The 71th special feature “New Progress of Batteries and Fuel Cells”
Quantitative Study of Solid Electrolyte Particle Dispersion and Compression Processes in All-Solid-State Batteries Using DEM
2025 年 93 巻 6 号 p. 063009
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2025 年 93 巻 6 号 p. 063009
All-solid-state batteries (ASSBs) are expected to be next-generation batteries owing to their safety and suitability for high-temperature operation. While traditional lithium-ion batteries use liquid electrolytes that enable easy electrolyte filling after electrode fabrication, ASSBs use solid electrolyte particles. Thus, electrolyte particles must be dispersed alongside the active materials and additives during electrode preparation. The dispersion state of the electrolyte influences subsequent electrode formation and structure; however, experimentally quantitatively controlling and evaluating the dispersion states remains challenging. This study used powder simulation to control the dispersion state quantitatively, based on the aggregation size of solid electrolyte particles. It also evaluated the compression process and the resulting electrode structure.
Lithium-ion batteries (LIBs) are increasingly being used in portable devices and electric vehicles, thereby driving the demand for further performance improvements.1 However, organic electrolytes in conventional LIBs are flammable and volatile, limiting their safety and usability at high temperatures; consequently, all-solid-state batteries (ASSBs) have gained attention.2 The solid electrolytes used in ASSBs are nonflammable and operable over a wide temperature range,3,4 making them suitable for use in electric vehicles.
While the structure of electrodes is important in LIBs, it plays an even more critical role in ASSBs. Ion conduction may be impeded by voids between particles, and ensuring contact between the active materials and solid electrolyte particles is essential for facilitating the reaction area. To establish the design guidelines for ASSBs, models predicting the ionic conductivity and reaction area of homogeneously dispersed cathode composites have been proposed.5–9 However, achieving uniform dispersion remains a challenge because of the particle-based nature of solid electrolytes. Unlike conventional processes, in which liquid electrolytes are introduced after electrode fabrication, ASSBs require pre-mixing and dispersion of electrolytes with electrode materials,10,11 as illustrated in Fig. 1.
Electrode and cell manufacturing process for a typical all-solid-state battery.
When the dispersion states vary, the electrode structures formed during compression differ, affecting the battery performance. However, experimental control and observation of dispersion are difficult, and quantitative evaluation is challenging. For a deeper quantitative understanding, this study used the Discrete Element Method (DEM) to control the dispersion states and analyze the compression processes and electrode structures. DEM simulations are increasingly used to model the pressing process in both traditional lithium-ion batteries and ASSBs.12–20 Although the smaller electrolyte particles are generally preferred to the active material for optimal performance,21 their tendency to aggregate presents a challenge. Therefore, this study employed DEM simulations to investigate how different degrees of aggregation (i.e., the number of particles clustered together) in the solid electrolyte affect the compression behavior and resulting structure of ASSB electrodes.
The simulations employed the Altair EDEM software based on the DEM. The Hertz-Mindlin with JKR model,22 which can consider particle collisions, rotations, friction, and adhesion was used for contact modeling. Hence, this model, which calculates the contact forces based on Eq. 1. The equivalent Young’s modulus ($E^{*}$) and radius ($R^{*}$) were derived using Eqs. 2 and 3, respectively:
| \begin{equation} F = -4\sqrt{\pi \gamma E^{*}} a^{\frac{3}{2}} + \frac{4E^{*}}{3R^{*}}a^{3} \end{equation} | (1) |
| \begin{equation} \frac{1}{E^{*}} = \frac{(1 - v_{i}^{2})}{E_{i}} + \frac{(1 - v_{j}^{2})}{E_{i}} \end{equation} | (2) |
| \begin{equation} \frac{1}{R^{*}} = \frac{1}{R_{i}} + \frac{1}{R_{j}} \end{equation} | (3) |
where a is the contact radius, which can be calculated from the overlap amount δ using the following formula:
| \begin{equation} \delta = \frac{a^{2}}{R^{*}} - \sqrt{\frac{4\pi\gamma a}{E^{*}}} \end{equation} | (4) |
The forces between aggregated particles were calculated using the built-in BondingV2 model in Altair EDEM, which is designed to simulate bonding and interactions within particle assemblies. This model introduces bonding forces between specific particles that break when specified stresses are exceeded, causing particle separation. The forces in the normal and shear directions were computed iteratively for each time step. The interparticle forces and torque are set to zero after the aggregation process and are recalculated based on Eqs. 5–8.
| \begin{equation} \delta F_{n} = -\upsilon_{n}S_{n}A\delta t \end{equation} | (5) |
| \begin{equation} \delta F_{t} = -\upsilon_{t}S_{t}A\delta t \end{equation} | (6) |
| \begin{equation} \delta M_{n} = -\omega_{n}S_{t}J\delta t \end{equation} | (7) |
| \begin{equation} \delta M_{t} = -\omega_{t}S_{n}\frac{J}{2}\delta t \end{equation} | (8) |
where υ is the normal and shear velocities, and ω is the normal and shear angular velocities, and A and J are calculated as follows:
| \begin{equation} A = \pi R_{B}^{2} \end{equation} | (9) |
| \begin{equation} J = \frac{1}{2}\pi R_{B}^{4} \end{equation} | (10) |
If the specified stress σmax in the normal direction or τmax in the shear direction exceeds the set threshold, the bond will break.
| \begin{equation} \sigma_{\textit{max}} < -\frac{F_{n}}{A} + \frac{2M_{t}}{J}R_{B} \end{equation} | (11) |
| \begin{equation} \tau_{\textit{max}} < -\frac{F_{t}}{A} + \frac{M_{n}}{J}R_{B} \end{equation} | (12) |
Table 1 lists the input parameters used in the simulation. LiNi1/3Co1/3Mn1/3O2 (NCM) was used as the active material, and Li6PS5Cl (LPSCl) was used as the solid electrolyte.23 Based on the particle sizes of the materials used in previous experiments,5 NCM was set at 5 µm and LPSCl at 0.7 µm. However, in the DEM calculations, according to the relationship in Eq. 13, when the particle mass is small, the number of calculation steps increases, resulting in longer computation times.
| \begin{equation} \delta t < \frac{2\pi}{\omega}\sqrt{\frac{m}{k}} \end{equation} | (13) |
Therefore, in this study, the calculations were performed at the particle size of the active material and solid electrolyte 100 times larger to reduce calculation time. Additionally, it was verified in advance that the relationship between compressive stress and density is consistent between the 1 times scale and the 100 times scale.
| Parameter | Value | Unit | Ref. | |
|---|---|---|---|---|
| Active Material |
LiNi1/3Co1/3Mn1/3O2 | — | — | — |
| Diameter | 500 | µm | — | |
| Density | 4.75 | g/cm3 | 19 | |
| Young’s Modulus | 71 | GPa | 19 | |
| Volume ratio | 79 | Vol% | 19 | |
| Coefficient of restitution | 0.25 | — | 19 | |
| Coefficient of static friction | 0.5 | — | 19 | |
| Coefficient of rolling friction | 0.01 | — | 19 | |
| Surface energy | 0.1 | J/m2 | 19 | |
| Solid Electrolyte |
Li6PS5Cl | — | — | — |
| Diameter | 70 | µm | 5 | |
| Density | 1.8 | g/cm3 | 5 | |
| Young’s Modulus | 22.1 | GPa | 23 | |
| Volume ratio | 21 | Vol% | — | |
| Critical stress | 1000 | GPa | — | |
| Coefficient of restitution | 0.25 | — | — | |
| Coefficient of static friction | 0.5 | — | — | |
| Coefficient of rolling friction | 0.01 | — | — | |
| Surface energy | 0.1 | J/m2 | — | |
| Geometry | Plate Young’s Modulus | 74 | GPa | — |
| Area | 62500 | µm2 | — | |
| Boundary Condition | periodic (X, Y) | — | — | |
We calculated the volume ratio of the solid electrolyte in range where the effects of dispersion are likely to be significant, specifically in areas with a low volume ratio of the solid electrolyte. Additionally, we focused on range within the electrode where the paths of the solid electrolyte are not blocked, ensuring that the battery can operate effectively. To determine these conditions, we referred to our previous reports.5 In this report, we varied the volume ratio of the solid electrolyte to the active material and measured the ionic conductivity experimentally. Sufficient ionic conductivity was measured up to a solid electrolyte ratio of 21 vol%, but at a solid electrolyte ratio of 10 vol%, there was a significant decrease in conductivity, suggesting that adequate ionic conduction paths were not established. Therefore, we focused on a solid electrolyte volume ratio of 21 vol%, where the paths of the solid electrolyte are maintained. The coefficients of restitution, static friction, and rolling friction were based on previous studies.19 The critical bonding strength of the aggregates is difficult to obtain from experiments or reference materials. In this study, parameters were pre-set, such that the bonding was maintained during the gravity filling process, and the value at which the bonding would break during the compression process was defined. The aggregates of solid electrolyte particles ranged from a single particle (ideal dispersion) to 307 particles.
The simulation procedure involved random placement of the active material and aggregated solid electrolyte particles in a domain with periodic boundaries, followed by gravity filling and compression using a flat plate. Regarding pressurization, it was conducted through pressure control. Since gravity filling was completed in 0.03 seconds, the pressure was gradually increased from 0.03 seconds to 0.057 seconds, reaching up to 1000 MPa.
To investigate the impact of solid electrolyte aggregation on electrode structure during the ASSBs manufacturing process, DEM simulations were conducted with varying degrees of aggregation. Figure 2 illustrates the behavior of these aggregates during random arrangement, gravity filling, and compression. As expected, the aggregates remained clustered after initial arrangement and gravity filling. However, during compression, the aggregated structures separated and deformed. Notably, with an aggregation number of 307, there was insufficient solid electrolyte to fill the gaps between the active materials, even with a uniform initial distribution. This highlights the importance of the initial dispersion state, as the solid electrolyte’s inability to penetrate between the active materials can significantly influence the final electrode structure. When the aggregation number is small, no clear changes are observed at present, and a more detailed analysis is required.
Compression calculation process for aggregation numbers of 1, 6, and 307. Gray spheres represent the active material, and yellow spheres represent the solid electrolyte. Aggregation numbers (a–d) 1, (e–h) 6, and (i–l) 307. Each figure shows the aggregation shape of the solid electrolyte and the corresponding compression process. (a, e, i) show the aggregation state of the solid electrolyte particles. (b, f, j) illustrate the initial random arrangement state, followed by gravity filling in (c, g, k), and the compressed state in (d, h, l).
The stress-density relationships for the aggregation numbers ranging from 1 to 307 are illustrated in Fig. 3. Relative density was calculated as the ratio of the volume of particle to the volume determined by the plate distance and area. Regardless of the aggregation number, the density increased with stress. However, as the number of aggregated particles increased, the density remained lower than that of a single aggregated particle. Even at a high pressure of 800 MPa, for small aggregation numbers, such as 4, the density decreased by approximately 2 %, indicating a high sensitivity to aggregation. A lower electrode density was expected to reduce the effective ionic conductivity of the composite electrodes,5,24 emphasizing the importance of solid electrolyte dispersion.
Compression pressure and relative density of each aggregation number.
The decrease in density can be attributed to changes in the contact conditions between the active material and the solid electrolyte particles during compression caused by aggregation. Figures 4a and 4b show the stress distributions at 1000 MPa for aggregation numbers 1 and 6, respectively, represented by a color map of the total force on each particle. The stress distribution was relatively uniform for a single aggregated particle, representing an ideally dispersed state; this is likely because the soft solid electrolyte disperses the stress among the hard active materials. Conversely, in the case of 6 aggregated particles, the stress distribution became uneven, with certain particles subjected to high stress. To clarify the cause, in Fig. 4c, the high-stress particles that over 0.04 N were extracted. This result revealing a connected force chain from the upper to lower calculate regions, primarily formed by the segregated active materials; this indicates that aggregation of the solid electrolyte prevents its insertion between the active materials, resulting in insufficient compression. Increased contact between active materials hinders density improvements and leads to stress concentration on the active materials, potentially causing them to crack.25 In ASSBs, cracks in the active materials prevent lithium-ion diffusion, which raised concerns regarding decreased rate characteristics owing to increased diffusion resistance.
(a) and (b) show the stress distributions for aggregation numbers 1 and 6, respectively, represented by a color map of the total force on each particle. (c) shows only the particles with an aggregation number of 6 that were subjected to a force greater than 0.04 N.
To ensure sufficient reaction surface area and shorten the diffusion distance of lithium ions within the active materials, it is important to secure a sufficient contact area between the active materials and the solid electrolyte. Therefore, due to concerns regarding the effects of solid electrolyte aggregation, calculations of the contact area for each aggregation number were performed. The contact area was calculated based on active material surface area and overlapping area of active material and solid electrolyte and normalized to the ideal dispersed state (aggregation number 1). Figure 5d shows the normalized contact area for different solid electrolyte aggregation numbers and diagrams of the electrode for aggregation numbers 1, 6, and 307. The contact area decreased as the aggregation number increased. Even with an aggregation number of 6, the contact area decreased by approximately 15 %, highlighting the significant impact of aggregation. Comparing Fig. 5a (ideal dispersed state) with Figs. 5b and 5c, it is evident that as the aggregation increases, less solid electrolyte is present between the active materials, which is the primary reason for the reduced contact area. Within the scope of this study, even in the case of 307 aggregates, no isolated active material without contacts with the solid electrolyte existed.
(a, b, c) Cross-sectional images of the electrode for aggregation numbers of 1 (a), 6 (b), and 307 (c). (d) Relationship between reaction area and aggregation number. The black particles represent the active material particles, and the yellow particles represent single particle of the solid electrolyte. Reaction area was normalized to the ideal dispersed state as 1.
The results of this study indicate that the structure observed when the aggregation numbers increase in size the structure resembles the structure described in the reports regarding the increase in the particle size ratio of the solid electrolyte to the active material.9,26,27 Previous reports have indicated that a smaller particle size ratio of the solid electrolyte to the active material results in higher dispersion and ensures a larger contact area between the active material and the solid electrolyte. In contrast, it has been reported that a larger particle size ratio leads to the segregation of the active material, which causes a decrease in the rate performance and cycling characteristics of the battery. The results of this study suggest that the factors exhibiting a similar trend to those observed in the particle size ratio investigation may be related to the initial structure before compression. In cases where aggregated form or when the particle size ratio is large, there are fewer solid electrolyte particles able to infiltrate the spaces between the active materials during the initial arrangement. Subsequently, during compression, even aggregates that can easily deform plastically are unable to enter the gaps between the active materials, resulting in a similar structure post-pressurization.
We simulated a monodisperse system; however, in actual systems, a polydisperse state exists. If there are particles with a high aggregation number, the effective particle count may decrease when considering aggregates as a single particle, which could lead to an insufficient number of particles to fill the gaps between the active materials. Therefore, based on these results, it is crucial to evaluate the dispersion state by considering the number of particles, counting aggregates as a single particle, when examining the actual dispersion state of the particles.
In this study, we quantitatively evaluated the compression properties and electrode structures of composite electrodes for all-solid-state batteries. Until now, there have been few reported examples in the study of dispersion due to the difficulty of quantitative control in experiments. Therefore, this result provides important findings that can serve as a guideline for dispersion processes. Control the dispersion state quantitatively, based on the aggregation size of solid electrolyte particles using DEM. As the solid electrolyte aggregation number increases, the compression properties exhibit a decrease in density under pressure. An analysis of the stress distribution revealed that higher aggregation numbers resulted in higher stress concentrations, where aggregates of active materials formed columns, creating force chains that degraded the compression properties. This decline in the compression properties raises concerns about the reduced ionic conductivity of the electrodes.
Regarding the electrode structure, the contact area between the active material and solid electrolyte decreased as the aggregation number of the solid electrolyte increased. This reduction in the contact area is associated with a decrease in the reaction surface area and an increase in the diffusion distance in active material, which may adversely affect electrode performance. These findings quantitatively demonstrate that the proper dispersion of the solid electrolyte is essential for achieving high battery performance.
Force (N)
γSurface energy (J m−2)
EElastic modulus (MPa)
$E^{*}$Equivalent Young’s modulus (MPa)
$R^{*}$Equivalent radius (mm)
RBBonding radius (mm)
aContact radius (mm)
ωAngular velocity (rad s−1)
υParticle velocity (m s−1)
MTorque (N m−1)
SStiffness (N m−3)
σmaxCritical normal stress (N m−2)
τmaxCritical shear stress (N m−2)
mMass (g)
kElasticity (Pa)
The authors were waived from the APC with the support of The Committee of Battery Technology, ECSJ.
Kazufumi Otani: Conceptualization (Lead), Data curation (Lead), Formal analysis (Lead), Investigation (Lead), Methodology (Lead), Software (Lead), Visualization (Lead), Writing – original draft (Lead)
Takeru Yano: Writing – review & editing (Equal)
Ken Akizuki: Project administration (Equal), Writing – review & editing (Equal)
Koichiro Aotani: Project administration (Lead), Writing – review & editing (Equal)
Gen Inoue: Supervision (Lead), Writing – review & editing (Equal)
The authors declare no conflict of interest.
A part of this paper has been presented in the 65th Battery Symposium in Japan in 2024 (Presentation #1G17).
K. Otani, K. Akizuki, K. Aotani, and G. Inoue: ECSJ Active Members
