From Meso-to-Macroscale Effective Transport Properties

From Meso-to-Macroscale Effective Transport Properties 

Understanding the effects of membrane structure, water content and water distribution on proton conductivity has to invoke additional theoretical tools. They have to bridge many length scales from molecular environments to random heterogeneous structure at macroscale. This involves phenomenological concepts and homogenization methods in order to average over microscopic details [65]. 

The conductivity of a single pore is determined by the charge density of protons p and the proton mobiUty p,. As discussed above, p and are fimctions of the position within the pore. In highly hydrated PEMs, p, is highest in the bulk and smallest close to the surface. The proton distribution from simple Poisson-Boltzmann theory decreases monotonously from the interface towards the pore center. Refined calculations of the proton distribution take into accoimt the finite size of protonated complexes and a repulsive part of the intermolecular potential near the pore surface. This modified PB approach predicts an excluded region for the hydrated protons close to the surface (mainly related to the finite size of proton complexes). A maximum in exists at about 1.5 A away from the interface. From this position p decreases continuously towards the center of the pore. This density profile is in reasonable agreement with results from MD simulations [84]. Further possible refinements, such as incorporating variations of dielectric constant with position within the pore and with pore size, were not included in these calculations. 

In the absence of correlation effects in proton transport, the conductance of a single membrane pore can be calculated straightforwardly using the distributions of proton density and mobilities. The conductance of a slab-like pore is given by 

The mobility in the pore includes molecular mechanisms of proton transport in bulk water and along the array of charged surface groups. An idealized two-state approach based on this distinction was considered in [82]. This simple model can reproduce a continuous transition from surface-like to 

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