Speaker : Professor Tai-Chia Lin (National Taiwan University)
Title : New Poisson-Boltzmann Type Equations
Time : 2012-11-08 (Thu) 15:00 - 16:00
Place : Lecture Hall, Inst. of Mathematics
Abstract: The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe electrostatic interactions between molecules in ionic solutions (electrolytes) and have many applications in the fields of chemical physics and biophysics. As the PB theory was useful as a characteristic model, especially for diluted solutions (without the boundary effects), over the years, there had been many work comparing both analytical and numerical solutions of the PB equation with experimental data. However, serious discrepancies had been found in these comparisons, especially those involving multivalent ions. This motivates us to study new types of PB equations. In this lecture, two types of PB equations will be introduced. One is of differential-integral equations derived from the steady state of Poisson-Nernst-Planck equations being a standard model of ion transport. The other comes from the energy functional with the repulsive part of Lennard-Jones potential to describe ion size effects. Both analytical and numerical results related to Debye and Stern layers will be presented.