Relaxation effects and molecular interactions

Abstract

The molecular rotational motion is one of the most important mechanisms determining relaxation of macroscopic, physical properties and spectral profiles in liquid crystals. Under these circumstances, the relaxation effects are interpreted in terms of a conditional probability P(Ω o; Ω, t) for the change of orientation from Ω o to Ω. When this is assumed to occur through small angular steps, P(Ω o; Ω, t) is the solution of a generalized diffusion equation in which the anisotropic pseudo-potential V(Ω) responsible for the liquid crystalline ordering is introduced [1]: ▪ where L is the operator generating infinitesimal rotations and D the diffusion tensor. In this way, information on the long-range interactions which give rise to the orientational ordering can be obtained from relaxation experiments. As and example, it is examined the effect of a `diffuse cone' or `tilted' rotation [2,3] in smectic-A mesophases on a variety of spectroscopical techniques, including NMR relaxation, ESR lineshapes, dielectric dispersion and neutron scattering. To describe the tilted rotation, the orientational potential is written as a sum of second and fourth-rank legendre polynomials: ▪ the parameters α and λ being adjusted to give selected order parametersP̄ 4. The validity of the diffusional model is theoretically supported by a general memory-function approach, which also provides additional information on the short-range frictional forces. The method is based on the three-variable expansion of the Mori equations [4, 5], adapted to anisotropic systems, where the generalized spherical harmonics are no longer independent variables. The Fourier transforms J MN(ω) of the correlation functions G MN( t) = δ d M( t, δ D N(O) x ) are found to be: ▪ where X and {λ} are eigenfunctions and eigenvalues of the anisotropic diffusion operator. The expansion parameters K 0, K 1 are related to mean-square angular velocity and (total) torque N, and l/γ to the torque relaxation time. The diffusion equation results are recovered under `strong anisotropic interaction limit' (SAIL) conditions [6], K 1,/ K 0 = N/kT ⪢ 1.