  We use computer simulations to study the relaxation dynamics of a model for
oil-in-water microemulsion droplets linked with telechelic polymers. This
system exhibits both gel and glass phases and we show that the competition
between these two arrest mechanisms can result in a complex, three-step decay
of the time correlation functions, controlled by two different localization
lengthscales. For certain combinations of the parameters, this competition
gives rise to an anomalous logarithmic decay of the correlation functions and a
subdiffusive particle motion, which can be understood as a simple crossover
effect between the two relaxation processes. We establish a simple criterion
for this logarithmic decay to be observed. We also find a further
logarithmically slow relaxation related to the relaxation of floppy clusters of
particles in a crowded environment, in agreement with recent findings in other
models for dense chemical gels. Finally, we characterize how the competition of
gel and glass arrest mechanisms affects the dynamical heterogeneities and show
that for certain combination of parameters these heterogeneities can be
unusually large. By measuring the four-point dynamical susceptibility, we probe
the cooperativity of the motion and find that with increasing coupling this
cooperativity shows a maximum before it decreases again, indicating the change
in the nature of the relaxation dynamics. Our results suggest that compressing
gels to large densities produces novel arrested phases that have a new and
complex dynamics.
