Mobility Reversal of Polyelectrolyte-Grafted Colloids in Monovalent Salt Solutions

We present molecular dynamics simulations on the electrophoresis of a negative colloid grafted with positive polyelectrolytes. Net-neutral colloids show a varying mobility in monovalent salt. For colloids with negative net charge the mobility is negative at low and positive at high salt concentrations. This mobility reversal is an electrokinetic effect, and thus different from that observed in multivalent salt. Our results agree with numerical calculations based on the Darcy-Brinkman formalism, with which we predict the mobility reversal to also occur for experimentally accessible colloids.

Figure 1

Reduced mobility ${\mu }_{\mathrm{red}}$ as a function of salt concentration $c_{\mathrm{s}}$ and the corresponding Debye length ${\lambda }_{\mathrm{D}}$. Simulations for a neutral soft colloid (blue squared) and a charged soft colloid with $Q_{\mathrm{net}}=-50e$ (red circles) are shown. Numerical results are depicted respectively by the dotted and solid lines of the same color. The dashed line shows the numerical result for a negatively charged soft colloid with the same core and net charge density as used for the red circles, but with $R_{\mathrm{col}}=1\mu \text{m}$. At the top three simulation snapshots are shown for the charged soft colloid at $c_{\mathrm{s}}=\{0.001,0.1,1.0\}M$ respectively from left to right. These show only a radius of $14\sigma$ from the center of the colloid and are cut in half. The snapshots show the neutral monomers (green), charged monomers (yellow), positive salt ions (red), negative salt ions (dark blue), the surface raspberry beads (grey), and charged central colloid bead (light blue). The applied electric field is from left to right in these pictures.

Figure 2

Radial density profiles for $c_s=0.001M$ (dashed black lines), $c_s=0.1M$ (dash-dotted blue lines), and $c_s=2M$ (dotted red lines) of the monomers ${\rho }_{\text{mono}}(r)$ and fluid charge, i.e., the sum of the ions’ charges excluding the charges fixed on the polymers, ${\rho }_{\mathrm{ch}}(r)$. Panels (a) and (b) show the data for the neutral soft colloid while panels (c) and (d) are for $Q_{\mathrm{net}}=-50e$. All curves are shifted vertically by factors of 0.35. The solid lines represent the values produced by the program from Hill et al. [42].