Fate of the Coulomb singularity in nonlinear Poisson-Boltzmann theory: The point charge as an electrically invisible object
Abstract
An absolute upper bound of Debye-Hückel form, U(rs)e-rr, is derived for solutions to the nonlinear, spherical, radial Poisson-Boltzmann equation for the problem of an isolated charged sphere, dimensionless radius rs, in an infinite volume of electrolyte. For rs<<1, U(rs)~rsln(1rs). Thus, as rs-->0, U(rs)-->0 and the shielding cloud around a point charge shrinks to zero radius. From any finite distance away, however small, the point charge is electrically invisible.
- Publication:
-
Physical Review A
- Pub Date:
- January 1980
- DOI:
- 10.1103/PhysRevA.21.362
- Bibcode:
- 1980PhRvA..21..362L