10.1007/s10634-008-2006-x

Abstract

Orientational interaction of macromolecules is inherent, to a certain extent, in all polymers [1]. Macromolecules in biopolymers and liquid crystal (LC) polymers are spontaneously oriented, whereas those in fiber and film materials are subjected to forced orientation. In recent years, hundreds of LC polymers have been synthesized. A new field of research is the developments of LC elastomers [2].The requirements for synthesis of oriented polymers are stimulating the study of the causes of ordering and of the effect of the structure of such polymers on their properties. To obtain polymers with desired properties, their structural dynamic properties should be studied. For polymers, this task is more challenging than for low-molecular-weight compounds since these properties depend on the molecular weight distribution and conformation of macromolecules [1,3].Oriented polymers are studied by different experimental methods. NMR spectroscopy has turned out to be an informative method of estimation of the order of orientation of macromolecules [4,5]. Stimulated echo NMR is usually used for measuring the translational diffusion in polymers [6]. However, the lack of a theory of NMR spectra for oriented macromolecules prevents establishment of a correlation between diffusion effects and NMR signals of these polymers.In this work, we developed a theory of NMR spectra of oriented polymers on the basis of the theory of free induction decay (FID) in isotropic polymer networks and quasi-networks of entanglements [7][8][9]. This theory makes it possible to determine the structural dynamic characteristics (the order of orientation S , diffusion coefficient D , correlation function) of polymers taking into account the molecular weight distribution of chains. The theory is applicable in a wide range of changes in temperature, orientation order, average chain length N 0 , and molecular weight distribution.To consider molecular motions, we used the dynamic model represented in [8] by three types of motions with corresponding correlation functions k i ( τ ) of molecular motions of a separate chain:(1)where k 1 ( τ ) and k 2 ( τ ) are the functions characterizing small-and large-scale motions of chain segments, respectively; N is the length of the chain with fixed ends expressed in statistical segment length units; and θ is the angle between the magnetic field direction and the radius vector of the chain. The correlation function of the motion of the entire polymer chain in the high-temperature temperature range T > T st + 100°ë was determined for all possible conformations of the polymer chain [7]:(2)The FID for a crosslinked polymer sample after isotropic averaging over all directions of chains and their lengths between chain nodes with the distribution function P ( N ) takes the form (3) The FID of the sample can be represented as where G 1 ( t ) and G 2 ( t ) are described in the Anderson-Weiss model with the corresponding correlation function [7]:(4) According to Eqs. (1)-(4), only the G 3 ( t ) function depends on the orientation o...