PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Hope Shaffer, Chun Liu, Fei Wang.

Title:Generalized Poisson Boltzmann and Differential Capacitance data: an inverse problem
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Nir Gavish, Technion – Israel Institute of Technology (Host: C Liu)
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 prescribed 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.

Room Reservation Information

Room Number:MB106
Date:03 / 02 / 2015
Time:02:30pm - 03:30pm