“Kinetic models for network-forming reactions to predict material properties”
Polymer networks are one of the most ubiquitous categories of materials in the world today. From car tires to contact lenses to advanced biomedical and personal care materials, they enable our transportation, health, and quality of life in a critical way. However, networks are also one of the most mysterious categories of soft materials because they have both irregular spatial and topological structure, making them difficult to characterize with most structural techniques. Therefore, although it is known that the complex connectivity of polymer networks influences their material properties, we still lack a quantitative understanding of the relationship connecting structure and properties.
Inspired by the modelling work of Stepto and by new experimental methods from Johnson’s lab at MIT, we have worked over the past several years to develop kinetic theories for simulating network-forming reactions as the basis for modelling the molecular configurations of polymers within networks and their resulting physical properties. These theories based both on kinetic Monte Carlo (KMC) and differential equation formalisms (called kinetic graph theory, KGT) allow extremely rapid simulation of polymer networks by considering a purely topological approach to network connectivity that appears to be valid in the reaction-limited regime that applies to many network systems. They have led to insightful predictions of both linear mechanical properties and fracture properties, and their implementation is currently being automated in a piece of web-based code that makes complex network design tasks accessible to a wide variety of molecular engineers. A key test of these theories that has also been explored is their ability to successfully move beyond simple model materials and predict properties in more complex networks used in industry, including those with side reactions and multiple different crosslinking mechanisms.
In addition to predicting molecular configurations and mechanical properties, KMC and KGT models for network formation have been able to predict gel point suppression. Extending these theories to the prediction of critical exponents near the gel point, the results suggest that gelation does not follow universal critical behavior because the critical exponents depend upon the reaction concentration used for network formation. Moreover, the theory predicts that the forward and reverse gel points do not align, a significant discrepancy with our current understanding of network polymers. Although we cannot yet explain the origins of these effects, we present detailed experiments that show that in experimental systems the forward and reverse gel points need not align, affirming that there is a need for significant revision of polymer network theory.