In the theory of hyperbranched polymerization, due to the difficulty of deriving isomers of conformations, the early Flory's probability method and Stockmayer's statistical mechanics method have been rarely used. In this work, a new and easy way to derive the total number of configurations is developed, which can extend the application of the two theoretical methods to obtain the size distribution functions of hyperbranched polymerization. Taking the example of AB_g type hyperbranched polymerization, the size distribution functions of the products are respectively deduced by the probability, statistical mechanics, and kinetic method. The same result is obtained, which shows the self-consistent relationship of these methods and can help people understand the mechanism of aggregation process. These theoretical methods have their own advantages, which can be combined to deal with complex hyperbranched polymerization.

中文翻译：

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超支化聚合产物尺寸分布函数的理论方法

在超支化聚合理论中，由于难以获得构象异构体，因此很少使用早期的Flory概率法和Stockmayer的统计力学方法。在这项工作中，开发了一种新的简单的方法来获得构型总数，可以扩展这两种理论方法的应用以获得超支化聚合的尺寸分布函数。以AB _g为例通过超支化聚合反应，通过概率，统计力学和动力学方法分别推导了产物的尺寸分布函数。获得了相同的结果，表明了这些方法之间的自洽关系，可以帮助人们了解聚合过程的机理。这些理论方法有其自身的优点，可以结合起来处理复杂的超支化聚合反应。