Two-Step Mechanism of Rotational Relaxation in Lamellar Phases of Rods: Accelerating Effect of the Addition of Spheres

By using computer simulation on a model colloidal rod-sphere mixture in its lamellar phase, the mechanism responsible for the rod rotational relaxation has been definitely identified and characterized. It consists of two steps: first, a rod, parallel to the director, has to escape from the layer in which it is located and go into the interlayer region mostly populated by spheres, perpendicular to the director; then, it has to insinuate again into one of the adjacent layers, with 50% of probability of resulting antiparallel to the director. While this mechanism is also operating in a pure smectic phase of rods, the presence of spheres increases notably its efficacy, thus promoting the rotational relaxation and facilitating its observation.

Figure 1

First rank orientational time correlation functions for rods in the smectic or lamellar phases. For both panels (a) and (b), the value of ${\varphi }_{\mathrm{tot}}$ and the largest value of ${\varphi }_s$ are indicated. The curve corresponding to this state point is indicated by the arrow while the other curves corresponding to less sphere-rich systems are met moving toward the right. The last curve on the right corresponds to a monodisperse smectic phase of rods.

Figure 2

Typical angular trajectories of a rod.

Figure 3

Contour maps of the $\log \Pi$ probability density function for the intervals of $P_2$ [$-0.5$; $-0.2$] (left) and [0.7;1.0] (right), and various time intervals $s$: $20.38t^{*}$ (top), $163.02t^{*}$ (center), and $652.08t^{*}$ (bottom).

Figure 4

${\Delta }_{\max }$ of parallel rods for different times $s$: $13.6t^{*}$ (dotted line), $27.2t^{*}$ (dashed line) and $54.4t^{*}$ (solid line).