Determining the Reaction Kinetics and Thermodynamics of a Diels–Alder Network Using Dynamic Gel Criteria

Abstract

We undertook a detailed rheological investigation to evaluate the kinetic parameters of the forward and reverse Diels–Alder (DA) reactions of a model network cross-linked using a furan prepolymer and a common aromatic bismaleimide. At high temperature where the Winter–Chambon’s criterion of frequency-independence was more applicable, a multiwave technique permitted van’t Hoff analysis and calculation of the reaction thermodynamic parameters, specifically the enthalpy and entropy of the reaction: ΔH° = −38.3 ± 5.2 kJ mol^–1 and ΔS° = −94.3 ± 13.4 J mol^–1. At mild temperatures where the G′–G″ crossover point is experimentally convenient to measure gelation, isothermal tests were used to obtain reasonable fDA kinetic parameters from Eyring analysis such as the apparent activation enthalpy and entropy of $\Delta H_{\mathrm{fDA}}^{‡}=76.8\pm 6.9{\mathrm{kJ}\mathrm{mol}}^{-1}$ and $\Delta S_{\mathrm{fDA}}^{‡}=-82.8\pm 22.2J{\mathrm{mol}}^{-1}{K}^{-1}$. Comparable rheokinetic methods include cross-linking density measurements and stress relaxation tests to calculate effective kinetics, whereas the critical gel conversion was consistently applied here. Rate data are fitted with the Arrhenius equation for comparison purposes and the Eyring equation to demonstrate its broader utility.