Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics
Abstract
We formulate and apply a non-replica equilibrium theory for the fluid-glass transition, glass thermodynamic properties, and jamming of hard spheres in three and all higher spatial dimensions. Numerical predictions for the zero complexity glass transition and jamming packing fractions, and a “densest” equilibrium glass, are made. The equilibrium glass equation of state is regarded as the practical continuation of its fluid analog up to jamming. The analysis provides a possible resolution to the inability of any fluid virial series re-summation based equation of state to capture jamming at a reasonable volume fraction. The numerical results are quantitatively compared with various simulation data for equilibrium hard sphere glasses in 3 to 12 dimensions. Although there are uncertainties in this comparison, the predicted zero complexity or configurational entropy and corresponding jamming packing fractions do agree well with two characteristic packing fractions deduced from the dynamic simulation data. The similarities and differences of our approach compared to the replica approach are discussed. Here, the high dimensional scaling of the equilibrium glass transition and jamming volume fractions are also derived. The developments in this paper serve as input to Paper II that constructs a self-consistent integral equation theory of the 3-dimensional hard sphere pairmore »
- Authors:
-
- Univ. of Illinois, Urbana, IL (United States)
- Publication Date:
- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1875154
- Grant/Contract Number:
- FG02-07ER46471
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 139; Journal Issue: 5; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Thermodynamics; Amorphous materials; Integral equations; Free energy landscapes; Glass transitions; Langevin dynamics; Sphere packings; Computer simulation; Equations of state; Nucleon single particle level
Citation Formats
Jadrich, Ryan, and Schweizer, Kenneth S. Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics. United States: N. p., 2013.
Web. doi:10.1063/1.4816275.
Jadrich, Ryan, & Schweizer, Kenneth S. Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics. United States. https://doi.org/10.1063/1.4816275
Jadrich, Ryan, and Schweizer, Kenneth S. Thu .
"Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics". United States. https://doi.org/10.1063/1.4816275. https://www.osti.gov/servlets/purl/1875154.
@article{osti_1875154,
title = {Equilibrium theory of the hard sphere fluid and glasses in the metastable regime up to jamming. I. Thermodynamics},
author = {Jadrich, Ryan and Schweizer, Kenneth S.},
abstractNote = {We formulate and apply a non-replica equilibrium theory for the fluid-glass transition, glass thermodynamic properties, and jamming of hard spheres in three and all higher spatial dimensions. Numerical predictions for the zero complexity glass transition and jamming packing fractions, and a “densest” equilibrium glass, are made. The equilibrium glass equation of state is regarded as the practical continuation of its fluid analog up to jamming. The analysis provides a possible resolution to the inability of any fluid virial series re-summation based equation of state to capture jamming at a reasonable volume fraction. The numerical results are quantitatively compared with various simulation data for equilibrium hard sphere glasses in 3 to 12 dimensions. Although there are uncertainties in this comparison, the predicted zero complexity or configurational entropy and corresponding jamming packing fractions do agree well with two characteristic packing fractions deduced from the dynamic simulation data. The similarities and differences of our approach compared to the replica approach are discussed. Here, the high dimensional scaling of the equilibrium glass transition and jamming volume fractions are also derived. The developments in this paper serve as input to Paper II that constructs a self-consistent integral equation theory of the 3-dimensional hard sphere pair structure, in real and Fourier space, in the metastable regime up to jamming. The latter is employed as input to a microscopic dynamical theory of single particle activated barrier hopping.},
doi = {10.1063/1.4816275},
journal = {Journal of Chemical Physics},
number = 5,
volume = 139,
place = {United States},
year = {Thu Aug 01 00:00:00 EDT 2013},
month = {Thu Aug 01 00:00:00 EDT 2013}
}
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