All-solid-state batteries represent a transformative advancement in energy storage technology, offering the potential for high energy density, enhanced safety, and extended cycle life compared to conventional liquid electrolyte-based systems. The absence of flammable liquid components mitigates thermal runaway risks, while the use of solid electrolytes enables the integration of high-capacity electrodes, such as lithium metal anodes. However, the development of practical all-solid-state batteries faces significant challenges, including interfacial instability, mechanical stress-induced degradation, and limited ion transport efficiency. Computational modeling and simulation have emerged as indispensable tools for elucidating the underlying mechanisms governing the behavior of solid-state batteries, enabling the optimization of materials, interfaces, and cell architectures. This article comprehensively reviews recent progress in multiscale modeling approaches—spanning atomic-scale molecular dynamics to cell-level multiphysics simulations—and discusses their role in accelerating the commercialization of all-solid-state batteries.
The performance of all-solid-state batteries is governed by complex interplay between electrochemical, mechanical, and thermal phenomena. Key challenges include the formation of resistive interphases, dendrite growth in lithium metal anodes, and stress accumulation during cycling. Molecular dynamics (MD) and density functional theory (DFT) simulations provide insights into ion transport mechanisms and interfacial reactions at the atomic scale. For instance, the ion conductivity $\sigma$ in sulfide-based solid electrolytes like Li$_6$PS$_5$Cl can be described by the Nernst-Einstein relation: $$\sigma = \frac{D z^2 F^2 c}{RT},$$ where $D$ is the diffusion coefficient, $z$ is the charge number, $F$ is Faraday’s constant, $c$ is the ion concentration, $R$ is the gas constant, and $T$ is the temperature. At the mesoscale, phase-field models and finite element analysis (FEA) capture microstructural evolution, while continuum models integrate electrochemistry and mechanics to predict cell-level performance. This review systematically examines modeling efforts across these scales, highlighting advances in understanding material properties, interface behavior, and multiphysics coupling in solid-state batteries.
Molecular Dynamics and Atomic-Scale Simulations
Atomic-scale simulations are critical for probing ion transport and defect dynamics in solid-state battery materials. Density functional theory (DFT) calculations enable the prediction of thermodynamic stability, electronic structure, and mechanical properties. For example, the elastic tensor $C_{ij}$ of a solid electrolyte can be derived from stress-strain relationships: $$\sigma_{ij} = C_{ijkl} \epsilon_{kl},$$ where $\sigma_{ij}$ and $\epsilon_{kl}$ are the stress and strain tensors, respectively. Molecular dynamics simulations, particularly ab initio MD (AIMD), track ion trajectories over time, providing diffusion coefficients and activation energies. Coarse-grained MD (CGMD) extends these capabilities to larger systems, such as electrode composites, by simplifying atomic interactions. Machine learning potentials are increasingly used to bridge accuracy and computational cost, enabling high-throughput screening of solid electrolyte candidates. Table 1 summarizes key parameters derived from MD and DFT studies for common solid electrolytes.
| Material | Ionic Conductivity (mS/cm) | Young’s Modulus (GPa) | Diffusion Coefficient (m²/s) |
|---|---|---|---|
| Li$_6$PS$_5$Cl | 2.4 | 25.3 | 2.1 × 10$^{-12}$ |
| Li$_7$La$_3$Zr$_2$O$_{12}$ | 0.3 | 150.5 | 5.6 × 10$^{-14}$ |
| Li$_{10}$GeP$_2$S$_{12}$ | 12.0 | 18.7 | 8.9 × 10$^{-11}$ |
| Li$_3$PS$_4$ | 0.2 | 22.1 | 1.4 × 10$^{-13}$ |
In sulfide-based solid electrolytes, such as argyrodites (e.g., Li$_6$PS$_5$X, X = Cl, Br, I), DFT calculations reveal that halogen doping alters the lattice energy landscape, facilitating Li$^+$ migration. The activation energy $E_a$ for ion hopping can be expressed as: $$D = D_0 \exp\left(-\frac{E_a}{kT}\right),$$ where $D_0$ is the pre-exponential factor and $k$ is Boltzmann’s constant. MD simulations further show that cooperative ion motion reduces energy barriers, enhancing conductivity. However, grain boundaries and surface defects act as traps for excess electrons, promoting Li dendrite nucleation. Phase-field models incorporating DFT-derived parameters simulate dendrite initiation and growth, providing strategies for interface engineering.
Modeling Key Materials and Interfaces
Positive Electrode Materials
Composite positive electrodes in all-solid-state batteries consist of active material particles, solid electrolyte, and conductive additives. Porous electrode theory, extended to account for mechanical deformation, describes ion and electron transport. The governing equations include: $$\frac{\partial c}{\partial t} = \nabla \cdot (D \nabla c) + \frac{j}{F},$$ where $c$ is the Li$^+$ concentration, $D$ is the diffusivity, and $j$ is the pore wall flux. Stress-coupled models incorporate chemical strain $\epsilon_c$: $$\epsilon_c = \beta \Delta c,$$ where $\beta$ is the chemical expansion coefficient. Discrete element method (DEM) and finite element analysis (FEA) simulate microstructural effects, such as particle cracking and interface delamination. For example, in LiNi$_x$Mn$_y$Co$_z$O$_2$ (NMC) composites, stress accumulation during lithiation leads to fracture, increasing impedance. Table 2 compares modeling approaches for positive electrodes.
| Model Type | Key Equations | Applications | Limitations |
|---|---|---|---|
| Porous Electrode Theory | $\frac{\partial c_s}{\partial t} = D_s \nabla^2 c_s$, $j = i_0 \left[\exp\left(\frac{\alpha F \eta}{RT}\right) – \exp\left(-\frac{(1-\alpha) F \eta}{RT}\right)\right]$ | Homogenized performance prediction | Neglects microstructural details |
| Discrete Element Method (DEM) | $m_i \frac{d\mathbf{v}_i}{dt} = \sum \mathbf{F}_{ij}$ | Particle packing and contact analysis | High computational cost |
| Finite Element Analysis (FEA) | $\nabla \cdot \boldsymbol{\sigma} = 0$, $\boldsymbol{\sigma} = \mathbf{C} : (\boldsymbol{\epsilon} – \boldsymbol{\epsilon}_c)$ | Stress and fracture prediction | Requires detailed microstructure data |
Mechanical pressure externally applied to solid-state batteries improves interfacial contact but induces stress. The stress-dependent diffusivity $D(\sigma)$ follows: $$D(\sigma) = D_0 \exp\left(-\frac{\sigma \Omega}{kT}\right),$$ where $\Omega$ is the activation volume. Simulations show that optimal pressure (~1–5 MPa) reduces porosity and enhances ion transport, while excessive pressure causes particle fracture. Cohesive zone models (CZM) simulate interface debonding, revealing that compliant solid electrolytes (Young’s modulus < 25 GPa) delay failure by accommodating volume changes.
Negative Electrode Materials
Lithium metal anodes in all-solid-state batteries offer high capacity but suffer from dendrite growth and void formation. Dendrite morphology—needle-like, mossy, or tree-like—depends on current density and interface properties. Phase-field models capture dendrite evolution using the Cahn-Hilliard equation: $$\frac{\partial \phi}{\partial t} = \nabla \cdot (M \nabla \mu),$$ where $\phi$ is the phase field variable, $M$ is the mobility, and $\mu$ is the chemical potential. Mechanical models incorporate plasticity and flow: $$\boldsymbol{\sigma} = \mathbf{C} : (\boldsymbol{\epsilon} – \boldsymbol{\epsilon}^p),$$ where $\boldsymbol{\epsilon}^p$ is the plastic strain. For silicon anodes, large volume changes (~300%) during lithiation are modeled using finite strain theory: $$\mathbf{F} = \mathbf{F}_e \mathbf{F}_p,$$ where $\mathbf{F}$ is the deformation gradient, and $\mathbf{F}_e$ and $\mathbf{F}_p$ are its elastic and plastic components. Simulations predict that hollow nanostructures alleviate stress and prevent fracture.
Table 3 summarizes key parameters for negative electrode materials.
| Material | Theoretical Capacity (mAh/g) | Volume Change (%) | Modeling Focus |
|---|---|---|---|
| Lithium Metal | 3860 | 100 | Dendrite suppression, interface stability |
| Silicon | 4200 | 300 | Stress management, fracture prevention |
| Graphite | 372 | 10 | Intercalation kinetics, SEI formation |
Solid Electrolyte Materials
Solid electrolytes are the core component of all-solid-state batteries, with sulfide-based materials like Li$6$PS$_5$Cl exhibiting high ionic conductivity (>1 mS/cm). Microstructural modeling uses resistor networks to simulate the effects of porosity and cracks on effective conductivity $\sigma{\text{eff}}$: $$\sigma_{\text{eff}} = \sigma_0 (1 – \phi)^{3/2},$$ where $\phi$ is the porosity and $\sigma_0$ is the intrinsic conductivity. Interface modeling addresses space-charge layers and contact loss. The Poisson-Nernst-Planck equations describe ion transport: $$\frac{\partial c}{\partial t} = \nabla \cdot (D \nabla c + \frac{D z F c}{RT} \nabla \Phi),$$ where $\Phi$ is the electric potential. Mechanical degradation, including fracture due to interphase formation, is simulated using phase-field damage models: $$\mathcal{G}_c \nabla^2 \phi – \frac{\partial \psi}{\partial \phi} = 0,$$ where $\mathcal{G}_c$ is the critical energy release rate and $\psi$ is the free energy density.
Ion transport mechanisms in sulfide solid electrolytes involve cooperative migration, where multiple Li$^+$ ions move simultaneously, reducing energy barriers. DFT calculations show that disorder in Li$_6$PS$_5$Cl, achieved by substituting S with Cl, enhances conductivity by creating Li$^+$ vacancies. External pressure improves interfacial contact but may accelerate crack propagation if the stack pressure exceeds the fracture toughness. Simulations indicate that a stack pressure of 20–30 MPa optimizes performance without causing mechanical failure.
Cell-Level Electrochemical and Mechanical Modeling
Cell-level models integrate electrode and electrolyte behavior to predict the performance of all-solid-state batteries. The pseudo-two-dimensional (P2D) model, extended for solid-state systems, couples Li$^+$ diffusion in particles with charge conservation: $$\frac{\partial c_s}{\partial t} = \frac{D_s}{r^2} \frac{\partial}{\partial r} \left(r^2 \frac{\partial c_s}{\partial r}\right),$$ $$\nabla \cdot (\kappa \nabla \Phi) + \nabla \cdot (\kappa_D \nabla \ln c) = 0,$$ where $c_s$ is the solid-phase concentration, $r$ is the particle radius, $\kappa$ is the ionic conductivity, and $\kappa_D$ is the diffusional conductivity. Mechanical models incorporate stress effects on equilibrium potential $U$: $$U = U_0 + \frac{\Omega \sigma_h}{F},$$ where $\sigma_h$ is the hydrostatic stress. Thermal models account for heat generation: $$q = j \eta + I^2 R,$$ where $j$ is the current density, $\eta$ is the overpotential, and $R$ is the resistance.
Multiphysics coupling is essential for accurate performance prediction. For example, the strain energy density $W$ influences Li$^+$ diffusion: $$\frac{\partial c}{\partial t} = \nabla \cdot \left(M c \nabla \frac{\delta W}{\delta c}\right).$$ Finite element simulations show that bending in thin-film solid-state batteries alters stress distribution, affecting capacity retention. Table 4 compares cell-level models for solid-state batteries.
| Model Type | Governing Equations | Applications |
|---|---|---|
| Extended P2D Model | $\frac{\partial c_s}{\partial t} = D_s \nabla^2 c_s$, $\nabla \cdot (\sigma \nabla \Phi_s) = a j$, $\nabla \cdot (\kappa \nabla \Phi_e) = -a j$ | Voltage response, capacity fade |
| Thermal-Electrochemical Model | $\rho C_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + q$ | Thermal management, safety analysis |
| Mechanical-Electrochemical Model | $\nabla \cdot \boldsymbol{\sigma} = 0$, $\boldsymbol{\sigma} = \mathbf{C} : (\boldsymbol{\epsilon} – \boldsymbol{\epsilon}_c)$ | Stress evolution, fracture prediction |
Three-dimensional models reconstruct electrode microstructures from X-ray tomography, enabling the analysis of local current density and stress concentrations. For instance, in Si-based anodes, FEA simulations reveal that particle size and spatial distribution critically influence interface stress. Models also predict that low-stiffness solid electrolytes reduce stress but may exacerbate Li dendrite penetration if interface adhesion is weak.
Conclusion and Future Perspectives
Modeling and simulation have profoundly advanced the understanding of all-solid-state batteries, from atomic-scale ion dynamics to cell-level performance. Key insights include the role of mechanical stress in interface stability, the impact of microstructural defects on ion transport, and the coupling between electrochemistry and mechanics. However, challenges remain in accurately capturing phase transformation kinetics, damage evolution, and multiphysics interactions under realistic operating conditions.
Future research should focus on:
- Multiscale Integration: Coupling DFT, MD, and continuum models to bridge atomic-scale mechanisms with macroscopic behavior.
- Machine Learning: Developing data-driven models for high-throughput material screening and parameter optimization.
- Interface Engineering: Modeling interphase formation and degradation to design stable electrode-electrolyte interfaces.
- Mechanical Reliability: Incorporating plasticity, fracture, and fatigue models to predict long-term degradation.
- Manufacturing Process Simulation: Linking processing parameters (e.g., pressure, temperature) to microstructure and performance.
By addressing these areas, modeling will accelerate the development of robust, high-performance solid-state batteries, paving the way for their widespread adoption in electric vehicles and grid storage. The integration of computational tools with experimental validation will be crucial for achieving this goal.