Isomeric and Non-isomeric Structures of <i>AB_m-</i>type Hyperbranched Polymers: An Approach Using Combinatorics

In the past few decades, the utility of hyperbranched polymers in coatings, drug and gene delivery, additives etc. has provided significant impetus to design molecular architectures with a broad range of physicochemical properties. One of the methods to synthesize these branched polymers is via step polymerization using -type multifunctional monomer. Here, we use combinatorics within the framework of graph theory to obtain structural information about branched polymers. Specifically, we establish one-to-one correspondence between polymer chains and tree data structures and develop various metrics to calculate the exact quantities of isomorphic/non-isomorphic and branched/linear polymer chains. Further, we use the traditional kinetic models to validate our findings. Our approach can be harnessed not only to determine the exact quantity of the hyperbranched polymers formed during synthesis but also be utilized to formulate strategies to optimize their structure, which is critical for the aforementioned applications.