Reformulating Time-Cure Superposition to Describe the Phase Transition in Rearranging Gel Networks

Rearranging hydrogels are used for applications that require tailored control of solid- and liquid-like properties. These applications necessitate pinpointing the phase transition, where a sample-spanning structure is formed or broken. To characterize the mechanical properties at the phase transition, we use time-cure superposition (TCS), which superimposes rheological properties as a function of increasing extents of gelation or degradation, p. We generally use reaction time to estimate p. However, dynamic materials undergo network rearrangements, which invalidates this assumption. In this work, we characterize the rheology of a rearranging hydrogel during degradation using multiple particle tracking microrheology (MPT). The logarithmic slope of the particle mean-squared displacements, α, is used to estimate p instead of time, because α is directly related to the cross-link density, ρ, and is independent of time. This reformulation identifies the phase transition unambiguously and more precisely, expanding the scope of the technique to quantify phase transitions in these types of hydrogels.