The two dimensional shapes of simple three and four junction ideal comb polymers

R. de Regt; M. Bishop; A. J. Barillas; T. Borgeson; Christian von Ferber

doi:10.1016/j.physa.2016.03.109

The two dimensional shapes of simple three and four junction ideal comb polymers

R. de Regt, M. Bishop, A. J. Barillas, T. Borgeson, Christian von Ferber

LIB Mathematics Support Centre

Manhattan College

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Abstract

We redesign and apply a scheme originally proposed by Wei (1995) [2,3] to produce numerical shape parameters with high precision for arbitrary tree-branched polymers based on their Kirchhoff matrix eigenvalue spectrum. This algorithm and a Monte Carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers. We find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory. We confirm that polymers with a complete set of interior branches display a more circular shape.

Original language	English
Pages (from-to)	391–398
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	458
Early online date	20 Apr 2016
DOIs	https://doi.org/10.1016/j.physa.2016.03.109
Publication status	Published - 15 Sept 2016

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Physica A: Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A: Statistical Mechanics and its Applications, [458, , (2016)] DOI:10.1016/j.physa.2016.03.
© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Keywords

Soft matter
Branched polymers
Analytic approach
Simulation

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title = "The two dimensional shapes of simple three and four junction ideal comb polymers",

abstract = "We redesign and apply a scheme originally proposed by Wei (1995) [2,3] to produce numerical shape parameters with high precision for arbitrary tree-branched polymers based on their Kirchhoff matrix eigenvalue spectrum. This algorithm and a Monte Carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers. We find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory. We confirm that polymers with a complete set of interior branches display a more circular shape.",

keywords = "Soft matter, Branched polymers, Analytic approach, Simulation",

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note = "NOTICE: this is the author{\textquoteright}s version of a work that was accepted for publication in Physica A: Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A: Statistical Mechanics and its Applications, [458, , (2016)] DOI:10.1016/j.physa.2016.03. {\textcopyright} 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International ",

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AU - de Regt, R.

AU - Bishop, M.

AU - Barillas, A. J.

AU - Borgeson, T.

AU - von Ferber, Christian

N1 - NOTICE: this is the author’s version of a work that was accepted for publication in Physica A: Statistical Mechanics and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica A: Statistical Mechanics and its Applications, [458, , (2016)] DOI:10.1016/j.physa.2016.03. © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

PY - 2016/9/15

Y1 - 2016/9/15

N2 - We redesign and apply a scheme originally proposed by Wei (1995) [2,3] to produce numerical shape parameters with high precision for arbitrary tree-branched polymers based on their Kirchhoff matrix eigenvalue spectrum. This algorithm and a Monte Carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers. We find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory. We confirm that polymers with a complete set of interior branches display a more circular shape.

AB - We redesign and apply a scheme originally proposed by Wei (1995) [2,3] to produce numerical shape parameters with high precision for arbitrary tree-branched polymers based on their Kirchhoff matrix eigenvalue spectrum. This algorithm and a Monte Carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers. We find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory. We confirm that polymers with a complete set of interior branches display a more circular shape.

KW - Soft matter

KW - Branched polymers

KW - Analytic approach

KW - Simulation

U2 - 10.1016/j.physa.2016.03.109

DO - 10.1016/j.physa.2016.03.109

M3 - Article

SN - 0378-4371

VL - 458

SP - 391

EP - 398

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

The two dimensional shapes of simple three and four junction ideal comb polymers

Abstract

Bibliographical note

Keywords

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Cite this