Nonequilibrium static growing length scales in supercooled liquids on approaching the glass transition

Journal of Chemical Physics

Volumn 138, Issue 12, 2013, Pages

  Marcotte, Étienne ^a   Stillinger, Frank H ^a   Torquato, Salvatore ^a,b  

^a PRINCETON UNIVERSITY   (United States)

^b Princeton University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHARACTERISTIC RELAXATION TIME; DIRECT CORRELATION FUNCTIONS; MAXIMALLY RANDOM JAMMED STATE; ORNSTEIN-ZERNIKE INTEGRAL EQUATIONS; POINT CONFIGURATIONS; STRUCTURE FACTORS; SUPERCOOLED LIQUIDS; THERMAL EQUILIBRIUMS;

COMPUTER SIMULATION; GLASS; GLASS TRANSITION; JAMMING; SUPERCOOLING;

INTEGRAL EQUATIONS;

EID: 84875662141     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4769422     Document Type: Article

References (37)

1. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge, 1995)
2. L. Berthier, G. Biroli, J.-P. Bouchaud, J. W. Kob, K. Miyazaki, and D. R. Reichman, J. Phys. Chem. 126, 184503 (2007). 10.1063/1.2721554
3. S. Karmakar, C. Dasgupta, and S. Sastry, Proc. Natl. Acad. Sci. U.S.A. 106, 3675 (2009). 10.1073/pnas.0811082106
4. D. Chandler and J. P. Garrahan, Ann. Rev. Phys. Chem. 61, 191 (2010). 10.1146/annurev.physchem.040808.090405
5. V. Lubchenko and P. G. Wolynes, Ann. Rev. Phys. Chem. 58, 235 (2006). 10.1146/annurev.physchem.58.032806.104653
6. G. M. Hocky, T. E. Markland, and D. R. Reichman, Phys. Rev. Lett. 108, 225506 (2012). 10.1103/PhysRevLett.108.225506
7. A. B. Hopkins, F. H. Stillinger, and S. Torquato, Phys. Rev. E 86, 021505 (2012). 10.1103/PhysRevE.86.021505
8. S. Torquato, T. M. Truskett, and P. G. Debenedetti, Phys. Rev. Lett. 84, 2064 (2000). 10.1103/PhysRevLett.84.2064
9. S. Torquato and F. H. Stillinger, Rev. Mod. Phys. 82, 2633 (2010). 10.1103/RevModPhys.82.2633
10. S. Torquato and F. H. Stillinger, J. Appl. Phys. 102, 093511 (2007); 10.1063/1.2802184
11. S. Torquato and F. H. Stillinger, J. Appl. Phys. 103, 129902 (2008). 10.1063/1.2947597
12. S. Torquato and F. H. Stillinger, Phys. Rev. E 68, 041113 (2003). 10.1103/PhysRevE.68.041113
13. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 3rd ed. (Academic, 2006)
14. A. Donev, F. H. Stillinger, and S. Torquato, Phys. Rev. Lett. 95, 090604 (2005). 10.1103/PhysRevLett.95.090604
15. J. P. K. Doye, D. J. Wales, F. H. M. Zetterling, and M. Dzugutov, J. Chem. Phys. 118, 2792 (2003). 10.1063/1.1534831
16. W. Kob and H. C. Andersen, Phys. Rev. Lett. 73, 1376 (1994). 10.1103/PhysRevLett.73.1376
17. M. D. Rintoul and S. Torquato, Phys. Rev. Lett. 77, 4198 (1996); 10.1103/PhysRevLett.77.4198
18. M. D. Rintoul and S. Torquato, J. Chem. Phys. 105, 9258 (1996). 10.1063/1.473004
19. K. S. Schweizer, J. Chem. Phys. 127, 164506 (2007). 10.1063/1.2780863
20. C. E. Zachary, Y. Jiao, and S. Torquato, Phys. Rev. Lett. 106, 178001 (2011); 10.1103/PhysRevLett.106.178001
21. C. E. Zachary, Y. Jiao, and S. Torquato, Phys. Rev. E 83, 051308 (2011); 10.1103/PhysRevE.83.051308
22. C. E. Zachary, Y. Jiao, and S. Torquato, Phys. Rev. E 83, 051309 (2011). 10.1103/PhysRevE.83.051309
23. The hyperuniformity of maximally random jammed packings has been extended to apply to polydisperse spheres and nonspherical objects in terms of the spectral density χ(k)
24. S. Torquato and G. Stell, J. Chem. Phys. 82, 980 (1985). 10.1063/1.448475
25. S. Torquato, Random Heterogeneous Materials (Springer, 2002)
26. R. J. Baxter, J. Chem. Phys. 52, 4559 (1970). 10.1063/1.1673684
27. Using expression to write S(k) for a single configuration, we can express S(k) as the product of a non-zero vector times its Hermitian transpose, the rank of which (equal to the number of non-zero eigenvalues) is 1. Taking an ensemble average of Eq. breaks this symmetry, since the sum of M vectors multiplied by their transpose has a rank of M if the vectors are linearly independent
28. W. G. Hoover, Phys. Rev. A 31, 1695 (1985). 10.1103/PhysRevA.31.1695
29. B. Widom, J. Chem. Phys. 52, 3888 (1970). 10.1063/1.1673203
30. P. G. Debenedetti and F. H. Stillinger, Nature (London) 410, 259 (2001). 10.1038/35065704
31. Note that we found a very small systematic error due to a combination of the following factors: the thermostat, relaxation during the compressibility computation, and the finite difference method. To correct for this systematic error, we added to the computed value of X a constant such as to ensure that X 0 for the high-temperature liquid phase, for which the compressibility relations are satisfied. This constant is equal to 0.05 for the Z2 Dzugutov potential, and 0.015 for the Kob-Andersen potential
32. R. Brüning, D. A. St-Onge, S. Patterson, and W. Kob, J. Phys.: Condens. Matter 21, 035117 (2009). 10.1088/0953-8984/21/3/035117
33. J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 19, 774 (1951). 10.1063/1.1748352
34. M. Hejna, P. J. Steinhardt, and S. Torquato, Nearly-hyperuniform network models of amorphous silicon. (unpublished)
35. G. Long, R. Xie, S. Weigand, S. Moss, S. Roorda, S. Torquato, and P. Steinhardt, in Proceedings of the Minerals, Metals and Materials Society, March 11-15, 2012, Orlando, FL (published online at http://www.programmaster.org/PM/ PM.nsf/ApprovedAbstracts/87AA55590C28BE69852578CD006C12AA?OpenDocument);
36. R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, Hyperuniformity in amorphous silicon: measurement of the infinite-wavelength limit of the structure factor. (unpublished)
37. P. G. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, NJ, 1996)