Characterizing the Molecular Architecture of Hydrogels and Crosslinked Polymer Networks beyond Flory–RehnerI. Theory

In the early 1940s, Paul Flory and John Rehner published a series of papers on the properties of swellable polymeric networks. Originally intended for vulcanized rubber, their development has since been extensively used and extended to much more complex systems, such as hydrogels, and used to estimate the mesh size of such networks. In this article, we take a look at the development of the Flory–Rehner equation and highlight several issues that arise when using such a theory for the described hydrogel networks. We then propose a new approach and equations to accurately calculate the backbone molecular weight in-between crosslinks while explicitly accounting for the molecular mass of the crosslinker and branch segments. The approach also provides more applicable mesh dimensions, for complex networks with macromeric crosslinkers and/or a high degree of branching, as is the case of biocompatible hydrogels. The approach is finally illustrated by a case study comparing the values obtained with our proposed approach to those using the state-of-the-art approach.