Models of Proton Transport at Mesoscopic Scale

There are different ways to depict membrane operation based on proton transport in it. The oversimplified scenario is to consider the polymer as an inert porous container for the water domains, which form the active phase for proton transport. In this scenario, proton transport is primarily treated as a phenomenon in bulk water [1,8,90], perturbed to some degree by the presence of the charged pore walls, whose influence becomes increasingly important the narrower are the aqueous channels. At the moleciflar scale, transport of excess protons in liquid water is extensively studied. Expanding on this view of molecular mechanisms, straightforward geometric approaches, familiar from the theory of rigid porous media or composites [ 104,105], coifld be applied to relate the water distribution in membranes to its macroscopic transport properties. Relevant correlations between pore size distributions, pore space connectivity, pore space evolution upon water uptake and proton conductivities in PEMs were studied in [22,107]. Random network models and simpler models of the porous structure were employed. 

At the molecular level, refined approaches could involve explicit correlations between sidechain fluctuations and proton mobility. More recently, molecular dynamics simulations, utilizing force-field parameterizations [60, 62-64,83,84,109] or ab initio calculations based on a quantum mechanical description, were employed in order to study such correlations and exam- 

In real membranes, transport properties of protons and water molecules can be obtained by an effective interpolation between the bulk and the interfacial mechanisms, as explored in [82]. Subsequently, we will consider theoretical approaches along this general scheme, increasing in complexity and covering scales from molecular to macroscopic. 

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