Time-temperature-composition equivalence of the viscoelastic behavior through the glass transition of digitally mixed 3D-printed polymers

Abstract

The linear viscoelastic behavior of a polymer shows an equivalence of loading frequency and temperature, the time-temperature equivalence (TTE). Horizontal shifting extends moduli measured over limited ranges to much wider ranges, through the glass transition. Multimaterial 3D printing has created digitally mixed polymers, a new class in which elastomeric and glassy resins are mixed voxel by voxel in prescribed ratios. Composition shifts the location and breadth of the glass transition and increases the rubbery modulus. Here we extend TTE to a time-temperature-composition equivalence (TTCE). Across all measured temperatures, frequencies, and compositions, the storage modulus collapses onto one master curve. Composition translates the transition and stretches its breadth, both linearly. The phase angle and relaxation spectrum superpose under the same operations, so the family shares one distribution of relaxation times. A single closed-form TTCE gives the storage and loss moduli of the family, guiding graded and architected designs for elasticity and dissipation.