Goldman-Type Transfer

The flux of an ion is directly proportional to the gradient of electrochanical potential and can be expressed by the Nemst-Planck equation  

If we assume as a first approximation that ( )(x) - ( ) (x) varies linearly across the interface, by introducing the constants y and y,  

Of course, the problem here is that the standard term( )f(x) = - j,f/Z F, which expresses the standard chemical potential, varies in a stepwise manner aaoss the mixed-solvent layer, say, 1 nm thick, whereas the potential drop varies in a monotonic way in the absence of specific adsorption across the two back-to-back diffuse layers, say 10 nm thick. As a result. Equation 1.30 is a very rough approximation, as soon as the Gibbs energy of transfer of the ion is larger than 5 kJ-mol.  

The second major assumption of this approach is to assume that the electrochemical mobility is constant throughout the interfacial region, in other words, that the viscous drag is the same in the two solvents, or that the diffusion coefficients are equal in the adjacent phases. Doing so, we have 

For small values of y. Equation 1.32 reduces to a simple diffusional flux equation  

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