  Power law rheology is of widespread occurrence in complex materials that are
characterized by the presence of a very broad range of microstructural length
and time scales. Although phenomenological models able to reproduce the
observed rheological features exist, in general a well-established connection
with the microscopic origin of this mechanical behavior is still missing. As a
model system, this work focuses on a fractal colloidal gel. We thoroughly
characterize the linear power law rheology of the sample and its age
dependence. We show that at all sample ages and for a variety of rheological
tests the gel linear viscoelasticity is very accurately described by a
Fractional Maxwell (FM) model, characterized by a power law behavior. Thanks to
a unique set-up that couples small-angle static and dynamic light scattering to
rheological measurements, we demonstrate that the power law rheology observed
in the linear regime originates from reversible non-affine rearrangements and
discuss the possible relationship between the FM model and the microscopic
structure of the gel.
