Charged nanoparticle in a nanochannel: Competition between electrostatic and dielectrophoretic forces

Nanochannels made in solid-state materials are used for various applications such as nanoparticle separation or DNA manipulation. In this work we examine the effects of the electric and dielectrophoretic forces on a charged nanoparticle confined in a nanochannel. To this end, we solve the Poisson equation for the nanochannel with a wedgelike geometry and consider how channel geometry and electrolyte concentration affect the electrostatic potential distribution and forces acting on nanoparticles of various sizes. On the basis of our calculations, we establish conditions necessary for the particle's attraction to the corners of a channel. We find that for large particles, the net force is attractive only for low concentrations of the electrolyte irrespective of the wedge angle, while small enough particles are attracted to the vertex for either larger electrolyte concentrations or small wedge angle.

Figure 1

Schematics of the $x\text{−}y$ cross section near a corner of a nanochannel that extends along the $z$ axis.

Figure 2

Contour plots of the electrostatic potential $\mathrm{\Phi }(r,\varphi )$ inside the wedge for $\alpha ={45}^{\circ },\alpha ={90}^{\circ }$, and $\alpha ={135}^{\circ }$, from top to bottom, for $C =$ 3 mM. The inset in each shows line plots of the electrostatic potential along certain angles.

Figure 3

Schematic representation of a spherical particle located at its position closest to the vertex of a nanochannel for $\alpha ={45}^{\circ },{90}^{\circ }$, and ${135}^{\circ }$, from left to right. Each outer (red) ring has a thickness of 0.4 nm and represents the thickness of the surface layer over which the charge is distributed.

Figure 4

Total potential $U_{\mathrm{total}}$ for different wedge angles $\alpha$ with $C =$ 3 mM along the bisecting angle of the wedge for $K=-1/2$ (plus-dashed blue line), 0 (dashed red line), 1/4 (dotted magenta line), 3/4 (dash-dotted black line), and 1 (solid green line). The black dashed line shows the location of the $r_{\min }$ value (see Table 1).

Figure 5

Same as in Fig. 4 but for $C=10$ mM.

Figure 6

Electrostatic potential $\mathrm{\Phi }$ versus ${\lambda }_{\max }$ calculated at a distance of 0.16 nm from the bottom surface of the nanochannel and at various distances from the vertex: 100 nm, black (top) line; 20 nm, red (middle) line; and 0.36 nm, blue (bottom) line. The plot clearly shows that the farther away from the vertex, the larger the upper limit of integration ${\lambda }_{\max }$ is required to obtain an accurate value of the potential.