## Finite-size ions in PB approach (12th of August 2013)

Poisson-Boltzmann (PB) approach is the simplest description of charge interactions in solutions (e.g. of interactions between
charged proteins in solutions of NaCl salt, which dissociates to Na^{+} i Cl^{-} ions). It combines two very
famous equations: Poisson's and Maxwell-Boltzmann's. Poisson's equation is a concise formulation of electrostatics, and
Maxwell-Boltzmann's equation (i.e. distribution) is a foundation of a classical statistical mechanics.

However, a usual combination of these two equations produces a PB equation which has a drawback as it does not account for
finite (and different) sizes of anions and cations (e.g.. Na^{+} i Cl^{-}, depending on the salt). In a
>> paper which I shortly present in this post, Marko Popović
and I tried to modify a standard PB approach so to approximately include the facts *(i)* that the mobile ions in the solution have
finite sizes and therefore prevent other ions from approaching the site they occupy, and *(ii)* that their sizes are
*not the same*. The paper was published on 8th of August in Physical Review E and you can
>> download it HERE.

For some papers, the illustration is secondary. The only "illustration" Marko and I made for the paper is shown in the image
above, and the paper could go on without it. Sometimes, the only "illustration" a paper needs is mathematics. The equation
(6) from our paper states:

Marko Popović leaves for PhD study in Dresden next month.

Last updated on 12th of August 2013.