New Solution for Counterion Condensation Theory
Abstract
We found a new, exact solution of the nonlinear Poisson-Boltzmann equation in cylindrical geometry describing the counter ion condensation on a strongly charged polymer. In contrast to the Manning condensation theory, the condensation occurs at the critical line charge density λ = 3/2, which is 3/2 times larger than in Manning's theory. In Manning theory the condensation occurs in cylindrical cell geometry when electrosasatic energy gain of bringing the counter ion to the surface 2λ logρ becomes comparable with the 2D entropy loss of the couter ions 2logρ. Our result describes condensation in a dilute solutions of polyelectrolytes. In this case the couter ion should be brought from the 3D space and the entropy loss is 3/2 times larger than in Manning' case. Therefore the onset of condensation occuers at higher chagre density.
- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- March 1997
- Bibcode:
- 1997APS..MAR.K3231L