Abstract
Recently it has been revealed that when approaching the glass-transition temperature, Tg, the dynamics of a liquid not only drastically slows down, but also becomes progressively more heterogeneous. From our simulations and experiments of six different glass-forming liquids, we find that the heterogeneous dynamics is a result of critical-like fluctuations of static structural order, contrary to a common belief that it is purely of dynamic origin. The static correlation length and susceptibility of a structural order parameter show Ising-like power-law divergence towards the ideal glass-transition point. However, this structural ordering accompanies little density change, which explains why it has not been detected by the static structure factor so far. Our results suggest a far more direct link than thought before between glass transition and critical phenomena. Indeed, the glass transition may be a new type of critical phenomenon where a structural order parameter is directly linked to slowness.
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References
Onuki, A. Phase Transition Dynamics (Cambridge Univ. Press, 2002).
Chaikin, P. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Univ. Press, 1995).
Angell, C. A. Formation of glasses from liquids and biopolymers. Science 267, 1924–1935 (1995).
Sillescu, H. Heterogeneity at the glass transition: A review. J. Non-Cryst. Solids 243, 81–108 (1999).
Ediger, M. D. Spatially heterogeneous dynamics in supercooled liquids. Annu. Rev. Phys. Chem. 51, 99–128 (2000).
Debenedetti, P. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).
Dyre, J. C. Colloquium: The glass transition and elastic models of glass-forming liquids. Rev. Mod. Phys. 78, 953–972 (2006).
Perera, D. & Harrowell, P. Stability and structure of a supercooled liquid mixture in two dimensions. Phys. Rev. E 59, 5721–5743 (1999).
Hurley, M. & Harrowell, P. Non-Gaussian behavior and the dynamical complexity of particle motion in a dense two-dimensional liquid. J. Chem. Phys. 105, 10521–10526 (1996).
Kegel, W. & van Blaaderen, A. Direct observation of dynamical heterogeneities in colloidal hard-sphere suspensions. Science 287, 290–293 (2000).
Weeks, E., Crocker, J., Levitt, A., Schofield, A. & Weitz, D. Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287, 627–631 (2000).
Kob, W., Donati, C., Plimpton, S., Poole, P. & Glotzer, S. Dynamical heterogeneities in a supercooled Lennard-Jones liquid. Phys. Rev. Lett. 79, 2827–2830 (1997).
Yamamoto, R. & Onuki, A. Kinetic heterogeneities in a highly supercooled liquid. J. Phys. Soc. Jpn 66, 2545–2548 (1997).
Lačević, N., Starr, F., Schroder, T. & Glotzer, S. Spatially heterogeneous dynamics investigated via a time-dependent four-point density correlation function. J. Chem. Phys. 119, 7372–7387 (2003).
Berthier, L. et al. Direct experimental evidence of a growing length scale accompanying the glass transition. Science 310, 1797–1800 (2005).
Adam, G. & Gibbs, J. On the temperature dependence of cooperative relaxation properties in glass-forming liquid. J. Chem. Phys. 43, 139–146 (1965).
Kirkpatrick, T. R., Thirumalai, D. & Wolynes, P. G. Scaling concepts for the dynamics of viscous liquids near an ideal glassy state. Phys. Rev. A 111, 1045–1054 (1989).
Xia, X. & Wolynes, P. G. Fragilities of liquids predicted from the random first order transition theory of glasses. Proc. Natl Acad. Sci. USA 97, 2990–2994 (2000).
Biroli, G., Bouchaud, J. P., Cavagna, A., Grigera, T. S. & Verrochio, P. Thermodynamic signature of growing amorphous order in glass-forming liquids. Nature Phys. 4, 771–775 (2008).
Sethna, J. P., Shore, J. D. & Huang, M. Scaling theory for the glass transition. Phys. Rev. B 44, 4943–4959 (1991).
Toninelli, C., Wyart, M., Berthier, L., Biroli, G. & Bouchaud, J.-P. Dynamical susceptibility of glass formers: Contrasting the predictions of theoretical scenarios. Phys. Rev. E 71, 041505 (2005).
Garrahan, J. P. & Chandler, D. Coarse-grained microscopic model of glass formers. Proc. Natl Acad. Sci. USA 100, 9710–9714 (2003).
Hedges, L. O., Jack, R. L., Garrahan, J. P. & Chandler, D. Dynamic order–disorder in atomistic models of structural glass formers. Science 323, 1309–1313 (2009).
Tarjus, G., Kivelson, S. A., Nussinov, Z. & Viod, P. The frustration-based approach of supercooled liquids and the glass transition: A review and critical assessment. J. Phys. Condens. Matter 17, R1143–R1182 (2005).
Tanaka, H. Two-order-parameter description of liquids. I. A general model of glass transition covering its strong to fragile limit. J. Chem. Phys. 111, 3163–3174 (1999).
Tanaka, H. Two-order-parameter model of the liquid-glass transition. II. Structural relaxation and dynamic heterogeneity. J. Non-Cryst. Solids 351, 3385–3395 (2005).
Widmer-Cooper, A., Harrowell, P. & Fynewever, H. How reproducible are dynamic heterogeneities in a supercooled liquid? Phys. Rev. Lett. 93, 135701 (2004).
Widmer-Cooper, A. & Harrowell, P. Predicting the long-time dynamic heterogeneity in a supercooled liquid on the basis of short-time heterogeneities. Phys. Rev. Lett. 96, 185701 (2006).
Widmer-Cooper, A., Perry, H., Harrowell, P. & Reichman, D. R. Irreversible reorganization in a supercooled liquid originates from localized soft modes. Nature Phys. 4, 711–715 (2008).
Shintani, H. & Tanaka, H. Frustration on the way to crystallization in glass. Nature Phys. 2, 200–206 (2006).
Kawasaki, T., Araki, T. & Tanaka, H. Correlation between dynamic heterogeneity and medium-range order in two-dimensional glass-forming liquids. Phys. Rev. Lett. 99, 215701 (2007).
Watanabe, K. & Tanaka, H. Direct observation of medium-range crystalline order in granular liquids near the glass transition. Phys. Rev. Lett. 100, 158002 (2008).
Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and gases. Phys. Rev. B 28, 784–805 (1983).
Berthier, L. & Tarjus, G. Nonperturbative effect of attractive forces in viscous liquids. Phys. Rev. Lett. 103, 170601 (2009).
Glaser, M. A. & Clark, N. A. Melting and liquid structure in two dimensions. Adv. Chem. Phys. 83, 543–709 (1993).
Conrad, J. C., Starr, F. W. & Weitz, D. A. Weak correlations between local density and dynamics near the glass transition. J. Phys. Chem. B 109, 21235–21240 (2005).
Widmer-Cooper, A. & Harrowell, P. Free volume cannot explain the spatial heterogeneity of Debye–Waller factors in a glass-forming binary alloy. J. Non-Cryst. Solids 352, 5098–5102 (2006).
Ebert, F., Keim, P. & Maret, G. Local crystalline order in a 2D colloidal glass former. Eur. Phys. J. E 28, 161–168 (2008).
Angell, C., Ngai, K., McKenna, G., McMillan, P. & Martin, S. Relaxation in glass forming liquids and amorphous solids. J. Appl. Phys. 88, 3113–3157 (2000).
Mittal, J., Errington, J. R. & Truskett, T. M. Quantitative link between single-particle dynamics and static structure of supercooled liquids. J. Phys. Chem. B 110, 18147–18150 (2006).
Ray, P. & Binder, K. Finite-size effect in the dynamics near the glass transition. Europhys. Lett. 27, 53–58 (1994).
Karmakara, S., Dasgupta, C. & Sastry, S. Growing length and time scales in glass-forming liquids. Proc. Natl Acad. Sci. USA 106, 3675–3679 (2009).
Auer, S. & Frenkel, D. Suppression of crystal nucleation in polydisperse colloids due to increase of the surface free energy. Nature 413, 711–713 (2001).
Aharonov, E. et al. Direct identification of the glass transition: Growing length scale and the onset of plasticity. Europhys. Lett. 77, 56002 (2007).
Chandra, P., Coleman, P. & Larkin, A. I. Ising transition in frustrated Heisenberg models. Phys. Rev. Lett. 64, 88–91 (1990).
Weber, C. et al. Ising transition driven by frustration in a 2D classical model with continuous symmetry. Phys. Rev. Lett. 91, 177202 (2003).
Torquato, S., Truskett, T. M. & Debenedetti, P. G. Is random close packing of spheres well defined? Phys. Rev. Lett. 84, 2064–2067 (2000).
Fisher, D. S. Activated dynamic scaling in disordered systems. J. Appl. Phys. 61, 3672–3677 (1987).
Mezard, M. & Parisi, G. Statistical physics of structural glasses. J. Phys. Condens. Matter 12, 6655–6673 (2000).
Bouchaud, J. P., Cugliandro, L. F., Kurchan, J. & Mezard, M. in Spin Glasses and Random Fields (ed. Young, A. P.) (World Science, 1997).
Tarzia, M. & Moore, M. A. Glass phenomenology from the connection to spin glasses. Phys. Rev. E 75, 031502 (2007).
Hecksher, T., Nielsen, A. I., Olsen, N. B. & Dyre, J. C. Little evidence for dynamic divergences in ultraviscous molecular liquids. Nature Phys. 4, 673–673 (2008).
Elmatad, Y. S., Chandler, D. & Garrahan, J. P. Corresponding states of structural glass formers. J. Phys. Chem. B 113, 5563–5567 (2009).
Acknowledgements
The authors thank A. Furukawa for valuable discussion and C. Paddy Royall for a critical reading of the manuscript. This work was partially supported by a grant-in-aid from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
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H.T. conceived and supervised the project, T.K. carried out simulations of 2DPC, 2DBL, 3DPC and 3DLJ, H.S. carried out simulations of 2DSL, K.W. carried out experiments of 2DGL, H.T. and T.K. analysed the data and H.T. wrote the manuscript.
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Tanaka, H., Kawasaki, T., Shintani, H. et al. Critical-like behaviour of glass-forming liquids. Nature Mater 9, 324–331 (2010). https://doi.org/10.1038/nmat2634
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DOI: https://doi.org/10.1038/nmat2634
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