The mechanism of Li-ion transport in carbonate-based electrolytes

Abstract

Molecular dynamics (MD) simulations were performed on a carbonate-based electrolyte, composed of 1 M lithium hexafluorophosphate (LiPF₆) dissolved in the mixture of ethylene carbonate (EC) and dimethyl carbonate (DMC) (1 : 1 v/v), at temperatures of 298.15 K, 273.15 K, 253.15 K, 233.15 K, and 213.15 K, respectively. The simulations revealed that as temperature decreases, the contribution of DMC to the first solvation shell of Li⁺ increases significantly, leading to the formation of more DMC-rich solvation structures. Meanwhile, Li⁺ increasingly tends to form solvent-separated ion pair (SSIP) with PF₆⁻. These dynamically sluggish solvation structures hinder Li⁺ transport in the electrolyte. Further analysis shows that a low-temperature suppresses solvent exchange and weakens the structural transport. These findings elucidate how temperature-induced changes in solvation structures and transport mechanisms jointly hinder Li⁺ transport, providing molecular-level insights for the rational design of next-generation electrolytes and for enhancing the low-temperature performance of lithium-ion batteries.

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Introduction

Lithium-ion batteries (LIBs) are widely used in portable electronics, grid energy storage, and electric vehicles owing to their high energy density and long cycle life.^1–7 Electrolytes based on ethylene carbonate (EC) are the most widely used commercial electrolytes. However, current commercial LIBs suffer from rapid capacity degradation under cold conditions, especially below 0 °C.^8–10 The poor low-temperature performance of LIBs is primarily attributed to the increased resistance of Li⁺ transport, including transferring across the electrode–electrolyte interface as well as the sluggish Li⁺ transport in the electrolyte.^11–13 Electrolyte engineering has been recognized as a promising strategy to enhance the low-temperature performance of LIBs.^14,15

Extensive research has been conducted on the low-temperature performance of LIBs, with most experimental studies focusing on improving performance by modifying the electrolyte composition. The strategies include blending EC with linear carbonates such as dimethyl carbonate (DMC), ethyl methyl carbonate (EMC), or diethyl carbonate (DEC) to reduce viscosity,^16–19 introducing novel solvents and adjusting solvent ratios,^20–23 as well as introducing functional additives.^24–26 Although these studies reported significant performance improvements, detailed mechanistic insights into Li⁺ transport are still welcome toward designing functional electrolytes,²⁷ since direct experimental determination of ion transport behavior at the molecular level remains challenging.

Molecular dynamics (MD) simulations are particularly well suited for investigating ion transport in electrolytes at the molecular level,^28,29 and have proven particularly effective for resolving solvation structures and coordination analysis in complex electrolyte environments.³⁰ Numerous MD studies have examined the solvation structure of the widely used EC/DMC system at room temperature, yet the relative contributions of each solvent component remain under debate. For example, Borodin et al. reported substantial coordination from both solvents in 1 : 1 EC/DMC mixtures, with slightly greater participation from DMC,³¹ whereas Uchida et al. found stronger EC involvement,³² and Tenney et al. concluded that EC possesses a superior solvation capability.³³ Moreover, studies on the EC/DMC system under low-temperature conditions are scarce. Several studies on similar systems under low-temperature conditions have been reported. Ringsby et al. examined the transport phenomena of the EC/EMC system and attributed the performance degradation primarily to the increase in viscosity.¹⁴ Rampal et al. investigated the LiPF₆/EC system and identified the presence of highly mobile clusters.³⁴ Overall, investigations into Li⁺ transport behavior at low temperatures remain markedly limited, particularly regarding the transport mechanisms that critically govern ion dynamics. Addressing this knowledge gap is therefore essential for guiding the rational design of advanced electrolytes with improved low-temperature performance.

In this study, MD simulations were performed on the widely used carbonate-based commercial electrolyte, 1 M LiPF₆ in EC/DMC (1 : 1 v/v), at five temperatures (298.15 K, 273.15 K, 253.15 K, 233.15 K, and 213.15 K). The simulation reliability was first validated against experimental data, and the changes in Li⁺ solvation structures and component-specific contributions of different temperatures were subsequently analyzed. Through the self-part of conditional van Hove function analysis, we uncovered slow-dynamics clusters that impede Li⁺ transport. Simultaneously, we elucidated the influence of low temperature on the transport mechanisms of Li⁺. These mechanistic insights into low-temperature transport behavior uncovered in this work will provide new perspectives for the rational optimization and design of electrolytes for enhancing the low-temperature performance.

Methods

MD simulations were performed using GROMACS package.³⁵ The simulated electrolyte system was composed of 100 LiPF₆, 750 EC, and 590 DMC, corresponding to a 1 : 1 volume ratio of EC to DMC. Initial configurations were generated in a cubic box by PACKMOL,³⁶ and subsequently energy-minimized using the steepest descent algorithm.³⁷ Then, the system was equilibrated in the NPT ensemble using the Parrinello–Rahman barostat³⁸ and Nosé–Hoover thermostat.³⁹ The temperature was gradually reduced from 600 K to 298.15 K with pressure simultaneously lowered to 1 bar. After equilibration, 5 ns NPT equilibrations were performed at 1 bar for the target temperatures (298.15 K, 273.15 K, 253.15 K, 233.15 K, and 213.15 K). At each temperature, five independent 100 ns production runs were conducted in the NVT ensemble. Equations of motion were integrated via the leapfrog algorithm⁴⁰ with a 2 fs timestep, and all C–H bonds were constrained using the LINCS algorithm.^41,42 A 12 Å cutoff was applied for van der Waals interactions described by the Lennard–Jones potential and electrostatic interactions calculated by Smooth Particle Mesh Ewald (SPME) method.⁴³ Trajectory data of production runs were saved every 100 steps (0.2 ps) and analyzed using in-house code, and the MD snapshots were visualized using VMD.⁴⁴

The force field parameters were taken from the OPLS force field.⁴⁵ The atomic charges were fitted with the restrained electrostatic potential (RESP) method,⁴⁶ with reference ab initio electrostatic potentials computed at the B3LYP/6-31G* level using Gaussian 16.⁴⁷ Charge scaling was only applied during MD simulations to account for electronic polarization effects,^48,49 while unscaled charges were used to calculate ionic conductivity.⁵⁰ Detailed force field parameters and atomic charges were summarized in Tables S1–S4 in (SI).

Results and discussion

We begin our discussion by examining the impact of temperature on ionic conductivity (σ), which determines the rate performance of batteries. σ was calculated from the Green–Kubo relation,⁵¹ which accounts for interionic correlations, i.e., in which e is the elementary charge, V is the volume of the cubic simulation box, k_B is the Boltzmann constant, and T is the temperature. z_i and z_j denote the charge numbers of the i-th and j-th ion (±1), N_i and N_j are the total number of ions i and j in the system, Δr_i(t) = r_i(t) − r_i(0)and Δr_j(t) = r_j(t) − r_j(0)represent the center-of-mass displacements of ions i and j, respectively, during the time interval t, and 〈⋯〉 represents the ensemble average. σ is contributed by the partial ionic conductivity of Li⁺ (σ_Li⁺) and PF₆⁻ (σ_PF6⁻), i.e., σ = σ_Li⁺ + σ_PF6⁻, in which σ_Li⁺ and σ_PF6⁻ are calculated by replacing N_i in eqn (1) by the number of Li⁺ (N_Li⁺) and the number of (N_PF6⁻), respectively, remembering N_i = N_Li⁺ + N_PF6⁻.

The charge mean square displacement , in which N_x denotes N_i, N_Li⁺, or N_PF6⁻, obtained over the time interval t at different temperatures, is depicted in Fig. S2 in SI. Fig. 1 presents the simulated σ and the transference numbers of Li⁺ (t⁺ = σ_Li⁺/σ). The simulated σ shows good agreement with experimental data (σ_exp),²⁰ and the simulated transference numbers are also consistent with previous studies,^52–54 remaining approximately 0.4. These results confirm the reliability of the force field parameters used in our MD simulations. As expected, both the σ and σ_Li⁺ decrease significantly with temperature, indicating the diminishing ion transport capacity at lower temperature, which would severely impair the rate performance of LIBs.

Fig. 1 Simulated ionic conductivity (σ), experimental ionic conductivity²⁰ (σ_exp), the individual ionic conductivities of Li⁺ (σ_Li⁺) and PF₆⁻ (σ_PF6⁻), the lithium-ion transference number (t⁺ = σ_Li⁺/σ), and the experimental lithium-ion transference number (t_exp⁺) at 298.15 K.^52–54

The solvation structures of Li⁺ in electrolytes are essential in determining the electrochemical performance of a battery system, including σ. To gain deeper insights into the temperature-dependent solvation structures in the 1 M LiPF₆/EC–DMC electrolyte, we adopted the strategy of Shi et al.,⁵⁵ who successfully resolved the solvation structures in PVDF-based electrolytes by examining Li⁺ RDFs with key atoms (e.g., F from anions). The radial distribution functions (RDFs) and the corresponding coordination numbers (CNs) around Li⁺ were calculated using:

where r_ij is the distance between central atom i and surrounding atom j, N_i is the number of atom i, and ρ_j is the average number density of atom j. δ(r_ij − r) is the Kronecker delta symbol, which equals 1 if r_ij ∈ [r,r + dr] and 0 otherwise, in which dr was set to 0.01 Å. 〈⋯〉 denotes the ensemble average.

Fig. 2 presents the RDFs and CNs between Li⁺ and the carbonyl oxygen atoms (O_C) of EC and DMC, g(r_Li⁺–OC) and n(r_Li⁺–OC), as well as the phosphorus atom (P) of PF₆⁻, g(r_Li⁺–P) and n(r_Li⁺–P). The RDFs and CNs for the ether oxygen atoms (O_E) of EC and DMC are shown in Fig. S3, but reveal that the negligible coordination with Li⁺ due to CNs is nearly zero around 3.2 Å, which is the first minimum in g(r_Li⁺–OC). The coordination with Li⁺ occurs almost exclusively through the O_C of EC and DMC, thus the contributions from ether oxygen are not considered in the subsequent analysis. As shown in Fig. 2a and b, both the g(r_Li⁺–OC) of EC and DMC exhibit a pronounced peak at 2.0 Å, with the peak for EC being lower than that for DMC. On the other hand, given the higher number density of EC in the system, integrating the g(r_Li⁺–OC)'s up to the first minimum at 3.2 Å (eqn (3)) gives the resulting n(r_Li⁺–OC)'s of 2.23 for O_C(EC) and 2.01 for O_C(DMC), indicating that EC contributes more to the first solvation shell of Li⁺ at 298.15 K. As shown in Fig. 2d, as the temperature decreases from 298.15 K to 213.15 K, the peak of g(r_{Li⁺–OC(EC)}) gradually diminishes, and CNs of O_C(EC) decreases from 2.23 to 2.05. In contrast, DMC exhibits the opposite trend, with the peak of g(r_{Li⁺–OC(DMC)}) becoming higher and CNs increasing from 2.01 to 2.25. These results suggest that while EC slightly dominates the solvation structure of Li⁺ at room temperature, DMC gradually becomes the primary coordinating solvent at lower temperatures. As shown in Fig. 2c, g(r_Li⁺–P) exhibits three distinct peaks located at approximately 3.7 Å, 6.5 Å, and 9.3 Å. These peaks correspond to first, second, and third solvation shells, respectively. As the temperature decreases, the peaks at 3.7 Å and 9.3 Å gradually diminish, while the peak at 6.5 Å increases. A consistent trend is also observed in g(r_Li⁺–F), as shown in Fig. S3c of the SI, where the first peak of g(r_Li⁺–F) at around 2.1 Å progressively decreases with decreasing temperature. This interesting trend indicates that PF₆⁻ tends to locate at the second solvation shell of Li⁺ at lower temperatures.

Fig. 2 RDFs (solid lines) and corresponding CNs (dashed lines) between Li⁺ and different atoms from 298.15 to 213.15 K. (a) Li⁺–O_C(EC); (b) Li⁺–O_C(DMC); (c) Li–P(PF₆⁻); (d) CNs between Li⁺–O_C(EC) and Li⁺–O_C(DMC).

To further elucidate the solvation environment of Li⁺, the existence states of Li⁺ were categorized into four types based on the relative positions of PF₆⁻: (1) contact ion pair (CIP), in which only one PF₆⁻ is located within the first solvation shell of Li⁺, and this PF₆⁻ does not coordinate with any other Li⁺; (2) solvent-separated ion pair (SSIP), in which no PF₆⁻ is present with the first solvation shell of Li⁺ and at least one PF₆⁻ appears in the second solvation shell of Li⁺, i.e., PF₆⁻ appears between the first and second solvation shell of Li⁺; (3) fully solvated Li⁺ (FSLi), in which no PF₆⁻ is present within the first and second solvation shells of Li⁺; (4) aggregate (AGG), formed through crosslinking of multiple Li⁺ and PF₆⁻ ions.

Fig. 3a shows the distribution of the four existence states of Li⁺. The majority of Li⁺ exists in SSIP and FSLi, with a small portion present in CIP, and AGG is negligible. This indicates that LiPF₆ salt is fully dissolved by EC and DMC solvents. Clearly, with decreasing temperature, CIP and FSLi clusters become less prevalent, while SSIP clusters become more dominant, consistent with the discussed RDF results of g(r_{Li⁺–P(PF6⁻)}) in Fig. 2. Furthermore, the detailed composition of the first solvation shell of Li⁺ was analyzed, as shown in Fig. 3b. The clusters were classified into two categories based on the CN, namely tetra-coordinated clusters (CN = 4) and penta-coordinated clusters (CN = 5). The proportion of tetracoordinated clusters gradually declines with decreasing temperature, while that of penta-coordinated clusters increases. Specifically, among the tetracoordinated clusters, the populations of the 1–4–0, 1–3–1, and 1–2–2 clusters declined significantly, whereas the 1–1–3 and 1–0–4 clusters showed increasing trends. Among the penta-coordinated clusters, although the overall population increased, the population of 1–4–1 clusters even decreased below 253.15 K, while the 1–1–4 clusters became more prevalent. These observations suggest that DMC contributes increasingly to the first solvation shell of Li⁺ at lower temperatures, which is consistent with the trend observed in the RDF analysis.

Fig. 3 (a) Percentage of CIP, SSIP, and FSLi clusters. (b) Percentage of various Li⁺ solvation structures. The notation 1–X–Y represents clusters with the first solvation shell composition of Li⁺–EC_X–DMC_Y; “other” refers to remaining clusters containing five solvent molecules in the first solvation shell. “CIP–X” denotes clusters with a CIP structure and X coordinated molecules in the first solvation shell. Due to the limited number of such clusters, they were not further subdivided by specific compositions.

The transport properties of Li⁺ in electrolytes are closely related to their solvation environments. In order to distinguish the transport of Li⁺ in various clusters, the self-part of conditional van Hove functions⁵⁶ of Li⁺ were calculated, i.e.,

where |r_i(t) − r_i(0)| denotes the displacement of the i-th Li⁺ over time t, N_Li⁺ is the number of Li⁺ in the PBC box, and 〈⋯〉 indicates an ensemble average. It should be noted that the criterion of determining which type of cluster a Li⁺ belongs to is only based on its coordinating configurations on time origins.

The normalized conditional G_s(r,t) of Li⁺ in CIP, SSIP, and FSLi is shown in Fig. 4a and b, at 298.15 K and 213.15 K, respectively. The results at other temperatures are summarized in Fig. S4. Li⁺ in the SSIP clusters exhibits smaller average displacements over the same time compared to those of Li⁺ in the CIP and FSLi clusters. This trend is also observed at different temperatures and time scales, indicating slower Li⁺ transport within SSIP clusters. Since the solvation structure of Li⁺ may change over time, the differences of its transport among various clusters can be more accurately assessed on shorter timescales. At a longer time scale, Li⁺ gradually “forgets” its initial solvation structure, and all the conditional G_s(r,t) curves should become indistinguishable. This behavior is clearly observed at 298.15 K. However, at 213.15 K, the conditional G_s(r,t) curves for different clusters are still distinguishable, which is attributed to sluggish dynamics of the system at low temperatures, and the 10 ns simulation timescale is still insufficient for Li⁺ to undergo multiple solvation structure transitions.

Fig. 4 The normalized self-part of conditional Gs(r,t) for Li⁺ in various solvation clusters at different time scales and temperatures. (a) 298.15 K and (b) 213.15 K for Li⁺ in CIP, SSIP, and FSLi. (c) 298.15 K and (d) 213.15 K for Li⁺ in Li⁺–EC_X–DMC_Y type clusters.

Furthermore, the conditional G_s(r,t) of more detailed solvation structures was analyzed. Based on the analysis above of the solvation structure, several dominant clusters were selected for further investigation. Given the tiny population of CIP in the system, only SSIP and FSLi were considered. Fig. 4c and d show the normalized conditional G_s(r,t) for Li⁺ in these representative clusters at 298.15 K and 213.15 K, respectively. The results at other temperatures are summarized in Fig. S4. Across different temperatures, the transport rates of Li⁺ in the representative clusters follow the order 1–4–0 > 1–3–1 > 1–2–2 > 1–1–3 > 1–0–4, and 1–3–2 > 1–2–3, with 1–4–0 clusters exhibiting the fastest transport, and 1–0–4 clusters being the slowest, indicating slower transport in clusters with a higher DMC content. From the above solvation structure analyses, the population of EC-rich clusters that migrate relatively fast decreases with temperature, which might account for the sluggish kinetics at lower temperatures.

According to the above analyses, the transport of Li⁺ involves the solvent exchange in a long time scale, as Li⁺ gradually “forgets” its initial solvation configuration. Fig. 5a illustrates a complete solvent exchange event, in which Li⁺ coordinates with an incoming EC, temporarily adopting a penta-coordinated structure as an intermediate state. Then, one original EC leaves the first solvation shell of Li⁺, restoring the CN to four. To further investigate the dynamics of solvent exchange, the residence time autocorrelation functions C_Li⁺–X(t) were calculated for EC and DMC molecules within the first solvation shell of Li⁺, which represents the probability that a given solvent molecule remains within the solvation shell of Li⁺ after time t. C_Li⁺–X(t) was calculated using:

where X denotes EC or DMC (only their carbonyl oxygen atom was considered as the coordinating atom), h_Li⁺–X(t) is equal to 1 if the Li⁺–X pair remains continuously within the first solvation shell over time t, otherwise 0, and 〈⋯〉 denotes an average over all time origins. In the long time, C_Li⁺–EC(t) decays exponentially as C_Li⁺–EC(t) = exp(−t/τ_Li⁺–X), thus the residence time τ_Li⁺–X that corresponds to the average duration time that a solvent molecule stays coordinated with Li⁺ can be estimated by fitting the corresponding C_Li⁺–X(t) curve. The fitted τ_Li⁺–X is summarized in Table S5. As shown in Fig. 5b and c, C_Li⁺–EC(t) decays faster than C_Li⁺–DMC(t), with τ_Li⁺–EC being significantly shorter than τ_Li⁺–DMC at the same temperature, indicating that EC exchanges more frequently than DMC within the first solvation shell of Li⁺. This may explain why clusters with more EC diffuse faster than clusters with more DMC. As the temperature decreases, C_Li⁺–X(t) decays slower and τ_Li⁺–X increases significantly, indicating that EC and DMC tend to stay coordinated with Li⁺ at lower temperatures, which evidently accounts for the population increase of penta-coordinated clusters.

Fig. 5 (a) Illustration of a solvent exchange event. The transparent molecules enclosed by dashed circles represent species outside the first solvation shell (i.e., not coordinated to Li⁺). Residence time autocorrelation functions for (b) Li⁺–EC and (c) Li⁺–DMC at different temperatures. (d) Transport index at different temperatures with different time windows of 0.5 ps, 1 ps, and 2 ps, respectively.

Two distinct transport mechanisms were identified: vehicular transport, where Li⁺ migrates together with its ligands, and structural transport, where Li⁺ migrates by continuously exchanging its ligands. The significant reduction of solvent exchange as the temperature decreases would clearly affect the transport mechanisms of Li⁺. In order to quantify the contribution of structural transport to total Li⁺ transport, referenced to the work of Lu et al.,⁵⁷ the transport index (TI) was introduced. TI is defined as eqn (6), in which N_v and N_s denote the numbers of Li⁺ undergoing vehicular and structural transport, respectively, with their sum equal to the total number of Li⁺. Δr_v(t)² and Δr_s(t)² correspond to the mean square displacement (MSD) of Li⁺ that transport via the vehicular and structural mechanisms over a given time t. The criterion for determining whether the MSD of a Li⁺ belongs to structural transport or vehicular transport is whether ligand exchange occurs within the time period t. It is worth noting that different time scales only affect the numerical values of the TI, without altering its overall trend, and that the results are only comparable when calculated at the same time scale. In this study, three different time scales (0.5 ps, 1 ps, and 2 ps) were examined to ensure the reliability of the analysis. As shown in Fig. 5d, TI decreases progressively as the temperature decreases from 298.15 K to 213.15 K across all time windows. This trend is attributed to the significant increase in the residence time τ_Li⁺–X (Table S5), and the formation of more DMC-rich clusters at low temperatures. These changes substantially weaken solvent exchange within the Li⁺ solvation shell, thereby reducing the contribution of the structural transport and ultimately leading to the observed decrease in TI with decreasing temperature.

Conclusions

In this study, MD simulations were employed to systematically investigate the solvation structure and transport mechanism of Li⁺ in a 1 M LiPF₆/EC–DMC electrolyte at low temperatures. As the temperature decreases, EC and DMC exhibit a crossover trend in their contributions to the first solvation shell of Li⁺, with DMC gradually becoming the dominant coordinating solvent at lower temperatures. Meanwhile, Li⁺ tends to form more SSIP, with fewer CIP and FSLi. In addition, the total CN increases with a growing proportion of pentacoordinated clusters. Li⁺ in SSIP and DMC-rich clusters exhibits slower transport behavior. Low temperature also significantly affects the transport mechanism of Li⁺. As the temperature decreases, the residence time of solvents increases, and the frequency of solvent exchange events decreases, thereby suppressing structural transport and further hindering Li⁺ transport.

Overall, the increased proportion of dynamically sluggish clusters and reduced solvent exchange in the electrolyte collectively hinder Li⁺ transport, contributing to the performance degradation of LIBs at low temperatures. This work provides molecular-level insights into how low temperatures influence Li⁺ transport, thereby laying the foundation for the development of novel low-temperature electrolytes, the outcomes of which will be presented in future studies.

Author contributions

Junyu Huang: conceptualization, methodology, software, formal analysis, investigation, visualization, writing – original draft, writing – review & editing. Tao Wang: software, writing – review & editing. Hongjin Li: software, writing – review & editing. Yuechao Wu: software, writing – review & editing. Shu Li: writing – review & editing. Bin Kan: writing – review & editing. Tianying Yan: conceptualization, methodology, supervision, funding acquisition, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The compositions and periodic boundary condition cell lengths of the model systems, as well as the force field parameters supporting the reproducibility of the molecular dynamics simulations in this article, together with additional calculated data, have been uploaded as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5ta08753h.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (No. 22273040).

References

1. M. Armand and J.-M. Tarascon, Nature, 2008, 451, 652–657.
2. P. G. Bruce, B. Scrosati and J. M. Tarascon, Angew. Chem., Int. Ed., 2008, 47, 2930–2946.
3. N.-S. Choi, Z. Chen, S. A. Freunberger, X. Ji, Y.-K. Sun, K. Amine, G. Yushin, L. F. Nazar, J. Cho and P. G. Bruce, Angew. Chem., Int. Ed., 2012, 51, 9994–10024.
4. J. Garcia-Barriocanal, A. Rivera-Calzada, M. Varela, Z. Sefrioui, E. Iborra, C. Leon, S. J. Pennycook and J. Santamaria, Science, 2008, 321, 676–680.
5. W. He and B. Wang, Adv. Energy Mater., 2012, 2, 329–333.
6. B. Kang and G. Ceder, Nature, 2009, 458, 190–193.
7. L.-X. Yuan, Z.-H. Wang, W.-X. Zhang, X.-L. Hu, J.-T. Chen, Y.-H. Huang and J. B. Goodenough, Energy Environ. Sci., 2011, 4, 269–284.
8. C. K. Huang, J. Sakamoto, J. Wolfenstine and S. Surampudi, J. Electrochem. Soc., 2000, 147, 2893.
9. H.-P. Lin, D. Chua, M. Salomon, H. Shiao, M. Hendrickson, E. Plichta and S. Slane, Electrochem. Solid-State Lett., 2001, 4, A71.
10. S. S. Zhang, K. Xu and T. R. Jow, Electrochim. Acta, 2004, 49, 1057–1061.
11. Z. Li, Y. X. Yao, S. Sun, C. B. Jin, N. Yao, C. Yan and Q. Zhang, Angew. Chem., Int. Ed., 2023, 135, e202303888.
12. N. Zhang, T. Deng, S. Zhang, C. Wang, L. Chen, C. Wang and X. Fan, Adv. Mater., 2022, 34, 2107899.
13. Q. Li, G. Liu, H. Cheng, Q. Sun, J. Zhang and J. Ming, Chem.–Eur. J., 2021, 27, 15842–15865.
14. A. J. Ringsby, K. D. Fong, J. Self, H. K. Bergstrom, B. D. McCloskey and K. A. Persson, J. Electrochem. Soc., 2021, 168, 080501.
15. X. Chen, M. Liu, S. Yin, Y. C. Gao, N. Yao and Q. Zhang, Angew. Chem., Int. Ed., 2025, 137, e202503105.
16. K. Xu, Chem. Rev., 2004, 104, 4303–4418.
17. K. Xu, Chem. Rev., 2014, 114, 11503–11618.
18. L. Xiao, Y. Cao, X. Ai and H. Yang, Electrochim. Acta, 2004, 49, 4857–4863.
19. S. Zhang, K. Xu, J. Allen and T. Jow, J. Power Sources, 2002, 110, 216–221.
20. Y.-G. Cho, Y.-S. Kim, D.-G. Sung, M.-S. Seo and H.-K. Song, Energy Environ. Sci., 2014, 7, 1737–1743.
21. A. Ramanujapuram and G. Yushin, Adv. Energy Mater., 2018, 8, 1802624.
22. M. Smart, B. Ratnakumar, A. Behar, L. Whitcanack, J.-S. Yu and M. Alamgir, J. Power Sources, 2007, 165, 535–543.
23. M. Smart, B. Ratnakumar, K. Chin and L. Whitcanack, J. Electrochem. Soc., 2010, 157, A1361.
24. Z. Wu, S. Li, Y. Zheng, Z. Zhang, E. Umesh, B. Zheng, X. Zheng and Y. Yang, J. Electrochem. Soc., 2018, 165, A2792.
25. B. Liu, B. Li and S. Guan, Electrochem. Solid-State Lett., 2012, 15, A77.
26. J. Shi, N. Ehteshami, J. Ma, H. Zhang, H. Liu, X. Zhang, J. Li and E. Paillard, J. Power Sources, 2019, 429, 67–74.
27. Y. Sun, T. Yang, H. Ji, J. Zhou, Z. Wang, T. Qian and C. Yan, Adv. Energy Mater., 2020, 10, 2002373.
28. N. Yao, X. Chen, Z.-H. Fu and Q. Zhang, Chem. Rev., 2022, 122, 10970–11021.
29. Y. Ma, Energy Environ. Mater., 2018, 1, 148–173.
30. N. N. Rajput, V. Murugesan, Y. Shin, K. S. Han, K. C. Lau, J. Chen, J. Liu, L. A. Curtiss, K. T. Mueller and K. A. Persson, Chem. Mater., 2017, 29, 3375–3379.
31. O. Borodin and G. D. Smith, J. Phys. Chem. B, 2009, 113, 1763–1776.
32. S. Uchida and T. Kiyobayashi, Phys. Chem. Chem. Phys., 2021, 23, 10875–10887.
33. C. M. Tenney and R. T. Cygan, J. Phys. Chem. C, 2013, 117, 24673–24684.
34. N. Rampal, S. E. Weitzner, S. Cho, C. A. Orme, M. A. Worsley and L. F. Wan, Energy Environ. Sci., 2024, 17, 7691–7698.
35. M. J. Abraham, T. Murtola, R. Schulz, S. Páll, J. C. Smith, B. Hess and E. Lindahl, SoftwareX, 2015, 1, 19–25.
36. L. A. Martínez, R. Birgin, E. G. Martínez and J. Mario, J. Comput. Chem., 2009, 30, 2157–2164.
37. M. C. Payne, M. P. Teter, D. C. Allan, T. Arias and J. Joannopoulos, Rev. Mod. Phys., 1992, 64, 1045.
38. M. Parrinello and A. Rahman, J. Appl. Phys., 1981, 52, 7182–7190.
39. S. Nosé, J. Chem. Phys., 1984, 81, 511–519.
40. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford university press, 2017.
41. B. Hess, H. Bekker, H. J. Berendsen and J. G. Fraaije, J. Comput. Chem., 1997, 18, 1463–1472.
42. B. Hess, J. Chem. Theory Comput., 2008, 4, 116–122.
43. U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee and L. G. Pedersen, J. Chem. Phys., 1995, 103, 8577–8593.
44. W. Humphrey, A. Dalke and K. Schulten, J. Mol. Graphics, 1996, 14, 33–38.
45. W. L. Jorgensen, D. S. Maxwell and J. Tirado-Rives, J. Am. Chem. Soc., 1996, 118, 11225–11236.
46. C. I. Bayly, P. Cieplak, W. Cornell and P. A. Kollman, J. Phys. Chem., 1993, 97, 10269–10280.
47. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, A. P. B. Peng, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman and D. J. Fox, Gaussian 16 Rev. B.01, Wallingford, CT, 2016.
48. I. Leontyev and A. Stuchebrukhov, Phys. Chem. Chem. Phys., 2011, 13, 2613–2626.
49. I. V. Leontyev and A. A. Stuchebrukhov, J. Chem. Theory Comput., 2012, 8, 3207–3216.
50. S. Blazquez, J. L. Abascal, J. Lagerweij, P. Habibi, P. Dey, T. J. Vlugt, O. A. Moultos and C. Vega, J. Chem. Theory Comput., 2023, 19, 5380–5393.
51. R. Kubo, J. Phys. Soc. Jpn., 1957, 12, 570–586.
52. L. Niedzicki, S. Grugeon, S. Laruelle, P. Judeinstein, M. Bukowska, J. Prejzner, P. Szczecinski, W. Wieczorek and M. Armand, J. Power Sources, 2011, 196, 8696–8700.
53. C. L. Berhaut, P. Porion, L. Timperman, G. Schmidt, D. Lemordant and M. Anouti, Electrochim. Acta, 2015, 180, 778–787.
54. J. Zhao, L. Wang, X. He, C. Wan and C. J. Jiang, J. Electrochem. Soc., 2008, 155, A292.
55. J. Shi, M. Sun, C. Liu, Y. Tian and Z. Zhou, Chem. Eng. Sci., 2025, 122353.
56. L. Van Hove, Phys. Rev., 1954, 95, 249.
57. D. Lu, R. Li, M. M. Rahman, P. Yu, L. Lv, S. Yang, Y. Huang, C. Sun, S. Zhang, H. Zhang, J. Zhang, X. Xiao, T. Deng, L. Fan, L. Chen, J. Wang, E. Hu, C. Wang and X. Fan, Nature, 2024, 627, 101–107.

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