Dec 9th, 2014 – Nir Gavish

Title: Generalized Poisson Boltzmann and Differential Capacitance data: an inverse problem


The contact between a charged object (metal surface, macromolecule, membrane, etc.) and an electrolyte solution results in the rearrangement of ion distribution near the interface and formation of the so-called electrical double layer.  One of the important experimentally available quantities for characterising the structure of electrolyte solutions near such interfaces are differential capacitance measurements.  From a mathematical point of view, the double layer structure is commonly modelled by the Poisson-Boltzmann equation and generalizations of it.

In this work, we conduct a systematic study of the differential capacitance data.  In particular, we focus on the inverse problem: Given differential capacitance data, we ask whether it is possible to derive a generalized Poisson-Boltzmann model which gives rise to the given data.  We show that such models do exist, characterise their variational action in terms of a PDE, and provide a method for solving the PDE and deriving the appropriate generalized Poisson-Boltzmann model.  This method does not yield a unique model, and so we find that a wide class of models can give rise to the same differential capacitance data.

Using our method, we derive generalized Poisson-Boltzmann models from differential capacitance data coming from either theoretical models or experimental measurements.  In particular, derive novel models which accurately recover experimental data.

This is a joint work with Keith Promislow.