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Topological Characteristics of Chain Molecules with Branching and Molar-Mass Distributions

机译：分支和摩尔质量分布的链分子的拓扑特征

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摘要

A graph-theoretical method is presented for characterizing the statistical and dynamic properties of randomly and fixed-branched chains that exhibit molecular weight distribution. The Wiener index, which is a topological index reflecting tree-shaped structures, of any branched chain estimated from its random-flight model (molecular graph) enables to express the radius of gyration and dynamic relaxation times of various chains with branching and molar-mass distributions. A homologous series of branched chains with random branching points can be obtained by comparing their Wiener indices with those of their corresponding primitive chains (where the subchains between adjacent branch or end points are reduced to single bonds). Moreover, the analogical growth of a fixed-branched structure during polymerization can be quantitatively analyzed using analogous functions, which are also determined by comparing the statistics and dynamic properties of branched polymers and their primitive chains.
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