Counterion Activity of Highly Charged Strong Polyelectrolytes

Comprehensive counterion activity studies have revealed clear influence of the polyelectrolyte concentration and chain length on the polyion−counterion interaction, neither of which is evident from the existing theoretical models. The counterion activity coefficient ( f a ) increases below the overlap concentration c * as calculated from Odijk's scaling approach. At dilutions where the Debye length ( l D ) exceeds the contour length ( L ), this increase is more pronounced. It is concluded that these changes in the ionic interactions are primarily responsible for the strong increase of the equivalent conductivity (Λ) below c *. The findings are not restricted to oligomers but apply to all chain lengths of polyelectrolytes at concentrations less than c *. The correlation of f a and Λ with both c * and the ratio l D / L leads to a general description of polyelectrolyte behavior. Experiments were performed above and below c * and over the range 0.1 ≤ l D / L ≤ 10 using a series of poly(vinylbenzyltrialkylammonium) model polyelectrolytes with contour lengths over a range 7 nm ≤ L ≤ 102 nm and characterized by a charge density parameter ξ = 2.85.