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Goldbart, Paul M. Peng, Weiqun 2012-06-04T18:17:07Z 2012-06-04T18:17:07Z 10000-01-01 2001 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. Submitted by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T18:17:07Z No. of bitstreams: 1 2001_Peng.pdf: 4379088 bytes, checksum: 74792513db5c610eb45ef22f70bac7d5 (MD5) Made available in DSpace on 2012-06-04T18:17:07Z (GMT). No. of bitstreams: 1 2001_Peng.pdf: 4379088 bytes, checksum: 74792513db5c610eb45ef22f70bac7d5 (MD5) Previous issue date: 2001 Restriction data tranferred 2014-07-01T11:34:43-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: thesis Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Elizabeth Kent (eckent2@illinois.edu) on 2012-06-04T18:17:07Z Item is restricted indefinitely. thesis U of I Only 4539080 http://hdl.handle.net/2142/31331 en ©2001 Weiqun Peng vulcanization transition The Vulcanization Transition and the Amorphous Solid State It Yields: A Statistical Mechanical Perspective Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.