Dynamical heterogeneity in lattice glass models

Journal of Chemical Physics

Volumn 132, Issue 4, 2010, Pages

  Darst, Richard K ^a   Reichman, David R ^a   Biroli, Giulio ^b,c  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b DIF   (France)

^c Centre National de la Recherche Scientifique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMISTIC SYSTEM; DYNAMICAL HETEROGENEITIES; FRAGILE GLASS; KINETICALLY CONSTRAINED MODELS; LATTICE GLASS MODEL; LATTICE MODELS; LENGTH SCALE; PARTICLE MOTIONS; STOKES-EINSTEIN RELATION; TIME-SCALES;

GLASS FORMING MACHINES; LIQUIDS;

GLASS;

EID: 75749125404     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3298877     Document Type: Article

References (83)

1. P. Debenedetti and F. Stillinger, Nature (London) NATUAS 0028-0836 410, 259 (2001). 10.1038/35065704 (Pubitemid 32218700)
2. M. Ediger, C. Angell, and S. Nagel, J. Phys. Chem. JPCHAX 0022-3654 100, 13200 (1996). 10.1021/jp953538d
3. J. Garrahan and D. Chandler, Phys. Rev. Lett. PRLTAO 0031-9007 89, 035704 (2002). 10.1103/PhysRevLett.89.035704
4. J. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 100, 9710 (2003). 10.1073/pnas.1233719100 (Pubitemid 37087006)
5. L. Hedges, R. Jack, J. Garrahan, and D. Chandler, Science SCIEAS 0036-8075 323, 1309 (2009). 10.1126/science.1166665
6. V. Lubchenko and P. G. Wolynes, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 58, 235 (2007). 10.1146/annurev.physchem.58.032806.104653 (Pubitemid 46880966)
7. J. Bouchaud and G. Biroli, J. Chem. Phys. JCPSA6 0021-9606 121, 7347 (2004). 10.1063/1.1796231
8. D. Kivelson, S. A. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, Physica A PHYADX 0378-4371 219, 27 (1995). 10.1016/0378-4371(95)00140-3
9. W. Gotze and L. Sjogren, Rep. Prog. Phys. RPPHAG 0034-4885 55, 241 (1992). 10.1088/0034-4885/55/3/001
10. K. Schweizer and E. Saltzman, J. Chem. Phys. JCPSA6 0021-9606 119, 1181 (2003). 10.1063/1.1578632
11. J. Dyre, Rev. Mod. Phys. RMPHAT 0034-6861 78, 953 (2006). 10.1103/RevModPhys.78.953 (Pubitemid 44496728)
12. J. Langer, Phys. Rev. Lett. PRLTAO 0031-9007 97, 115704 (2006). 10.1103/PhysRevLett.97.115704 (Pubitemid 44396700)
13. A. Heuer, J. Phys. Condens. Matter JCOMEL 0953-8984 20, 373101 (2008). 10.1088/0953-8984/20/37/373101
14. S. Butler and P. Harrowell, J. Chem. Phys. JCPSA6 0021-9606 95, 4454 (1991). 10.1063/1.461768
15. M. Hurley and P. Harrowell, Phys. Rev. E PLEEE8 1063-651X 52, 1694 (1995). 10.1103/PhysRevE.52.1694
16. W. Kob, C. Donati, S. Plimpton, P. Poole, and S. Glotzer, Phys. Rev. Lett. PRLTAO 0031-9007 79, 2827 (1997). 10.1103/PhysRevLett.79.2827
17. R. Yamamoto and A. Onuki, Phys. Rev. E PLEEE8 1063-651X 58, 3515 (1998). 10.1103/PhysRevE.58.3515
18. K. Schmidt-Rohr and H. Spiess, Phys. Rev. Lett. PRLTAO 0031-9007 66, 3020 (1991). 10.1103/PhysRevLett.66.3020
19. M. Ediger, Annu. Rev. Phys. Chem. ARPLAP 0066-426X 51, 99 (2000). 10.1146/annurev.physchem.51.1.99
20. I. Chang and H. Sillescu, J. Phys. Chem. B JPCBFK 1089-5647 101, 8794 (1997). 10.1021/jp9640989
21. M. Cicerone and M. Ediger, J. Chem. Phys. JCPSA6 0021-9606 104, 7210 (1996). 10.1063/1.471433
22. Y. Jung, J. Garrahan, and D. Chandler, Phys. Rev. E PLEEE8 1063-651X 69, 061205 (2004). 10.1103/PhysRevE.69.061205
23. X. Xia and P. Wolynes, J. Phys. Chem. B JPCBFK 1089-5647 105, 6570 (2001). 10.1021/jp004616m (Pubitemid 35339026)
24. G. Tarjus and D. Kivelson, J. Chem. Phys. JCPSA6 0021-9606 103, 3071 (1995). 10.1063/1.470495
25. L. Berthier, D. Chandler, and J. Garrahan, Europhys. Lett. EULEEJ 0295-5075 69, 320 (2005). 10.1209/epl/i2004-10401-5 (Pubitemid 40209759)
26. D. Stariolo and G. Fabricius, J. Chem. Phys. JCPSA6 0021-9606 125, 064505 (2006). 10.1063/1.2221309 (Pubitemid 44239105)
27. P. Chaudhuri, L. Berthier, and W. Kob, Phys. Rev. Lett. PRLTAO 0031-9007 99, 060604 (2007). 10.1103/PhysRevLett.99.060604 (Pubitemid 47263149)
28. E. Saltzman and K. Schweizer, Phys. Rev. E PLEEE8 1063-651X 77, 051504 (2008). 10.1103/PhysRevE.77.051504 (Pubitemid 351768340)
29. S. F. Swallen, K. Traynor, R. J. McMahon, M. D. Ediger, and T. E. Mates, J. Phys. Chem. B JPCBFK 1089-5647 113, 4600 (2009). 10.1021/jp808912e
30. L. Berthier, Phys. Rev. E PLEEE8 1063-651X 69, 020201 (2004). 10.1103/PhysRevE.69.020201
31. A. Pan, J. Garrahan, and D. Chandler, Phys. Rev. E PLEEE8 1063-651X 72, 041106 (2005). 10.1103/PhysRevE.72.041106
32. G. Szamel and E. Flenner, Phys. Rev. E PLEEE8 1063-651X 73, 011504 (2006). 10.1103/PhysRevE.73.011504 (Pubitemid 43256601)
33. N. Lačević, F. Starr, T. Schrøder, and S. Glotzer, J. Chem. Phys. JCPSA6 0021-9606 119, 7372 (2003). 10.1063/1.1605094
34. C. Dasgupta, A. Indrani, S. Ramaswamy, and M. Phani, Europhys. Lett. EULEEJ 0295-5075 15, 307 (1991). 10.1209/0295-5075/15/3/013
35. S. Franz and G. Parisi, J. Phys.: Condens. Matter JCOMEL 0953-8984 12, 6335 (2000). 10.1088/0953-8984/12/29/305 (Pubitemid 30906135)
36. L. Berthier, G. Biroli, J. Bouchaud, W. Kob, K. Miyazaki, and D. Reichman, J. Chem. Phys. JCPSA6 0021-9606 126, 184503 (2007). 10.1063/1.2721554 (Pubitemid 46745219)
37. S. Franz and A. Montanari, J. Phys. A JPHAC5 0305-4470 40, F251 (2007). 10.1088/1751-8113/40/11/F01
38. G. Biroli, J. Bouchaud, A. Cavagna, T. Grigera, and P. Verrocchio, Nat. Phys. ZZZZZZ 1745-2473 4, 771 (2008). 10.1038/nphys1050
39. L. Berthier, G. Biroli, J. Bouchaud, L. Cipelletti, D. Masri, D. L'Hote, F. Ladieu, and M. Pierno, Science SCIEAS 0036-8075 310, 1797 (2005). 10.1126/science.1120714 (Pubitemid 41818947)
40. G. Biroli, J. Bouchaud, K. Miyazaki, and D. Reichman, Phys. Rev. Lett. PRLTAO 0031-9007 97, 195701 (2006). 10.1103/PhysRevLett.97.195701 (Pubitemid 44707961)
41. S. Karmakar, C. Dasgupta, and S. Sastry, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 106, 3675 (2009). 10.1073/pnas.0811082106
42. G. Fredrickson and H. Andersen, Phys. Rev. Lett. PRLTAO 0031-9007 53, 1244 (1984). 10.1103/PhysRevLett.53.1244
43. W. Kob and H. Andersen, Phys. Rev. E PLEEE8 1063-651X 48, 4364 (1993). 10.1103/PhysRevE.48.4364
44. F. Ritort and P. Sollich, Adv. Phys. ADPHAH 0001-8732 52, 219 (2003). 10.1080/0001873031000093582
45. G. Biroli, J. Bouchaud, and G. Tarjus, J. Chem. Phys. JCPSA6 0021-9606 123, 044510 (2005). 10.1063/1.1955527 (Pubitemid 41164743)
46. D. Chandler and J. Garrahan, J. Chem. Phys. JCPSA6 0021-9606 123, 044511 (2005). 10.1063/1.1955528 (Pubitemid 41164744)
47. L. Hedges and J. Garrahan, J. Phys. A: Math. Theor. ZZZZZZ 1751-8113 41, 324006 (2008). 10.1088/1751-8113/41/32/324006
48. L. Hedges and J. Garrahan, J. Phys. Condens. Matter JCOMEL 0953-8984 19, 205124 (2007). 10.1088/0953-8984/19/20/205124 (Pubitemid 46653756)
49. L. Berthier, Phys. Rev. E PLEEE8 1063-651X 76, 011507 (2007). 10.1103/PhysRevE.76.011507 (Pubitemid 47119581)
50. G. Biroli and M. Ḿzard, Phys. Rev. Lett. PRLTAO 0031-9007 88, 025501 (2001). 10.1103/PhysRevLett.88.025501
51. G. McCullagh, D. Cellai, A. Lawlor, and K. Dawson, Phys. Rev. E PLEEE8 1063-651X 71, 030102 (2005). 10.1103/PhysRevE.71.030102
52. K. Dawson, S. Franz, and M. Sellitto, Europhys. Lett. EULEEJ 0295-5075 64, 302 (2003). 10.1209/epl/i2003-00174-3 (Pubitemid 37358059)
53. M. Pica Ciamarra, M. Tarzia, A. de Candia, and A. Coniglio, Phys. Rev. E PLEEE8 1063-651X 67, 057105 (2003). 10.1103/PhysRevE.67.057105
54. M. Pica Ciamarra, M. Tarzia, A. de Candia, and A. Coniglio, Phys. Rev. E PLEEE8 1063-651X 68, 066111 (2003). 10.1103/PhysRevE.68.066111
55. It should be noted that LGMs of the type described here involve extreme constraints that must be globally satisfied and are thus not realistic translations of off-lattice particle-based models. Such constraints might indeed induce artificial behavior, especially at higher densities. It would be most interesting to investigate "soft" versions of such models where constraints may be locally violated at the cost of an energy penalty. In this regard, such models would be the configurational analog of KCMs where dynamical constraints may be broken at the cost of an energy penalty. D. Chandler and J. P. Garrahan, " Dynamics on the Way to Forming Glass: Bubbles in Space-Time.," Annu. Rev. Phys. Chem. ARPLAP 0066-426X (in press).
56. A. Bortz, M. Kalos, and J. Lebowitz, J. Comput. Phys. JCTPAH 0021-9991 17, 10 (1975). 10.1016/0021-9991(75)90060-1
57. A subtle issue arises in the nature of glassy behavior observed in the t154 model outlined in this work. LGMs could have a dynamical percolation-like transition, as in the spiral model. This has been indeed found in some LGMs on the Bethe lattice and would slow down the dynamics for reasons completely different from the diminishing of the configurational entropy. If there is a low-lying crystal phase then one can show that this dynamical percolation-like transition cannot take place in finite dimension. Although we have not found a crystal phase for the model, the existence of such a transition seems unlikely and irrelevant for our present work. First, it can be shown that blocked structures, if they exist, have to verify much more constraints than in the spiral model. Second, we have found that the relaxation time growth of the persistence functions with increasing density in local canonical Monte Carlo simulations are similar to those under grand-canonical dynamics, which cannot contain any blocked structure. The union of these two facts render the dynamical blocking scenario highly unlikely.
58. U. Balucani and M. Zoppi, Dynamics of the Liquid State (Oxford University Press, New York, 1994).
59. W. Kob and H. Andersen, Phys. Rev. E PLEEE8 1063-651X 51, 4626 (1995). 10.1103/PhysRevE.51.4626
60. G. Wahnström, Phys. Rev. A PLRAAN 1050-2947 44, 3752 (1991). 10.1103/PhysRevA.44.3752
61. T. Sarlat, A. Billoire, G. Biroli, and J. Bouchaud, J. Stat. Mech.: Theory Exp. 2009, P08014). 10.1088/1742-5468/2009/08/P08014 1742-5468
62. L. Berthier and T. A. Witten, Europhys. Lett. EULEEJ 0295-5075 86, 10001 (2009). 10.1209/0295-5075/86/10001
63. P. Chaudhuri, S. Sastry, and W. Kob, Phys. Rev. Lett. PRLTAO 0031-9007 101, 190601 (2008). 10.1103/PhysRevLett.101.190601
64. C. Toninelli, G. Biroli, and D. Fisher, Phys. Rev. Lett. PRLTAO 0031-9007 92, 185504 (2004). 10.1103/PhysRevLett.92.185504
65. C. Donati, J. Douglas, W. Kob, S. Plimpton, P. Poole, and S. Glotzer, Phys. Rev. Lett. PRLTAO 0031-9007 80, 2338 (1998). 10.1103/PhysRevLett.80.2338
66. C. Donati, S. Glotzer, P. Poole, W. Kob, and S. Plimpton, Phys. Rev. E PLEEE8 1063-651X 60, 3107 (1999). 10.1103/PhysRevE.60.3107
67. B. Doliwa and A. Heuer, J. Phys. Condens. Matter JCOMEL 0953-8984 11, 025 (1999). 10.1088/0953-8984/11/10A/025
68. G. Appignanesi, J. Rodríguez Fris, R. Montani, and W. Kob, Phys. Rev. Lett. PRLTAO 0031-9007 96, 057801 (2006). 10.1103/PhysRevLett.96.057801 (Pubitemid 43273474)
69. F. Stillinger, J. Chem. Phys. JCPSA6 0021-9606 89, 6461 (1988). 10.1063/1.455365
70. A. Widmer-Cooper, P. Harrowell, and H. Fynewever, Phys. Rev. Lett. PRLTAO 0031-9007 93, 135701 (2004). 10.1103/PhysRevLett.93.135701
71. R. K. Darst, D. R. Reichman, and G. Biroli (unpublished).
72. F. Stillinger and J. Hodgdon, Phys. Rev. E PLEEE8 1063-651X 50, 2064 (1994). 10.1103/PhysRevE.50.2064
73. C. Liu and I. Oppenheim, Phys. Rev. E PLEEE8 1063-651X 53, 799 (1996). 10.1103/PhysRevE.53.799
74. M. Ḿzard and A. Montanari, J. Stat. Phys. JSTPBS 0022-4715 124, 1317 (2006). 10.1007/s10955-006-9162-3 (Pubitemid 44581231)
75. R. Stein and H. Andersen, Phys. Rev. Lett. PRLTAO 0031-9007 101, 267802 (2008). 10.1103/PhysRevLett.101.267802
76. R. Jack and J. Garrahan, J. Chem. Phys. JCPSA6 0021-9606 123, 164508 (2005). 10.1063/1.2075067 (Pubitemid 41527655)
77. R. Richert and C. Angell, J. Chem. Phys. JCPSA6 0021-9606 108, 9016 (1998). 10.1063/1.476348
78. L. Martinez and C. Angell, Nature (London) NATUAS 0028-0836 410, 663 (2001). 10.1038/35070517 (Pubitemid 32293575)
79. A. Crisanti and F. Ritort, Europhys. Lett. EULEEJ 0295-5075 51, 147 (2000). 10.1209/epl/i2000-00524-7
80. L. Berthier and R. Jack, Phys. Rev. E PLEEE8 1063-651X 76, 041509 (2007). 10.1103/PhysRevE.76.041509 (Pubitemid 350023321)
81. R. Candelier, O. Dauchot, and G. Biroli, Phys. Rev. Lett. PRLTAO 0031-9007 102, 088001 (2009). 10.1103/PhysRevLett.102.088001
82. G. Biroli and C. Toninelli, Eur. Phys. J. B EPJBFY 1434-6028 64, 567 (2008). 10.1140/epjb/e2008-00029-9
83. O. Rivoire, G. Biroli, O. Martin, and M. Mezard, Eur. Phys. J. B EPJBFY 1434-6028 37, 55 (2003). 10.1140/epjb/e2004-00030-4