The relentless pursuit of higher energy density and enhanced safety in electrochemical energy storage has positioned the solid-state battery as a paramount frontier in next-generation technology. Replacing the flammable liquid electrolyte with a solid ion conductor fundamentally mitigates risks of leakage and thermal runaway. However, the persistent challenge of lithium dendrite growth at the anode interface remains a critical barrier, threatening cycle life, coulombic efficiency, and ultimately, the safety of solid-state batteries. Dendrites, metallic protrusions formed during lithium plating, can penetrate the solid electrolyte, causing internal short circuits. While the superior mechanical strength of solid electrolytes offers a natural defense compared to their liquid counterparts, it is often insufficient to completely arrest dendrite propagation. Consequently, advanced microstructural engineering of battery components is essential. This article employs a comprehensive phase-field modeling approach, coupled with mechanical, thermal, and electrochemical fields, to systematically investigate how optimized morphologies of nanoskeletons within the electrode and artificial separators within the electrolyte can effectively suppress lithium dendrite growth in solid-state batteries.
The phase-field method is a powerful computational tool for simulating interfacial evolution, making it ideal for studying the complex, non-equilibrium growth of lithium dendrites. In this model, a conserved order parameter (e.g., lithium ion concentration) and non-conserved order parameters (representing phases like lithium metal, solid electrolyte, nanoskeleton, or separator) describe the system. The total free energy of the system governs the evolution. For a solid-state battery system incorporating nanoskeletons and artificial separators, the electrochemical-thermal-mechanical coupled model can be conceptualized. The evolution of the lithium metal phase (ξ=1) within a solid electrolyte (ξ=0) and other structural phases is driven by the minimization of the total free energy functional F:
$$F = \int_{V} \left[ f_{\text{chem}}(\xi, \psi, \phi, c_{\text{Li}^+}) + f_{\text{grad}}(\nabla\xi, \nabla\psi, \nabla\phi) + f_{\text{els}}(\xi, \epsilon_{ij}) + f_{\text{elec}}(c_{\text{Li}^+}, \phi) \right] dV$$
Here, \(f_{\text{chem}}\) is the chemical free energy density, \(f_{\text{grad}}\) is the gradient energy density accounting for interfaces, \(f_{\text{els}}\) is the elastic strain energy density, and \(f_{\text{elec}}\) is the electrostatic energy density. The variables \(\psi\) and \(\phi\) are additional phase-field variables representing the nanoskeleton and artificial separator phases, respectively. The chemical energy density for a system with a nanoskeleton and separator can be expressed using multi-obstacle or double-well potentials:
$$
f_{\text{chem}} = W \xi^2(1-\xi)^2 + W_1 \psi^2(1-\psi)^2 + W_2 \phi^2(1-\phi)^2 + M_{\xi\psi} \xi^2\psi^2 + M_{\xi\phi} \xi^2\phi^2 + RT c_{\text{Li}^+} \left( \ln \frac{c_{\text{Li}^+}}{c_0} – 1 \right)
$$
Where \(W, W_1, W_2\) are energy barrier heights, and \(M_{\xi\psi}, M_{\xi\phi}\) are interaction coefficients between phases. The kinetics of phase transformation and lithium deposition are described by the Allen-Cahn equation for non-conserved order parameters and the Cahn-Hilliard equation for lithium ion diffusion:
$$
\frac{\partial \xi}{\partial t} = -L_{\sigma} \frac{\delta F}{\delta \xi} = -L_{\sigma} \left[ \frac{\partial f_{\text{chem}}}{\partial \xi} – \kappa_{\xi} \nabla^2 \xi + \frac{\partial f_{\text{els}}}{\partial \xi} – L_{\eta} h'(\xi) \eta_{\alpha} \right]
$$
$$
\frac{\partial c_{\text{Li}^+}}{\partial t} = \nabla \cdot \left( D_{\text{eff}} \nabla c_{\text{Li}^+} + \frac{D_{\text{eff}} c_{\text{Li}^+}}{RT} F \nabla \phi \right) – \chi \frac{\partial \xi}{\partial t}
$$
The effective properties, such as diffusion coefficient \(D_{\text{eff}}\) and elastic modulus \(E_{\text{eff}}\), are interpolated across phases using smooth interpolation functions \(h(\xi)\), \(g(\psi)\), etc.:
$$
D_{\text{eff}} = D_{\text{Li}} h(\xi) + D_{\text{SE}} [1-h(\xi)]g(\psi) + D_{\text{SS}}[1-h(\xi)][1-g(\psi)]
$$
$$
E_{\text{eff}} = E_{\text{Li}} h(\xi) + E_{\text{NS}} g(\psi) + E_{\text{SE}} [1-h(\xi)-g(\psi)]
$$
The coupled electrical potential is solved via the Poisson equation: \(\nabla \cdot (\sigma_{\text{eff}} \nabla \phi) = F \partial \xi / \partial t\). Key parameters used in the phase-field simulations for the solid-state battery model are summarized in the table below.
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Interface Mobility | \(L_{\sigma}\) | 1×10⁻⁶ | m³/(J·s) |
| Reaction Constant | \(L_{\eta}\) | 0.5 | s⁻¹ |
| Energy Barrier Height | \(W\) | 3.75×10⁵ | J/m³ |
| Gradient Coefficient | \(\kappa_0\) | 1×10⁻¹⁰ | J/m |
| Anisotropy Strength | \(\delta\) | 0.1 | – |
| Charge Transfer Number | \(n\) | 1 | – |
| Anode Conductivity | \(\sigma_e\) | 1×10⁷ | S/m |
| Electrolyte Conductivity | \(\sigma_s\) | 0.1 | S/m |
| Li Diffusion in Anode | \(D_e\) | 1.7×10⁻¹⁵ | m²/s |
| Li Diffusion in Electrolyte | \(D_s\) | 2×10⁻¹⁵ | m²/s |
| Anode Young’s Modulus | \(E_e\) | 7.8 | GPa |
| Electrolyte Young’s Modulus | \(E_s\) | 1 | GPa |
| Standard Li Concentration | \(c_0\) | 1×10³ | mol/m³ |
The Role of Nanoskeleton Morphology in a Solid-State Battery
Integrating a nanoskeleton—a porous, mechanically robust framework—into the lithium metal anode or composite electrolyte is a promising strategy for stabilizing the solid-state battery interface. The nanoskeleton serves multiple functions: it provides structural support to accommodate volume changes, homogenizes lithium-ion flux, and poses a physical barrier to dendrite penetration. The effectiveness of this approach is highly dependent on the nanoskeleton’s morphology, including its architecture, porosity, and surface characteristics.
Common architectures include vertically aligned nanotube/nanowire arrays and hierarchical porous networks. The phase-field model allows us to introduce the nanoskeleton as a distinct phase (\(\psi\)). Simulations comparing a baseline solid-state battery with one containing a regular nanotube array skeleton reveal significant differences. The skeleton forces lithium to deposit within its porous channels, delaying the onset of dendritic instability. The primary dendrite height is notably reduced, and the growth of secondary side branches is suppressed as lithium ions are guided along the skeleton walls, promoting denser plating. The von Mises stress distribution shows that the skeleton absorbs and redistributes mechanical stress generated during plating, reducing stress concentration at the dendrite tips, which is a key driver for piercing the solid electrolyte in a solid-state battery.
A critical but less explored factor is the uniformity of the nanoskeleton’s surface roughness. Simulations were conducted for two skeletons: a nanotube array and a hierarchical structure, each with two surface conditions—uniformly rough (regular triangular patterns) and non-uniformly rough (irregular asperities). The results are quantified in the table below.
| Nanoskeleton Type | Surface Condition | Primary Dendrite Height Reduction/Increase | Key Observation |
|---|---|---|---|
| Nanotube Array | Uniformly Rough | -16.62% | Dendrite growth confined to channels; lateral growth encouraged. |
| Nanotube Array | Non-uniformly Rough | +17.87% | Local hotspots for ion flux accelerate vertical penetration. |
| Hierarchical Porous | Uniformly Rough | -21.04% | High volume fraction impedes growth; ion path tortuosity increased. |
| Hierarchical Porous | Non-uniformly Rough | +25.57% | Uneven pores create easy penetration paths, weakening inhibition. |
The mechanism is clear: a uniformly rough surface creates consistent nucleation sites and evenly distributed ionic pathways, preventing localized current hot spots. Conversely, non-uniform roughness leads to preferential ion aggregation at sharper or larger asperities, creating localized fast tracks for dendrite growth that can compromise the integrity of the solid-state battery. The hierarchical structure shows greater sensitivity to roughness uniformity due to its interconnected pore network.
Optimizing Artificial Separator Morphology for a Solid-State Battery
Beyond the anode, engineering the solid electrolyte separator itself is crucial. An artificial separator here refers to a designed, often multi-layered, microstructure within the solid electrolyte meant to regulate lithium-ion transport and block dendrites. The phase-field variable \(\phi\) is used to define this separator phase with distinct properties. Key morphological parameters are thickness (\(t\)), pore size/porosity (\(p\)), and cross-sectional shape.
Simulations with a double-layer porous separator show that it effectively disrupts the direct, linear path for dendrite propagation. Lithium ions are forced to navigate through曲折的 pores, which increases the diffusion overpotential locally and promotes more uniform deposition before the separator. Dendrites that approach the separator must re-nucleate and grow through its pores, consuming additional energy and slowing progress.
1. Effect of Pore Size and Thickness: A parametric study reveals the interplay between separator thickness and pore spacing. Reducing pore size increases the separator’s tortuosity and mechanical resistance, significantly hindering dendrite penetration. Increasing thickness also improves inhibition but with diminishing returns if the pores remain large. The most effective strategy is co-optimization. For instance, increasing thickness from 0.2 µm to 0.4 µm while simultaneously decreasing pore spacing from 0.5 µm to 0.4 µm leads to a dramatic 17.70% reduction in dendrite height, compared to a mere 6.95% reduction when only thickness is increased for a large-pore (0.5 µm) separator. This synergistic effect highlights the importance of integrated design for the solid-state battery separator.
2. Innovative Cross-Sectional Morphology: Moving beyond conventional rectangular or cylindrical pore shapes, we propose and model a “tile”-shaped cross-section for the separator walls. This design features a wavy, corrugated structure. The phase-field simulation demonstrates its superior performance. Compared to a standard rectangular-section separator, the tile-shaped design reduces the maximum dendrite height by an additional 12.75%. The mechanism involves enhanced ion flux regulation: the concave regions of the tile structure act as energy sinks, slowing down dendrite advancement, while the convex regions deflect the growth direction laterally and downward, away from the direct vertical path toward the cathode. This continuously redirects the dendrite growth energy, making vertical penetration significantly more difficult and enhancing the safety of the solid-state battery.
Conclusion and Perspectives for the Solid-State Battery
This phase-field modeling study underscores the profound impact that microstructural engineering of internal components can have on mitigating the dendrite challenge in solid-state batteries. The key findings are:
- Nanoskeleton Uniformity is Critical: A nanoskeleton with a uniformly rough surface can significantly suppress primary and secondary dendrite growth by homogenizing lithium-ion flux and providing guided deposition pathways. Non-uniform roughness deteriorates performance, potentially accelerating failure.
- Artificial Separator Requires Co-optimization: The inhibitory effect of a porous artificial separator is maximized by concurrently reducing pore size and increasing thickness. A single-parameter adjustment offers limited benefits.
- Morphological Innovation Yields Gains: Advanced separator geometries, such as the modeled tile-shaped cross-section, can outperform traditional designs by dynamically regulating lithium-ion transport and dissipating dendrite growth energy more effectively.
The phase-field method, with its ability to couple multiple physical fields, serves as an indispensable virtual laboratory for screening and optimizing these complex morphologies before costly experimental fabrication. Future work for the solid-state battery community should focus on exploring more bio-inspired and fractal geometries for both nanoskeletons and separators, investigating the dynamic evolution of these structures during cycling, and integrating these localized morphological optimizations into full-cell models to predict overall solid-state battery performance and longevity.