Effects of chain length and anions on ion transport in PEO-lithium salt systems

ABSTRACT
 Understanding the transport mechanism of Li+ in solid polymer electrolytes is beneficial for improving the safety and energy density of lithium-ion batteries. In this work, we investigate the effects of chain length of poly (ethylene oxide) (PEO) and anions (TfO-, TFSI-, PFSI-) on ion transport properties in PEO-lithium salt systems using all-atom molecular dynamics simulations. We found that the Li+ and PEO monomers are co-diffusion, regardless of the PEO chain length and the type of anion. The diffusion of Li+ becomes slower with PEO chain length and reaches an asymptotic value. In addition, the motion of the Li+ is the slowest in PEO/LiTfO systems. We conclude that the free volume of the systems plays a decisive role in the transport properties of Li+.


Introduction
In recent years, energy and environmental issues are becoming more prominent with the increase in energy demand. As an emerging energy storage medium, lithium-ion battery [1,2] has been widely applied in portable electronic devices and new energy vehicles [3]. In traditional liquid lithium-ion battery, the separator and liquid electrolytes occupy a large volume and mass. The lithium dendrites can pierce the separator and result in short circuit. Moreover, the liquid electrolytes may undergo side chemical reactions or even combustion at high temperatures, which can cause many safety issues [4]. However, solid polymer electrolytes (SPEs) have the advantages of low flammability, low leakage issue, high energy density, and high electrochemical stability compared with conventional liquid electrolytes and have gained considerable attention [3,[5][6][7][8].
Although SPEs has many advantages over liquid electrolytes, it exhibits low conductivity at room temperature and low Li + transfer numbers hindering its commercial applications [4,[9][10][11]. Among different kinds of SPEs, poly (ethylene oxide) (PEO) has been widely studied as the matrix of SPEs due to the oxygen coordination sites from the ethylene oxide monomers and the flexible backbone which promote the ion transport [12][13][14][15]. Even though the ionic conductivity of PEO-based SPEs can be improved by increasing temperature, high temperature will result in a poor mechanical strength. Numerous experiments and computer simulations have proved that through material modification such as copolymerization [16][17][18][19], grafting [20][21][22], blending [23][24][25] and adding filler [23,24,[26][27][28], one can improve both ionic conductivity and mechanical strength of PEO-based SPEs.
The mixture of PEO and LiTFSI is the most commonly used polymer electrolyte for lithium-ion batteries due to its good solvation properties [3,29,30]. The CF 3 SO 2 -group in the structure of TFSIhas a strong electron absorption effect and makes the salt have high solubility [3,31]. Although the room temperature conductivity of PEO-based/LiTFSI SPEs remains below acceptability [32], this is one of the most promising materials developed to date [8,14,[32][33][34][35][36]. Experimental researchers have been able to effectively improve the Li + conductivity and interfacial properties by designing structures of anions through introducing specific groups [37,38] or extending the length of perfluorinated alkyl chains [39][40][41]. Although many works focus on the effects of anions structures on the ion transport properties in polymerized ionic liquids that have been reported [42][43][44][45][46], the relevant works on PEO-based SPEs are scarce. For instance, Ganesan et al. [45] performed all-atom molecular dynamics (MD) simulations to study a cationic polymerized ionic liquids with eight different anions and explored the influence of different anions on the decoupled conductivity contributed by polymer segment dynamics. Qu et al. [44] studied the ion transport properties in ionic liquids/poly(vinyl-idene fluoride) (ILs/PVDF) mixtures where six different anions (Cl -, Br -, BF 4 -, PF 6 -, TfOand TFSI -) are considered. Inspired by the works above, in this work, we will investigate the effect of the anionic structure on ion transport properties in the PEO-based SPEs. Specifically, we use atomistic MD simulations to study the transport properties of theLi + in the PEO-lithium salt SPEs with three anions: trifluoromethyl sulfate (TfO -), bis (trifluoromethyl sulfonyl) imide (TFSI -) and bis (pentafluoroethyl sulfonyl) imide (PFSI -).
In addition to this, we will also investigate the effect of the PEO chain length on Li + transport in the PEO-lithium salt systems. Teran et al. [47] have measured the ionic conductivity using AC impedance spectroscopy in the PEO/LiTFSI SPEs, where the molecular weight (M n ) is ranged from 0.2 to 5000 kg/mol. Devaux et al. [8] experimentally studied the effect of polymer molecular weight on the conductivity of Li + in the PEO/LiTFSI systems and found that the isothermal conductivity at 333 K reached a plateau when the molecular weight is higher than 9 kg/mol. Timachova et al. [48] tested PEG-NMR experiments to measure Li + and TFSIdiffusion over a range of molecular weights and ionic concentrations, where M n = 0.6-100 kg/mol and the concentration ratio of Li + to ethylene oxide (EO) monomer is ranged from 0.02 to 0.08. They reported that ion motion becomes limited to the segmental motion of the polymer chains and the transfer number of cations approaches a plateau when M n > 10 kg/mol. In fact, the use of experimental methods to study the ion transport mechanism of SPEs is very limited, because the dynamical properties at the microscopic level are difficult to be captured using experimental equipments in such a complex system. Allatom MD simulation can trace the trajectories of each atom, which is a complementary tool for exploring the ion transport mechanism in SPEs. Recently, Chattoraj et al. [49] investigated ion microscopic transport mechanisms in PEO-based SPEs with different PEO chain lengths (N = 5, 10, 20, 54) using MD simulations and a theoretical approach based on the Rouse model, they found that the cation and anion diffusion exhibit a similar chain-length dependence but a different temperature dependence. Although a thorough understanding of ion transport in SPEs plays a significant role in development of high performance SPEs, a comprehensive study of the effect of polymer chain length (or molecular weight) and the type of anions on diffusion dynamics of Li + in SPEs has not been conducted.
In this work, we investigated the effects of PEO chain length and lithium salts on the microscopic mechanisms of ion transport properties in the PEO-based SPEs using allatom MD simulations. We found that the self-diffusion coefficients of anions and cations decrease with increasing chain length, as reported by experiments [48]. Furthermore, we tried to understand how the size and symmetry of the anions affect the ion transport in the PEO-based SPEs. The chemical structures of PEO and lithium salts are shown in Figure 1.

Models and force fields
We prepare PEO with four different degrees of polymerizations (DP), i.e. DP = 20, 50, 100, and 200, and three kinds of anions (TfO -, TFSI -, PFSI -) (see Table 1 for details). The total number of monomers of PEO and the number of Li + in all systems are set to 4000 and 80, respectively. Therefore, the ratio of Li + to ether oxygen (EO) monomers is r = [Li]/ [EO] = 0.02. The total molar mass of PEO in each system is determined by the chain length and the chain number. Particularly, a PEO chain includes three parts: the begin group (BEG), the middle group (MID) and the end group (END). The molar mass for BEG, MID and END are m BEG = 89 g/ mol, m MID = 44 g/mol and m END = 89 g/mol, respectively (see Figure 1). The molar mass of PEO with a specific DP is M (see Table  1), which is calculated through m BEG + m END + (DP − 2) × m MID . Then, the total molar mass of PEO is calculated through M × 4000/DP.
In this work, we employ a force field based on the framework of Optimized Potentials for Liquid Simulations (OPLS) force field [50]. For PEO and Li + , the force field parameters come from the work [50] with the exception of partial charges. The quantity of charge on each atom is from the OPLS R force field proposed by Fang et al. [51]. In their work, two kinds of charge scaling factors (0.8 and 0.55 for PEO and ions, respectively) are used to mimic the coupling effects of charge transfer and polarization. The force fields for anions are taken from the recently-developed OPLS parameters for ionic liquids [52,53]. In this work, we only list the more important nonbonded parameters (i.e. the van der Waals parameters and partial charges) in Table 2. Note that the listed charges are unscaled.

Simulation procedure
The PEO chains and lithium salts are packed randomly in a cubic box via Packmol software [54] followed by the energy minimization and then executing an equilibrium simulations (see section 1 and Table S1 in SI for details) attaining 160 ns are performed in the NPT ensemble, in which the temperature and pressure of the system are kept at 363 K and 1.0 bar, respectively. The production runs are all carried out in the NVT ensemble (600 ns), in which the temperature of the systems is fixed at 363 K. The trajectories of the systems are saved every 5 ps for further analysis.
All simulation are conducted using the GROMACS 2021.4 [55] package with time step of 1 fs. Periodic boundary conditions (PBC) were applied to the system cell in all three directions. The cut off of the van der Waals (vdW) and short-range electrostatic potentials are 1.2 nm where the vdW interactions are smoothly shifted to zero starting from 0.8 nm. Long-range part of the electrostatic interactions is evaluated by the Particle Mesh Ewald (PME) [56,57]. Temperature and pressure are controlled using the v-rescale thermostat and benendsen barostats with the coupling time constants of 0.1 and 0.5 ps, respectively.
The density is shown in Table 3, which is calculated by using the last 5 ns of the NPT equilibration after the annealing procedure. The densities of all simulated systems are around 1.1 g/cm 3 which are very close to the experimental values [3,8].

Structural analysis
The structural characteristics of the system plays a significant role in the behavior of ion transport. Hence, we first briefly introduce two commonly-used structural functions: the radial distribution function (RDF) and free volume ratio (V r ). RDF represents the probability of finding another species (i.e. B) around the central one (i.e. A) which can be obtained by the following equation, where V is the volume of system and N B is the number of B particle in the whole system. r is the radical distance relative to the central particle A, thus 4πr 2 dr is the volume of the thick spherical shell with a thickness dr and a radius r. In this spherical shell, the number of B particle is n B . In this work, all RDFs are obtained by using the command gmx rdf in GROMACS package. It is worth to note that the RDF for the anion is calculated by using its center of mass (COM) as the reference site and the RDF for the monomer in PEO is calculated by using the COM of the ether oxygen (EO) atoms as the reference site. We next calculate the ether oxygen coordination number (CN) of Li + via Eq. (2), where ρ and r c are the average number density of the ether oxygen atoms in the system and the radius of Li-O's first solvation shell (FSS), respectively. The free volume ratio (V r ) is calculated via Eq. (3), where V free , V occupy , and V are the free volume of the system, the occupied volume of the atoms, and the total volume of the system, respectively. Specifically, V free is the volume consisting of defects in the polymer chain stacking and system vacancies and, V occupy is the total volume of all atoms themselves. Therefore, V free is equal to V minus V occupy . Actually, V free can be obtained directly by the high-efficiency package Multiwfn [58]. The relevant data in Table S2 are from the average of 10 different frames of trajectories.

Dynamical analysis
To study the diffusion behavior of the species in the system, the mean square displacement (MSD) are calculated by using the command gmx msd in GROMACS. The diffusion coefficients where r i (t) is the position of particle i at time t, r i (0) is the position of particle i at time 0, and the symbol < > represents the ensemble average.

Microstructure of Li +
To investigate the transport mechanism of Li + in SPEs, it is important to understand the Li + solvation microstructures. Therefore, we first study the RDFs relevant to Li + . Figure 2 shows the RDFs in systems with PEO/LiTFSI SPEs at DP = 100, where the COM of TFSIare selected as the reference site in all cases. According to Figure 2a, we find that the position of the first peak is at around 0.2 nm, which is agreement with the experimental [59] and simulation observations [51,60,61]. We also note that the magnitude of the first peak is about 20 and is much larger than other species (see the first peaks of RDFs in Figure 2b), which strongly indicates that the interactions between Li + and ether oxygen atoms is the strongest compared with the interactions between Li + and other species. And the oxygen CN of Li + is 5.215 (≈ 5), which is also agreement with the experimental [59,62] and simulation observations [33,51,63,64]. Additionally, the RDFs for Li-Li and TFSI-TFSI shown in Figure 2b are very close to the work from Chiu and co-workers [51] suggesting the correctness of the force fields and simulation protocols.

Effects of PEO chain length on Li + transport
In Section 3.1, we showed the solvation microstructures of Li + for the cases when DP = 100. In this section, we will investigate the effect of PEO chain length on the Li + transport. Here we take the PEO/LiTFSI systems as an example. We first explore the effect of polymer chain length on the solvation microstructure of Li + . According Figure 3a, we can find that the chain length of PEO has slight influence on the first peak of the Li-O RDF. As shown in the inset, the magnitude of the first peak decreases with DP and reaches an asymptotic value when DP is larger than 100. In addition, we find that PEO chain length has no evident effect on the RDF between Li + and TFSI -(see Figure 3b). It suggests that the interactions between Li + and TFSIare not dependent on the chain length of PEO. By following the commonly-used definition of the FSS, the radius of the FSS can be determined through the position of the first minimum of the RDF. According to Figure 3a, it shows that the chain length of PEO does not show remarkable influence on the size of the FSS between Li + and the EO atoms. Consequently, the EO CN of Li + are nearly the same (approximately 5.22 for four DPs). It is worth to note that the radii (r c ) of the FSS between Li + and the EO atoms in the systems with different PEO chain lengths are 3.52 Å (DP = 20), 3.44 Å (DP = 50), 3.40 Å (DP = 100), and 3.40 Å (DP = 200). Moreover, the similar phenomena can also be found in the PEO/LiTfO and PEO/LiPFSI systems with different PEO chain lengths (see Figures S3 and S4 in SI), which suggest that the interactions among PEO, cations, and anions are insensitive to the chain length of PEO.
Although the microstructures around PEO monomers and ions are insensitive to the chain length of PEO, the dynamic properties of Li + and PEO monomers are strongly dependent on the chain length. In this section, we investigate the effect of PEO chain length on MSD. In particular, we calculate the MSD of all ether oxygen atoms of PEO, which was rarely reported in the literature due to the high computational cost. Interestingly, Figure 4 shows that the MSD of Li + and EO are close to each other. This phenomenon indicates that the strong interactions between Li + and EO (see Figure 3a) make the migration of Li + be strongly dependent on the motion of EO. In other words, the Li + and EO in PEO-based SPEs show Li-EO co-diffusion [4]. We have to note that the MSD of Li + and EO for the longer PEO are not as close as the shorter PEO. In fact, this phenomenon is to be expected when the ether oxygen atom is attached to the -CH 2 -CH 2 -backbone. As the chain length increases, the chain segment movement becomes slower due to the reduced free volume, which will limit the migration of the ether oxygen atom. We should note that it will take a long time for the solid polymer system to reach the diffusion regime (see section 2 in SI for details). Therefore, in this present work, we do not calculate the diffusion coefficient of EO. However, according to Figure 4 and EO become slower with PEO chain length and reaches an asymptotic value when the chain length is sufficiently large. Moreover, according to Figure 5a, we find that the diffusion coefficients of both cations and anions decrease with PEO chain length. Interestingly, although the size of anions is much larger than the one of cations, the motion of anions is much faster than cations. The result agrees with reported experimental datas [48,[65][66][67][68]. The reason of this phenomenon is that the Li + has multiple coordination sites with the EO atoms (that is to say, most of the Li + are coordinated with the EO atoms, and vice versa) but the TFSIdoes not. Therefore, the motions of Li + are slowed down by the EO atom, while the motions of TFSIare relatively independent. Furthermore, there is another question to be considered: why do the motions of the EO atom and TFSIbecome slower with PEO chain length? In order to answer this question, we calculate the density and free volume ratio of the systems with different chain lengths. According to Figure 5b, the   density of the system is increased with the PEO chain length. This indicates that the system becomes more compact (i.e. smaller free volume) because the conformational entropy of chain prefers to reduce the excess space surrounding itself. Particularly, the trend of the free volume ratio (V r ) is almost the same with the one of diffusion coefficient. Therefore, we conclude that the origin of the slowing down of the EO atoms and anions is the reduction of the free volume of the system with longer PEO chains. In addition, PEO/LiTfO and PEO/LiPFSI systems also show similar chain length-dependent behavior (see Figures S5-S8).
We have to note that our diffusion coefficients are of the same order of magnitude as the experimental values [41,48], but there are still some deviations due to the differences between simulations and the real experimental systems. For example, the diffusion coefficient of Li + (≈0.6 × 10 −11 m 2 /s) and TFSI -(≈2.5 × 10 −11 m 2 /s) for DP = 100 in our work are slightly less than the experimental values [48] (D Li ≈1.4 × 10 −11 m 2 /s and D TFSI ≈4.1 × 10 −11 m 2 /s). And the diffusion coefficient of TFSI -(≈2.2 × 10 −11 m 2 /s) for DP = 200 is very close to the experimental value (≈3 × 10 −11 m 2 /s) from Xiao Ming et al. [41]. Moreover, our results are consistent with the ones from simulation works [33,48,69]. Therefore, we think that our results are reliable.

Effects of anions on Li + transport
Besides the chain length of PEO, we also focus on the effect of the size and symmetry of anions on the transport properties of Li + in the PEO-based SPEs.
We first study the effect of anions on the solvation microstructure of Li + . According to Figure 6, the first peaks of g Li PEO(O) (r) and g Li Anions (r) show that Li + is mainly coordinated to the EO atoms and weakly coordinated to the anions. Moreover, according to Figure 6b, the first peak of the g Li Anions (r) decreases with the size of anions: TfO > TFSI > PFSI. In the meanwhile, the RDFs become wider and flatter, which indicates that the interaction between Li + and anions with a larger size is weaker. In addition, the symmetry of anions' structures also influences the interactions between Li + and anions. For example, TFSIand PFSIare both symmetric structures with a higher degree of charge dispersion. Therefore, the interaction between Li + and TfOis the strongest one among those three anions. Consequently, the anion-dependent variation tendency of the first peak of the g Li PEO(O) (r) is: PFSI > TFSI > TfO.
By following the analysis of the microstructures around Li + , we also explore the effect of anions on MSD. In Figure 7, we only show the MSDs for DP = 20 and 200 because they are more representative. The MSDs for DP = 50 and 100 can be found in Figure S12. Both Figures 7 and S12 show again that the MSDs of Li + and EO are very close to each other regardless of the type of anion. Therefore, we do not show the corresponding diffusion coefficient because of the difference between the diffusion coefficients is comparable to the error of the diffusion coefficient fitting. However, some interesting phenomena can be observed via MSD.
According to the bottom panel in Figure 7a, it is expected that the motion of PFSIis the lowest due to the largest size (the strongest steric hindrance). Interestingly, although the size of TfOis the smallest (V PFSI ≈1.35V TFSI ≈2.47V TfO , where V PFSI , V TFSI , and V TfO are the volumes of anions, see details in Table S2), its motion is almost the same with the one of TFSI -. As shown in Figure 7a, the motion of anions is much larger than the one of Li + . Therefore, we think that the dynamics of TfOis slowed down by the Li + due to the strong interaction between Li + and TfO -(see Figures 6b and S9-10). More interestingly, the motions of Li + is the slowest in the PEO/LiTfO systems, and the motions of Li + in PEO/TFSI and PEO/PFSI systems are almost the same. In order to understand this phenomenon, we calculate the free volume ratios (V r ) in systems with different anions. According to Figure 8, the V r in the PEO/LiTfO is the lowest. The lowest free volume means the strongest steric hindrance in systems. Therefore, the dynamics of PEO monomer is the slowest in PEO/LiTfO system. Consequently, the motion of Li + is the slowest due to the co-diffusion characteristic with EO atoms. According to Figure  8, the free volumes of PEO/TFSI and PEO/PFSI systems are close relatively. In a word, the free volume of system plays a decisive role in the transport properties of Li + .
Moreover, when the PEO chain is long enough (e.g. DP = 200), the extremely small free volumes make the dynamics of each species in PEO-based SPEs is insensitive to the type of anions. In particular, the MSD of EO is almost the same in the systems with different types of anions, while the MSDs of Li + and anions are sensitive to the type of anions. The MSD of PFSIis small compared to other two anions due to its larger volume. And the MSD of Li + in the PEO/LiPFSI SPEs is larger than the ones in other two systems, which is due to the larger size and structural symmetry of PFSI -, resulting in a weaker interaction between Li + and anions (see Figures 6b).

Conclusions
In this work, in order to understand the mechanism of Li + transport in solid polymer electrolytes (SPEs), we systematically studied the effects of PEO chain length and the size and symmetry of anions on the mean square displacement, diffusion coefficient, and free volume of PEO/Lithium salt systems.
Regardless of the PEO chain length and the type of anion, the Li + transport is determined by the dynamics of ether oxygen (EO) atoms, i.e. the Li + and EO atoms are co-diffusion. The motion of Li + become slower with PEO chain length and reaches an asymptotic value when the chain length is large enough. The origin of this chain length-dependent phenomenon is the reduction of the free volume of the system with longer PEO chains. Moreover, the dynamics of the Li + is the slowest in PEO/LiTfO SPE systems, regardless of the PEO chain length. We found that the free volume of the systems also plays a decisive role in the anion-dependent transport properties of Li + . In the PEO/LiTfO SPEs, the free volume is the smallest. In addition, we found that although the size of TfOis the smallest, the MSDs of TfOand TFSIare almost the same. The reason of this phenomenon is that the motion of TfOis slowed down by the Li + due to the strong interactions between them.
Actually, in order to support our conclusions above, we need more direct evidences such as the average volume of the pores in the system. However, at present, we do not find a suitable method to calculate this quantity. We eagerly hope that our present work can provide some new insights in understanding of the Li + transport mechanism in SPEs.

Supporting information
Equilibration procedure; diffusive transport regime; the RDFs, the MSDs, diffusion coefficients, density and free volume ratio for the PEO/LiTfO and PEO/LiPFSI systems with different chain lengths.

Disclosure statement
No potential conflict of interest was reported by the author(s).