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.
|Number of pages||9|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Early online date||20 Apr 2016|
|Publication status||Published - 15 Sep 2016|
Bibliographical noteNOTICE: 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.
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- Soft matter
- Branched polymers
- Analytic approach