Strong stretching theory for pH-responsive polyelectrolyte brushes in large salt concentrations

In this paper, we develop a theory for describing the thermodynamics, configuration, and electrostatics of strongly-stretched, pH-responsive polyelectrolyte (PE) brushes in the presence of large salt concentrations. The aim of the paper, therefore, is to study the properties of a PE brush in a salt concentration regime (namely, large concentrations of several molars) that has been hitherto unexplored theoretically in the context of PE brushes but can be routinely encountered in molecular scale simulations of the problem. The brushes are modelled using our recently developed augmented Strong Stretching Theory (SST), while the effect of the presence of the large salt concentration is accounted for by including the contributions of three different types of non-Poisson-Boltzmann (non-PB) effects to the free energy description of the PE brush induced electric double layer (EDL). These non-PB effects are ionic non-mean-field ion-ion correlations, solvent polarization, and the finite size effect of the ions and water dipoles. We study the individual influences of these different effects and show that the ion-ion correlations and solvent polarization effect reduce the brush height which consequently enhances the monomer density and leads to an electrostatic potential distribution of the brush induced EDL that has a larger magnitude at near-wall locations and becomes zero at shorter distances from the wall. The finite size effect, on the other hand, increases the brush height and therefore, weakens the monomer density and leads to a smaller near-wall magnitude of the EDL potential that becomes zero at larger distances from the wall. Eventually, we consider the impact of all the three non-PB effects simultaneously and show that the ion-ion correlations and solvent polarization effect dominate the size effects and dictate the overall brush configuration and the EDL electrostatics. We also point out that the influence of all the three non-PB effects becomes the largest for a larger salt concentration and a smaller bulk pH. Finally, we compare our theoretical predictions with those obtained from our recently developed all-atom MD simulation model and obtain an excellent match.