Local know model of entangled polymer chains. 2. Theory of probe fluctuation and diffusion coefficient of a single local knot

The local knot (LK) theory is tested by computer simulations in parts 1 and 2. Here, theoretical problems of the simulations are mainly discussed. The probe fluctuation found in part 1 is studied theoretically, and a method for separating the Markov motion of a LK from its probe fluctuation is proposed. A detailed discussions on the mechanism of the probe fluctuation and the uncertainty principal are given. A modified expression of the diffusion coefficient of a LK is derived that cancels the interference of the probe fluctuations, and its numerical calculation is performed. A correction for short memory effects of LK motion is also done. The theoretical value of d0 thus computed is 0.0393 bond2/u.t. (u.t. - unit time) which is comparable to its simulation value 0.0172 bond2/u.t. obtained in part 1. Finally, it is concluded that the LK theory is proved by the results of parts 1 and 2 and, by this, a true molecular theory of entanglement has been first established. 13 refs., 7 figs., 1 tab