Understanding lithium transport in SEI films: a nonequilibrium molecular dynamics simulation

ABSTRACT The transport properties of the solid electrolyte interphase (SEI) play an important role in the charging and discharging process of lithium-ion batteries (LIBs). We used nonequilibrium molecular dynamics (NEMD) simulation to mimic the lithium permeability of SEI films with different chemical compositions, thicknesses and densities. We found the order of permeability to be Li2CO3 > LiF > compound > Li2O > LiOH. Permeability is likely more affected by the binding energy between the lithium ions and the SEI atoms than by structural qualities such as surface area and porosity. The density profiles indicate lithium ions tend to accumulate on the SEI–vacuum interface when the film is less permeable. The transport process does not satisfy Einstein’s diffusion equation, thereby revealing the nonequilibrium nature. The relationship between the chemical compositions, densities, thicknesses and permeabilities of each film is expressed by an empirical equation, which can be used to quickly predict the transport properties of SEI films.


Introduction
Lithium-ion batteries (LIBs) are efficient energy storage devices which have been widely used in portable electronics and electric vehicles due to their high energy density and recyclability. However, one disadvantage of LIBs is that the capacity decreases significantly after a few charge/discharge cycles. The primary cause for this capacity decrease is the formation of a solid electrolyte interface (SEI) film on the electrode, which has lower electrical conductivity and lower penetrability for lithium ions [1]. The formation of the SEI film also consumes lithium ions, which contributes to irreversible lithium capacity. On the other hand, a thin SEI film can benefit LIBs as the film filters solvent molecules from the electrode and prevents further reactions between the electrode and the solution. Very recently, it has been found that by controlling the conditions of SEI film formation, the coulombic efficiency of a LIB reaches 99% [2][3][4].
The formation of an SEI film is due to reactions between the electrode, ions and solvent. The typical thickness of the film is 0-90 nm [5], and its chemical composition includes both organic and inorganic components. Typical organic components are ROCO 2 Li, ROCOLi, ROLi and RCOOLi, where R stands for alkyl groups [1,[6][7][8][9][10][11], and typical inorganic components are Li 2 CO 3 , LiF, Li 2 O, LiOH and lithium sulphide [6,[12][13][14][15][16][17][18][19][20][21]. The organic and inorganic components are separated in the film, which forms into a multilayer structure with a higher content of inorganic components compared with organic components [22][23][24]. The organic components form into a porous structure and more heavily concentrated in the outer layer, which is permeable to both solvent molecules and lithium ions. In contrast, the inorganic components form into a more compact structure more heavily concentrated in the inner layer, which is permeable only to lithium ions [25][26][27][28][29]. Therefore, we can assume the inorganic part of the SEI film plays a more important role in the transport process. Additionally, in Kranz et al.'s recent studies [30,31], it has also been noticed that electrolytes could penetrate the SEI film which further affect the lithium transport. Kranz et al. also found that the diffusion coefficient of lithium ions and redox molecules are very similar implying that the ions could transport across the electrolyte-filled SEI film.
Understanding the mechanism for how the SEI film affects the transport of lithium ions is an important consideration for controlled synthesis of LIBs. Many theoretical studies have been proposed to give insight into this issue, and most of them are based on quantum density functional theory (QDFT). For example, based on QDFT, Li et al. [32] used a two-layer/two-mechanism diffusion model to calculate the lithium diffusion in an SEI film. Li et al. found that only the dense inorganic layer can effectively prevent the transport of lithium ions and they proposed a method to accelerate the transport process. Chen et al. [15] used QDFT and nudged elastic band methods to calculate the diffusion of lithium ions in three components of SEI film: Li 2 CO 3 , Li 2 O and LiF. Chen et al. found that the transport of lithium ions in Li 2 CO 3 and Li 2 O can be very fast if there are lithium vacancies available but the transport in LiF is very slow. Chen et al.'s study reveals the intrinsic interactions between lithium ions and the components of SEI film; however, as the Li 2 CO 3 , Li 2 O and LiF are modelled as perfect crystals, and these elements are not present as perfect crystals in SEI films, Chen et al.'s results may not precisely predict experimental results. These QDFT studies can predict the binding energy and energy barrier in the transport process, however, it is difficult for QDFT to calculate entropy effects due to thermal motion, which is another predominant factor in the transport process. Molecular dynamics (MD) is a reasonable method to approximate entropy effects and has been widely used to study molecular transport. For example, Qian et al. [33] used equilibrium MD simulations and experiments to study the cycling stability of lithium metal anodes, and found that a 4 M LiFSI/DME electrolyte could increase the stability of an SEI film and therefore has the optimal cycling performance. Ryan et al. [34] introduced a new force field for LiPF 6 in ethylene carbonate by using ab initio molecular dynamics (AIMD) simulation, which was further used to examine the structure of the SEI film. Leung et al. [35] used AIMD simulations and thermodynamic integration methods to predict the free energy barrier of lithium transport from a LiC 6 anode to the bulk electrolyte. Leung et al. found that the surface charge on the electrode/electrolyte interface is key to lithium transport. Leung et al. [36] introduced an atomic layer deposition (ALD) technique to passivate the electrode in LIB by using AIMD, QDFT and experimental data. In Leung et al.'s work, both AIMD and QDFT were used to predict the structural and free energy information of the system, and the AIMD method was found to be more reliable than QDFT. However, there lack of direct simulation on how lithium transport through SEI films. In this work, we will use a nonequilibrium molecular dynamics simulation to provide an insight into this transport process.

Modelling
We mimicked the charging process of an LIB using nonequilibrium molecular dynamics simulation. As shown in Figure 1, the simulation box (24.6 nm × 2.46 nm × 2.04 nm) is divided into three regions along the x axis: the electrode, the SEI film and the vacuum, respectively. The electrode is modelled by a set of graphene layers parallel to the xoy plane and the interlayer spacing is 0.34 nm. The SEI film is modelled as an amorphous structure with a thickness of 3 nm, and the molecular structure is generated by the Amorphous Cell module of Material Studio software.
The MD simulation is performed in a NVT ensemble by the Forcite module of Material Studio software. In the initial state, 150 lithium ions are placed in the right side of the vacuum region, which is 10 nm away from the SEI film. To mimic the electric field in the charging process, additional negative charge is added to the carbon atoms of the electrode. To make the calculation box neutral, the net charge of the electrode is numerically equal to the charge on the lithium ions. In this case, the net charge density is 260 mAh/g, which generates an initial electric field of 1.7 × 10 9 V/m. In the MD simulation, the electrode and the SEI film are assumed to be rigid. The Van de Waals interaction is modelled by the Universal Force Field (UFF) and the charge on the SEI atoms is parameterised by the QEq method (detailed numbers are listed in Table 1). The long range tail of the Van de Waals potential is truncated at r = 1 nm, the electrostatic interaction is calculated using Ewald summation with an accuracy level of 10 −4 kcal/mol. The temperature of the system is set as 298 K, which was controlled by the Nose method. The time length and time step of the MD simulation is 2 ns and 1 fs, respectively. For each system, the results are averaged from 20 independent simulations.

Results and discussion
As shown in Table 2, we considered 11 types of inorganic SEI films, where the compositions of the first four are pure Li 2 CO 3 , LiF, LiOH and Li 2 O, respectively, and the others (compound 1compound 2 ) are the mixtures of the four components with a ratio Li 2 CO 3 :LiF:LiOH:Li 2 O = 1:1:1:1. The densities for the four pure component films is 1.5 g/cm 3 , and the density for compound x is x g/cm 3 . The macroscopic structural information of the films is shown in Table 1 and the microscopic molecular structures are shown in Figure 2 and Figure S1. At 1.5 g/cm 3 , Li 2 O has both the lowest specific surface area (71 m 2 /g) and the lowest porosity (0.0054). In contrast, Li 2 CO 3 has both the highest specific surface area (1619 m 2 /g) and the highest porosity (0.17). The properties of the mixture (compound 1.5 ) seems the interpolation of the four pure components. Such differences imply that the composition of an SEI film plays an important role in the transport process. For the compounds, when density ρ increases from 1 to 2 g/cm 3 , both the specific surface area and the porosity decrease by 98%. By using power law fitting, the surface area and the porosity are proportional to ρ −3.8 .
The molecular structure of the transport process is shown in Figure S2 in the supporting information. Lithium ions start to enter the SEI film when t > 1.6 ps and enter the electrode when t > 5.6 ps; when t > 1 ns the system appears to be in equilibrium. To examine the transfer rate of the lithium ions     [15]. As mentioned above, Chen et al. mimic the SEI film as a perfect crystal where lithium ions can pass through the film only when there are lithium vacancies available. However, as has been shown previously [4,23,32,37], the structure of an SEI film is amorphous. The SEI film should behave more like a porous film than a defective crystal. In this case, predictions from molecular simulations may be more reasonable. Comparing to Table 2, where both the porosity and specific surface area of LiOH are higher than Li 2 O, LiOH is less permeable than Li 2 O. This may be due to the attractions between the SEI film and the lithium ions. As the polarity of LiOH is stronger than that of Li 2 O, the attraction between LiOH and lithium ion is stronger. Therefore, the absorbance of lithium ion in the LiOH film will increase, and the presence of lithium ion in the SEI film will partially shield the external electric field and generate local free energy barriers, resulting in reduced permeability for lithium ion in the LiOH film. The attraction is further examined by the radial distribution function (RDF) and potential mean force (PMF) between the lithium ion and the O atoms in SEI film. As shown in Figure 4, the peak of the RDF and the well of the PMF indicates the attraction between Li + and the four components are as follows: LiOH > Li 2 O > LiF > Li 2 CO 3 , which is consistent with the order of permeability. The minimum of the PMFs is approximately 3 kJ/ mol, implying a weak hydrogen bonding interaction.
To give a more detailed understanding of the transport process, we examined the density distribution of lithium ions in the material, which is shown in Figures 5 and S3. For LiOH, which is the least permeable film to lithium ions, lithium ions are highly accumulated on the interface between the SEI film and the vacuum. For the other films, when the permeability increases, the peak on the SEI-vacuum interface decreases accordingly. In contrast to the SEI-vacuum interface, the density on the electrode-SEI interface reaches a minimum for all films. Such a distribution reveals poor transport properties of the SEI film.
The densities and thicknesses of the SEI films are two other important factors in the transport process. Figure 6(a,c) summarises the influence of density and thickness on the transition time. According to Figure 6(a,b), ρ = 1.3 g/cm 3 is a critical density level for lithium transport: when ρ < 1.3 g/cm 3 , the transition time is 5.5 ps, which is nearly independent of the density and the composition; when ρ > 1.3 g/cm 3 , the transition time increases, and the increment depends on the composition of the film. According to Figure S4, there is a power law relationship between the SEI density and the transition time. The power law function is given by: t = 5.5 + ar 6.5 (1) where a = 0.05, 0.082, 0.12, 0.4 and 0.62 for Li 2 CO 3 , LiF, compound, LiOH, and Li 2 O, respectively. According to Figure 6(a, c), the relationship between the transition time τ and film thickness L does not satisfy the Einstein's diffusion equation, where the displacement (which corresponds to the thickness of an SEI film in this work) L is proportional to τ 1/2 . One potential reason is that Einstein's diffusion equation is based on the free diffusion model, where thermal motion is the dominating factor,  and the equation is true for equilibrium systems. However, lithium transport under a strong electric field is a typical nonequilibrium process; the driving force from the electric field is comparable with and even exceeds the thermal motion, thus rendering Einstein's diffusion equation inappropriate in this case. By using power law fitting, the transition time τ is proportional to L 0.56 − L 1.29 depending on the composition of the film. Such a power is in between the two limits of transport: τ ∼ L 2 (Einstein's diffusion equation) and τ ∼ L 1/2 (Newton's law), suggesting the combined effects of these two elements.
The power of L is less than that of ρ, indicating the permeability is more sensitive to density than it is to thickness. Porosity is another important structural property of transport, which concerns more details of the film. As shown in Figure 6(d), there exists a universal correlation between the porosity and the transition time, which is less dependent of the chemical composition. More specifically, for the same porosity, LiOH still has the longest transition time, which is consistent with the previous discussions. The correlation can be fitted into a pow law function with power −0.23, and the deviation R 2 = 0.8967 implies a good correlation.
To consider the influence of chemical composition, SEI density and film thickness comprehensively, we introduced an empirical function to predict the transition time/permeability based on the MD predictions, which is given by: where x i is the mass fraction of component i and the unit of τ is ps. C(x i ) is the chemical factor for the SEI film, which is given by: where c i = 0.0627, 0.0712, 0.2914 and 0.1954 ps for Li 2 CO 3 , LiF, LiOH and Li 2 O, respectively, which is the value of C(x i ) for pure component. S(ρ, L) is the structural factor of the film, which is given by: where ρ 0 = 3 g/cm 3 , and the unit of L is nm. The empirical  method is applied to 54 types of SEI films, and compared with MD simulations in Figure 7 and Table S1. The root mean square deviation (RMSD) Δ = 0.8736 ps indicates the good agreement between the empirical method and MD simulation as well as the potential to extend the empirical method to other systems. As mentioned above, it has been found that electrolytes could penetrate the SEI film and affect the transport of lithium ions. Therefore, we mimic the lithium transport through an electrolyte-filled SEI film. The film is constructed by inserting electrolyte molecules dimethyl carbonate (DMC) into the pore of the SEI film (the pore diameter is 0.8 nm, the density and width of the SEI film is 1.75 g/cm 3 and 3 nm, respectively). Figure 8 shows the transition time as a function of the DMC loadings. Obviously, there is a linear correlation between the adsorption of the electrolyte and transition time. The slope is 0.23 ps/(mg/g) indicating that the adsorption of electrolyte does not highly increase the transition time as the electrolyte molecule is much larger than the lithium ions. This is consistent with Kranz et al. experimental findings that lithium ions could transport across the electrolyte-filled SEI films [30,31].

Conclusions
We have used nonequilibrium molecular dynamics simulation to study lithium transport in SEI films. Films with different chemical compositions, densities and thicknesses were examined. We have found that the order of permeability for SEI films to lithium ions is as follows: Li 2 CO 3 > LiF > compound > Li 2 O > LiOH. The transport is likely more affected by the adsorption strength between the SEI film and the lithium ions than the pore size and surface area. Lithium ions tend to accumulate on the SEI-vacuum interface due to poor transport properties of the film. The permeability of the SEI film is more sensitive to density than it is to thickness, and the dependence on density is more dramatic when ρ > 1.3 g/ cm 3 . The transport of lithium ion does not satisfy Einstein's diffusion equation due to strong driving forces that result in a typical nonequilibrium effect. The influence of chemical composition, film density and film thickness on the permeability is summarised in an empirical function, which can be used for permeability predictions.