• Corpus ID: 219792563

# Segment Distribution around the Center of Gravity of Branched Polymers

@article{Suematsu2020SegmentDA,
title={Segment Distribution around the Center of Gravity of Branched Polymers},
author={Kazumi Suematsu and Haruo Ogura and S. Inayama and Toshihiko Okamoto},
journal={arXiv: Soft Condensed Matter},
year={2020}
}
• Published 12 June 2020
• Physics
• arXiv: Soft Condensed Matter
Mathematical expressions for mass distributions around the center of gravity are derived for branched polymers with the help of the Isihara formula. We introduce the Gaussian approximation for the end-to-end vector, $\vec{r}_{G\nu_{i}}$, from the center of gravity to the $i$th mass point on the $\nu$th arm. Then, for star polymers, the result is \varphi_{star}(s)=\frac{1}{N}\sum_{\nu=1}^{f}\sum_{i=1}^{N_{\nu}}\left(\frac{d}{2\pi\left\langle r_{G\nu_{i}}^{2}\right\rangle}\right…
1 Citations

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## References

SHOWING 1-10 OF 48 REFERENCES
Excluded Volume Effects of Branched Molecules
The expansion factor, $\alpha^{2}=\langle s_{N}^{2}\rangle/\langle s_{N}^{2}\rangle_{0}$, of branched molecules in the melt state is estimated. The equilibrium expansion factor is determined as the
Alternative Approach to the Excluded Volume Problem The Critical Behavior of the Exponent $\nu$
• Physics
• 2018
We present the alternative derivation of the excluded volume equation. The resulting equation is mathematically identical to the one proposed in the preceding paper. As a result, the theory
Volume Expansion of Branched Polymers
The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this
Excluded volume effect in flexible dendron systems: A self-consistent field theory
• Physics
• 2016
We have studied the conformation and scaling behavior of a flexible dendron (the primary branch of a dendrimer) immersed in neutral or good solvents. A self-consistent field theory combined with a
The Rouse Dynamic Properties of Dendritic Chains: A Graph Theoretical Method
• Mathematics
• 2017
The eigen-polynomials of the Rouse matrix for the G-generation dendritic chains with arbitrary spacer length (n), and functionalities of the central segment (f0) and outer segments (f) are derived
Configurational Statistics of Highly Branched Polymer Systems
• Mathematics
• 1964
Applications of the theory of branching processes to polymer systems can be so formulated, that all statistical parameters emerge automatically in a form which applies to the soluble part of the
Dependence of the cyclization behavior of multifunctional network molecules on molecular size
The tendency for cyclization of nonlinear network molecules is quantitatively expressed by the cyclization probability, defined as the ratio of cyclization to total reaction rate. In contrast to
Random walk with shrinking steps
• Mathematics
• 2004
We outline the properties of a symmetric random walk in one dimension in which the length of the nth step equalsl, with l,1. As the number of steps N→`, the probability that the end point is at x
Statistics of « starburst » polymers
• Materials Science
• 1983
. 2014 We discuss the growth of completely branched polymer, based on tertiary amine branch points conected by flexible linear portions (« spacers ») each of P monomers. The method is a modified
Marginally compact hyperbranched polymer trees.
• Materials Science
Soft matter
• 2017
This work generates by means of a proper fractal generator hyperbranched polymer trees which are marginally compact and shows that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time τp of mode p must scale as τp ∼ (N/p)5/3 rather than the usual square power law for linear chains.