Conformation of weakly charged polyelectrolytes at a solid–liquid interface

The adsorption characteristics of polyelectrolyte chains on a plane surface are derived. The approach uses the mean-field arguments first developed by de Gennes [Rep. Prog. Phys. 32, 187 (1969)] and Richmond and Jones and Richmond [J. Chem. Soc. Faraday Trans. 73, 1062 (1977)] for the evaluation of the configuration probability of a neutral chain at an interface. Electrostatic interactions among monomers are treated through the linearized Poisson–Boltzmann equation. The treatment is restricted to dilute solutions and to weakly charged polyelectrolytes. Simply analytical expressions are derived for the concentration profile and the adsorption isotherm which are expressed in terms of two characteristic lengths L1 which characterizes the range of surface forces and L2, the Debye–Hückel length, which characterizes the range of electrical forces. Once these variables are fixed, it appears that the adsorption cannot exceed a critical value Γm which is tuned by the temperature.