Loops versus Branch Functionality in Model Click Hydrogels

Through the use of macromolecular design and efficient chemical reactions it is now possible to control the composition of polymer networks and gels with excellent precision: In contrast, topological defects are still impossible to avoid and are generally difficult to quantify. For example, primary loops that form when a bifunctional monomer (A(2)) reacts twice with the same f functional (f> 2) monomer (B-f) during formation of an end-linked A(2) + B-f network represent a pervasive defect that has a detrimental effect on mechanical integrity. Methods for the quantitative analysis of primary loops in such materials have recently emerged; however, these methods have only been applied to the simplest network structure: A(2) + B-3. Herein, we report strategies for counting primary loops in tetrafunctional (A(2) + B-4) networks and networks with mixed tri- and tetrafunctional (A(2) + B-3/B-4) junctions. We apply these strategies to-the quantitative analysis of primary loops in a series of end-linked poly(ethylene glycol) hydrogels synthesized via copper-catalyzed azide-alkyne cydoaddition click chemistry. Our results show that A(2) + B-4 networks are particularly susceptible to cyclic defects compared to A(2) + B-3 networks and that higher-order cyclic species must play a significant role in the gel point of the former materials. Our experimental results were compared to rate theory and Monte Carlo simulations. This Work reveals new structural insights into a widely studied family of materials and sets the stage for the development of strategies to tune network defects in such gels.