First-Passage-Time Distributions of the Freedericksz Transition in Nematic Liquid Crystals

Abstract

A two-stage transient statistical investigation of the Freedericksz transition in Nematic Liquid Crystals (NLC) is presented. After applying an external field that exceeds the Freedericksz critical value, the director of the NLC relaxes from its unstable equilibrium state with the effect of noise. The statistical properties of this transient process can be characterized by the First Passage Time (FPT). We separate the whole process into two stages with the time when the distribution function of the director has its variance equal to the variance of the steady-state distribution at the critical point. The first stage is considered as an Ornstein-Uhlenbeck process and the second stage as a deterministic nonlinear transformation of the distribution function of the director. The explicit expression of the FPT distribution is analytically derived with this consideration. Monte Carlo simulations shown that the present theory describes the transient behavior of the NLC much better than the previous asymptotic approach. The mean, the variance and the skewness of our explicit FPT distribution function show excellent agreement with the numerical simulation.

Key Words:

• Nematic liquid crystal
• first passage time
• Freedericksz transition
• transient process