Helical motions of aliphatic chains in molecular crystals the incoherent quasi-elastic neutron scattering law

Abstract

The incoherent quasi-elastic neutron scattering (IQNS) law for the restricted diffusive motion of a particle along a spiral (helical motion) is derived in order to model correlated rotational and translational motions of molecules in the dynamically disordered phases of organic molecular crystals. In addition, we present a unified formulation to calculate the scattering laws for restricted translational diffusion, uniaxial restricted rotational diffusion and uncorrelated restricted translations and rotations. We therefore discuss the various experimental geometries needed to analyse in detail these motions. Spectra are simulated and analysed on the basis of IQNS experiments performed to study the dynamics of n-nonadecane molecules in various crystalline environments. We also discuss the existence of correlated and uncorrelated rotational and translational motions in the ‘rotator’ phase of pure n-nonadecane samples.