Stochastic-molecular theory of spin–relaxation for liquid crystals

Abstract

The theory of spin relaxation for liquid crystals is examined with the objective of properly analyzing the statistical i n t e rdependence of the faster rotational reorientation of the individual spin‐bearing molecules and the (slower) director or order‐parameter fluctuations. The analysis is presented in terms of a composite Markov process including both types of motions. It is shown that one recovers a sum of spectral‐density terms which, in lowest order in fluctuations, correspond to (1) reorientation of the molecule relative to the equilibrium potential of mean torque, (2) effects of director fluctuations, and (3) a negative cross‐term between these two processes which bears a simple relation to (2). Detailed results are given for the particular models of director fluctuations in the nematic phase, quasicritical order fluctuations on either side of the isotropic–nematic phase transition, and slow fluctuations in the local structure. Effects of localized cooperative modes of molecular reorientation are also included. Explicit expressions for NMR and ESR relaxation and line shapes are given. The results obtained here clearly demonstrate some weaknesses in previous treatments which were presumed to be based on an assumption of the statistical independence of the different motional processes. Discussion is also given on how to formulate director fluctuations as a multidimensional Markov process, and on the applicability of motional narrowing theory in these cases where director fluctuations have very slowly relaxing components.