The Vulcanization Transition and the Amorphous Solid State It Yields: A Statistical Mechanical Perspective

The vulcanization transition is a crosslink-density-controlled equilibrium phase transition from the liquid to the amorphous solid state. In order to understand the origins and consequences of the universal aspects of this transition and the emergent solid state, we construct a minimal model in the spirit of the Landau approach to continuous phase transitions. At the mean-field level this model produces the essential features of the liquid state and, especially, the amorphous solid state, such as the fraction of randomly localized particles and the scaling function that describes the statistical distribution of localization lengths. Our investigation of the vulcanization transition beyond the mean-field level, via both a perturbative renormalization group approach and a diagrammatic analysis of the two- and three-point vertex functions to all orders in perturbation theory, shows that percolation theory correctly captures the critical phenomenology of the vulcanization transition associated with percolative aspects of the liquid and critical states. In addition, we study certain density correlators associated with the vulcanization transition, which are accessible via various experimental techniques. These correlators turns out to contain essential information about both the vulcanization transition and the emergent amorphous solid state.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Peng, Weiqun

Contributors dc:contributor

• Goldbart, Paul M.

• vulcanization transition

Statement dc:rights

• ©2001 Weiqun Peng

Language dc:language

en

Identifier

4539080

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31331