The coulomb condensate of the nonlinear Poisson-Boltzmann equation: A unified theory
Abstract
A general form of the one-dimensional nonlinear Poisson-Boltzmann (PB) equation for a simple electrolyte is studied, namely r-m(d/d r{ rmdψ (m)/dr} = sinh ψ (m), where r and ψ (m) are dimensionless distance and potential respectively, and m = 2, 1 and 0 correspond to the spherical, cylindrical and planar equations respectively. Since analytic solutions are not available for this general PB equation, its properties are here studied via suitable upper bounds, both relative and absolute, on its solutions. When the final results are specialized to the sphere ( m = 2) and cylinder ( m = 1) cases, there are recovered the σ-funcfion condensate theorems for a point charge and line charge respectively, previously proven by the author. Since the point-charge and line-charge condensates are hereby shown to have a common origin, it is suggested that they both be called simply "Coulomb condensates", in recognition of their physical origin.
- Publication:
-
Chemical Physics
- Pub Date:
- March 1982
- DOI:
- 10.1016/0301-0104(82)85064-7
- Bibcode:
- 1982CP.....65..143L