  Colloids that attractively bond to only a few neighbors (e.g., patchy
particles) can form equilibrium gels with distinctive dynamic properties that
are stable in time. Here, we use a coarse-grained model to explore the dynamics
of linked networks of patchy colloids whose average valence is macroscopically,
rather than microscopically, constrained. Simulation results for the model show
dynamic hallmarks of equilibrium gel formation and establish that the
colloid-colloid bond persistence time controls the characteristic slow
relaxation of the self-intermediate scattering function. The model features
re-entrant network formation without phase separation as a function of linker
concentration, centered at the stoichiometric ratio of linker ends to
nanoparticle surface bonding sites. Departures from stoichiometry result in
linker-starved or site-starved networks with reduced connectivity and shorter
characteristic relaxation times with lower activation energies. Underlying the
re-entrant trends, dynamic properties vary monotonically with the number of
effective network bonds per colloid, a quantity that can be predicted using
Wertheim's thermodynamic perturbation theory. These behaviors suggest
macroscopic in situ strategies for tuning the dynamical response of colloidal
networks.
