Rotational relaxation of molecules in isotropic and anisotropic fluids

Abstract

A theory of rotational relaxation in isotropic and anisotropic liquids is presented. The Debye rotational diffusion model is generalized so as to include reorientations of arbitrary angle with the use of a nonlocal in orientation master equation for the orientational conditional probability. For isotropic media, we have previously demonstrated that spectral line shapes (Fourier transforms of time correlation functions) appropriate to, for example, Raman and ir line broadening spectroscopy, are always superpositions of Lorentzian lines. We present here an algebraic formulation which gives the linewidths of the Lorentzian lines in terms of the transition probability describing the reorientational motion. Several models and general trends for these linewidths are discussed in order to facilitate the comparison of experimental results and this theory. For anisotropic media, such as liquid crystals or small molecules ordered by liquid crystals, a nonlocal reorientational mechanism leads to a continuous spectrum and singular eigenfunctions in the eigenvalue-eigenvector decomposition of the conditional probability. This leads to formal line shape expressions which, while certainly non-Lorentzian, are difficult to evaluate. For a special model transition probability and for the long times relevant to line shape measurements, explicit asymptotic expressions for the time correlation functions can be obtained which also lead to non-Lorentzian line shapes.