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Article

Primitive Path Networks Generated by Annealing and Geometrical Methods: Insights into Differences

Sachin Shanbhag*^†^‡ and Martin Kröger^§

School of Computational Science, Florida State University, Tallahassee, Florida 32306-4120, Department of Chemical and Biomedical Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32310-6046, and Polymer Physics, Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 10, CH-8093 Zurich, Switzerland

Macromolecules, 2007, 40 (8), pp 2897–2903

DOI: 10.1021/ma062457k

Publication Date (Web): March 24, 2007

Corresponding author. Present address: School of Computational Science, Dirac Science Library, Florida State University, Tallahassee, FL 32306-4120. Telephone: 850.644.6548. E-mail: sachins@scs.fsu.edu.

†

School of Computational Science, Florida State University.

‡

Department of Chemical and Biomedical Engineering, FAMU−FSU College of Engineering.

Polymer Physics, Department of Materials, ETH Zurich.

‖

E-mail: mk@mat.ethz.ch.

Abstract

Existing methods to obtain the primitive path network for monodisperse, linear polymers in the molten state are critically compared. A connection is established between the original “annealing” and newer geometrical approaches. A discrepancy of about 15% is observed in the mean primitive path length obtained by these methods for well-entangled polymers. This deviation is attributed to disentanglement that occurs during annealing. A number of well-equilibrated polymeric systems and some toy-configurations (rings) were studied to estimate the relative contributions of slip and constraint release by end-looping to the observed disentanglement. We found that about half (≈ 7.7%) of the discrepancy persists for ring polymers in which end-looping is not possible, and may be attributed to slip alone. It is argued that the characteristics of the network obtained by annealing become practically equivalent to those obtained by geometrical methods in the asymptotic limit of small chain diameter and rapid quenching.

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