The shapes of ideal dendrimers in two and three dimensions

Robin de Regt; Christian von Ferber; Marvin Bishop; Timothy Hamling

doi:10.1016/j.physa.2018.09.196

The shapes of ideal dendrimers in two and three dimensions

Robin de Regt, Christian von Ferber, Marvin Bishop, Timothy Hamling

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

The properties of nine, twelve, twenty-one and thirty-nine branch dendrimers in the ideal regime in both two and three dimensions are investigated. A method based on the Kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers and a scheme originally proposed by Benhamou et al., (2004), are applied to calculate the radii of gyration ratios, the asphericity, shape parameters, and the form factors of these structures. Monte Carlo simulations using a growth algorithm are also employed to determine these properties. It is found that the extrapolated property values obtained by these methods are in excellent agreement with each other and available theory. Dendrimers with a higher generation and a greater number of branches have a more symmetrical shape.

Original language	English
Pages (from-to)	50-57
Number of pages	8
Journal	Physica A: Statistical Mechanics and its Applications
Volume	516
Early online date	15 Oct 2018
DOIs	https://doi.org/10.1016/j.physa.2018.09.196
Publication status	Published - 15 Feb 2019

Funding

We thank the Manhattan College Computer Center, USA and the Kakos Center for Scientific Computing, USA for generous grants of computer time and Professor Paula Whitlock for helpful discussions. Timothy Hamling and Marvin Bishop were supported by Manhattan College Summer Research, USA grants. CvF acknowledges support by FP7 Projects PIRSES-295302 SPIDER and PIRSES-269139 DCP-PhysBio.

Keywords

Analytical approach
Dendrimer
MC simulation
Soft matter

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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10.1016/j.physa.2018.09.196

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abstract = "The properties of nine, twelve, twenty-one and thirty-nine branch dendrimers in the ideal regime in both two and three dimensions are investigated. A method based on the Kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers and a scheme originally proposed by Benhamou et al., (2004), are applied to calculate the radii of gyration ratios, the asphericity, shape parameters, and the form factors of these structures. Monte Carlo simulations using a growth algorithm are also employed to determine these properties. It is found that the extrapolated property values obtained by these methods are in excellent agreement with each other and available theory. Dendrimers with a higher generation and a greater number of branches have a more symmetrical shape.",

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AU - de Regt, Robin

AU - von Ferber, Christian

AU - Bishop, Marvin

AU - Hamling, Timothy

PY - 2019/2/15

Y1 - 2019/2/15

N2 - The properties of nine, twelve, twenty-one and thirty-nine branch dendrimers in the ideal regime in both two and three dimensions are investigated. A method based on the Kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers and a scheme originally proposed by Benhamou et al., (2004), are applied to calculate the radii of gyration ratios, the asphericity, shape parameters, and the form factors of these structures. Monte Carlo simulations using a growth algorithm are also employed to determine these properties. It is found that the extrapolated property values obtained by these methods are in excellent agreement with each other and available theory. Dendrimers with a higher generation and a greater number of branches have a more symmetrical shape.

AB - The properties of nine, twelve, twenty-one and thirty-nine branch dendrimers in the ideal regime in both two and three dimensions are investigated. A method based on the Kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers and a scheme originally proposed by Benhamou et al., (2004), are applied to calculate the radii of gyration ratios, the asphericity, shape parameters, and the form factors of these structures. Monte Carlo simulations using a growth algorithm are also employed to determine these properties. It is found that the extrapolated property values obtained by these methods are in excellent agreement with each other and available theory. Dendrimers with a higher generation and a greater number of branches have a more symmetrical shape.

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KW - MC simulation

KW - Soft matter

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JO - Physica A: Statistical Mechanics and its Applications

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ER -

The shapes of ideal dendrimers in two and three dimensions

Abstract

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Keywords

ASJC Scopus subject areas

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