Polyelectrolytes : A Fuzzy Sphere Model

The expansion factor α of polyelectrolytes is calculated on the assumption that at least one member of each interacting pair of charged segments is immersed in a segment cloud having the average sement density, here given by a uniform distribution inside a sphere. The counterion concentration is assumed to be much larger inside the sphere than the byion concentration, and a binding parameter is introduced via an effective dielectric constant. As a consequence α3 is predicted to be linear in the reciprocal square root of ionic strength. The dominant source of expansion is repulsion between segments such that one member of an interacting pair is inside and the other outside the background cloud. This same repulsion makes the free energy a minimum when the polymer shape is spherical.