  We present an integrated experimental and quantitative theoretical study of
the mechanics of self-crosslinked, neutral, repulsive pNIPAM microgel
suspensions over concentration (c) range spanning the fluid, glassy and
putative "soft jammed" regimes. In the glassy regime we measure a linear
elastic dynamic shear modulus over 3 decades which follows an apparent power
law concentration dependence G'~$c^{5.64}$, followed by a sharp crossover to a
nearly linear growth at high concentrations. We formulate a theoretical
approach to address all three regimes within a single conceptual Brownian
dynamics framework. A minimalist single particle description is constructed
that allows microgel size to vary with concentration due to steric de-swelling
effects. Using a Hertzian repulsion interparticle potential and a suite of
statistical mechanical theories, quantitative predictions under quiescent
conditions of microgel collective structure, dynamic localization length,
elastic modulus, and the structural relaxation time are made. Based on a
constant inter-particle repulsion strength parameter which is determined by
requiring the theory to reproduce the linear elastic shear modulus over the
entire concentration regime, we demonstrate good agreement between theory and
experiment. Theoretical predictions of how quiescent structural relaxation time
changes under deformation, and how the yield stress and strain change as a
function of concentration has been made. Reasonable agreement with our
observations is obtained. To the best of our knowledge, this is the first
attempt to quantitatively understand structure, quiescent relaxation and shear
elasticity, and nonlinear yielding of dense microgel suspensions using
microscopic force based theoretical methods that include activated hopping
processes. We expect our approach will be useful for other soft polymeric
particle suspensions in the core-shell family.
