Strongly entangled polymer chains in a melt. Description of n.m.r. properties associated with a submolecule model

Abstract

A model is proposed to illustrate properties of the transverse magnetic relaxation function, G( t), of proton pairs linked to strongly entangled polymer chains in a melt. According to this model, any polymer molecule is described as a freely jointed chain and it is divided into submolecules of equal contour length L v e. Every link is supposed to carry a proton pair; dipolar spin couplings between different proton pairs are neglected. The disentanglement relaxation time is supposed to be much longer than any characteristic time of the spin system; consequently, any submolecule observed on an n.m.r. time scale is supposed to have fixed ends. It is considered that the residual spin-coupling energy resulting from such a constraint governs the magnetic relaxation process. The free induction decay is expressed as a contour length function; its time evolution is shown to exhibit two ranges, which might be characterized by two relaxation times. The model is easily extended to rotating methyl groups. Theoretical results are compared with magnetic relaxation properties observed on entangled real chains: polydimethylsiloxane (PDMS) and cis-1,4-polybutadiene (PB). An attempt to adjust the contour length value to experimental results leads to the determination of average submolecule molecular weights M v e equal to 8200 and 2000 for PDMS and PB, respectively; the values usually obtained from viscoelastic plateau modulus measurements are 8100 and 1900, respectively.