Topological Theory of Entanglement: A Polymer Chain and a Fixed Barrier. II. Frictional Coefficient of the Center of Mass

Abstract

In the previous paper, a system composed of a polymer chain and a fixed barrier has been studied and a diffusion equation has been derived for a simultaneous distribution function in regard to a few normal coordinates Q_α and a few topological variables T_α. In this paper, the following are given: (i) The nature of the diffusion equation is examined qualitatively and it is shown that the entanglement effect on the motion of the center of mass of the polymer chain is caused by fluctuations of the topological variables T_α² around their equilibrium values, (ii) an average force acting an the center of mass is calculated exactly along its fixed trajectory and an expression of frictional coefficient ζ of the center of mass is derived. Numerical calculations of ζ are given in the following paper.