NMR TRANSVERSE RELAXATION FUNCTION CALCULATED FOR CONSTRAINED POLYMER-CHAINS - APPLICATION TO ENTANGLEMENTS AND NETWORKS

A general method is presented for calculating the NMR transverse relaxation function due to dipolar interactions between a spin pair, rigidly attatched to a constrained polymer chain. The constraints considered are those restricting the dynamics of the end-to-end vector of an arbitrary group of consecutive polymer segments. A direct application is made to the motion of polymer chains, as perceived by NMR, in deformed cross-linked systems. The ability to handle this type of constraint enables a more general hierarchical chain structure to be created, where the dynamics on one scale can be quite different from those operating on another scale, so that entanglements as well as cross-links can be included. General results are given for the relaxation function in a form that is shown to be dynamically scale invariant. The methods presented and in particular the incorporation of the constraints are entirely novel and lead to an exact calculation of the transverse NMR relaxation function. As a result the conditions under which the NMR relaxation is exponential or otherwise are clearly shown. The general results are explicitly illustrated by the case of a chain, consisting of two levels of structure, i.e., a small-scale structure with relatively fast (with respect to the NMR time) relaxation and a larger scale structure subjected to deformation and governed by slower dynamics. © 1990, American Chemical Society. All rights reserved.