Decay of angular correlation functions by multiple rotational potential diffusion in polymer chains, with applications to NMR relaxation in paraffin chains of lipid bilayers

Abstract

Spectroscopic techniques as NMR give information about correlation functions of the motion. For polymer chains, this motion is the result of internal rotations about several bonds. These rotations are supposed to be independent of each other and are described by one-dimensional rotational diffusion in a suitable potential. The general case is described and calculations are made for a trigonometric potential with three minima. The free rotational diffusion and the trans-gauche model are limiting cases of this model. The correlation functions decay on two time scales, for short times due to motion within the wells of the potential, which however not causes a decay to zero. On a longer time scale the functions decay further to zero by passage over the potential barriers. The model is applied to NMR-relaxation in hydro-carbon chains of lipid bilayers, where it gives another dependence upon chain position than previous models.