Simon Daubner

Microstructure design of battery electrodes is key to enable fast charge and higher capacity in next-generation lithium and sodium ion batteries. While porous-electrode (Doyle–Fuller–Newman-type) models capture the coupled transport–reaction physics governing cell performance, they typically treat the electrode as a homogenized medium and encode microstructure only through fitted, scalar “effective” parameters (e.g., Bruggeman-type tortuosity). This assumption is often adequate for uniform electrodes, but it breaks down for modern architectures with graded porosity, binder migration, bimodal particle distributions, or bilayer designs, where transport resistance is heterogeneous and reaction rates localize, leading to non-uniform utilization and premature rate limitations.

Pattern-forming dynamics govern the behavior of many quantum, electrochemical, and soft-matter systems, yet learning and controlling the corresponding partial differential equation (PDE) models on realistic geometries remains challenging. In this work, we develop a unified, differentiable framework for free-energy-based PDEs that enables end-to-end parameter inference and optimal control directly on image-based domains. Starting from a variational description in terms of an energy or free energy functional, we combine PDE-based smoothing of segmented geometries, the smoothed boundary method, advanced integrators for stiff pattern-forming PDEs, and memory-efficient automatic differentiation implemented in JAX to construct scalable PDE solvers amenable to gradient-based optimization. We demonstrate the capabilities of this framework across four classes of applications: (1) learning Cahn-Hilliard and Allen-Cahn free energies and kinetic laws from noisy spatiotemporal data on complex battery electrode microstructures; (2) designing time-dependent wetting boundary conditions that steer phase boundaries to desired orientations; (3) optimizing spatially varying reaction rates, interpreted as surface coatings, to suppress phase separation in intercalation electrode models; and (4) computing time-dependent trapping potentials that transfer Bose-Einstein condensates between ground states of qualitatively different Gross-Pitaevskii potentials while minimizing excitations. Together, these results show that variational PDE models, when equipped with differentiable solvers on complex domains, provide a versatile substrate for data-driven discovery, design, and control of pattern-forming materials and quantum fluids, and they point toward tighter integration of physics-based PDE modeling with modern optimization and machine learning pipelines.

Materials science inherently spans disciplines: experimentalists use advanced microscopy to uncover micro- and nanoscale structure, while theorists and computational scientists develop models that link processing, structure, and properties. Bridging these domains is essential for inverse material design where you start from desired performance and work backwards to optimal microstructures and manufacturing routes. Integrating high-resolution imaging with predictive simulations and data-driven optimization accelerates discovery and deepens understanding of process-structure-property relationships. The differentiable physics framework evoxels is based on a fully Pythonic, unified voxel-based approach that integrates segmented 3D microscopy data, physical simulations, inverse modeling, and machine learning.

Optimal microstructure design of battery materials is critical to enhance the performance of batteries for tailored applications such as high power cells. Accurate simulation of the thermodynamics, transport, and electrochemical reaction kinetics in commonly used polycrystalline battery materials remains a challenge. Here, we combine state-of-the-art multiphase field modelling with the smoothed boundary method to accurately simulate complex battery microstructures and multiphase physics. The phase-field method is employed to parameterize complex open pore cathode microstructures and we present a formulation to impose galvanostatic charging conditions on the diffuse boundary representation. By extending the smoothed boundary method to the multiphase-field method, we build a simulation framework which is capable of simulating the coupled effects of intercalation, anisotropic diffusion, and phase transitions in arbitrary complex polycrystalline agglomerates. This method is directly compatible with voxel-based data, e.g., from X-ray tomography. The simulation framework is used to study the reversible phase transitions in Li _X NiO₂ in dense and nanoporous agglomerates. Based on the thermodynamic consistency of phase-field approaches with ab-initio simulations and the open circuit potential, we reconstruct the Gibbs free energies of four individual phases (H1, M, H2 and H3) from experimental cycling data. The results show remarkable agreement with previously published DFT results. From charge simulations, we discover a strong influence of particle morphology on the phase transition behaviour, in particular a shrinking core-like behaviour in dense polycrystalline structures and a particle-by-particle mosaic behavior in nanoporous samples. Overall, the proposed simulation framework enables the detailed study of phase transitions in intercalation materials to enhance microstructure design and fast charging protocols.

The present work addresses the simulation of pore emptying during the drying of battery electrodes. For this purpose, a model based on the multiphase-field (MPF) method is used, since it is an established approach for modeling and simulating multiphysical problems. A model based on phase fields is introduced that takes into account fluid flow, capillary effects, and wetting behavior, all of which play an important role in drying. In addition, the MPF method makes it possible to track the movement of the liquid-air interface without computationally expensive adaptive mesh generation. The presented model is used to investigate pore emptying in real hard carbon microstructures. For this purpose, the microstructures of real dried electrodes are used as input for the simulations. The simulations performed here demonstrate the importance of considering the resolved microstructural information compared to models that rely only on statistical geometry parameters such as pore size distributions. The influence of various parameters such as different microstructures, fluid viscosity, and the contact angle on pore emptying are investigated. In addition, this work establishes a correlation between the capillary number and the breakthrough time of the solvent as well as the height difference of the solvent front at the time of breakthrough. The results indicate that the drying process can be optimized by doping the particle surface, which changes the contact angle between the fluids and the particles.

The reliable computation of microstructure metrics such as specific surface area and tortuosity factors is key to bridge the gap between the battery microscale and fast, homogenized cell models. In this work, we present an approach to compute the surface area of phases based on pixelated image data which is both easy-to-implement and computationally efficient. The concept is inspired from the diffuse surface representation in phase-field methods. Subsequently, the approach is validated and compared with common python libraries on two benchmark cases and actual battery microstructure data. The results underline the reliability and fast computational performance of the approach. Furthermore, the concept of through-feature connectivity in pixelated image data is introduced and explored to quantify the reliability of tortuosity factor computations. Overall, this work enhances the computational tools to bridge the scale from battery microstructures to cell models and gives an overview of state-of-the-art methodology. The developed code is published to further accelerate the scientific progress in this field.

The research of new electrode materials such as sodium intercalation compounds is key to meet the challenges of future demands of sustainable energy storage. For these batteries, the intercalation behavior on the micro-scale is governed by a complex interplay of chemical, electrical and mechanical forces strongly influencing the overall cell performance. The multiphase-field method is a suitable tool to study these multi-physics and bridge the scale from ab-initio methods to the cell level. In this work, we follow a combined approach of experiments, density functional theory (DFT) calculations and multiphase-field simulations to predict thermodynamic and kinetic properties for the P2-type Na_XNi_1/3Mn_2/3O₂ sodium-ion cathode material. Experimentally, we obtain the thermodynamic potential and diffusion coefficients at various sodium contents using electrochemical techniques and discuss limitations of the experimentally applied methods. DFT is used to identify stable phases by calculating an energy hull curve. Then, the influence of long-range dispersion interactions and the exchange-correlation functional on the voltage curve is investigated by comparison with experimental results. Finally, multiphase-field simulations are performed based on inputs from experiments and DFT. The fitting of phase-specific chemical free energies from DFT calculations and experimental data is discussed. Our results highlight the thermodynamic consistency of all three approaches close to thermodynamic equilibrium. Furthermore, the phase-field method accurately describes the kinetics of the system including multiple phase transitions, by which we unravel the mechanism of the P2-O2 phase transition in a single crystal under the influence of intercalation reaction, bulk diffusion and elastic deformation. The model is able to predict the kinetic capacity loss depending on charging rate in agreement with C-rate experiments.

The research of new electrode materials such as sodium intercalation compounds is key to meet the challenges of future demands of sustainable energy storage. For these batteries, the intercalation behaviour on the micro-scale is governed by a complex interplay of chemical, electrical and mechanical forces strongly influencing the overall cell performance. The multiphase-field method is a suitable tool to study these multi-physics and bridge the scale from ab-initio methods to the cell level. In this work, we follow a combined approach of experiments, density functional theory (DFT) calculations and multiphase-field simulations to predict thermodynamic and kinetic properties for the P2-type Na_XNi_1/3Mn_2/3O₂ sodium-ion cathode material. Experimentally, we obtain the thermodynamic potential and diffusion coefficients at various sodium contents using electrochemical techniques and discuss limitations of the experimentally applied methods. DFT is used to identify stable phases by calculating an energy hull curve. Then, the influence of long-range dispersion interactions and the exchange-correlation functional on the voltage curve is investigated by comparison with experimental results. Finally, multiphase-field simulations are performed based on inputs from experiments and DFT. The fitting of phase-specific chemical free energies from DFT calculations and experimental data is discussed. Our results show that the single- and two-phase regions can be precisely reproduced at low C-rates close to thermodynamic equilibrium. Furthermore, the inclusion of a Butler-Volmer-type boundary condition allows to study the kinetics of the system as a competition of surface reaction, bulk diffusion and elastic deformation upon phase transformations. The model is able to predict kinetic capacity loss due to bulk diffusion limitation and the overpotential depending on charging rate.