The statistical mechanics of continuous random networks

Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order parameter, resulting from a statistical-mechanical approach, captures information concerning this heterogeneity via a certain joint probability distribution. This joint probability distribution describes the variations in the positional and orientational localization of the particles, reflecting the random environments experienced by them, as well as further information characterizing the thermal motion of particles. A complete solution, valid in the vicinity of the amorphous solidification transition, is constructed essentially analytically for the amorphous solid order parameter. Knowledge of this order parameter allows us to draw certain conclusions about the stucture and heterogeneity of randomly covalently bonded atomic or molecular network solids in the vicinity of the amorphous solidification transition. These conclusions are then compared to the results of moleculardynamics simulations of the model and are found to be in good agreement with them. Results of simulations of the system far from the transition are also presented. Robustness of the results of the simulations supports the conclusion that the results obtained are not limited to the context of the particular model presented here, but are, instead, a consequence of the symmetries of the system.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Shakhnovich, Konstantin A.

Contributors dc:contributor

• Goldbart, Paul M.

• statistical mechanics
• constinuous random networks
• joint probability distribution

Statement dc:rights

• ©2001 Shakhnovich

Language dc:language

en

Identifier

4423491

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/31338