Rotational diffusion of shape switching particles in nematic liquid crystals

The theory of rotational diffusion of particles of various symmetry embedded in a liquid crystal host, essential to interpret a variety of spectroscopic observables, has been available for some time, but only for the case of rigid molecules. Here we generalize the treatment and present a theory to describe the rotational diffusion of shape-changing particles dispersed in nematic liquid crystals. The interaction of the particles with the environment is modeled by an effective field potential, while the particles are allowed to assume an arbitrary discrete number of shapes. The transition between shapes is modeled by a Markovian process which is combined with rotational diffusion. Our model is applied to the simple case of a particle that can exchange between three shapes: a rod, a disk, and a sphere. We consider in detail the effect of shape transitions in some selected correlation functions which are relevant for experiments.

Figure 1

The shape switching process between rodlike, spherical and disklike ellipsoidal particles.

Figure 2

Angular correlation functions for the particle described in Table 1. The curves were obtained using $p_0\left(\chi \right)=1/3$ for all shapes $\chi$. We have switching rate ${\zeta }^{*}=0$ (A), 0.01 (B), 0.05 (C), 0.1(D), 0.5 (E), 1(F), 5 (G), 20 (H).

Figure 3

Correlation functions of the shape deformation for parallel (a) and perpendicular axis (b). The parameters used in the calculations are described in Table 1. The curves correspond to $p_0\left(\chi \right)=1/3$ for all shapes $\chi$ and switching rate ${\zeta }^{*}=0.01$ (A), 0.05 (B), 0.1 (C), 0.5 (D), 1 (E), 5(F), 20 (G).

Figure 4

Correlation times ${\tau }^2$ for $p_0\left(\text{rod}\right)/p_0\left(\text{disk}\right)=0.2$ (A), 0.5 (B), 1(C), 2 (D), 5 (E), and 10 (F).

Figure 5

Angular correlation functions for the particle described in Table 1. Here $\zeta =1$ and $p_0\left(\text{rod}\right)/p_0\left(\text{disk}\right)=\left(\mathrm{A}\right)\infty$, (prolate); (B) 10; (C) 5; (D) 2; (E) 1; (F) 0.5; (G) 0.2; (H) 0.0.