The Poisson-Boltzmann equation for aqueous solutions of stong polyelectrolytes without added salt: The cell model revisited
- Leiden Univ. (Netherlands)
An extensive discussion of the analytical solution for the Poisson-Boltzmann equation in cylindrical symmetry for strong polyelectrolytes in the cell model is presented. The reduced mean electrostatic potential {mu} at finite dilutions is discussed in terms of its dependence on the polyelectrolyte equivalent concentration C{sub e}, its charge density parameter {xi}, and the distance of closest approach a of the counterions to the polyion. It is shown that in the limit a {yields} 0 counterion condensation is expected. For more realistic nonzero values of a, the reduced potential {mu} at a given relative position r/R in the cell with radius R is practically independent of the linear charge density for {xi} > 2, but its value depends on the product a{sup 2}C{sub e}. The value {mu}(a) of the reduced potential near the surface of the polyion is {xi}-dependent, however, under the same conditions. A large fraction of all the counterions in the cell accumulate, on the average, in the neighborhood of the polyion, this fraction being larger the higher {xi} is and the lower the product a{sup 2}C{sub e} is. The fraction of ions accumulated between the polyion surface at a and a distance from the polyion axis equal to the screening length 1/{chi} is high, reaching values exceeding 80% and being higher the smaller a{sup 2}C{sub e} is. This fraction of counterions (the {open_quotes}associated{close_quotes} counterions) occupies a smaller part of the total cell volume than the counterions situated between 1/{chi} and R, which are characterized by a relatively low electrostatic interaction energy with the polyion, {mu} < 1 (the {open_quotes}free{close_quotes}counterions). 22 refs., 11 figs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 411965
- Journal Information:
- Journal of Physical Chemistry, Vol. 96, Issue 10; Other Information: PBD: 14 May 1992
- Country of Publication:
- United States
- Language:
- English
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