Influence of weak groups on polyelectrolyte mobilities

The ionization of dissociable groups in weak polyelectrolytes does not occur in a homogenous fashion. Monomer connectivity imposes constraints on the localization of the dissociated (charged) monomers that affect the local electric potential. As a result, the mean bare charge along a weak polyelectrolyte can vary depending on the proximity to topological features (e.g. presence of crosslinks or dangling ends). Using reaction-ensemble Monte-Carlo simulations we calculate the dissociation inhomogeneities for a few selected PE configurations, linear, rod-like, flexible four-arm star, and a star with stiff arms. An ensemble preaverage is used to obtain the annealed bare charge profile for these different polymer configurations. Using molecular dynamics simulations within a Lattice-Boltzman fluid, we investigate how the electrophoretic mobility is affected by the bare charge inhomogeneities arising from the annealed weak polyelectrolytes. Surprisingly, the mobility obtained for the situations corresponding to the predicted charge profile for annealed weak polyelectrolytes are not significantly different than the mobility obtained when all the monomers have an identical charge (under the constraint that the total polyelectrolyte bare charge is the same). This is also true for the stiff rod-like variants where conformational changes induced from the localization of the monomer charges are negligible. In salty solutions, we find that counterions are affected by the electric potential modulations induced by the topological features. Since the counterions crowd in regions where the electric potential caused by the dissociated monomers is highest, they wash-out the bare charge inhomogeneities and contribute to a more uniform effective backbone charge.