Breaking the trade-off between lithium purity and lithium recovery: A comprehensive mathematical modeling based on membrane structure-property-performance relationships

The application of nanofiltration (NF) membranes for resource recovery, particularly lithium (Li) extraction from high magnesium (Mg) brines, is a rapidly growing research area. However, the trade-off between high Li⁺ purity and recovery remains challenging. In our study, we extend the widely adopted Donnan Steric Pore Model with Dielectric Exclusion (DSPM-DE) to analyze membrane structure-property-performance relationships at the process scale. For the first time, we quantify how membrane intrinsic parameters (e.g., pore size, effective thickness, and charge density) affect Li⁺ purity and recovery under module-scale processes. Under this framework, we demonstrate that electrically neutral and positively charged membranes outperform negatively charged membranes, albeit at the cost of slightly higher required hydraulic pressure. Notably, positively charged membranes with smaller pore size yet high water permeance (40-80 L m^-2 h^-1 bar^-1) are preferred, which could simultaneously achieve excellent Li⁺ purity (∼98 %) and high Li⁺ recovery (∼93 %) in the single-pass process, effectively overcoming the purity-recovery trade-off correlation. We further demonstrate that negative Li⁺ rejection plays a crucial role in overcoming the trade-off correlation by significantly increasing Li⁺ recovery. Nevertheless, poor system flux distribution is inadvertently observed in the regions where strong negative rejection occurs, highlighting the need for careful consideration of the balance between system stability and lithium extraction performances. Our study identifies critical membrane parameters for achieving optimal lithium extraction performance at the process scale, offering fundamental insights for designing high-performance membranes for resource recovery.