Mathematical modeling of transport properties of proton-exchange membranes containing immobilized nanoparticles

•The model is based on effective medium approach.•Nanoparticles are localized in the meso- and macropores.•Conductivity increases when particles' double layer replaces electroneutral solution.•Effect of nanoparticles increases with dilution of the bathing solution.

Immobilization of inorganic nanoparticles (like ZrO2, TiO2 and SiO2) allows essential improvement of proton-exchange membrane properties pertinent for fuel cell applications. We propose a model for describing the effect of nanoparticles on the membrane electrical conductivity, diffusion permeability and permselectivity. The basis is the microheterogeneous two-phase model, which, in turn, is built on the irreversible thermodynamics and effective medium approach. The model considers the presence of three different domains, each of them characterized by their own parameters (such as the diffusion coefficients): charged gel, electrically neutral solution filling the intergel spaces, and nanoparticles. The nanoparticles are localized in the meso- and macropores, which form the intergel solution. The comparison of calculations with literature experimental data shows a good agreement. With increasing content of nanoparticles, the membrane conductivity passes through a maximum, while diffusion permeability decreases and permselectivity increases. The effect is due to the fact that the nanoparticle replaces the electrically neutral solution, which occupies the inner part of macro- and mesopores.

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