Semimicroscopic theory of elasticity near the vulcanization transition

Semimicroscopic theory of elasticity near the vulcanization transition

Randomly cross-linked macromolecules undergo a liquid to amorphous-solid phase transition at a critical cross-link concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence of a nonzero static shear modulus. In this paper, a semimicroscopic statistical mechanical theory of the elastic properties of the amorphous solid state i...

Theory & Practice Of Vulcanization

Density-correlator signatures of the vulcanization transition

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal...

Connecting the vulcanization transition to percolation.

The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wavelength behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it ...

Emergent Physics at the Vulcanization Transition

The Essay starts with an overview of the percolation approach and classical elasticity theory of the vulcanization transition of rubber, describing their assumptions and their limitations. Thereafter we discuss a third approach, the Vulcanization Theory (VT) which incorporates the effects of thermal fluctuations and quenched random disorder. The VT is an order parameter theory in the true Landa...