Random Branching of Polymer Chains with Schulz–Zimm Distribution. 2. Radius of Gyration and Maximum Span Length,Macromolecular Theory and Simulations

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Random Branching of Polymer Chains with Schulz–Zimm Distribution. 2. Radius of Gyration and Maximum Span Length
Macromolecular Theory and Simulations ( IF 1.8 ) Pub Date : 2020-02-05 , DOI: 10.1002/mats.201900057
Hidetaka Tobita ₁

Affiliation

Mean‐square radius of gyration Rg² and the maximum span length L_MS of each polymer molecule are investigated for the random branching of primary chains that follow the Schulz–Zimm distribution, by using the Monte Carlo simulation method. It is found that the expected g‐ratio of Rg² of the branched molecule to that of a linear molecule for a given number of branch points k does not change with the branching density. The expected g‐ratio becomes larger for the primary chains with broader distribution. An approximate formula for the relationship between g‐ratio and k that accounts for the distribution breadth is proposed. The relationship between the weight fraction of the maximum span chain L_MS/(degree of polymerization) and k shows the analogous behavior with that for g‐ratio and k. The magnitude of Rg² is proportional to L_MS, with Rg² = 0.18 L_MS, irrespective of the breadth of the primary polymer chain length distribution.

中文翻译：

具有Schulz-Zimm分布的聚合物链的随机分支。2.回转半径和最大跨度

回转均方半径RG ²和最大跨距长度大号_MS每个聚合物分子进行了研究用于跟随的舒尔茨-席姆分布，通过使用蒙特卡罗模拟法初级链的随机支化。发现对于给定数目的分支点k，支链分子的Rg ²与线性分子的Rg ²的预期g比不会随支化密度而改变。分布较广的主链的预期g比值会变大。g比率与k之间的关系的近似公式提出了解决分布宽度问题的建议。最大跨度链的重量分数L _MS /（聚合度）与k的关系显示出与g比率和k相似的行为。的幅度RG ²正比于大号_MS，用RG ² = 0.18大号_MS，而不管主聚合物链长分布的宽度的。

更新日期：2020-02-05

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