Charged Polymers Transport under Applied Electric Fields in Periodic Channels

Abstract

By molecular dynamics simulations, we investigated the transport of charged polymers in applied electric fields in confining environments, which were straight cylinders of uniform or non-uniform diameter. In the simulations, the solvent was modeled explicitly and, also, the counterions and coions of added salt. The electrophoretic velocities of charged chains in relation to electrolyte friction, hydrodynamic effects due to the solvent, and surface friction were calculated. We found that the velocities were higher if counterions were moved away from the polymeric domain, which led to a decrease in hydrodynamic friction. The topology of the surface played a key role in retarding the motion of the polyelectrolyte and, even more so, in the presence of transverse electric fields. The present study showed that a possible way of improving separation resolution is by controlling the motion of counterions or electrolyte friction effects.

Keywords: confinement; molecular dynamics; polyelectrolytes.

Figure 1

Cross-section schematic illustration (from top to bottom) of constant radius ($6\sigma$) and variable diameter straight cylinders of increasing surface undulations. The depth of surface undulations is constant, $25\%$ of the cylinder radius. $P_0$ denotes the combination of straight cylinders and parallel applied electric fields ${\overrightarrow{E}}_{\parallel }$, $T_0$ denotes the combination of straight cylinders and both parallel and transverse applied fields ${\overrightarrow{E}}_{\left|\right|}+{\overrightarrow{E}}_{\perp }$, etc.

Figure 2

Schematic illustration of fluid control volume, $A_1$, around an arbitrary monomer of a charged chain, which has instantaneous velocity ${\overrightarrow{v}}_i$. The local fluid velocity at the position of monomer i is noted ${\overrightarrow{v}}_f$.

Figure 3

The axial component of the fluid velocity around the polyion as a function of radial distance r, for $N=180$. The legend notation is the same as in Figure 1.

Figure 4

(Top) Electrolyte friction ${\xi }_C$ as a function of distance r from the polyelectrolyte ($N=180$) for limiting cases of smooth and, respectively, wavy surfaces, in parallel (geometries $P_0$, $P_{16}$) and in parallel with perpendicular applied fields (geometries $T_0$, $T_{16}$). (Bottom) Plateau values (large r) of electrolyte friction ${\xi }_C$ as a function of chain length N for the same geometries, $P_0$, $T_0$, $P_{16}$ and $T_{16}$.

Figure 5

Electrophoretic velocities of charged chains of length N in uniform (index “0”) and variable diameter straight cylinders (indices “2”, “4”, “12” and “16” are in the increasing order of the number of undulations per wavelength, as shown in Figure 1). (Top) The constant applied electric field has both longitudinal and transverse components. (Bottom) The constant applied electric field is parallel to the symmetry axis.

Figure 6

(a) Contour plot of average number density distribution of counterions and (b) coions of added salt in a cross-section perpendicular to the axis of the cylinder geometry, $T_{12}$. The applied field has both a longitudinal, ${\overrightarrow{E}}_{\parallel }$, and a transversal component, ${\overrightarrow{E}}_{\perp }$; (c) Similar contour plots of average number density distribution of polymer chain monomers (in the largest section area) in longitudinal fields and (d) in both longitudinal and transversal applied fields; (e) Similar distribution of fluid monomers in geometry, $T_{12}$. In the vicinity of the walls, the monomers arrange themselves in layers.

Figure 7

Average number of contacts with the walls, normalized by chain length N as a function of geometry (see Figure 1). The top curve is for applied fields with both longitudinal and transversal components, and the bottom curve is for fields parallel to the symmetry axis.

Figure 8

Projections of charged chain extension on the z-axis, normalized by average bond length b, and chain length N, as a function of chain size (for legend, see Figure 1).

Figure 9

Average electrophoretic velocities as a function of chain length, N, for the case of pulsed transverse fields and pulsed longitudinal fields. During the first half of the pulse, the driving field is ${\overrightarrow{E}}_{\parallel }+{\overrightarrow{E}}_{\perp }$, while in the second half of the pulse, the field is switched to $-{\overrightarrow{E}}_{\parallel }$.