  Electrophoretic (EP) mobility reversal is commonly observed for strongly
charged macromolecules in multivalent salt solutions. This curious effect takes
place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so
that the counterion-dressed surface charge reverses its sign, leading to the
inversion of the polymer drift driven by an external electric field. In order
to characterize this seemingly counterintuitive phenomenon that cannot be
captured by electrostatic mean-field theories, we adapt here a previously
developed strong-coupling-dressed Poisson-Boltzmann approach to the cylindrical
geometry of the polyelectrolyte-salt system. Within the framework of this
formalism, we derive an analytical polymer mobility formula dressed by charge
correlations. In qualitative agreement with polymer transport experiments, this
mobility formula predicts that the increment of the monovalent salt, the
decrease of the multivalent counterion valency, and the increase of the
dielectric permittivity of the background solvent, suppress charge correlations
and increase the multivalent bulk counterion concentration required for EP
mobility reversal. These results are corroborated by coarse-grained molecular
dynamics simulations showing how multivalent counterions induce mobility
inversion at dilute concentrations and suppress the inversion effect at large
concentrations. This re-entrant behavior, previously observed in the
aggregation of like-charged polymer solutions, calls for verification by
polymer transport experiments.
