Theoretical Methods of the Size Distribution Function for the Products of Hyperbranched Polymerization

Abstract

AbstractIn 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 ABg 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.