Abstract
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- line and the slope- line in log-log plot, and the tube diameter can be obtained by recording the time at which data start to leave the slope- 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 data to reach the slope- regime, this could be the best way to find the entanglement length from microscopic consideration.
Highlights
Modern theories of polymer dynamics and rheology describe the universal aspects of the viscoelastic behavior based on the idea that molecular entanglements confine individual filaments to a one-dimensional, diffusive dynamics in tube-like regions in space [1].Entanglements are transient topological constraints arising from the restriction that the backbones of fluctuating chain molecules cannot cut through each other [2,3]
Based on the concept of primitive path, the topological approach proposed by Everaers et al is the so-called primitive path analysis (PPA), which can directly provide the statistical information of the primitive path mesh [4,5]
Based on the methods introduced in the last section, both tube step length (TSL) and tube diameter (TD) can be estimated from monomer mean-square displacement (MSD) data
Summary
Modern theories of polymer dynamics and rheology describe the universal aspects of the viscoelastic behavior based on the idea that molecular entanglements confine individual filaments to a one-dimensional, diffusive dynamics (reptation) in tube-like regions in space [1]. Mesh size is one of most important quantities in tube theory. A quick method to predict mesh size is required and it should be easy to realize in computer simulations. An alternative method by using the monomer MSD was firstly proposed by Likhtman and McLeish [8]. This method is based on the scaling argument of the behaviors of MSD in different time regimes. Seeking a quick and easy method to determine the mesh size in medium-length entangled system is the aim of this paper.
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