A Simple Relationship Relating Linear Viscoelastic Properties and Chemical Structure in a Model Diels–Alder Polymer Network

Although the gel point conversion of a thermoreversible polymer network is certainly a key parameter in determining the material properties, it is not a conventional liquid–solid transition as in common, irreversible networks. Rather, the material’s viscosity is time-dependent and finite at the gel point and beyond, as bond breakage works in concert with diffusion to relax stresses imposed on the forming transient network of the material. For example, in a model Diels–Alder network with functionality 3.8 and a stoichiometric ratio of 10:6 furan:maleimide used here, a crossover frequency (0.52, 0.32, and 0.12 rad/s) was measured below the temperature corresponding to gelation (3, 5, and 10 °C below, respectively). In this work, we describe this complex process occurring in model thermoreversible networks with a simple relationship from the work of Semenov and Rubinstein on associative transient networks. This relationship provides a toolkit for the prediction of the important engineering and rheological properties of the material in the postgel regime, such as viscosity, plateau modulus, and relaxation time, based upon the straightforward estimation of two material-dependent parameters: the gel point conversion <i>p</i>_gel and a proportionality constant <i>C</i>. We show key agreement between theory and experiment as the gel point conversion estimated from network dynamics matches the classical prediction of the gel point within 4% conversion. We discuss the applicability criteria of the Semenov–Rubinstein scaling relationship and compare it to time–temperature superposition methods of describing transient network relaxation