Poisson-Boltzmann theory of pH-sensitive (annealing) polyelectrolyte brush

We present a self-consistent field analytical theory of a polymer brush formed by weakly charged pH-sensitive (annealing) polyelectrolytes tethered to a solid-liquid interface and immersed in buffer solution of low molecular weight salt. We use the Poisson-Boltzmann framework, applied by us previously to polyelectrolyte (PE) brushes with quenched charge (Zhulina, E. B.; Borisov, O. V. J. Chem. Phys. 1997, 107, 5952). This approach allows for detailed analysis of the internal structure of annealing PE brush in terms of polymer density distribution, profiles of electrostatic potential and of local degree of chain ionization as a function of buffer ionic strength and pH without any assumptions on mobile ion distribution imposed in earlier scaling-type models. The presented analytical theory recovers all major asymptotic dependences for average brush properties predicted earlier. In particular, a nonmonotonic dependence of brush thickness on ionic strength and grafting density is confirmed and specified with accuracy of numerical coefficients including crossover regions. Moreover, the theory predicts qualitatively new effects, such as, e.g., disproportionation of tethered polyions into weakly charged concentrated proximal and strongly charged sparse distal brush domains at low salt and moderate grating densities. The presented results allow us to quantify responsive features of annealing PE brushes whose large-scale and local conformational properties can be manipulated by external stimuli.