Critical fluctuations and molecular dynamics at liquid-crystalline phase transitions. I. Theoretical aspects of the nematic–smectic-A transition

Abstract

A theoretical model is developed for treating molecular dynamics at the nematic–smectic‐A (N–S_A) phase transition, which is frequently second order. This model is motivated by electron‐spin‐resonance (ESR) spin‐relaxation studies of molecular probes. The critical dynamics of the hydrodynamic modes is described in accordance with dynamic scaling arguments of Brochard. Following Zager and Freed, the molecular dynamics of a probe molecule (governed by the molecular orientation and/or rotational diffusion) is assumed to couple to fluctuations in the smectic order parameter, because these molecular properties are a function of the precise location of the probe within the transient smecticlike layer. Two limiting cases of (1) (nearly) free translational diffusion of the probe across the smecticlike layer; and (2) expulsion of the probe to the aliphatic chains with highly hindered diffusion (i.e., jump diffusion) across the smecticlike layer are considered. The relevant spectral density shows critical types of divergence, where the exponent depends strongly on the details of the model. It is found that only the (near) zero‐frequency spectral densities can show such divergences. It is pointed out that spectral densities available for spin relaxation do not truly diverge as the N–S_A transition is approached arbitrarily closely, because ultimately motional‐narrowing theory will no longer be valid, and fluctuations begin to be frozen on the ESR time scale. This matter is briefly analyzed. Also considered briefly are the effects of anisotropies in the smectic phase and of fluctuations in nematic director near the N–S_A transition.