THE POISSON-BOLTZMANN EQUATION FOR AQUEOUS-SOLUTIONS OF STRONG POLYELECTROLYTES WITHOUT ADDED SALT - THE CELL MODEL REVISITED

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 u at finite dilutions is discussed in terms of its dependence on the polyelectrolyte equivalent concentration C(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 --> 0 counterion condensation is expected. For more realistic nonzero values of a, the reduced potential u 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 a2C(e). The value u(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 a2C(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 a2Ce is. This fraction of counterions (the "associated" 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, u < 1 (the "free" counterions).