Vulcanization and the random solid state it yields: A statistical mechanical perspective.

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition, known as the vulcanization transition, to a random solid state. In this random solid state, particles are permanently but randomly localized, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. The aims of this paper are two-fold: First, the briefest sketch will be given of aspects of the mean-field theory of the vulcanization transition and the emergent random solid state. (These aspects have been reviewed elsewhere rather recently.) Second, a more detailed account will be given of various new results on the vulcanization transition beyond mean-field theory. [ABSTRACT FROM AUTHOR]