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Updated: Jul 4, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Analytic expressions for the statistics of the primitive-path length in entangled polymers
Renat N Khaliullin1, Jay D Schieber
1Department of Chemical and Biological Engineering, and Center for Molecular Study of Condensed Soft Matter, Illinois Institute of Technology, 10 W. 33rd Street, Chicago, Illinois, USA.
Abstract:
An analytic expression is proposed for the primitive-path length of entangled polymer chains. The expression is derived from statistical mechanics of a chain that is a random walk with randomly scattered entanglements. The only parameters are the number of Kuhn steps in the chain and a dimensionless parameter beta that contains information about the entanglement density and Kuhn step size. The expression is found to compare very favorably with numerical results recently found from examining topological constraints in microscopic simulations. The comparison also predicts well the plateau modulus of polyethylene, suggesting that the slip-link model is a viable intermediate in the search for true ab initio rheology predictions. Since the expression is analytic, it can be used to make predictions where the simulations cannot reach, and hence is applicable for coarse graining.
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