{"title":"Linear Relationship between Mean-Square Radius of Gyration and Graph Diameter, and Its Application to Network Polymers","authors":"Hidetaka Tobita","doi":"10.1002/mats.202200055","DOIUrl":null,"url":null,"abstract":"<p>Mean-square radius of gyration <i>Rg</i><sup>2</sup> and the graph diameter <i>D</i> of the random crosslinked network polymers are investigated to find a linear relationship, <i>Rg</i><sup>2</sup> = <i>a D</i>. The proportionality coefficient, <i>a</i> is dominated by the cycle (circuit) rank, or the number of intramolecular crosslinks <i>k</i><sub>c</sub>, and a convenient equation is proposed for the relationship between <i>a</i> and <i>k</i><sub>c</sub>. This relationship makes it possible to estimate <i>Rg</i><sup>2</sup> based on <i>D</i> and <i>k</i><sub>c</sub>, which can reduce the required computational time to determine the <i>Rg</i><sup>2</sup>-values greatly. This new method is applied to find that the contraction factor <i>g</i> decreases with <i>k</i><sub>c</sub>, and the differences in the primary chain length distribution that constitute the network polymers vanish for large <i>k</i><sub>c</sub>-values.</p>","PeriodicalId":18157,"journal":{"name":"Macromolecular Theory and Simulations","volume":"32 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Macromolecular Theory and Simulations","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mats.202200055","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"POLYMER SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Mean-square radius of gyration Rg2 and the graph diameter D of the random crosslinked network polymers are investigated to find a linear relationship, Rg2 = a D. The proportionality coefficient, a is dominated by the cycle (circuit) rank, or the number of intramolecular crosslinks kc, and a convenient equation is proposed for the relationship between a and kc. This relationship makes it possible to estimate Rg2 based on D and kc, which can reduce the required computational time to determine the Rg2-values greatly. This new method is applied to find that the contraction factor g decreases with kc, and the differences in the primary chain length distribution that constitute the network polymers vanish for large kc-values.
研究了随机交联网络聚合物的旋转均方半径Rg2和图径D之间的线性关系Rg2 = a D，比例系数a由环(电路)秩或分子内交联数kc决定，并提出了a与kc之间的关系式，该关系式使得基于D和kc来估计Rg2成为可能。这样可以大大减少确定rg2值所需的计算时间。应用该方法发现，收缩因子g随kc值的增大而减小，并且当kc值较大时，构成网络聚合物的主链长度分布的差异消失。
期刊介绍：
Macromolecular Theory and Simulations is the only high-quality polymer science journal dedicated exclusively to theory and simulations, covering all aspects from macromolecular theory to advanced computer simulation techniques.
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