Mechanical, vibrational, and dynamical properties of amorphous systems near jamming

Abstract

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.

Keywords

jamming / amorphous systems / critical phenomena / glass transition

References

[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

[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

[6] A. J. Liu and S. R. Nagel, Nature (London), 1998, 396: 21

[7] V. Trappe, V. Prasad, L. Cipelletti, P. N. Segre, and D. A. Weitz, Nature (London), 2001, 411: 772

[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

[9] P. G. Debenedetti and F. H. Stillinger, Nature (London), 2001, 410: 259

[10] C. A. Angell, J. Non-Cryst. Solids, 1991, 131: 13

[11] C. A. Angell, Science, 1995, 267: 1924

[12] A. Cavagna, Phys. Rep., 2009, 476: 51

[13] W. Kauzmann, Chem. Rev., 1948, 43: 219

[14] G. Adams and J. H. Gibbs, J. Chem. Phys., 1965, 43: 139

[15] M. Goldstein, J. Chem. Phys., 1969, 51: 3728

[16] E. Leutheusser, Phys. Rev. A, 1984, 29: 2765

[17] F. H. Stillinger, Science, 1995, 267: 1935

[18] E. Lerner, I. Procaccia, and J. Zylberg, Phys. Rev. Lett., 2009, 102: 125701

[19] R. Yamamoto and A. Onuki, Phys. Rev. E, 1998, 58: 3515

[20] N. Lačević, F. W. Starr, T. B. Schrøder, and S. C. Glotzer, J. Chem. Phys., 2003, 119: 7372

[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

[22] J. D. Eaves and D. R. Reichman, PNAS, 2009, 106: 15171

[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

[25] T. Nakayama, K. Yakubo, and R. L. Orbach, Rev. Mod. Phys., 1994, 66: 381

[26] R. O. Pohl, X. Liu, and E. Thompson, Rev. Mod. Phys., 2002, 74: 991

[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

[28] D. G. Cahill, S. K. Watson, and R. O. Pohl, Phys. Rev. B, 1992, 46: 6131

[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

[30] W. Losert, L. Bocquet, T. C. Lubensky, and J. P. Gollub, Phys. Rev. Lett., 2000, 85: 1428

[31] D. Howell, R. P. Behringer, and C. Veje, Phys. Rev. Lett., 1999, 82: 5241

[32] N. Xu, C. S. O’Hern, and L. Kondic, Phys. Rev. Lett., 2005, 94: 016001

[33] N. Xu, C. S. O’Hern, and L. Kondic, Phys. Rev. E, 2005, 72: 041504

[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

[37] J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys., 1971, 54: 5237

[38] W. Kob and H. C. Andersen, Phys. Rev. E, 1995, 51: 4626

[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

[43] D. J. Durian, Phys. Rev. Lett., 1995, 75: 4780

[44] D. J. Durian, Phy. Rev. E, 1997, 55: 1739

[45] T. C. Hales, Ann. Math., 2005, 162: 1065

[46] J. D. Bernal, Nature (London), 1960, 188: 910

[47] C. S. O’Hern, S. A. Langer, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2002, 88: 075507

[48] C. S. O’Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E, 2003, 68: 011306

[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

[51] H. A. Makse, D. L. Johnson, and L. M. Schwartz, Phys. Rev. Lett., 2000, 84: 4160

[52] E. Somfai, M. van Hecke, W. G. Ellenbroek, K. Shundyak, and W. van Saarloos, Phys. Rev. E, 2007, 75: 020301(R)

[53] K. Shundyak, M. van Hecke, and W. van Saarloos, Phys. Rev. E, 2007, 75: 010301(R)

[54] S. Torquato, T. M. Truskett, and P. G. Debenedetti, Phys. Rev. Lett., 2000, 84: 2064

[55] N. Xu, J. Blawzdziewicz, and C. S. O’Hern, Phys. Rev. E, 2005, 71: 061306

[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

[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

[59] M. Mailman, C. F. Schreck, C. S. O’Hern, and B. Chakraborty, Phys. Rev. Lett., 2009, 102: 255501

[60] Z. Zeravcic, N. Xu, A. J. Liu, S. R. Nagel, and W. van Saarloos, Europhys. Lett., 2009, 87: 26001

[61] L. N. Zou, X. Cheng, M. L. Rivers, H.M. Jaeger, and S. R. Nagel, Science, 2009, 326: 408

[62] N. Xu and E. S. C. Ching, Soft Matter, 2010, 6: 2944

[63] N. Xu, arXiv: 0911.1576, 2009

[64] A. Donev, F. H. Stillinger, and S. Torquato, Phys. Rev. Lett., 2005, 95: 090604

[65] L. E. Silbert and M. Silbert, Phys. Rev. E, 2009, 80: 041304

[66] N. Xu, A. J. Liu, and T. C. Lubensky, unpublished

[67] D. J. Durian, Phys. Rev. E, 1997, 55: 1739

[68] T. S. Majmudar, M. Sperl, S. Luding, and R. P. Behringer, Phys. Rev. Lett., 2007, 98: 058001

[69] P. Olsson and S. Teitel, Phys. Rev. Lett., 2007, 99: 178001

[70] T. Hatano, arXiv: 0804.0477, 2008

[71] L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2005, 95: 098301

[72] M. Wyart, S. R. Nagel, and T. A. Witten, Europhys. Lett., 2005, 72: 486

[73] M. Wyart, L. E. Silbert, S. R. Nagel, and T. A. Witten, Phys. Rev. E, 2005, 72: 051306

[74] J. A. Drocco, M. B. Hastings, C. J. O. Reichhardt, and C. Reichhardt, Phys. Rev. Lett., 2005, 95: 088001

[75] W. G. Ellenbroek, E. Somfai, M. van Hecke, and W. van Saarloos, Phys. Rev. Lett., 2006, 97: 258001

[76] A. S. Keys, A. R. Abate, S. C. Glotzer, and D. J. Durian, Nature Physics, 2007, 3: 260

[77] D. A. Head, Phys. Rev. Lett., 2009, 102: 138001

[78] N. Xu, V. Vitelli, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2009, 102: 038001

[79] V. Vitelli, N. Xu, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. E, 2010, 81: 021301

[80] P. W. Anderson, Phys. Rev., 1958, 109: 1492

[81] E. Duval, A. Boukenter, and T. Achibat, J. Phys.: Condens. Matter, 1990, 2: 10227

[82] T. Keyes, J. Phys. Chem. A, 1997, 101: 2921

[83] W. Schirmacher, G. Diezemann, and C. Ganter, Phys. Rev. Lett., 1998, 81: 136

[84] P. Lunkenheimer, U. Schneider, R. Brand, and A. Loidl, Contemp. Phys., 2000, 41: 15

[85] D. A. Parshin and C. Laermans, Phys. Rev. B, 2001, 63: 132203

[86] J.W. Kantelhardt, S. Russ, and A. Bunde, Phys. Rev. B, 2001, 63: 064302

[87] T. Nakayama, Rep. Prog. Phys., 2002, 65: 1195

[88] V. L. Gurevich, D. A. Parshin, and H. R. Schober, Phys. Rev. B, 2003, 67: 094203

[89] T. S. Grigera, V. Martin-Mayor, G. Parisi, and P. Verrocchio, Nature (London), 2003, 422: 289

[90] H. Shintani and H. Tanaka, Nature Mater., 2008, 7: 870

[91] W. A. Phillips, J. Low Temp. Phys., 1972, 7: 351

[92] C. Kittel, Phys. Rev., 1949, 75: 972

[93] M. Wyart, Ann. Phys. (Paris), 2005, 30: 1

[94] N. Xu, M. Wyart, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2007, 98: 175502

[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

[97] X. Mao, N. Xu, and T. C. Lubensky, Phys. Rev. Lett., 2010, 104: 085504

[98] L. E. Silbert, A. J. Liu, and S. R. Nagel, Phys. Rev. E, 2009, 79: 021308

[99] Z. Zeravcic, W. van Saarloos, and D. R. Nelson, Europhys. Ning XU, Front. Phys. Lett., 2008, 83: 44001

[100] H. R. Schober and G. Ruocco, Phil. Mag., 2004, 84: 1361

[101] P. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten, Phil. Mag. B, 1999, 79: 1715

[102] A. Widmer-Cooper, H. Perry, P. Harrowell, and D. R. Reichman, Nature Phys., 2008, 4: 711

[103] C. Liu and S. R. Nagel, Phys. Rev. Lett., 1992, 68: 2301

[104] C. Liu and S. R. Nagel, Phys. Rev. B, 1993, 48: 15646

[105] X. Jia, C. Caroli, and B. Velicky, Phys. Rev. Lett., 1999, 82: 1863

[106] X. Jia, Phys. Rev. Lett., 2004, 93: 154303

[107] P. B. Allen and J. L. Feldman, Phys. Rev. Lett., 1989, 62: 645

[108] P. B. Allen and J. L. Feldman, Phys. Rev. B, 1993, 48: 12581

[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

[111] C. Heussinger and J. L. Barrat, Phys. Rev. Lett., 2009, 102: 218303

[112] M. P. Ciamarra, and A. Coniglio, Phys. Rev. Lett., 2009, 103: 235701

[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

[114] N. Xu, T. K. Haxton, A. J. Liu, and S. R. Nagel, Phys. Rev. Lett., 2009, 103: 245701

[115] W. Kob and H. C. Andersen, Phys. Rev. E, 1995, 52: 4134

[116] Y. S. Elmatad, D. Chandler, and J. P. Garrahan, J. Phys. Chem. B, 2009, 113: 5563

[117] G. Lois, J. Blawzdziewicz, and C. S. O’Hern, Phys. Rev. Lett., 2008, 100: 028001

[118] P. J. Lu, E. Zaccarelli, F. Ciulla, A. B. Schofield, F. Sciortino, and D. A. Weitz, Nature (London), 2007, 453: 499

[119] G. J. Gao, J. Blawzdziewicz, C. S. O’Hern, and M. Shattuck, Phys. Rev. E, 2009, 80: 061304

[120] A. R. Abate and D. J. Durian, Phys. Rev. E, 2006, 74: 031308

[121] X. Cheng, Phys. Rev. E, 2010, 81: 031301

[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

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