The Vulcanization Transition and the Amorphous Solid State It Yields: A Statistical Mechanical Perspective
Peng, Weiqun
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https://hdl.handle.net/2142/31331
Description
Title
The Vulcanization Transition and the Amorphous Solid State It Yields: A Statistical Mechanical Perspective
Author(s)
Peng, Weiqun
Issue Date
2001
Doctoral Committee Chair(s)
Goldbart, Paul M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
vulcanization transition
Language
en
Abstract
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.
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