Kinetics of phase ordering in uniaxial and biaxial nematic films.

Abstract

The phase ordering process following a quench to both the uniaxial and biaxial nematic phases of a quasi-two-dimensional nematic liquid crystal is investigated numerically. The time dependences of the correlation function, structure factor, energy density, and number densities of topological defects are computed. It is found that the correlation function and the structure factor apparently collapse on to scaling curves over a wide range of times. The correlation length ${\mathit{L}}_{\mathrm{cor}}$(t) is found to grow as a power law in the time since the quench t, with a growth exponent of ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{cor}}$=0.407\ifmmode\pm\else\textpm\fi{}0.005. The growth exponents of the characteristic length scales obtained from the energy length (${\mathrm{\ensuremath{\varphi}}}_{\mathrm{en}}$) and the defect number densities (${\mathrm{\ensuremath{\varphi}}}_{\mathrm{def}}$), however, are found to differ from ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{cor}}$. The discrepancy between ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{cor}}$ and ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{def}}$ indicates a violation of dynamical scaling, a violation that is not apparent from our data for the correlation function alone. The observation that all the measured growth exponents are smaller than 0.5 (i.e., the value expected from dimensional analysis) is addressed in terms of properties of point defects in two dimensions, and the annihilation process of an isolated defect pair in a uniaxial nematic phase is investigated. Following the quench to the biaxial nematic phase, there are four topologically distinct defect species present in the system, the populations of which are studied in detail. It is found that only two types of defects are observed in large numbers at late times, and a mechansim for the selection of the prevailing defect species is proposed.