Generalized gaussian model for uniaxial rotational motion: application to the calculation of spectroscopic responses

An exact model aimed at describing uniaxial rotational motions, based on a rotational adapted Gaussian statistics, is presented. In its simplest form, it depends on only two parameters, an order parameter which can vary from 1 (perfect order) to 0 (isotropic diffusion) and a time-dependent correlation parameter rho which varies from 1 to 0 between initial and infinite times. This model yields closed form expressions for the correlation functions relevant to the main spectroscopic techniques (dielectric absorption, light and neutron scattering, NMR line shape, spin-lattice relaxation, etc.) for all values of the two parameters. According to the functional form postulated for rho(t), in particular forms decaying as power laws at long times, one obtains shapes for the spectroscopic correlation functions and spectra that are similar to those experimentally observed in a large variety of complex systems (liquid crystals, polymers, gels, and amorphous and glassy materials), especially in confined geometries, which often resemble "stretched" exponentials. A simple way to introduce time coherent effects through a modification of rho(t) is proposed. Examples of theoretical correlation functions and spectra are presented. Important remarks concerning the application of this model to the analysis of real data are made. This model is the rotational analogue of the Gaussian translational model developed recently (Volino et al. J. Phys. Chem B 2006, 110, 11217).