Effect of the Particle Size Distribution on the Cahn-Hilliard Dynamics in a Cathode of Lithium-Ion Batteries

• Main Authors: Pavel L’vov, Renat Sibatov
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Batteries
• Subjects: lithium-ionbattery; Cahn-Hilliard equation; intercalation; particle size distribution
• Online Access: https://www.mdpi.com/2313-0105/6/2/29

The phase-field model based on the Cahn-Hilliard equation is employed to simulate lithium intercalation dynamics in a cathode with particles of distributed size. We start with a simplified phase-field model for a single submicron particle under galvanostatic condition. We observe two stages associated with single-phase and double-phase patterns typical for both charging and discharging processes. The single-phase stage takes approximately 10%–15% of the process and plays an important role in the intercalation dynamics. We establish the laws for speed of front propagation and evolution of single-phase concentration valid for different sizes of electrode particles and a wide range of temperatures and C-rates. The universality of these laws allows us to formulate the boundary condition with time-dependent flux density for the Cahn-Hilliard equation and analyze the phase-field intercalation in a heterogeneous cathode characterized by the particle size distribution.