The Dynamic Interplay of Cross-Linking and Exchange Reaction Probabilities during Vitrimer Synthesis: A Monte Carlo Approach

Abstract

Covalent adaptable networks (CANs) are based on an associative exchange mechanism, and hence, vitrimers have been shown to be an attractive candidate for the synthesis of sustainable cross-linked materials due to synergetic structural stability and reprocessability. Herein, matrix-based kinetic Monte Carlo (kMC) simulations are performed to increase our mechanistic understanding of vitrimer synthesis, selecting step-growth vinylogous carbamothioate (VC)-based CANs as dynamic chemistry. Novelties are (i) the consideration of 8 elementary reaction categories differentiating between cross-linking and exchange reactions as well as inter- and intramolecular reactions (22 in total); and (ii) a dedicated tuning strategy of both intrinsic and diffusion parameters, employing experimental data from Fourier transform infrared spectroscopy and rheological measurements. Upon a model validation at different temperatures (30–60 °C), revealing a key role for mobility constraints due to viscosity increases, emphasis is on the evolution of molecular properties such as the branching density, the reduced mass-average degree of polymerization, the mass-average molar mass, and the mass fraction of the sol, to understand the relationship of kinetics, reaction probabilities, and molecular network properties. The simulation results demonstrate that increasing the temperature to, e.g., 60 °C, sufficiently promotes the exchange rate, leading to a gel point realization at higher conversion enabling the production of more uniform cross-linked structures. They also show that at higher yield, more intramolecular reactions come in to play, complicating the network structural arrangement. It is further shown that the traditional Flory and Macosko–Miller theories are no longer applicable to predicting gel points and molecular properties in dynamic network systems with higher exchange rates. Moreover, the generation of branched and cross-linked structures can be delayed with the increase of the molar ratio of primary amine groups to acetoacetate groups. The current study provides an in-depth understanding of the reaction kinetics for the synthesis of VC-based CANs, and it is an important step toward a generalized elementary reaction step driven kinetic model as well as chemistry design for vitrimer synthesis.