Propagating Director Bend Fluctuations in Nematic Liquid Crystals

We show, by molecular simulation, that for a range of standard, coarse-grained, nematic liquid crystal models, the director bend fluctuation is a propagating mode. This is in contrast to the generally accepted picture of nematic hydrodynamics, in which all the director modes (splay, twist, bend, and combinations thereof) are overdamped. By considering the various physical parameters that enter the equations of nematodynamics, we propose an explanation of this effect and conclude that propagating bend fluctuations may be observable in some experimental systems.

Figure 1

Time correlation functions $c(k,t)$ plotted versus time $t$ for model GB(3.0, 5.0, 1, 3) at $\rho =0.3$, $T=3.4$: (a) splay, (b) twist, (c) bend. Points with error bars are simulation results. Lines are the fits to an exponential decay or to Eq. (1), as discussed in the text. Different curves correspond to different wave numbers $k=n2\pi /L$ where $L$ is the simulation box length: $n=1$ (diamonds, cyan), $n=2$ (down triangles, red), $n=3$ (up triangles, gray), $n=4$ (circles, blue), $n=5$ (squares, green). All quantities are in simulation units defined in the text.

Figure 2

Decay rates $\nu$ and oscillation frequencies $\omega$, obtained by fitting Eq. (1) to $c_{\text{bend}}(k,t)$, as functions of $k^2$, for the same system as Fig. 1. Points with error bars are simulation results. Lines are linear least-squares fits. All quantities are in simulation units defined in the text. We also give a schematic illustration of the director variation $\mathbf{n}$ and coupled velocity field $\mathbf{v}$ for the bend mode.