  Understanding the behavior of charged complex fluids is crucial for a
plethora of important industrial, technological, and medical applications.
Using coarse-grained molecular dynamics simulations, here we investigate the
properties of a polyelectrolyte solution, with explicit counterions and
implicit solvent, that is driven by a steady electric field. By properly tuning
the interplay between interparticle electrostatics and the applied electric
field, we uncover two nonequilibrium continuous phase transitions as a function
of the driving field. The first transition occurs from a homogeneously mixed
phase to a macroscopically charge segregated phase, in which the
polyelectrolyte solution self-organizes to form two lanes of like-charges,
parallel to the applied field. We show that the fundamental underlying factor
responsible for the emergence of this charge segregation in the presence of
electric field is the excluded volume interactions of the drifting
polyelectrolyte chains. As the drive is increased further, a re-entrant
transition is observed from a charge segregated phase to a homogeneous phase.
The re-entrance is signaled by the decrease in mobility of the monomers and
counterions, as the electric field is increased. Furthermore, with multivalent
counterions, a counterintuitive regime of negative differential mobility is
observed, in which the charges move progressively slower as the driving field
is increased. We show that all these features can be consistently explained by
an intuitive trapping mechanism that operates between the oppositely moving
charges, and present numerical evidence to support our claims. Parameter
dependencies and phase diagrams are studied to better understand charge
segregation in such driven polyelectrolyte solutions.

Soft Condensed Matter;Materials Science;Statistical Mechanics