Time and length scales in supercooled liquids

Ludovic Berthier

doi:10.1103/PhysRevE.69.020201

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Time and length scales in supercooled liquids

Ludovic Berthier^*

Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom

^*Also at Laboratoire des Verres, Université Montpellier II, 34095 Montpellier, France.

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Phys. Rev. E 69, 020201(R) – Published 27 February, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.020201

Abstract

We numerically obtain a quantitative demonstration that development of spatial correlations of mobility as temperature is lowered is responsible for the “decoupling” of transport properties of supercooled liquids. This result further demonstrates the necessity of a spatial description of the glass formation and therefore seriously challenges a number of popular alternative theoretical descriptions.

References (27)

P.G. Debenedetti and F.H. Stillinger, Nature (London) 410, 259 (2001).
F. Fujara, B. Geil, H. Sillescu, and G. Fleischer, Z. Phys. B: Condens. Matter 88, 195 (1992).
J.-L. Barrat, J.-N. Roux, and J.-P. Hansen, Chem. Phys. 149, 197 (1990).
M.T. Cicerone and M.D. Ediger, J. Chem. Phys. 104, 7210 (1996); S.F. Swallen, P.A. Bonvallet, R.J. McMahon, and M.D. Ediger, Phys. Rev. Lett. 90, 015901 (2003).
J.A. Hodgdon and F.H. Stillinger, Phys. Rev. E 48, 207 (1993); G. Tarjus and D. Kivelson, J. Chem. Phys. 103, 3071 (1995); ibid.D.N. Perera and P. Harrowell, 104, 2369 (1996); Y.J. Jung, J.P. Garrahan, and D. Chandler, e-print cond-mat/0311396.
H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999); M.D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000).
J.P. Garrahan and D. Chandler, Phys. Rev. Lett. 89, 035704 (2002).
L. Berthier and J.P. Garrahan, J. Chem. Phys. 119, 4367 (2003).
M.M. Hurley and P. Harrowell, Phys. Rev. E 52, 1694 (1995); Y. Hiwatari and T. Muranaka, J. Non-Cryst. Solids 235-237, 19 (1998); C. Bennemann, C. Donati, J. Baschnagel, and S.C. Glotzer, Nature (London) 399, 246 (1999); S.C. Glotzer, V.N. Novikov, and T. B Schrøder, J. Chem. Phys. 112, 509 (2000); B. Doliwa and A. Heuer, Phys. Rev. E 61, 6898 (2000).
U. Tracht, M. Wilhelm, A. Heuer, H. Feng, K. Schmidt-Rohr, and H.W. Spiess, Phys. Rev. Lett. 81, 2727 (1998); S.A. Reinsberg, X.H. Qiu, M. Wilhelm, H.W. Spiess, and M.D. Ediger, J. Chem. Phys. 114, 7299 (2001).
X.H. Qiu and M.D. Ediger, J. Phys. Chem. B 107, 459 (2003).
W. Kob and H.C. Andersen, Phys. Rev. Lett. 73, 1376 (1994).
S. Plimpton, J. Comput. Phys. 117, 1 (1995).
L. Berthier, Phys. Rev. Lett. 91, 055701 (2003).
S.C. Glotzer, J. Non-Cryst. Solids 274, 342 (2000).
S. Whitelam, L. Berthier, and J.P. Garrahan, e-print cond-mat/0310207.
R. Yamamoto and A. Onuki, Phys. Rev. E 58, 3515 (1998).
L. Andreozzi, A. Di Schino, M. Giordano, and D. Leporini, Europhys. Lett. 38, 669 (1997).
L. Berthier and J.P. Garrahan, Phys. Rev. E 68, 041201 (2003).
J. Jäckle, J. Phys. C 14, 1423 (2002); J.P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003).
D. Kivelson, S.A. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, Physica A 219, 27 (1995).
X. Xia and P.G. Wolynes, Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000).
W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 55 (1992).
Y. Brumer and D. R. Reichman, Phys. Rev. E. (to be published). e-print cond-mat/0306580.
In S. Franz and G. Parisi, J. Phys. C 12, 6335 (2000), the volume integral of Eq. (2) is shown to diverge at $T_{c}$ in the fully-connected spherical p-spin glass model. This suggests that nontrivial dynamic spatial correlations might underlie the mode-coupling instability at ${T = T}_{c} .$
D. Turnbull and M.H. Cohen, J. Chem. Phys. 29, 1049 (1958); G.S. Grest and M.H. Cohen, Adv. Chem. Phys. 48, 454 (1981).
M. Goldstein, J. Chem. Phys. 51, 3728 (1969); F.H. Stillinger, Science 267, 1935 (1995); D. J. Wales, Energy Landscapes (Cambridge University Press, Cambridge, 2003).

[c1] P.G. Debenedetti and F.H. Stillinger, Nature (London) 410, 259 (2001).

[c2] F. Fujara, B. Geil, H. Sillescu, and G. Fleischer, Z. Phys. B: Condens. Matter 88, 195 (1992).

[c3] J.-L. Barrat, J.-N. Roux, and J.-P. Hansen, Chem. Phys. 149, 197 (1990).

[c4] M.T. Cicerone and M.D. Ediger, J. Chem. Phys. 104, 7210 (1996); S.F. Swallen, P.A. Bonvallet, R.J. McMahon, and M.D. Ediger, Phys. Rev. Lett. 90, 015901 (2003).

[c5] J.A. Hodgdon and F.H. Stillinger, Phys. Rev. E 48, 207 (1993); G. Tarjus and D. Kivelson, J. Chem. Phys. 103, 3071 (1995); ibid.D.N. Perera and P. Harrowell, 104, 2369 (1996); Y.J. Jung, J.P. Garrahan, and D. Chandler, e-print cond-mat/0311396.

[c6] H. Sillescu, J. Non-Cryst. Solids 243, 81 (1999); M.D. Ediger, Annu. Rev. Phys. Chem. 51, 99 (2000).

[c7] J.P. Garrahan and D. Chandler, Phys. Rev. Lett. 89, 035704 (2002).

[c8] L. Berthier and J.P. Garrahan, J. Chem. Phys. 119, 4367 (2003).

[c9] M.M. Hurley and P. Harrowell, Phys. Rev. E 52, 1694 (1995); Y. Hiwatari and T. Muranaka, J. Non-Cryst. Solids 235-237, 19 (1998); C. Bennemann, C. Donati, J. Baschnagel, and S.C. Glotzer, Nature (London) 399, 246 (1999); S.C. Glotzer, V.N. Novikov, and T. B Schrøder, J. Chem. Phys. 112, 509 (2000); B. Doliwa and A. Heuer, Phys. Rev. E 61, 6898 (2000).

[c10] U. Tracht, M. Wilhelm, A. Heuer, H. Feng, K. Schmidt-Rohr, and H.W. Spiess, Phys. Rev. Lett. 81, 2727 (1998); S.A. Reinsberg, X.H. Qiu, M. Wilhelm, H.W. Spiess, and M.D. Ediger, J. Chem. Phys. 114, 7299 (2001).

[c11] X.H. Qiu and M.D. Ediger, J. Phys. Chem. B 107, 459 (2003).

[c12] W. Kob and H.C. Andersen, Phys. Rev. Lett. 73, 1376 (1994).

[c13] S. Plimpton, J. Comput. Phys. 117, 1 (1995).

[c14] L. Berthier, Phys. Rev. Lett. 91, 055701 (2003).

[c15] S.C. Glotzer, J. Non-Cryst. Solids 274, 342 (2000).

[c16] S. Whitelam, L. Berthier, and J.P. Garrahan, e-print cond-mat/0310207.

[c17] R. Yamamoto and A. Onuki, Phys. Rev. E 58, 3515 (1998).

[c18] L. Andreozzi, A. Di Schino, M. Giordano, and D. Leporini, Europhys. Lett. 38, 669 (1997).

[c19] L. Berthier and J.P. Garrahan, Phys. Rev. E 68, 041201 (2003).

[c20] J. Jäckle, J. Phys. C 14, 1423 (2002); J.P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003).

[c21] D. Kivelson, S.A. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, Physica A 219, 27 (1995).

[c22] X. Xia and P.G. Wolynes, Proc. Natl. Acad. Sci. U.S.A. 97, 2990 (2000).

[c23] W. Götze and L. Sjögren, Rep. Prog. Phys. 55, 55 (1992).

[c24] Y. Brumer and D. R. Reichman, Phys. Rev. E. (to be published). e-print cond-mat/0306580.

[c25] In S. Franz and G. Parisi, J. Phys. C 12, 6335 (2000), the volume integral of Eq. (2) is shown to diverge at $T_{c}$ in the fully-connected spherical p-spin glass model. This suggests that nontrivial dynamic spatial correlations might underlie the mode-coupling instability at ${T = T}_{c} .$

[c26] D. Turnbull and M.H. Cohen, J. Chem. Phys. 29, 1049 (1958); G.S. Grest and M.H. Cohen, Adv. Chem. Phys. 48, 454 (1981).

[c27] M. Goldstein, J. Chem. Phys. 51, 3728 (1969); F.H. Stillinger, Science 267, 1935 (1995); D. J. Wales, Energy Landscapes (Cambridge University Press, Cambridge, 2003).

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Time and length scales in supercooled liquids

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