Complex Formation between Poly ( dimethyldiallylammonium chloride ) and Carboxylated Starburst Dendrimers

Polyelectrolytes interact strongly with oppositely charged colloid particles. This phenomenon takes many forms: colloid flocculation in water treatment and paper-making,l stabilization of colloidal suspensions,2 association of DNA with basic protein^,^ and complexation of proteins with synthetic polyelectrolyte^.^ The consequences of these interactions are similarly varied; they may lead to precipitation, coacervation, or the formation of soluble complexes. The commonality among these diverse systems is the strong Coulomb interaction between the polyion and the colloidal surface. Thus, the key parameters should be the polyelectrolyte linear charge density (61, the colloid surface charge density (a), and the ionic strength (I)-or the related Debye length K K ~ . Theoretical treatments have been offered for a rather similar problem, the binding of a polyelectrolyte to an oppositely charged planar ~urface,~-lO and these show how the magnitude of the interaction increases with 6, u, and K-I. All of these treatments find phase transition behavior, generally expressed as a critical temperature at which, for a given set of conditions (corresponding to a set of 6, 0, and K ) , a bound polymer state appears. The temperature appears in these formulations through a Boltzmann term and is not a particularly meaningful parameter, as these treatments neglect temperature-induced changes in ion solvation and water structure, which may in fact be dominant. More usefully, these analyses predict that a polyelectrolyte of charge density 6 in a medium of some given ionic strength will not electrostatically adsorb onto a surface until that surface’s charge density exceeds some critical value. In general, all of these formulations lead to expressions of the form