Electrochemical modeling of solid-state battery interfaces provides critical insights into the complex phenomena governing ion transport, interfacial stability, and mechanical behavior in next-generation energy storage systems. The solid-state architecture introduces unique challenges compared to conventional liquid electrolyte systems, particularly at the electrode-electrolyte interface and grain boundaries within the ceramic or polymer electrolyte. Three primary challenges dominate the modeling efforts: interfacial resistance, dendrite growth, and contact mechanics. These factors collectively determine the performance, safety, and longevity of solid-state batteries.

Interfacial resistance arises from the imperfect contact between solid materials, where lattice mismatches, chemical incompatibilities, and space charge layers impede ion transport. The governing equations for ion transport across these interfaces combine Poisson-Nernst-Planck theory with Butler-Volmer kinetics, modified to account for solid-state specific phenomena. The Poisson equation describes the electric potential distribution, while the Nernst-Planck equation governs ion flux under concentration gradients and electric fields. At the interface, the Butler-Volmer equation is adapted to include the energy barriers associated with ion hopping between dissimilar crystal structures. The resulting interfacial resistance is often quantified through the area-specific resistance (ASR), which can range from 10 to 1000 ohm-cm² depending on material pairing and processing conditions.

Dendrite growth in solid-state systems follows different mechanisms compared to liquid electrolytes, with mechanical penetration through the solid electrolyte becoming a dominant failure mode. Models incorporate stress-coupled electrodeposition, where the overpotential drives both ionic current and mechanical deformation. The governing equations combine electrochemical phase-field models with fracture mechanics. The phase-field approach tracks the moving boundary between the metal electrode and electrolyte, while the stress distribution is computed using linear elasticity theory with eigenstrains representing deposition-induced expansion. Critical parameters include the shear modulus of the electrolyte, interfacial energy, and exchange current density. Simulations show that dendrite propagation speeds can vary from 0.1 to 10 µm/s under typical operating conditions, with ceramic electrolytes exhibiting higher resistance to penetration than polymer electrolytes.

Contact mechanics play a pivotal role in maintaining interfacial integrity during cycling. The models must account for elastic and plastic deformation at the electrode-electrolyte interface, as well as the evolution of contact area under stack pressure. Hertzian contact theory provides the foundation, augmented with electrochemical creep and diffusion terms. The governing equations relate the local pressure to the interfacial gap distance, which in turn affects the local current density distribution. A key finding from these models is the existence of a critical stack pressure, typically in the range of 1-10 MPa, below which interfacial delamination occurs and performance degrades rapidly.

Material selection benefits significantly from electrochemical modeling by identifying compatibility metrics for electrode-electrolyte pairs. The chemical potential mismatch between materials can be quantified through density functional theory (DFT) calculations of interfacial energies, which are then fed into larger-scale continuum models. Interface engineering strategies such as buffer layers or graded compositions can be virtually tested before experimental validation. For example, models predict that a 5-10 nm lithium lanthanum zirconium oxide (LLZO) interlayer between a lithium metal anode and sulfide electrolyte can reduce interfacial resistance by up to 80% while suppressing dendrite nucleation.

Grain boundary effects in polycrystalline solid electrolytes require special consideration in the models. The space charge layer at grain boundaries creates local potential variations that divert ion transport paths. The governing equations here extend the Mott-Schottky theory to include multiple mobile species and anisotropic conductivity. Simulations reveal that grain boundary resistance can contribute 30-50% of the total cell resistance in oxide electrolytes, while in sulfides the effect is less pronounced due to their softer lattice structures.

The models employ various numerical techniques to handle the multiphysics nature of the problem. Finite element methods dominate for continuum-scale simulations, while molecular dynamics and kinetic Monte Carlo approaches address atomistic processes. Recent advances in computational power enable full 3D simulations of realistic microstructures, capturing the interplay between electrochemical, mechanical, and thermal effects. These simulations guide the design of optimized interface morphologies, such as fractal surfaces that maximize contact area without compromising mechanical stability.

Validation of the models relies on specialized experimental techniques including impedance spectroscopy with distribution of relaxation times analysis, in situ X-ray tomography for interface visualization, and atomic force microscopy for nanoscale mechanical measurements. The agreement between model predictions and experimental data has improved significantly in recent years, with discrepancies now typically below 20% for key parameters like interfacial resistance and critical current density.

Future developments in electrochemical modeling will focus on incorporating more sophisticated material behaviors such as viscoelasticity in polymer-ceramic composites, anisotropic ion transport in single-crystal electrolytes, and the effects of defects generated during cycling. The ultimate goal remains the creation of predictive tools that can accelerate the development of solid-state batteries with superior performance and reliability, moving beyond empirical optimization to rationally designed interfaces.