Modelling multicomponent ion transport in layer-by-layer modified cation exchange membranes for selective lithium recovery in electrodialysis

Selective lithium recovery from complex systems remains challenging due to high Mg 2+ /Li + ratios and competing monovalent cations (Na + , K + ), particularly in electrodialysis processes. Layer-by-layer (LbL) modification of cation exchange membranes (CEMs) has emerged as an effective strategy to enhance Li + /Mg 2+ selectivity; however, the mechanistic understanding of ion transport in LbL-modified CEMs in multicomponent conditions remains limited. Existing ion transport modelling studies are largely restricted to single or binary electrolyte systems or lack a unified framework linking membrane multilayer properties and operating conditions to ion transport and selectivity. To address these gaps, a one-dimensional Nernst–Planck–Poisson (NPP) model was developed to investigate ion transport in LbL-modified CEMs in multicomponent systems. The model investigated the effect of multilayer thickness, fixed charge density, bilayer number, feed concentration, and applied voltage on separation performance. The results reveal that as voltage increases, the ion transport transitions from substrate membrane-controlled to multilayer-mediated divalent ion exclusion, with monovalent/divalent selectivity increasing until it reaches a plateau near the limiting current density. Moreover, ion competition strongly affects performance, with multi-ionic systems showing higher ion fluxes and limiting current densities but lower Li + /Mg 2+ permselectivity than binary systems. A multilayer thickness of 50–100 nm, fixed charge density of at least 1000 mol m −3 , and bilayer number up to 5.5 provide a favourable balance between Li + /Mg 2+ permselectivity and ion flux while minimising unnecessary transport resistance. Overall, the study establishes a predictive structure–transport–selectivity framework for the design and optimisation of LbL-modified CEMs for lithium recovery in electrodialysis.