A generalized Langevin equation approach to reorientational dynamics in nematic liquid crystals

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Abstract
A new model of reorientational dynamics in nematic liquid crystals, based on a linear generalized Langevin equation (GLE) representation of the dynamics of a probe molecule, is developed. Derived in the limit of high order, the linearized angular motion of a probe molecule under the influence of director fluctuations is analyzed when the time scale of rotational relaxation is comparable to that of the cooperative modes of the liquid crystal solvent. This model allows negative total solvent contributions (director fluctuations plus a negative cross term) to the spectral density J1(ω) relative to the rotational diffusion contribution, a result predicted experimentally by least-squares data fits. This result cannot be justified in terms of existing theories that assume a separation of time scales between the probe molecule motion and relaxation of the cooperative modes of the solvent. Results from the GLE-based model (and the standard model) are compared to measured spectral densities of a highly ordered spin probe dissolved in a nematic liquid crystal [W. H. Dickerson, R. R. Vold, and R. L. Vold, J. Phys. Chem. 87, 166 (1983)]. Because the frequencies involved are low, the model predictions are very similar and excellent numerical agreement is found with both models. However, because the total solvent contribution is observed to involve inhibition of relaxation relative to the rotational diffusion, the standard model must be rejected on the basis of being physically unreasonable. The GLE model, on the other hand, is on firm physical ground and completely reasonable. The observed negative total solvent contribution to the spectral density can be explained in terms of a coupling of cooperative solvent modes with the molecular reorientation of the probe molecule that interferes with relaxation.

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