Brachiation of a polymer chain in the presence of a dynamic network

The viscoelastic behavior of a physically crosslinked gel involves a spectrum of molecular relaxation processes, which at the single-chain level involve the chain undergoing transient hand-to-hand motion through the network. We develop a self-consistent theory for describing transiently associating polymer solutions that captures these complex dynamics. A single polymer chain transiently binds to a viscoelastic background that represents the polymer network formed by surrounding polymer chains. The viscoelastic background is described in the equation of motion as a memory kernel, which is self-consistently determined based on the predicted rheological behavior from the chain itself. The solution to the memory kernel is translated into rheological predictions of the complex modulus over a wide range of frequencies to capture the time-dependent behavior of a physical gel. Using the loss tangent predictions, a phase diagram is shown for the sol-gel transition of polymers with dynamic association affinities. This theory provides a predictive, molecular-level framework for the design of associating gels and supramolecular assemblies with targeted rheological properties.