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We present an integrated experimental and quantitative theoretical study ofthe mechanics of self-crosslinked, neutral, repulsive pNIPAM microgelsuspensions over concentration (c) range spanning the fluid, glassy andputative "soft jammed" regimes. In the glassy regime we measure a linearelastic dynamic shear modulus over 3 decades which follows an apparent powerlaw concentration dependence G'~$c^{5.64}$, followed by a sharp crossover to anearly linear growth at high concentrations. We formulate a theoreticalapproach to address all three regimes within a single conceptual Browniandynamics framework. A minimalist single particle description is constructedthat allows microgel size to vary with concentration due to steric de-swellingeffects. Using a Hertzian repulsion interparticle potential and a suite ofstatistical mechanical theories, quantitative predictions under quiescentconditions of microgel collective structure, dynamic localization length,elastic modulus, and the structural relaxation time are made. Based on aconstant inter-particle repulsion strength parameter which is determined byrequiring the theory to reproduce the linear elastic shear modulus over theentire concentration regime, we demonstrate good agreement between theory andexperiment. Theoretical predictions of how quiescent structural relaxation timechanges under deformation, and how the yield stress and strain change as afunction of concentration has been made. Reasonable agreement with ourobservations is obtained. To the best of our knowledge, this is the firstattempt to quantitatively understand structure, quiescent relaxation and shearelasticity, and nonlinear yielding of dense microgel suspensions usingmicroscopic force based theoretical methods that include activated hoppingprocesses. We expect our approach will be useful for other soft polymericparticle suspensions in the core-shell family.

Linear and Nonlinear Rheology and Structural Relaxation in Dense Glassy and Jammed Soft Repulsive Microgel Suspensions