
Mechanical, vibrational, and dynamical properties of amorphous systems near jamming
Front. Phys. ›› 0
Mechanical, vibrational, and dynamical properties of amorphous systems near jamming
Amorphous systems undergo the jamming transition when the density increases, temperature drops, or external shear stress decreases, as described by the jamming phase diagram which was proposed to unify different processes such as the glass transition, random close packing, and yielding under shear stress. At zero temperature and shear stress, the jamming transition occurs at a critical density at Point J. In this paper, we review recent studies of the material properties of marginally jammed solids and the glassy dynamics in the vicinity of Point J. As the only singular point in the jamming phase diagram, Point J exhibits special criticality in both mechanical and vibrational quantities. Dynamics approaching the glass transition in the vicinity of Point J show critical scalings, suggesting that the molecular glass transition and the colloidal glass transition are equivalent in the hard sphere limit. All these studies shed light on the long-standing puzzles of the glass transition and unusual properties of amorphous solids.
jamming / amorphous systems / critical phenomena / glass transition
[1] |
A. J. Liu and S. R. Nagel, Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic scales, New York: Taylor & Francis, 2001
|
[2] |
M. van Hecke, J. Phys.: Condens. Matter, 2010, 22: 033101
CrossRef
ADS
Google scholar
|
[3] |
A. J. Liu, S. R. Nagel, W. van Saarloos, and M. Wyart, http://www.ilorentz.org/∼saarloos/Papers/jammingreview.pdf, 2010
|
[4] |
A. J. Liu and S. R. Nagel, Ann. Rev. Condens. Matt. Phys., 2010 (to be published)
|
[5] |
G. Parisi and F. Zamponi, Rev. Mod. Phys., 2010, 82: 789
CrossRef
ADS
Google scholar
|
[6] |
A. J. Liu and S. R. Nagel, Nature (London), 1998, 396: 21
CrossRef
ADS
Google scholar
|
[7] |
V. Trappe, V. Prasad, L. Cipelletti, P. N. Segre, and D. A. Weitz, Nature (London), 2001, 411: 772
CrossRef
ADS
Google scholar
|
[8] |
Z. Zhang, N. Xu, D. T. N. Chen, P. Yunker, A. M. Alsayed, K. B. Aptowicz, P. Habdas, A. J. Liu, S. R. Nagel, and A. G. Yodh, Nature (London), 2009, 459: 230
CrossRef
ADS
Google scholar
|
[9] |
P. G. Debenedetti and F. H. Stillinger, Nature (London), 2001, 410: 259
CrossRef
ADS
Google scholar
|
[10] |
C. A. Angell, J. Non-Cryst. Solids, 1991, 131: 13
CrossRef
ADS
Google scholar
|
[11] |
C. A. Angell, Science, 1995, 267: 1924
CrossRef
ADS
Google scholar
|
[12] |
A. Cavagna, Phys. Rep., 2009, 476: 51
CrossRef
ADS
Google scholar
|
[13] |
W. Kauzmann, Chem. Rev., 1948, 43: 219
CrossRef
ADS
Google scholar
|
[14] |
G. Adams and J. H. Gibbs, J. Chem. Phys., 1965, 43: 139
CrossRef
ADS
Google scholar
|
[15] |
M. Goldstein, J. Chem. Phys., 1969, 51: 3728
CrossRef
ADS
Google scholar
|
[16] |
E. Leutheusser, Phys. Rev. A, 1984, 29: 2765
CrossRef
ADS
Google scholar
|
[17] |
F. H. Stillinger, Science, 1995, 267: 1935
CrossRef
ADS
Google scholar
|
[18] |
E. Lerner, I. Procaccia, and J. Zylberg, Phys. Rev. Lett., 2009, 102: 125701
CrossRef
ADS
Google scholar
|
[19] |
R. Yamamoto and A. Onuki, Phys. Rev. E, 1998, 58: 3515
CrossRef
ADS
Google scholar
|
[20] |
N. Lačević, F. W. Starr, T. B. Schrøder, and S. C. Glotzer, J. Chem. Phys., 2003, 119: 7372
CrossRef
ADS
Google scholar
|
[21] |
L. Berthier, G. Biroli, J. P. Bouchaud, L. Cipelletti, D. El Masri, D. L′Hôte, F. Ladieu, and M. Pierno, Science, 2005, 310: 1797
CrossRef
ADS
Google scholar
|
[22] |
J. D. Eaves and D. R. Reichman, PNAS, 2009, 106: 15171
CrossRef
ADS
Google scholar
|
[23] |
Amorphous Solids. Low Temperature Properties, edited by W. A. Phillips, Berlin: Springer-Verlag, 1981
|
[24] |
A. P. Sokolov, U. Buchenau, W. Steffen, B. Frick, and A. Wischnewski, Phys. Rev. B, 1995, 52: R9815
CrossRef
ADS
Google scholar
|
[25] |
T. Nakayama, K. Yakubo, and R. L. Orbach, Rev. Mod. Phys., 1994, 66: 381
CrossRef
ADS
Google scholar
|
[26] |
R. O. Pohl, X. Liu, and E. Thompson, Rev. Mod. Phys., 2002, 74: 991
CrossRef
ADS
Google scholar
|
[27] |
A. I. Chumakov, I. Sergueev, U. van Bürck, W. Schirmacher, T. Asthalter, R. Rüffer, O. Leupold, and W. Petry, Phys. Rev. Lett., 2004, 92: 245508
CrossRef
ADS
Google scholar
|
[28] |
D. G. Cahill, S. K. Watson, and R. O. Pohl, Phys. Rev. B, 1992, 46: 6131
CrossRef
ADS
Google scholar
|
[29] |
D. M. Mueth, G. F. Debregeas, G. S. Karczmar, P. J. Eng, S. R. Nagel, and H. M. Jaeger, Nature (London), 2000, 406: 385
CrossRef
ADS
Google scholar
|
[30] |
W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, Phys. Rev. Lett., 2000, 85: 1428
CrossRef
ADS
Google scholar
|
[31] |
D. Howell, R. P. Behringer, and C. Veje, Phys. Rev. Lett., 1999, 82: 5241
CrossRef
ADS
Google scholar
|
[32] |
N. Xu, C. S. O’Hern, and L. Kondic, Phys. Rev. Lett., 2005, 94: 016001
CrossRef
ADS
Google scholar
|
[33] |
N. Xu, C. S. O’Hern, and L. Kondic, Phys. Rev. E, 2005, 72: 041504
CrossRef
ADS
Google scholar
|
[34] |
H. A. Barnes, J. Rheology, 1989, 33: 329
|
[35] |
E. Brown, N. A. Forman, C. S. Orellana, H. Zhang, B. W. Maynor, D. E. Betts, J. M. DeSimone, and H. M. Jaeger, arXiv: 0907.4999, 2009
|
[36] |
N. J. Wagner and J. F. Brady, Phys. Today, 2009, 62: 27
CrossRef
ADS
Google scholar
|
[37] |
J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys., 1971, 54: 5237
CrossRef
ADS
Google scholar
|
[38] |
W. Kob and H. C. Andersen, Phys. Rev. E, 1995, 51: 4626
CrossRef
ADS
Google scholar
|
[39] |
W.H. Press, B.P. Flannery, S. A. Teukolsky, and W.T. Vetterling, Numerical Recipes in Fortran 77, New York: Cambridge University Press, 1986
|
[40] |
http://www.eecs.northwestern.edu/∼nocedal/lbfgs.html
|
[41] |
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Oxford: Oxford University Press, 1987
|
[42] |
N. Xu and C. S. O’Hern, Phys. Rev. Lett., 2005, 94: 055701
CrossRef
ADS
Google scholar
|
[43] |
D. J. Durian, Phys. Rev. Lett., 1995, 75: 4780
CrossRef
ADS
Google scholar
|
[44] |
D. J. Durian, Phy. Rev. E, 1997, 55: 1739
CrossRef
ADS
Google scholar
|
[45] |
T. C. Hales, Ann. Math., 2005, 162: 1065
CrossRef
ADS
Google scholar
|
[46] |
J. D. Bernal, Nature (London), 1960, 188: 910
CrossRef
ADS
Google scholar
|
[47] |
C. S. O’Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2002, 88: 075507
CrossRef
ADS
Google scholar
|
[48] |
C. S. O’Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E, 2003, 68: 011306
CrossRef
ADS
Google scholar
|
[49] |
D. Frenkel, Random close packing: Time for a new Kepler conjecture? http://www.physics.leidenuniv.nl
|
[50] |
C. Song, P. Wang, and H. A. Makse, Nature (London), 2008, 453: 629
CrossRef
ADS
Google scholar
|
[51] |
H. A. Makse, D. L. Johnson, and L. M. Schwartz, Phys. Rev. Lett., 2000, 84: 4160
CrossRef
ADS
Google scholar
|
[52] |
E. Somfai, M. van Hecke, W. G. Ellenbroek, K. Shundyak, and W. van Saarloos, Phys. Rev. E, 2007, 75: 020301(R)
CrossRef
ADS
Google scholar
|
[53] |
K. Shundyak, M. van Hecke, and W. van Saarloos, Phys. Rev. E, 2007, 75: 010301(R)
CrossRef
ADS
Google scholar
|
[54] |
S. Torquato, T. M. Truskett, and P. G. Debenedetti, Phys. Rev. Lett., 2000, 84: 2064
CrossRef
ADS
Google scholar
|
[55] |
N. Xu, J. Blawzdziewicz, and C. S. O’Hern, Phys. Rev. E, 2005, 71: 061306
CrossRef
ADS
Google scholar
|
[56] |
N. Xu, D. Frenkel, and A. J. Liu, unpublished
|
[57] |
A. Donev, I. Cisse, D. Sachs, E. Variano, F. H. Stillinger, R. Connelly, S. Torquato, and P. M. Chaikin, Science, 2004, 303: 990
CrossRef
ADS
Google scholar
|
[58] |
W. N. Man, A. Donev, F. H. Stillinger, M. T. Sullivan, W. B. Russel, D. Heeger, S. Inati, S. Torquato, and P. M. Chaikin, Phys. Rev. Lett., 2005, 94: 198001
CrossRef
ADS
Google scholar
|
[59] |
M. Mailman, C. F. Schreck, C. S. O’Hern, and B. Chakraborty, Phys. Rev. Lett., 2009, 102: 255501
CrossRef
ADS
Google scholar
|
[60] |
Z. Zeravcic, N. Xu, A. J. Liu, S. R. Nagel, and W. van Saarloos, Europhys. Lett., 2009, 87: 26001
CrossRef
ADS
Google scholar
|
[61] |
L. N. Zou, X. Cheng, M. L. Rivers, H.M. Jaeger, and S. R. Nagel, Science, 2009, 326: 408
CrossRef
ADS
Google scholar
|
[62] |
N. Xu and E. S. C. Ching, Soft Matter, 2010, 6: 2944
CrossRef
ADS
Google scholar
|
[63] |
N. Xu, arXiv: 0911.1576, 2009
|
[64] |
A. Donev, F. H. Stillinger, and S. Torquato, Phys. Rev. Lett., 2005, 95: 090604
CrossRef
ADS
Google scholar
|
[65] |
L. E. Silbert and M. Silbert, Phys. Rev. E, 2009, 80: 041304
CrossRef
ADS
Google scholar
|
[66] |
N. Xu, A. J. Liu, and T. C. Lubensky, unpublished
|
[67] |
D. J. Durian, Phys. Rev. E, 1997, 55: 1739
CrossRef
ADS
Google scholar
|
[68] |
T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer, Phys. Rev. Lett., 2007, 98: 058001
CrossRef
ADS
Google scholar
|
[69] |
P. Olsson and S. Teitel, Phys. Rev. Lett., 2007, 99: 178001
CrossRef
ADS
Google scholar
|
[70] |
T. Hatano, arXiv: 0804.0477, 2008
|
[71] |
L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2005, 95: 098301
CrossRef
ADS
Google scholar
|
[72] |
M. Wyart, S. R. Nagel, and T. A. Witten, Europhys. Lett., 2005, 72: 486
CrossRef
ADS
Google scholar
|
[73] |
M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Witten, Phys. Rev. E, 2005, 72: 051306
CrossRef
ADS
Google scholar
|
[74] |
J. A. Drocco, M. B. Hastings, C. J. O. Reichhardt, and C. Reichhardt, Phys. Rev. Lett., 2005, 95: 088001
CrossRef
ADS
Google scholar
|
[75] |
W. G. Ellenbroek, E. Somfai, M. van Hecke, and W. van Saarloos, Phys. Rev. Lett., 2006, 97: 258001
CrossRef
ADS
Google scholar
|
[76] |
A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, Nature Physics, 2007, 3: 260
CrossRef
ADS
Google scholar
|
[77] |
D. A. Head, Phys. Rev. Lett., 2009, 102: 138001
CrossRef
ADS
Google scholar
|
[78] |
N. Xu, V. Vitelli, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2009, 102: 038001
CrossRef
ADS
Google scholar
|
[79] |
V. Vitelli, N. Xu, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. E, 2010, 81: 021301
CrossRef
ADS
Google scholar
|
[80] |
P. W. Anderson, Phys. Rev., 1958, 109: 1492
CrossRef
ADS
Google scholar
|
[81] |
E. Duval, A. Boukenter, and T. Achibat, J. Phys.: Condens. Matter, 1990, 2: 10227
CrossRef
ADS
Google scholar
|
[82] |
T. Keyes, J. Phys. Chem. A, 1997, 101: 2921
CrossRef
ADS
Google scholar
|
[83] |
W. Schirmacher, G. Diezemann, and C. Ganter, Phys. Rev. Lett., 1998, 81: 136
CrossRef
ADS
Google scholar
|
[84] |
P. Lunkenheimer, U. Schneider, R. Brand, and A. Loidl, Contemp. Phys., 2000, 41: 15
CrossRef
ADS
Google scholar
|
[85] |
D. A. Parshin and C. Laermans, Phys. Rev. B, 2001, 63: 132203
CrossRef
ADS
Google scholar
|
[86] |
J.W. Kantelhardt, S. Russ, and A. Bunde, Phys. Rev. B, 2001, 63: 064302
CrossRef
ADS
Google scholar
|
[87] |
T. Nakayama, Rep. Prog. Phys., 2002, 65: 1195
CrossRef
ADS
Google scholar
|
[88] |
V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B, 2003, 67: 094203
CrossRef
ADS
Google scholar
|
[89] |
T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Nature (London), 2003, 422: 289
CrossRef
ADS
Google scholar
|
[90] |
H. Shintani and H. Tanaka, Nature Mater., 2008, 7: 870
CrossRef
ADS
Google scholar
|
[91] |
W. A. Phillips, J. Low Temp. Phys., 1972, 7: 351
CrossRef
ADS
Google scholar
|
[92] |
C. Kittel, Phys. Rev., 1949, 75: 972
CrossRef
ADS
Google scholar
|
[93] |
M. Wyart, Ann. Phys. (Paris), 2005, 30: 1
CrossRef
ADS
Google scholar
|
[94] |
N. Xu, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2007, 98: 175502
CrossRef
ADS
Google scholar
|
[95] |
N. Xu, V. Vitelli, A. J. Liu, and S. R. Nagel, 2010, 90: 56001
|
[96] |
A. Souslov, A. J. Liu, and T. C. Lubensky, Phys. Rev. Lett., 2009, 103: 205503
CrossRef
ADS
Google scholar
|
[97] |
X. Mao, N. Xu, and T. C. Lubensky, Phys. Rev. Lett., 2010, 104: 085504
CrossRef
ADS
Google scholar
|
[98] |
L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E, 2009, 79: 021308
CrossRef
ADS
Google scholar
|
[99] |
Z. Zeravcic, W. van Saarloos, and D. R. Nelson, Europhys. Ning XU, Front. Phys. Lett., 2008, 83: 44001
CrossRef
ADS
Google scholar
|
[100] |
H. R. Schober and G. Ruocco, Phil. Mag., 2004, 84: 1361
CrossRef
ADS
Google scholar
|
[101] |
P. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten, Phil. Mag. B, 1999, 79: 1715
CrossRef
ADS
Google scholar
|
[102] |
A. Widmer-Cooper, H. Perry, P. Harrowell, and D. R. Reichman, Nature Phys., 2008, 4: 711
CrossRef
ADS
Google scholar
|
[103] |
C. Liu and S. R. Nagel, Phys. Rev. Lett., 1992, 68: 2301
CrossRef
ADS
Google scholar
|
[104] |
C. Liu and S. R. Nagel, Phys. Rev. B, 1993, 48: 15646
CrossRef
ADS
Google scholar
|
[105] |
X. Jia, C. Caroli, and B. Velicky, Phys. Rev. Lett., 1999, 82: 1863
CrossRef
ADS
Google scholar
|
[106] |
X. Jia, Phys. Rev. Lett., 2004, 93: 154303
CrossRef
ADS
Google scholar
|
[107] |
P. B. Allen and J. L. Feldman, Phys. Rev. Lett., 1989, 62: 645
CrossRef
ADS
Google scholar
|
[108] |
P. B. Allen and J. L. Feldman, Phys. Rev. B, 1993, 48: 12581
CrossRef
ADS
Google scholar
|
[109] |
A. F. Ioffe and A. R. Regel, Prog. Semicond., 1960, 4: 237
|
[110] |
L. Cipelletti and L. Ramos, J. Phys.: Condens. Matter, 2005, 17: R253
CrossRef
ADS
Google scholar
|
[111] |
C. Heussinger and J. L. Barrat, Phys. Rev. Lett., 2009, 102: 218303
CrossRef
ADS
Google scholar
|
[112] |
M. P. Ciamarra, and A. Coniglio, Phys. Rev. Lett., 2009, 103: 235701
CrossRef
ADS
Google scholar
|
[113] |
J. Mattsson, H. M. Wyss, A. Fernandez-Nieves, K. Miyazaki, Z. Hu, D. R. Reichman, and D. A. Weitz, Nature (London), 2009, 462: 83
CrossRef
ADS
Google scholar
|
[114] |
N. Xu, T. K. Haxton, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2009, 103: 245701
CrossRef
ADS
Google scholar
|
[115] |
W. Kob and H. C. Andersen, Phys. Rev. E, 1995, 52: 4134
CrossRef
ADS
Google scholar
|
[116] |
Y. S. Elmatad, D. Chandler, and J. P. Garrahan, J. Phys. Chem. B, 2009, 113: 5563
CrossRef
ADS
Google scholar
|
[117] |
G. Lois, J. Blawzdziewicz, and C. S. O’Hern, Phys. Rev. Lett., 2008, 100: 028001
CrossRef
ADS
Google scholar
|
[118] |
P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, Nature (London), 2007, 453: 499
CrossRef
ADS
Google scholar
|
[119] |
G. J. Gao, J. Blawzdziewicz, C. S. O’Hern, and M. Shattuck, Phys. Rev. E, 2009, 80: 061304
CrossRef
ADS
Google scholar
|
[120] |
A. R. Abate and D. J. Durian, Phys. Rev. E, 2006, 74: 031308
CrossRef
ADS
Google scholar
|
[121] |
X. Cheng, Phys. Rev. E, 2010, 81: 031301
CrossRef
ADS
Google scholar
|
[122] |
X. Cheng, arXiv: 0911.1943, 2009
|
[123] |
K. Chen, W. G. Ellenbroek, Z. Zhang, D. T. N. Chen, P. Yunker, S. Henkes, C. Brito, O. Dauchot, W. van Saarloos, A. J. Liu, and A. G. Yodh, arXiv: 1003.3065, 2010
|
[124] |
P. Yunker, Z. Zhang, K. B. Aptowicz, and A. G. Yodh, Phys. Rev. Lett., 2009, 103: 115701
CrossRef
ADS
Google scholar
|
/
〈 |
|
〉 |