Structure Matters: A Scale-Resolved Numerical Operando Approach for Lithium-Sulfur Batteries

TL;DR

The paper tackles the challenge of predicting how porous cathode structure governs rate performance in Lithium–Sulfur Batteries by introducing a scale-resolved numerical operando framework. It combines a 3D scale-resolved model with a homogenized 1D counterpart through a rigorous spatial coarse-graining approach, underpinned by a postulated microscopic continuum model and a scaling analysis that yields Damköhler numbers $A$, $B$, and $C$. The methodology features a DG spatial discretization, a suite of time-stepping strategies, and an HPC-enabled solver to enable whole-discharge simulations; it demonstrates that low-current behavior can be calibrated with 1D models while high-current performance requires 3D scale-resolved insights to capture local effects. The results show good agreement between 1D and 3D models at low currents, but reveal pronounced local gradients and phase distributions in the cathode at higher discharge rates, validating the core claim that Structure matters for performance. The work advances predictive capability for LSB cathode design and highlights pathways for further methodological enhancements and adjoint-based calibration to enable optimization of aerospace-relevant energy-dense batteries.

Abstract

Lithium-Sulfur batteries (LSBs) are believed to have a high potential for aerospace applications due to their high gravimetric energy density. However, despite decades of research and advances, they still suffer from poor rate capability and low power output, eventually preventing their practical implementation. One particular aspect we want to shed light on is the influence of the porous cathode structure on the rate performance during discharge. Therefore, we present a scale-resolved simulation methodology that aims to provide structural insights into the electrochemical cell behavior that are experimentally hardly accessible even for modern operando methods. Our numerical operando approach employs high-performance computing (HPC) and is based on a coarse-grained continuum model. The latter is spatially discretized with a Discontinuous Galerkin (DG) method and advanced in time by an adaptive controller. The models and methods as well as HPC aspects of our toolbox will be critically discussed, finally showcasing the capabilities of our workflow to improve LSBs.

Figures (16)

• Figure 1: Illustrative perspective on the spatial modelling: (a) Schematic of the LSB including the modelling domain. (b) Detailed sketch of the modelling domain. (c) Porous cathode model created with the open-source tool Blender and the corresponding SEM/TEM images of the dominant carbon support material Printex XE2-B at different spatial resolutions. The SEM/TEM images were provided by Fraunhofer IWS in Dresden.
• Figure 2: Reaction mechanisms of LSBs with moderately solvating electrolytes (MSE). (a) Detailed Chemistry as reported in Liu_2021. (b) Reduced Chemistry usually employed in LSB models. (c) Tradeoff Chemistry developed and used within this work.
• Figure 3: Illustration on spatial coarse-graining in a porous multiphase system with liquid-solid-interface ($L/S$). The arbitrary coarse-graining scale $l$ is highlighted in red.
• Figure 4: Adaptive time stepping strategy based on a naive feedback-controller with respect to successful convergence of the solver.
• Figure 5: Adaptive time stepping strategy with the H211b controller using error control on the time step width $\Delta t$.