Determine Mesh Size through Monomer Mean-Square Displacement

A dynamic method to determine the main parameter of the tube theory through monomer mean-square displacement is discussed in this paper. The tube step length can be measured from the intersection of the slope- [Formula: see text] line and the slope- [Formula: see text] line in log-log plot, and the tube diameter can be obtained by recording the time at which [Formula: see text] data start to leave the slope- [Formula: see text] regime. According to recent simulation data, the ratio of the tube step length to the tube diameter was found to be about 2 for different entangled polymer systems. Since measuring the tube diameter does not require [Formula: see text] data to reach the slope- [Formula: see text] regime, this could be the best way to find the entanglement length from microscopic consideration.