Investigation of Local Motions in Polymers by the Method of Molecular Dynamics

Abstract

The main features of local motions in linear polymer chains and in cross-linked macromolecules were studied by the method of molecular dynamics. The chain model consists of particles connected by rigid bonds and interacting with each other and with solvent particles with Lennard-Jones potential forces. Chains with various numbers of units were considered at various concentrations and temperatures. The characteristics of local motions (translational and rotational mobility), normal modes, and cooperative motions and the effect of cross-linking on local chain mobility were investigated. The results of numerical experiments (NE) are compared with analytical results for a viscoelastic Hearst-Harris (H-H) model. It is shown that the char- acteristics of both local motions and normal modes are close to those of viscoelastic models. The dependence of the characteristic relaxation times of normal modes on the wavenumber virtually coincides with that for the H-H model. The present study suggests that in cross-linked systems the translational and rotational mobility of the cross-link and the adjoining chain elements are greatly hindered. The relationship between the characteristic times obtained in NE and experimental results on dielectric relaxation and polarized luminescence is discussed. The molecular theory of equilibrium properties of polymers in solution, in the melt and in bulk, is based on the principles and methods of conformational statistics of macromolecules developed by Flory and co-workers,2 V~lkenstein,~~ Ptitsyn and Bir~htein,~~ and others. This theory started from simple models of a polymer chain describing qualitatively the observed relationships. Models of real chains as developed at present permit the deter- mination of numerical values of physical parameters. In contrast, in the molecular theory of the nonequilibrium relaxation process in polymers we are only at the beginning of our path. The dynamic theory of polymers uses mainly semiphenomenological viscoelastic models that describe the average motion of chain segments containing many units. The transition to models in which the kinetic ele- ment is represented by a rigid link or a monomer unit rather than by a flexible subchain is difficult, because their analytical description involves substantial mathematical difficulties. These difficulties increase on passing from the description of the motion of a single chain in a continuous viscous medium to a more detailed description in which the interactions of polymer particles with each other and the solvent are explicitly taken into account. Computer simulation of molecular motion is the most suitable method for solving these problems. According to the degree of precision desired, different models and corresponding methods of motion simulation may be used. In lattice chain models, motion occurs as a result of random local rearrangements of chain elements. The mechanism of local mobility (various types of elementary jumps) is postulated and its manifestations in various dynamic chain characteristics are considered. Monte-Carlo methods are used for computer simulation of the motion of such mod- els+