Behavior of surface-anchored poly(acrylic acid) brushes with grafting density gradients on solid substrates: 2. Theory

We apply a molecular theory to predict the structural properties of poly(acrylic acid) macromolecules grafted via one of their ends to solid surfaces. The theory explicitly incorporates the acid-base equilibrium responsible for the charge regulation of the acrylic groups, as well as the conformations, size, shape, and charge distributions of all the molecular species present. We compare the predictions of the theory with experimental observations presented in the preceding article for the height of the layer as a function of ionic strength for different polymer molecular weight and polymer surface coverage. The calculated heights are found to be in good agreement with-the experimental observations. The theory predicts the distribution of charges within the layer. We find that the counterions adsorb to the grafting surface, overcompensating the charge of the polymer. The charge regulation within the polymer layer is,determined by the interplay between the bulk pH, the ionic strength, and the density of polymer. The system tends to become uncharged with decreasing ionic strength of the solution and increasing polymer density. In all cases the charge regulation acts in order to minimize the electrostatic repulsions in the system. The local distribution of protons within the polymer layer is predicted to be very different from that of the bulk solution. The local pH within the polymer layer can be tuned by varying the solution ionic strength and the Polymer surface coverage; the variation can be large as two pH units, relative to the bulk pH. This large variation of the local pH within a couple of nanometers within the brush can be used in the design of biosensors.