Intrinsic charge and Donnan potentials of grafted polyelectrolyte layers determined by surface conductivity data

In order to characterize grafted polyelectrolyte layers based on electrokinetic measurements a theory of the surface conductivity Ksigma was developed, starting from the model of thick polyelectrolyte layers with uniform segment distribution and dissociable groups with an unknown pK value. According to this model the inner part of the polyelectrolyte layer adjacent to the substrate is considered to be isopotential while the potential decay occurs in a zone near the solution side of the layer. A simple equation for the Donnan potential psiD as a function of pH, pK, electrolyte concentration C0, and volume charge density rho was obtained. In the derived equation Ksigma is directly related to psiD while the other terms have less influence on the magnitude of Ksigma and can be accounted for in a second approximation using psiD as determined from the measured Ksigma. Evaluation of the suggested model indicates that Ksigma measurements provide an effective method to characterize polyelectrolyte layers by analyzing the dependence of psiD on pH and C0: The magnitude of Ksigma yields information about the surface charge at complete dissociation of the ionizable groups. The dependence of Ksigma on pH and C0 can be used for the determination of the pK value of the dissociating functions and the segment volume fraction of the polyelectrolyte can be estimated using the measured value of rho.