Evanescent gels: Competition between sticker dynamics and single-chain relaxation

Solutions of polymer chains are modeled using nonequilibrium Brownian dynamics simulations, with physically associative beads which form reversible cross-links to establish a system-spanning physical gel network. Rheological properties such as the zero-shear-rate viscosity and relaxation modulus are investigated systematically as functions of polymer concentration and the binding energy between associative sites. It is shown that a system-spanning network can form regardless of the binding energy at a sufficiently high concentration. However, the contribution to the stress sustained by this physical network can decay faster than other relaxation processes, even single-chain relaxations. If the polymer relaxation time scales overlap with short-lived associations, the mechanical response of a gel becomes “evanescent,” decaying before it can be rheologically observed, even though the network is instantaneously mechanically rigid. In our simulations, the concentration of elastically active chains and the dynamic moduli are computed independently. This makes it possible to combine structural and rheological information to identify the concentration at which the sol-gel transition occurs as a function of the binding energy. Furthermore, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines whether the gel is in the evanescent regime.