Unified theory of orientational relaxation

In liquids, the autocorrelation function for angular velocity, <ω x (t)ω x (0)>, and the corresponding correlation time, τω , where can be determined only indirectly. Several methods are discussed: computer experiments; measurement of reorientation correlation times, τl , and the determination of τω through the Hubbard relation, measurement of spin-rotational correlation times, τ sr, by measn of magnetic resonance and the subsequent identification of τ sr with τ ω; and the analysis of spectral lineshapes, Il (ω), and the approximate relationship of <ωx (t)ωx (0)> to the Fourier transform of ω 2 Il (ω). By the application of a previously constructed theory, the unified theory of orientational relaxation (UTOR), expressions are obtained for τω and τωτl in terms of intermolecular torques, and these formulae can be recast in terms of experimentally measurable moments of spectral lineshapes. We discuss the significance and short-comings of each of these methods. We find that in the rotational diffusion limit, τω is very much smaller than times characteristic of nuclear motions. This fact can be understood if <ωx (t)ωx (0)> becomes negative after some short, but physically reasonable time, τf τl; or if, at a given instant, most of the molecules are held clamped in torsional potential wells formed by the surrounding liquid.