  This is an integrated experimental and theoretical study of the dynamics and
rheology of self-crosslinked, slightly charged, temperature responsive soft
Poly(N-isopropylacrylamide) (pNIPAM) microgels over a wide range of
concentration and temperature spanning the sharp change in particle size and
intermolecular interactions across the lower critical solution temperature
(LCST). Dramatic, non-monotonic changes in viscoelasticity are observed with
temperature, with distinctive concentration dependences in the dense fluid,
glassy, and soft-jammed states. Motivated by our experimental observations, we
formulate a minimalistic model for the size dependence of a single microgel
particle and the change of interparticle interaction from purely repulsive to
attractive upon heating. Using microscopic equilibrium and time-dependent
statistical mechanical theories, theoretical predictions are quantitatively
compared with experimental measurements of the shear modulus. Good agreement is
found for the nonmonotonic temperature behavior that originates as a
consequence of the competition between reduced microgel packing fraction and
increasing interpar-ticle attractions. Testable predictions are made for
nonlinear rheological properties such as the yield stress and strain. To the
best of our knowledge, this is the first attempt to quantitatively understand
in a unified manner the viscoelasticity of dense, temperature-responsive
microgel suspensions spanning a wide range of temperatures and concentrations.
