Spatially dependent dielectric coefficient

Before we discuss the above results, we note that for a spatially dependent dielectric coefficient, a good approximation can be found by simply replacing the exponential terms in Eq. [22] or [23] with... 

Going beyond an atomistic description of the aqueous phase and the membrane, Paddison and coworkers [79-88] employed statistical mechanical models, incorporating solvent friction and spatially dependent dielectric properties, to the calculation of the proton diffusion coefficient in Nation and PEEKK membrane pores. They concluded from their studies that, in accordance with NMR based evidence [50], the mechanism of proton transport is more vehicular (classical ion transport) in the vicinity of the pore surface and more Grotthus-like in the center. 

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