Theory of universal fast orientational dynamics in the isotropic phase of liquid crystals

Abstract

A theoretical treatment is presented that demonstrates universal dynamical behavior in the isotropic phase of liquid crystals on ultrafast time scales and short distance scales. The theoretical development generates a temperature independent power law for the short time scale decay of the molecular orientational correlation function. This provides a theoretical rationale for the postulate of universal behavior based on recent experimental observations on two liquid crystal systems. A temperature independent power law decay with the identical exponent, 0.63, was observed for the two systems. First, an alternative theoretical approach reproduces the Landau de Gennes results for the long distance scale, slow time scale orientational dynamics in the isotropic phase. This approach is also capable of examining the short distance scale and short time scale dynamics, and yields a temperature independent power law decay with exponent 0.5. Then critical correlations of fluctuations and local symmetry considerations are included. The Ising model of critical systems is employed. This detailed analysis yields the experimentally observed exponent, 0.63, without recourse to adjustable parameters. Modern theories of dynamic critical phenomena like dynamic scaling theory, the kinetic Ising model and the stochastic model of Karder–Parisi–Zhang are considered as alternative approaches. While these theories can generate some of the features found in experiment, it is not possible to reproduce the observed experimental results without internal inconsistencies or unwarranted adjustable parameters.