Simulating Proton Transport in a Pore

In order to simulate proton transport in a realistic pore model that more closely resembles the structure of polymer-water interfaces, one has to resort to classical or 

The mobility in the pore includes molecular mechanisms of proton transport in bulk water and along the array of charged surface groups. Coulomb barriers for proton mobility could arise in the vicinity of the anionic surface groups in the case of strong electrostatic pinning of protons. 

Near the surface, AG is dominated by the Coulomb energy profile and, therefore, it is approximately equal to the difference of the electrostatic potentials at the proton positions before and after the transfer. This difference depends strongly on the distance of the proton from the surface. Values of AG were found in the range of 0.5 eV. This value decreases, however, to the activation energy of proton transport in bulk water when the proton-surface separation exceeds 3 A (the thickness of one monolayer of water). Moreover, the electrostatic activation energy is a function of the separation between surface charges, which lies in the range of 7 to 15 A. 

A simple model of pore conductance, presented in Eikerhng et al. (2001) can reproduce a continuous transition from surface-like to bulk-like proton conductance upon increasing the water content in a pore. In calculations of pore eonductances, it was taken into account that the average separation between SOJ surface groups varies with pore size, and that the dielectric constant is a function of pore size. In nanopores, the reduced orientational flexibility in the stiffer hydrogen bond network offers more resistance to water reorganization resulting in a decrease of the dielectric constant (Booth, 1951 Kornyshev and Leikin, 1997 Paul and Paddison, 2001). 

The bulk conductance is mainly affected by the reduced concentration of protons (z), which decreases from pore surface to center. On the other hand, surface mobility of protons in the vicinity of the SOJ groups could be suppressed due to the existence of Coulomb barriers. A higher density of SO groups diminishes Coulomb barriers and, thus, facilitates proton motion near the surface. With increasing water content in the pore, the trade-off between proton concentration and mobility shifts in favor of the bulk conductance. 

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