Multiscale modeling of transport phenomena in batteries represents a critical approach to understanding and optimizing the complex interplay of ion and electron movement across different components. This methodology integrates various computational techniques to bridge the gap between atomic-scale interactions and macroscopic battery performance. By combining density functional theory (DFT), molecular dynamics (MD), and continuum-scale simulations, researchers can accurately predict transport properties and identify bottlenecks in lithium-ion and solid-state battery systems.

At the atomic scale, DFT calculations provide insights into the electronic structure of electrode and electrolyte materials. These quantum mechanical simulations predict key properties such as lithium-ion migration barriers, electronic conductivity, and interfacial stability. For example, DFT has been used to evaluate the activation energy for lithium hopping in common cathode materials like lithium cobalt oxide (LiCoO₂), revealing values in the range of 0.2 to 0.5 eV depending on crystallographic direction. Similarly, DFT studies of solid electrolytes like lithium lanthanum zirconium oxide (LLZO) have identified preferential conduction pathways through specific lattice sites.

Molecular dynamics simulations extend these insights by modeling the collective motion of ions and molecules over longer timescales and larger systems. Classical MD with empirically parameterized force fields can simulate lithium-ion diffusion in liquid electrolytes, capturing the solvation shell dynamics and ion pairing effects. All-atom MD of common carbonate-based electrolytes has shown lithium-ion diffusivities on the order of 10⁻¹⁰ to 10⁻⁹ m²/s at room temperature, consistent with experimental measurements. For solid-state systems, reactive force field MD enables the study of grain boundary effects on ion transport, where reduced conductivity by one to two orders of magnitude has been observed compared to bulk crystalline regions.

The mesoscale bridges atomistic and continuum descriptions by addressing phenomena such as phase separation in electrodes, pore-scale transport in porous electrodes, and the formation of solid-electrolyte interphases (SEI). Kinetic Monte Carlo methods simulate lithium insertion and extraction processes in electrode particles, accounting for site-blocking effects and surface reactions. Phase-field models capture the evolution of lithium concentration gradients and associated stress development during cycling, which is particularly important for high-capacity electrodes like silicon that experience large volume changes.

Continuum-scale models employ partial differential equations to describe mass, charge, and energy transport across full cell geometries. The Newman-style porous electrode theory remains widely used, solving coupled equations for lithium conservation in solid and liquid phases, charge conservation in electrodes and electrolyte, and energy balance for thermal effects. These models require effective transport properties as inputs, which are derived from lower-scale simulations through upscaling techniques.

Upscaling represents a crucial step in multiscale modeling, where microscopic heterogeneity is homogenized into effective macroscopic properties. Mathematical homogenization methods, volume averaging, and renormalization group approaches are commonly employed. For example, the effective ionic conductivity of a composite cathode containing active material, binder, and conductive additives is determined by considering percolation pathways and interfacial resistances. Similarly, the tortuosity factor of porous electrodes, typically ranging from 2 to 6 for commercial designs, is extracted from reconstructed microstructures or stochastic models.

In solid-state batteries, multiscale modeling faces additional challenges due to the complex interplay between bulk, grain boundary, and interfacial transport. First-principles calculations predict bulk ionic conductivities for promising solid electrolytes like lithium thiophosphates (10⁻³ to 10⁻² S/cm), while MD simulations reveal grain boundary resistances that can dominate overall cell impedance. Continuum models must incorporate these interfacial effects through effective medium approximations or explicit boundary conditions.

Experimental validation of multiscale transport models employs various characterization techniques. Impedance spectroscopy measures bulk and interfacial resistances, with typical solid-state electrolyte interfacial resistances ranging from 10 to 100 Ω·cm². Neutron and X-ray diffraction provide lithium concentration profiles during operation, while tomography reconstructs 3D microstructures for direct comparison with simulated morphologies. Advanced techniques like pulsed field gradient NMR directly measure diffusion coefficients, with values for liquid electrolytes typically agreeing within 20% of MD predictions.

Recent advances in multiscale modeling focus on coupling between physical phenomena. Thermo-electrochemical models incorporate heat generation from joule heating and entropy changes, important for predicting thermal runaway. Mechanical-electrochemical models address stress-coupled diffusion, particularly relevant for silicon anodes where stresses can exceed 1 GPa during lithiation. Machine learning accelerates these simulations by developing surrogate models trained on high-fidelity data, enabling rapid exploration of material combinations and cell designs.

The predictive power of multiscale transport modeling has guided several battery improvements. Simulations identified optimal porosity gradients in thick electrodes to balance energy density and rate capability. Interface engineering strategies, such as buffer layers between solid electrolytes and electrodes, emerged from atomic-scale studies of reactivity. Electrolyte formulations have been optimized by screening solvent mixtures through combined DFT and MD approaches before experimental testing.

Challenges remain in fully capturing the dynamic evolution of battery materials during operation. SEI growth, electrode cracking, and interface degradation require coupled chemical-mechanical models across scales. The integration of manufacturing process simulations with transport models will enable direct links between processing conditions and performance. As computational power increases and methods improve, multiscale modeling will play an even greater role in accelerating battery development cycles and enabling next-generation energy storage systems.

Future directions include the development of universal interatomic potentials for more accurate MD simulations, improved coarse-graining techniques for mesoscale models, and enhanced data transfer protocols between simulation domains. The increasing availability of high-performance computing resources allows for larger-scale simulations with atomistic detail, while machine learning approaches help overcome the timescale limitations of traditional methods. These advances will further establish multiscale modeling as an indispensable tool for understanding and optimizing battery transport phenomena.