Extended Smoluchowski models for interpreting relaxation phenomena in liquids

Interpretation of the dynamical behaviour of single molecules or collec- tive modes in liquids has been increasingly centered, in the last decade, on complex liquid systems, including ionic solutions, polymeric liquids, super- cooled fluids and liquid crystals. This has been made necessary by the need of interpreting dynamical data obtained by advanced experiments, like optical Kerr effect, time dependent fluorescence shift experiments, two- dimensional Fourier-transform and high field electron spin resonance and scattering experiments like quasi-elastic neutron scattering. This commu- nication is centered on the definition, treatment and application of several extended stochastic models, which have proved to be very effective tools for interpreting and rationalizing complex relaxation phenomena in liq- uids structures. First, applications of standard Fokker-Planck equations for the orientational relaxation of molecules in isotropic and ordered liquid phase are reviewed. In particular attention will be focused on the inter- pretation of neutron scattering in nematics. Next, an extended stochastic model is used to interpret time-domain resolved fluorescence emission ex- periments. A two-body stochastic model allows the theoretical interpre- tation of dynamical Stokes shift effects in fluorescence emission spectra, performed on probes in isotropic and ordered polar phases. Finally, for the case of isotropic fluids made of small rigid molecules, a very detailed model is considered, which includes as basic ingredients a Fokker-Planck descrip- tion of the molecular librational motion and the slow diffusive motion of a persistent cage structure together with the decay processes related to the changing structure of the cage.