Schilling, Rolf ; Scheidsteger, Thomas (2008)
Mode coupling approach to the ideal glass transition of molecular liquids: Linear molecules.
In: Physical Review E, 1997, 56 (3)
Artikel, Zweitveröffentlichung, Postprint
Kurzbeschreibung (Abstract)
The mode coupling theory (MCT) for the ideal liquid glass transition, which was worked out for simple liquids mainly by Gotze, Sjogren, and their co-workers, is extended to a molecular liquid of linear and rigid molecules. By use of the projection formalism of Zwanzig and Mori an equation of motion is derived for the correlators S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t) of the tensorial one-particle density rho [sub lm]([bold q],t), which contains the orientational degrees of freedom for l(greater-than)0. Application of the mode coupling approximation to the memory kernel results into a closed set of equations for S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t), which requires the static correlators S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q]) as the only input quantities. The corresponding MCT equations for the nonergodicity parameters f[sub l][sup m](q)(equivalent)f[sub lm,lm](q[bold e][sub 3]) are solved for a system of dipolar hard spheres by restricting the values for l to 0 and 1. Depending on the packing fraction cursive-phi and on the temperature T, three different phases exist: a liquid phase, where translational (TDOF's) (l=0) and orientational (ODOF's) (l=1) degrees of freedom are ergodic, a phase where the TDOF are frozen into a (nonergodic) glassy state, whereas the ODOF's remain ergodic, and finally a glassy phase where both, TDOF's and ODOF's, are nonergodic. From the nonergodicity parameters f[sub 0][sup 0](q) and f[sub 1][sup 1](q) for q=0, we may conclude that the corresponding relaxation strength of the alpha peak of the compressibility can be much smaller than the corresponding strength of the dielectric function.
| Typ des Eintrags: |
Artikel
|
| Erschienen: |
2008 |
| Autor(en): |
Schilling, Rolf ; Scheidsteger, Thomas |
| Art des Eintrags: |
Zweitveröffentlichung |
| Titel: |
Mode coupling approach to the ideal glass transition of molecular liquids: Linear molecules |
| Sprache: |
Englisch |
| Publikationsjahr: |
17 Oktober 2008 |
| Ort: |
Darmstadt |
| Publikationsdatum der Erstveröffentlichung: |
1997 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: |
Physical Review E |
| Jahrgang/Volume einer Zeitschrift: |
56 |
| (Heft-)Nummer: |
3 |
| URL / URN: |
https://tuprints.ulb.tu-darmstadt.de/1131 |
| Zugehörige Links: |
|
| Kurzbeschreibung (Abstract): |
The mode coupling theory (MCT) for the ideal liquid glass transition, which was worked out for simple liquids mainly by Gotze, Sjogren, and their co-workers, is extended to a molecular liquid of linear and rigid molecules. By use of the projection formalism of Zwanzig and Mori an equation of motion is derived for the correlators S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t) of the tensorial one-particle density rho [sub lm]([bold q],t), which contains the orientational degrees of freedom for l(greater-than)0. Application of the mode coupling approximation to the memory kernel results into a closed set of equations for S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q],t), which requires the static correlators S[sub lm,l[sup (prime)]m[sup (prime)]]([bold q]) as the only input quantities. The corresponding MCT equations for the nonergodicity parameters f[sub l][sup m](q)(equivalent)f[sub lm,lm](q[bold e][sub 3]) are solved for a system of dipolar hard spheres by restricting the values for l to 0 and 1. Depending on the packing fraction cursive-phi and on the temperature T, three different phases exist: a liquid phase, where translational (TDOF's) (l=0) and orientational (ODOF's) (l=1) degrees of freedom are ergodic, a phase where the TDOF are frozen into a (nonergodic) glassy state, whereas the ODOF's remain ergodic, and finally a glassy phase where both, TDOF's and ODOF's, are nonergodic. From the nonergodicity parameters f[sub 0][sup 0](q) and f[sub 1][sup 1](q) for q=0, we may conclude that the corresponding relaxation strength of the alpha peak of the compressibility can be much smaller than the corresponding strength of the dielectric function. |
| Freie Schlagworte: |
cond-mat, Soft Condensed Matter, mode coupling theory, Gotze, Sjogren,projection formalism of Zwanzig and Mori, mode coupling approximation, nonergodicity parameter, translational, orientational degrees of freedom, memory kernel, dipolar hard spheres, packing fraction, static correlators |
| Schlagworte: |
| Einzelne Schlagworte | Sprache |
|---|
| cond-mat, Soft Condensed Matter, mode coupling theory, Gotze, Sjogren,projection formalism of Zwanzig and Mori, mode coupling approximation, nonergodicity parameter, translational, orientational degrees of freedom, memory kernel, dipolar hard spheres, packing fraction, static correlators | Englisch |
|
| Status: |
Postprint |
| URN: |
urn:nbn:de:tuda-tuprints-11317 |
| Zusätzliche Informationen: |
PACS96: 61.20.Lc Time-dependent properties; relaxation PACS96: 61.25.Em Molecular liquids PACS96: 61.43.Fs Glasses |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): |
500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): |
05 Fachbereich Physik |
| Hinterlegungsdatum: |
19 Jun 2024 14:16 |
| Letzte Änderung: |
19 Jun 2024 14:16 |
| PPN: |
|
| Schlagworte: |
| Einzelne Schlagworte | Sprache |
|---|
| cond-mat, Soft Condensed Matter, mode coupling theory, Gotze, Sjogren,projection formalism of Zwanzig and Mori, mode coupling approximation, nonergodicity parameter, translational, orientational degrees of freedom, memory kernel, dipolar hard spheres, packing fraction, static correlators | Englisch |
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Mode coupling approach to the ideal glass transition of molecular liquids: Linear molecules. (deposited 19 Jun 2024 14:16)
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