On the Theory of NMR Line Shapes in Amorphous Regions of Uniaxially Oriented Polymers

Abstract

A theory of NMR of protons belonging to highly-stretched polymer chains with fixed ends, e.g. tie molecules of amorphous regions of oriented semicrystalline polymers, is presented. Analysis is carried out in terms of the model of freely-jointed chains. All contributions to the line shape from the intramolecular dipole-dipole interactions (DDI) are taken into account. Expressions are derived for the residual time independent component of DDI and the second moments of the fluctuating DDI. The NMR spectra are described in terms of the Anderson-Weiss approximation. A number of spectra are calculated for polyethylene. It is shown that the linewidth of high lemperature spectrum rapidly grows with stretching and approaches that of crystallite polymer. It is demonstrated that the distribution function of tie molecules can, in principle, be obtained from the dependence of the spectra on the stretching ratio.

Key Words:

• NMR spectra
• freely-jointed chains
• molecular-weight distribution function
• tie molecules
• amorphous region.