Statistical Physics of Soft Random Solids: Vulcanization, Heterogeneity, and Elasticity

107 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008.In the second part of this thesis, Chapters 3, 4, and 5, spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the structure of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their elastic properties. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in the vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid to random solid transition. The resulting free energy of these Goldstone modes can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids, in terms of residual stress and Lam'e-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlation functions involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD