Gibbs' dividing surface between a fixed-charge membrane and an electrolyte solution. Application to electrokinetic phenomena in charged pores

The Gibbs model for the boundary between two phases consists of replacing the finite interfacial region, where the properties of the system change gradually, by a dividing surface which acts as a third phase of zero volume in which some magnitudes change abruptly. This thermodynamic concept was recently applied to a planar interface between a fixed charge membrane and an electrolyte solution.(1) The continuous decrease of counterions with the distance from the charged surface is replaced by a step function, so that the diffuse double layer is ideally represented by a charged region depleted of all co-ions. Here the cylindrical geometry is analyzed, and the planar case is revisited by proposing a slightly different step function for ion concentration. By starting from Boltzmann distributions of ions in solution, simple formulas are obtained for the distance between the charged interface and the dividing surface in both geometries. For the purpose of applying this model to charged, microporous membranes, expressions are given for some of the coefficients LU Of the Onsager phenomenological relations in a model membrane composed of identical, parallel, and cylindrical pores. A comparison is made between the Values for conductance and streaming potential in a homogeneously charged pore predicted by the Gibbs model and the classical space charge model. Despite the obvious simplifications inherent to the model, good agreement is found for conductivity, while only qualitative agreement is found between streaming potential predictions.