Condensed Matter


Poisson Boltzmann Equation Cannot be Solved Using Dirichlet Boundary Condition

Authors: Rajib Chakraborty

The Poisson-Boltzmann equation (PBE) gives us very simple formula for charge density distribution $(\rho_e)$ within ionic solutions. PBE is widely solved by specifying values to electrostatic potential ($\psi$) at different boundaries; this type of boundary condition (BC) is known as Dirichlet condition (DC). Here we show that DC cannot be used to solve the PBE, because it leads to unphysical consequences. For example, when we change the reference for $\psi$, the functional forms of $\psi$ and $\rho_e$ change in non-trivial ways i.e. it changes the physics, which is not acceptable. Our result should have far reaching effects on many branches of physical, chemical and biological sciences.

Comments: 2 Pages.

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Submission history

[v1] 2017-02-09 11:33:29

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