LOCAL KNOT MODEL OF ENTANGLED POLYMER-CHAINS .1. COMPUTER-SIMULATIONS OF LOCAL KNOTS AND THEIR COLLECTIVE MOTION

The local knot (LK) theory recently proposed is confirmed by computer simulations of entangled ring polymer chains. The simple cubic lattice model chains (ring) of length L = 512 (volume fraction c = 0.5) is used. By tracing local maxima of Gauss integral along polymer chains, many "true" LKs (lifetime tau(true) = infinity) and "temporary" LKs (lifetime tau(temp) = 2.3 M u.t.; u.t. = unit of time) are found. It is observed that the orders of true and temporary LKs along rings are conserved and that they perform a collective motion (reptation) as predicted by the theory. Various strange motions of true LKs, such as "merging effect", "multipeak effect", "ghost effect", and "probe fluctuations", are found. In this (part 1) and the following paper (part 2), we discuss in detail how to separate the true Markov motion of LKs and their collective motions from these non-Markov motions. The average number of true and temporary LKs per ring (L = 512) are estimated to be n(true)BAR = 3.44 and n(temp)BAR = 3.0(6). The average chain length per true LKs is L(true)BAR = 149. The diffusion coefficient of single LK is estimated to be d0 = 0.01 72 bond 2/u.t. The mean-square displacement of LK coordinate-xi along a ring, g(t) = [(xi(t) - xi(0))2], approaches the Markov line computed for the diffusion coefficient d0/(n(true)BAR + n(temp)BAR); this suggests that the temporary LKs join to the collective motion of LKs. The empirical entanglement spacing n(e) of this system is estimated to be 230 or slightly less; this n(e) is much larger than n(e) = 120-133 estimated by Skolnick et al.