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Int. J. Mol. Sci. 2009, 10(11), 5054-5089; doi:10.3390/ijms10115054
Review

Combined Molecular Algorithms for the Generation, Equilibration and Topological Analysis of Entangled Polymers: Methodology and Performance

1,*  and 2,*
Received: 6 October 2009 / Revised: 17 November 2009 / Accepted: 20 November 2009 / Published: 23 November 2009
(This article belongs to the Special Issue Algorithms and Molecular Sciences)
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Abstract

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.
Keywords: polymer; simulation; Monte Carlo; primitive path; knot; entanglement; random packing; hard-sphere; melt; system size effect; polydispersity polymer; simulation; Monte Carlo; primitive path; knot; entanglement; random packing; hard-sphere; melt; system size effect; polydispersity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Karayiannis, N.C.; Kröger, M. Combined Molecular Algorithms for the Generation, Equilibration and Topological Analysis of Entangled Polymers: Methodology and Performance. Int. J. Mol. Sci. 2009, 10, 5054-5089.

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