**Tuning the selective permeability of polydisperse polymer networks**

WK Kim and R Chudoba and S Milster and R Roa and M Kanduc and J Dzubiella, SOFT MATTER, 16, 8144-8154 (2020).

DOI: 10.1039/d0sm01083a

We study the permeability and selectivity ('permselectivity') of model membranes made of polydisperse polymer networks for molecular penetrant transport, using coarse-grained, implicit-solvent computer simulations. In our work, permeability P is determined on the linear-response level using the solutiondiffusion model, P = KDin, i.e., by calculating the equilibrium penetrant partition ratio K and penetrant diffusivity D-in inside the membrane. We vary two key parameters, namely the network- network interaction, which controls the degree of swelling and collapse of the network, and the network-penetrant interaction, which tunes the selective penetrant uptake and microscopic energy landscape for diffusive transport. We find that the partitioning K covers four orders of magnitude and is a non-monotonic function of the parameters, well interpreted by a second-order virial expansion of the free energy of transferring one penetrant from a reservoir into the membrane. Moreover, we find that the penetrant diffusivity D-in in the polydisperse networks, in contrast to highly ordered membrane structures, exhibits relatively simple exponential decays. We propose a semi-empirical scaling law for the penetrant diffusion that describes the simulation data for a wide range of densities and interaction parameters. The resulting permeability P turns out to follow the qualitative behavior (including maximization and minimization) of partitioning. However, partitioning and diffusion are typically anti-correlated, yielding large quantitative cancellations, controlled and fine-tuned by the network density and interactions, as rationalized by our scaling laws. We finally demonstrate that even small changes of network-penetrant interactions, e.g., by half a k(B)T, modify the permselectivity by almost one order of magnitude.

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