Brush Theory of Tethered Chains with a Charged Group at the Free End

Abstract

We consider the problem of end-grafted polymer molecules with a charged group attached to the free end both by an analytical and a numerical method. In the analytical approach the Gaussian model for the polymer chains is used. In this model volume interactions are ignored and analytical solutions for special type of boundary conditions are found. We consider both a repulsive surface, and a critical adsorption energy surface. The complete Poisson-Boltzmann equation is used and deviations from local electroneutrality are considered in a perturbation methd scheme. It is found that deviations of local electroneutrality both scale inversely with the chain length (N -1 and inversely with the ionic strength (Φ s -1 ). In the numerical method we apply a self-consistent-field scheme of freely jointed chains in Θ conditions. Results of the analytical model compare favorably to those obtained by the numerical method.