  It is well established that when multivalent counterions or salts are added
to a solution of highly-charged polyelectrolytes (PEs), correlation effects can
cause charge inversion of the PE, leading to electrophoretic mobility (EM)
reversal. In this work, we use coarse-grained molecular dynamics simulations to
unravel the less understood effect of coion valency on EM reversal for rigid
DNA-like PEs. We find that EM reversal induced by multivalent counterions is
suppressed with increasing coion valency in the salt added and eventually
vanishes. Further, we find that EM is enhanced at fixed low salt concentrations
for salts with monovalent counterions when multivalent coions with increasing
valency are introduced. However, increasing the salt concentration causes a
crossover that leads to EM reversal which is enhanced by increasing coion
valency at high salt concentration. Remarkably, this multivalent coion-induced
EM reversal persists even for low values of PE linear charge densities where
multivalent counterions alone cannot induce EM reversal. These results
facilitate tuning PE-PE interactions and self-assembly with both coion and
counterion valencies.
