We investigate the behavior of single polyelectrolytes in multivalent salt solutions under the action of electric fields through computer simulations. The chain is unfolded in a strong electric field and aligned parallel to the field direction, and the chain size shows a sigmoidal transition. The unfolding electric field E* depends on the salt concentration and scales as V (-1/2) with V being the ellipsoidal volume occupied by the chain. The magnitude of the electrophoretic mobility of chain drastically increases during the unfolding. The fact that E* depends on the chain length provides a plausible mechanism to separate long charged homopolymers by size in free solution electrophoresis via the unfolding transition of globule polyelectrolytes condensed by multivalent salt.

We study conformational and electrophoretic properties of polyelectrolytes (PEs) in tetravalent salt solutions under the action of electric fields by means of molecular dynamics simulations. Chain conformations are found to have a sensitive dependence on the salt concentration C(s). As C(s) is increased, the chains first shrink to a globular structure and subsequently re-expand above a critical concentration C(s)*. An external electric field can further alter the chain conformation. If the field strength E is larger than a critical value E*, the chains are elongated. E* is shown to be a function of C(s) by using two estimators E(I)* and E(II)* through the study of the polarization energy and the onset point of chain unfolding, respectively. The electrophoretic mobility of the chains depends strongly on C(s), and the magnitude increases significantly, accompanying the chain unfolding, when E>E(II)*. We study the condensed ion distributions modified by electric fields and discuss the connection of the modification with the change of chain morphology and mobility. Finally, E* is studied by varying the chain length N. The inflection point is used as a third estimator E(III)*. E(III)* scales as N(-0.63(4)) and N(-0.76(2)) at C(s) =0.0 and C(s)*, respectively. E(II)* follows a similar scaling law to E(III)* but a crossover appears at C(s) =C(s)* when N is small. The E(I)* estimator fails to predict the critical field, which is due to oversimplifying the critical polarization energy to the thermal energy. Our results provide valuable information to understand the electrokinetics of PE solutions at the molecular level and could be helpful in micro/nanofluidic applications.