Polyelectrolytes in Multivalent Salt Solutions under the Action of DC Electric Fields

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 salt concentration $C_s$. As $C_s$ is increased, the chains first shrink to a globular structure and subsequently reexpand 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/nano-fluidics applications.