{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80664"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80664","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Statistical Mechanics of the Amorphous Solid State of Randomly Cross-Linked Macromolecules","abstract":"In the third part of this work, a semi-microscopic statistical-mechanical theory of the elastic properties of the amorphous solid state is presented that accounts for both thermal fluctuations and quenched disorder. It is found that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess crosslink density. It is also found that, quite surprisingly, the external stresses do not spoil the spherical symmetry of the localization clouds of the particles near the transition.","abstract_html":"In the third part of this work, a semi-microscopic statistical-mechanical theory of the elastic properties of the amorphous solid state is presented that accounts for both thermal fluctuations and quenched disorder. It is found that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess crosslink density. It is also found that, quite surprisingly, the external stresses do not spoil the spherical symmetry of the localization clouds of the particles near the transition.","abstract_has_math":false,"creators":["Castillo, Horacio Emilio"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Goldbart, Paul M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"10000-01-01","date_published":"10000-01-01","updated_at":"2026-07-22T22:26:14Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9921669"],"render_values":[{"text":"(MiAaPQ)AAI9921669","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80664","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goldbart, Paul M."]},{"key":"dc:creator","label":"Author","values":["Castillo, Horacio Emilio"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["10000-01-01","1999","2015-09-25T20:03:30Z"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/80664","(MiAaPQ)AAI9921669"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In the third part of this work, a semi-microscopic statistical-mechanical theory of the elastic properties of the amorphous solid state is presented that accounts for both thermal fluctuations and quenched disorder. 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