  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, $-3\nu/2$ [Netz, Phys. Rev. Lett. 90
(2003) 128104], and the one obtained by simulations in tetravalent salt
solutions, $-0.453(3)$ [Hsiao and Wu, J. Phys. Chem. B 112 (2008) 13179]. It
demonstrates that the scaling exponent depends sensitively on the salt valence.
Hence, it is easier to unfold chains condensed by multivalent salt of smaller
valence. Moreover, the absolute value of chain electrophoretic mobility
increases drastically when the chain is unfolded in an electric field. The
dependence of the mobility on electric field and 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 an U-shaped structure. The formation of this structure in
our study is purely a result of the electric polarization, but not of the
elasto-hydrodynamics dominated in sedimentation of polymers.
