  Solutions of polymer chains are modelled using non-equilibrium Brownian
dynamics simulations, with physically associative beads which form reversible
crosslinks 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 binding energy at 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 modulii 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 binding energy. Further, it is shown that the
competition of scales between the sticker dissociation time and the
single-polymer relaxation time determines if the gel is in the evanescent
regime.
