Time-temperature superposition of polybutadiene vitrimers

A vitrimer has covalent cross-links that preserve network connectivity but permit topology fluctuations through dynamic exchange reactions. In this work, we investigate the linear rheology of polybutadiene (PB) vitrimers bearing cross-links that exchange via dioxaborolane metathesis. PB vitrimers are cross-linked in solution using photoinitiated thiol-ene click chemistry. As the targeted cross-link density is increased, both the insoluble fraction and glass transition temperature increase. Linear viscoelasticity is studied using a combination of small amplitude oscillatory shear (SAOS), creep, and stress relaxation measurements. In SAOS, the elastic modulus is approximately constant while the viscous modulus increases as angular frequency decreases. In creep, the compliance displays power law behavior that persists for at least 8 hrs. In stress relaxation, the modulus transitions from a rubbery plateau into a power law regime. Both SAOS and creep data are visually superposed into master curves using horizontal shift factors that exhibit Arrhenius behavior. However, application of these determined shift factors to stress relaxation curves fail to align the data into a single master curve. SAOS shift factors (a_SAOS) collapse the short time relaxation data and their activation energy (E_a^SAOS) matches the effective Williams-Landel-Ferry activation energy for PB homopolymer, indicating that the short time dynamics correspond to network strand segment relaxations. Creep shift factors (a_creep) collapse the long time relaxation data and their activation energy (E_a^creep) is significantly larger than the energies predicted by established theoretical models for transient networks. We speculate the discrepancy between experiment and theory is due to the temperature dependence of the cross-linker mobility within the vitrimer matrix, which is not fully captured by established theoretical models.