Dynamics of field-driven population inversion in a confined colloidal mixture

We study, using Langevin dynamics simulations, the change in composition of a binary colloidal mixture confined in a finite-length channel, induced by an external field. The field-induced transition from a near-bulk composition to an inverted population is studied as a function of time, for different field strengths and system parameters. For state points corresponding to reversible field cycles, the cyclic filling and emptying of the channel by the minority species are compared. Extrapolation of the physical relaxation times to the colloidal regime is performed through a series of simulations at increasing value of the damping parameter. For state points at which the mixture is unstable at zero field, reproducible irreversible cycles are illustrated. For reversible field cycles, the scaling with the particles size of the characteristic cycling time is discussed.

Figure 1

Plot of the WCA potentials for the 1-1 and 2-2 interactions (solid line) and the nearly additive (dashed line) and nonadditive (dotted line) mixtures (1-2 interaction).

Figure 2

Slit pore geometry used in the simulations. Lengths are in units of ${\sigma }_{\text{HS}}$.

Figure 3

Distribution of the applied field across the system. The arrow length is proportional to the field strength.

Figure 4

Density profiles at zero field of (a) dipolar spheres and (b) apolar spheres for MC (crosses) versus MD (${\gamma }^{*}=0.046$, circles and squares) simulations. Circles and squares correspond to initial ($q^{*}=0$) and final ($q^{*}=14.3\to 0$) states, respectively. Note the difference in the $y$-axis scale. The lines are guides to the eye.

Figure 5

Plot of the MD (${\gamma }^{*}=0.046$) density profiles in the channel for $q^{*}=14.3$. White and black circles correspond to dipolar and apolar spheres, respectively. The sampling in the $x$ direction was restricted to $x/{\sigma }_{\text{HS}}\in [-2.5,2.5]$; cf. Fig. 6.

Figure 6

The 2D density-composition profiles $({\rho }_{\text{T}},x_2)$ from MD simulation with ${\gamma }^{*}=0.046$. The charge densities in the three steps of the field cycle are (a) $q^{*}=0$, (b) $q^{*}=0\to 14.3$, and (c) $q^{*}=14.3\to 0$.

Figure 7

Filling and emptying dynamics of dipolar spheres inside a channel containing a nearly additive mixture during a cycle $q^{*}=0\to 14.3\to 0$. Here and in the following figures, up and down arrows indicate when the field is turned on and off, respectively. The reduced friction coefficient is ${\gamma }^{*}=0.046$.

Figure 8

Filling and emptying of the channel for the cycle $q^{*}=0\to 14.3\to 0$ for nearly additive (red) and nonadditive (green) mixtures. The nearly additive plot was shifted when emptying. The friction coefficient is ${\gamma }^{*}=0.46$.

Figure 9

Filling and emptying versus rescaled time for the cycles $q^{*}=14.3\to 0$ using several dampings. The parameter $\alpha$ with up and down arrows gives the scaling factor for the filling and the emptying, respectively.

Figure 10

Filling dynamics for the cycle $q^{*}=0\to 14.3$: pure dipoles (red) vs the nearly additive mixture (green). The friction coefficient ${\gamma }^{*}=0.46$.

Figure 11

Filling and emptying for the cycles $q^{*}=14.3/4$, $14.3/2$, and $14.3\to 0$ of the nearly additive mixture. The friction coefficient is ${\gamma }^{*}=0.46$.

Figure 12

Cycling the field $q^{*}=0\to 14.3/2\to 0$ for the nearly additive (red) and the nonadditive (green) mixtures. The bulk density and the composition are ${\rho }^{\text{b}}=0.6$ and $x_2^{\text{b}}=0.1$, respectively. The lowest friction coefficient ${\gamma }^{*}=0.046$ was used to speed up the simulation.

Figure 13

The 2D density-composition profiles $({\rho }_{\text{T}},x_2)$ from MD simulation with ${\gamma }^{*}=0.046$. The bulk density and composition are ${\rho }^{\text{b}}=0.6$ and $x_2^{\text{b}}=0.1$, respectively. The charge densities in the three steps of the field cycle are (a) $q^{*}=0$, (b) $q^{*}=0\to 14.3/2$, and (c) $q^{*}=14.3/2\to 0$.

Figure 14

Reversibly switchable irreversible cycles in the nonadditive mixture. The charge density is $q^{*}=0\to 14.3/2\to 0$. The other parameters are given in the text.

Figure 15

Interaction strength ${\epsilon }_{11}/k_{\text{B}}T$ of the WCA potential versus colloid diameter ${\sigma }_{\text{HS}}$. The inset shows a close-up for small ${\sigma }_{\text{HS}}$.