Unfolding polyelectrolytes in trivalent salt solutions using dc electric fields: A study by Langevin dynamics simulations

We study the behavior of single linear polyelectrolytes condensed by trivalent salt under the action of electric fields through computer simulations. The chain is unfolded when the strength of the electric field is stronger than a critical value. This critical electric field follows a scaling law against chain length, and the exponent of the scaling law is −0.77(1), smaller than the theoretical prediction, $−3ν/2$ [R. R. Netz, Phys. Rev. Lett. 90, 128104 (2003)], and the one obtained by simulations in tetravalent salt solutions, −0.453(3) [P.-Y. Hsiao and K.-M. Wu, J. Phys. Chem. B 112, 13177 (2008)]. It demonstrates that the scaling exponent depends sensitively on the salt valence. Hence, it is easier to unfold chains condensed by multivalent salt of a smaller valence. Moreover, the absolute value of chain electrophoretic mobility increases drastically when the chain is unfolded in an electric field. The fact that the mobility depends on electric field and on chain length provides a plausible way to impart chain-length dependence in free-solution electrophoresis via chain unfolding transition induced by electric fields. Finally, we show that, in addition to an elongated structure, a condensed chain can be unfolded into a U-shaped structure. The formation of this structure in our study is purely a result of the electric polarization, not of the elastohydrodynamics dominated in sedimentation of polymers.