.The simulated structures were validated by their increasing system density with increasing LiTFSI content.Our results showed that the lithium-ion diffusion coefficient decreased with increasing LiTFSI content, i.e., 9.03 x 10 -10 , 5.95 x 10 -10 , and 4.38 x 10 -10 cm 2 /s for 10, 15, and 20% LiTFSI, respectively.The coordination environments around the lithium ions were analyzed using the RDF and coordination number of Li + -O.The decrease in the lithium-ion diffusion coefficient was related to the decrease in lithium-ion coordination number with oxygen atoms in the CMCS polymer chain and the increase in the lithium-ion coordination number with oxygen atoms in the TFSI -ion.The values of the Li + -OTFSI coordination numbers in CMCS/LiTFSI-10, 15, and 20% were IOP Publishing doi:10.1088/1742-6596/2734/1/0120516 1.39, 1.58, and 1.92, respectively, while the Li + -OCMCS coordination numbers were 4.32, 4.07, and 3.36, respectively.The study highlighted the relationship between salt concentration and the self-diffusion coefficient of lithium ions in CMCS-based SPE, shedding light on the role of TFSI -anions in developing an electrolyte system with favorable ionic transport.

Figure 2 .
Figure 2. a) Diffusion coefficients of Li + (  + ) and b) TFSI -(  − ) ions in the simulated CMCS/LiTFSI systems, c) radial distribution function (RDF) curve, d) coordination number (n(r)) between Li + ions and the oxygen (O) atoms in TFSI -ions and CMCS polymer chains in the CMCS/LiTFSI-10% system, e) summary of Li + -O coordination numbers in the simulated systems.