Molecular translation — rotational coupling contribution to neutron incident line broadening in nematic liquid crystals

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Abstract
The component of the neutron quasi elastic line broadening in the oriented nematic phase, originating from the translation-rotational molecular coupling, is investigated. The molecules, approximated by ellipsoides, are assumed to undergo simple diffusion and a rotational Brownian motion along the long body axes. It is shown that in the nematic phase the translation, as modulated by the rotation, leads to the neutron scattering cross section for the center of mass motion which depends upon the relative magnitude of the term Q4⊥(ΔD)2body/ R2. Here, Q⟩ is the component of neutron scattering vector perpendicular to the optical axis, (ΔD) body is the difference of molecular self diffusion constants along the short and the intermediate body axes and R is the rotational diffusion coefficient along the long molecular axis. The center of mass neutron scattering cross section is represented by a single Lorentzian or by the sum of Lorentzian terms. In the former case the weak hindering approximation is applicable in this phase. It is suggested that for PAA, the temperature dependence of the laboratory self diffusion constants D∥ and D ⊥ (∥ and ⟩ to the optical axis) might be governed by the temperature dependence of the order parameter

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