Conformational Relaxation

Abstract

The fundamental model of macromolecular dynamics in an entangled system, which was formulated in the previous chapter, imitates the basic isotropic stochastic motion of the particles of the chain among the neighbouring chains, and includes a special non-linear effect – reptation motion of the macromolecule. The system of equations allows one to find correlation functions of coordinates and calculate conformational relaxation times of macromolecular coils. In the analytic investigation, some approximations of the fundamental system will be considered: instead of a single non-linear equation, we shall consider two particular cases: linear mesoscopic equation for weakly entangled systems and the original non-amended reptation-tube model for strongly entangled systems. We consider these two models as complementary models and combine the results, unless an analysis of unified non-linear model is available. The numerical investigation of complete non-linear model allows us to calculate the times of relaxation of the macromolecular coil, while the transition point between two modes of relaxation (diffusive and reptation) is evaluated as 10M _e. Both for the weakly and strongly entangled systems, in contrast to relaxation behaviour of the macromolecule in a viscous liquid, two relaxation branches emerge as characteristics of the relaxation behaviour of a macromolecular coil in a system of entangled macromolecules.