Anisotropic reaction–transport dynamics in Ti-substituted tunnel sodium cathodes: A three-dimensional critical-rate framework
Year: 2026
Type: article
Abstract: High-rate performance in anisotropic sodium-ion cathodes emerges from coupled particle-scale transport and reaction processes that cannot be represented adequately by a single effective diffusion coefficient. This study establishes a three-dimensional finite-element framework for rod-like Ti-substituted Na₄TiᵧMn₉₋ᵧO₁₈ tunnel cathodes by coupling tunnel-informed anisotropic Na transport, state-dependent diffusivity, concentration-dependent Butler–Volmer kinetics, finite electronic transport, and composition-dependent material properties. A model-derived critical rate, C crit , is introduced to identify the transition from quasi-uniform Na redistribution to transport-limited operation using the coupled evolution of concentration heterogeneity, reaction localization, and Na utilization. For the reference low-Ti particle, C crit was 2.35 ± 0.18C2.35\pm0.18 C. Increasing transport anisotropy raised C crit from 1.92 C at AD= 2–2.61 C at A D = 10, followed by a decline to 2.48 C at AD= 20, revealing diminishing benefit once transverse redistribution becomes limiting. Ti substitution produced a similarly non-monotonic response, with C crit increasing from 1.95 C for the Ti-free composition to 2.55 C at x Ti = 0.29, before decreasing to 1.88 C at x Ti = 0.56. Increasing particle aspect ratio from 3 to 8 reduced the threshold from 2.72 C to 1.86 C. Independent validation produced a GITT deviation of 9.7%, a rate-response NRMSE of 5.64%, and a MAPE of 6.38%. Notably, reaction localization emerged before pronounced loss of average Na utilization, identifying spatial reaction heterogeneity as an early marker of transport instability. The framework defines a composition–anisotropy–morphology design space for particle-scale control of high-rate sodium storage rather than a single optimum material configuration.
Source: Next Nanotechnology
Institutions: INTI International University, Al-Ahliyya Amman University, Jain University, Siksha O Anusandhan University, Institute of Medical Sciences and Sum Hospital, Sharda University, Chandigarh University, University of Education, The Women University Multan, Islamic Azad University, Tehran, Islamic Azad University Central Tehran Branch
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,280
OpenAlex ID: W7225329129