Intrinsic relationships between proton conductivity and nanopore size and functionalization

• We model water and charge transport in nanostructured aqueous systems.
• Charge transport is described by acidity, confinement and connectivity.
• There is an optimal surface coverage of acid groups for a given pore radius.
• There remains room for improvement in experimentally synthesized membranes.

A fundamental understanding of the relationship between the nanoscale structure of proton exchange membranes (PEMs) and their proton conductivity would be exceedingly useful in optimizing existing and designing new materials. In this work, a set of structural descriptors, accounting for nanopore size, functionalization and connectivity are employed to predict proton conductivities in PEMs. The model reproduces experimentally determined conductivities in two PEMs. The model is applied to water-filled cylindrical nanopores functionalized on their interior surface with acid groups. It is demonstrated that for cylindrical nanopores of a given radius there is an optimal surface coverage of acid groups. The optimum can be sharply peaked, indicating that non-optimal surface coverages (either too low or too high) drastically reduce the conductivity of the pore. The theoretical maximum conductivity through a cylindrical nanopore is calculated to be about 0.70 S/cm at 300 K.

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