Quantitative analysis of ion crossover in bacterial cellulose membranes separating diffusion behaviour from membrane thickness effects

Ion-selective membranes are crucial in bioelectrochemical systems (BES), such as microbial fuel cells (MFCs), microbial electrolysis cells (MECs), and microbial electrosynthesis systems (MES), where they separate anodic and cathodic compartments while enabling ionic transport. However, undesired crossover of other cations can affect membrane selectivity, pH stability, and overall electrochemical efficiency. In this study, cation transport across bacterial cellulose (BC)-based membranes with different structures, thicknesses, and compositions (stacked BC, dispersion-cast BC (dBC), and BC–graphene oxide (dBC-GO) composites) was systematically investigated and compared with Nafion 117. Ion crossover experiments were analyzed using numerical solutions of Fick's law to determine effective apparent diffusion coefficients ( D g ) and to evaluate the combined influence of membrane structure and thickness on ion transport behaviour. For all membranes, D g values were several orders of magnitude lower than D g in bulk water, indicating that ion transport is strongly influenced by ion–membrane interactions, while membrane microstructure governs the effective diffusion pathways. Monovalent ions diffused faster than divalent cations, highlighting the influence of ion valence and adsorption phenomena. Although apparent crossover rates decreased with increasing membrane thickness, thickness-normalized analysis revealed distinct transport behaviours: dBC membranes exhibited the highest apparent diffusion coefficients, whereas Nafion 117 showed the lowest. Modelling was further used to estimate membrane thicknesses required to limit cumulative crossover of the fastest ion to approximately 1% after 6 h. The results indicate that ion crossover can be effectively regulated by membrane thickness, providing a quantitative framework for designing cellulose-based membranes for BES and related electrochemical systems.