Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential

We report a Brownian dynamics simulation study of a two-dimensional system of repulsive colloidal particles in a channel geometry with a sinusoidal substrate potential under influence of a constant driving. The effect of this driving on the structure, mobility, and diffusion is discussed as well as the appearance of kink and antikink solitons. The competing order principles of the hexagonal crystal structure, the period of the substrate, and the layering due to the confining walls can be either commensurable or incommensurable. The combination of those three leads to new effects. The simultaneous occurrence of kinks and antikinks can be observed, due to the energy difference between boundary- and midlanes, and similarities to the electron-hole conductivity in a semiconductor can be found.

Figure 1

Snapshot of a channel section (a) without periodic potential and without external force ($V_p=F=0$), (b) with periodic potential $V_p=10$ and without driving force, and (c) with high driving force $F=40$ in channel direction.

Figure 2

(a) The mean-square displacement in the $x$ direction. (b) From the long-time limit the mean particle velocities $\overline{v}$ as a function of external force $F$ can be extracted. The free velocity $\overline{v}=F$ (solid line) and the solution for a single particle for $V_p\gg 1$ and $V_p=10$ (dashed lines) are plotted as reference.

Figure 3

The mean-square displacement in the $y$ direction. Points with $F<F_1$ are filled, and the others are open.

Figure 4

The mean-square displacement in the $x$ direction relative to the center of mass for (a) low and (b) high forces.

Figure 5

(a) Double-logarithmic plot of the mobility $\overline{v}/F$, the diffusion coefficient in the $x$ direction around the center-of-mass position $D_X$, and an effective orthogonal diffusion coefficient $D_Y$ as a function of external force. Equation (7) gives an approximation for $D_X$ of noninteracting particles. (b) Snapshots at $F=40$, taken at four times, increasing from top to bottom. The boundary particles move slower than the inner particles.

Figure 6

[(a) and (c)] The mean drift velocity $\overline{v}$ of the particles as a function of external forces $F$ for different periods $\lambda$ of the washboard potential. The solid curve is the result for a free particle. The dashed line gives the solution for a single particle in a one-dimensional channel. (b) Snapshots of the equilibrium positions for different periods $\lambda$ on the color-coded substrate potential (bright, maximum; dark, minimum). Red ellipses ($\lambda =2.1$), kinks; blue ellipses ($\lambda =1.5$), antikinks.

Figure 7

Snapshot of particle positions for different forces $F$. Fast particles are marked orange (light gray). The fast particles are around additional particles at the boundary (kinks) and vacancies in the midlanes (antikinks). A video is provide in the Supplemental Material [38].