VH light scattering from triphenyl phosphite: Coupling of shear modes to molecular rotation

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Abstract
The light-scattering spectrum of liquid triphenyl phosphite (TPP) has been studied over a temperature range in which the parameter (k 2η/Γoρ) varies from 0·17 to 50, where k is the scattering vector, η the shear viscosity, ρ the mass density and Γ0 the rotational correlation frequency determined from the HH spectrum. The VH spectrum changes markedly in character over this temperature range and can be explained in terms of molecular rotations coupled to shear modes. A single coupling parameter, dependent upon a time-dependent correlation function, is required to fit the spectrum; this parameter (R) is about equal to 0·45 and is independent of temperature and of k. The spectrum is a function of the parameter (k 2η/Γ0ρ) which includes variations with viscosity, temperature and scattering angle. A statistical theory is presented which yields a different explicit expression for the spectrum from that obtained previously; the difference is essential at large values of (k 2η/Γ0ρ). The coefficient of shear viscosity is independent of frequency, and the rotational relaxation frequency Γ0 obeys an extended Debye formula with an effective rotational radius aκ1/3, where a is the ‘true’ molecular radius obtained by means of molar refraction and κ = 0·55 is independent of temperature and is a measure of the coupling between rotations and translational shear modes. κ is closely related to the coupling parameter R, and ηR is the rotational contribution to the shear viscosity. A relation is obtained between the multiparticle parameter κ and its single particle equivalent κs; it is likely that κs < κ for TPP.