A full-atom multiscale modelling for sodium chloride diffusion in anion exchange membranes

A novel full-atom multiscale method, combining different computational approaches and aimed to describe diffusion of multiple ions in anion exchange membranes (AEM), is presented. The method is used to evaluate diffusion of chloride and sodium ions in polysulfone tetramethylammonium (PSU-TMA) membranes, with particular attention to the co-ion diffusion. The hydration of the PSU-TMA is computed as a function of the membrane ionic exchange capacity via Density Functional Theory (DFT) and used for carrying out molecular dynamics simulations (MD). An upgraded DFT-based approach is proposed to obtain the atoms’ charges used in the force field for the MD simulations. Three approaches have been adopted to evaluate the chloride self-diffusion coefficients, the first based on the Mean Square Displacement, while the others use two analytical models: Mackie-Meares and Yasuda-Lamaze-Ikenberry. For membranes with ideal selectivity, the computed chloride diffusion coefficients result in good agreement with literature values, highlighting the critical role of the water content on the diffusion of ions as the water uptake decreases. The full-atom modelling allows to reproduce the transition from normal to anomalous diffusion when decreasing the water volume fraction as expected experimentally. Moreover, to simulate real conditions, counter-ion and co-ion concentrations inside the AEM have been determined using the Donnan-Manning model. In this case, four approaches have been tested to balance the excess of charge obtained from the DFT calculations, finding, for one of them, a good agreement between theoretical and experimental diffusion coefficients. Finally, the calculation of fundamental quantities, necessary for the modelling of the sodium chloride diffusion, without resorting to adjustable parameters represents the guideline of the proposed methodology.