Dynamics of Fluctuations in Nematic Liquid Crystals

In a nematic system, the molecular axes tend to be aligned parallel to each other, but there are some fluctuations in the alignment. They give rise to a strong scattering of light. By a frequency analysis of the outgoing light, one can measure the power spectrum of these fluctuations, i.e., their dynamical behavior. The small motions of an incompressible nematic liquid crystal with coupled flows and molecular rotations are analyzed here in terms of the Leslie equations. The structure of the modes depends essentially on the parameter ${\mathrm{\mu \hspace{0.17em}=\hspace{0.17em}K}}_{\mathrm{\rho \eta }}^{\text{−2}}$ , where $K$ is an average elastic constant, $\rho$ is the density, and $\eta$ is an average viscosity. In the most usual case of small $\mu$ values the modes are purely dissipative. For a given wave vector q and polarization α there is one slow mode describing the relaxation of a twisted nematic configuration and a fast mode where the molecules exert no torque on the hydrodynamic motion. The light‐scattering data should measure the relaxation frequency of the slow mode: from such data taken at different $q$ values the six friction coefficients introduced by Leslie may in principle be determined.