Salt-Induced Counterion-Mobility Anomaly in Polyelectrolyte Electrophoresis

We study the electrokinetics of a single polyelectrolyte chain in salt solution using hydrodynamic simulations. The salt-dependent chain mobility compares well with experimental DNA data. The mobility of condensed counterions exhibits a salt-dependent change of sign, an anomaly that is also reflected in the counterion excess conductivity. Using Green’s function techniques this anomaly is explained by electrostatic screening of the hydrodynamic interactions between the chain and counterions.

Figure 1

Simulation cell for a DNA segment with counterions (dark gray) and coions (light gray). Periodic boundary conditions are applied along the projected end-to-end distance $H$ of the DNA segment. The external electric field is applied either parallel (${\mathit{E}}_{\Vert }$) or perpendicular (${\mathit{E}}_{\perp }$) to the PE axis.

Figure 2

Hydrodynamic simulations of DNA in aqueous NaCl solution of various ionic strengths $I$ at $20°\mathrm{C}$. (a) Electrophoretic DNA mobility ${\mu }_m$ as obtained from simulations (solid symbols) and experiments (open symbols) as a function of $I$, compared to theories by Stigter [6] (dashed line) and Manning [7] (dotted line). (b) Mobility of neutralizing counterions ${\mu }_{\mathrm{nct}}$, and condensed counterions ${\mu }_{\mathrm{cct}}$. (c) Counterion excess conductivity $A_{\mathrm{nct}}$ according to Eq. (1).

Figure 3

Results for a weakly charged PE with Manning parameter ${\xi }_{\mathrm{M}}=|q_{\mathrm{ct}}{q}_m{\ell }_{\mathrm{B}}/b|=0.4$. (a) Coion mobility ${\mu }_{\mathrm{co}}(r_{\perp },0)$ for various fixed distances $r_{\perp }$ from the PE as a function of $(\kappa a{)}^2$. The hydrodynamic drag exerted by the PE on the coions increases their mobility as compared to the case without PE, Eq. (3) ($r_{\perp }/a\to \infty$, solid line). The latter compares well with hydrodynamic simulations of a simple salt solution (solid symbols). (b) Counterion mobility ${\mu }_{\mathrm{ct}}(r_{\perp },0)$ at distance $r_{\perp }$ from the PE which exhibits a sign change. For small $r_{\perp }$ and low salt, counterions are dragged along with the PE [(${\mu }_{\mathrm{ct}}(r_{\perp },0)<0$]. (c) Comparison of theoretical predictions (solid lines) and hydrodynamic simulations (solid symbols) for the PE mobility ${\mu }_m$, neutralizing counterion mobility ${\mu }_{\mathrm{nct}}$ and condensed counterion mobility ${\mu }_{\mathrm{cct}}$. The condensed counterion mobility changes sign. We also show the parallel and perpendicular PE mobilities ${\mu }_m^{\parallel }$ (dotted line) and ${\mu }_m^{\perp }$ (short-dashed line).