Transport properties of glass-forming liquids suggest that dynamic crossover temperature is as important as the glass transition temperature

It is becoming common practice to partition glass-forming liquids into two classes based on the dependence of the shear viscosity η on temperature T. In an Arrhenius plot, ln η vs 1/T, a strong liquid shows linear behavior whereas a fragile liquid exhibits an upward curvature [super-Arrhenius (SA) behavior], a situation customarily described by using the Vogel–Fulcher–Tammann law. Here we analyze existing data of the transport coefficients of 84 glass-forming liquids. We show the data are consistent, on decreasing temperature, with the onset of a well-defined dynamical crossover η×, where η× has the same value, η× ≈ 103 Poise, for all 84 liquids. The crossover temperature, T×, located well above the calorimetric glass transition temperature Tg, marks significant variations in the system thermodynamics, evidenced by the change of the SA-like T dependence above T× to Arrhenius behavior below T×. We also show that below T× the familiar Stokes–Einstein relation D/T ∼ η-1 breaks down and is replaced by a fractional form D/T ∼ η-ζ, with ζ ≈ 0.85.

[1]  Bishop,et al.  Power-law behavior in the viscosity of supercooled liquids. , 1986, Physical review. B, Condensed matter.

[2]  F. Mallamace,et al.  A possible scenario for the fragile-to-strong dynamic crossover predicted by the extended mode-coupling theory for glass transition , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[3]  K. Hess,et al.  Universal representation of viscosity in glass forming liquids , 1998 .

[4]  K. Herwig,et al.  Observation of fractional Stokes-Einstein behavior in the simplest hydrogen-bonded liquid. , 2007, Physical review letters.

[5]  I. Procaccia,et al.  Statistical mechanics and dynamics of a three-dimensional glass-forming system. , 2009, Physical review letters.

[6]  Jeppe C. Dyre,et al.  Colloquium : The glass transition and elastic models of glass-forming liquids , 2006 .

[7]  W. Gotze,et al.  Relaxation processes in supercooled liquids , 1992 .

[8]  J. P. Garrahan,et al.  Corresponding states of structural glass formers. II. , 2009, The journal of physical chemistry. B.

[9]  R. McMahon,et al.  Self-diffusion of tris-naphthylbenzene near the glass transition temperature. , 2003, Physical review letters.

[10]  Chung-Yuan Mou,et al.  Pressure dependence of fragile-to-strong transition and a possible second critical point in supercooled confined water. , 2005, Physical review letters.

[11]  Peter G. Wolynes,et al.  The shapes of cooperatively rearranging regions in glass-forming liquids , 2006 .

[12]  David Chandler,et al.  Space-time thermodynamics of the glass transition. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[13]  John C. Mauro,et al.  Viscosity of glass-forming liquids , 2009, Proceedings of the National Academy of Sciences.

[14]  S. Buldyrev,et al.  Glass transition in biomolecules and the liquid-liquid critical point of water. , 2006, Physical Review Letters.

[15]  K. Nelson,et al.  Impulsive stimulated light scattered from glass‐forming liquids. II. Salol relaxation dynamics, nonergodicity parameter, and testing of mode coupling theory , 1995 .

[16]  H. Stanley,et al.  Connection between Adam-Gibbs theory and spatially heterogeneous dynamics. , 2002, Physical review letters.

[17]  Frank H. Stillinger,et al.  Supercooled liquids, glass transitions, and the Kauzmann paradox , 1988 .

[18]  Marie K. Mapes,et al.  Self-diffusion of supercooled o-terphenyl near the glass transition temperature. , 2006, The journal of physical chemistry. B.

[19]  H. Stanley,et al.  Appearance of a Fractional Stokes-Einstein Relation in Water and a Structural Interpretation of Its Onset , 2009 .

[20]  G. Tarjus,et al.  BREAKDOWN OF THE STOKES-EINSTEIN RELATION IN SUPERCOOLED LIQUIDS , 1995 .

[21]  Ranko Richert,et al.  Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy , 1998 .

[22]  Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Heterogeneity and growing length scales in the dynamics of kinetically constrained lattice gases in two dimensions. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Kaori Ito,et al.  Thermodynamic determination of fragility in liquids and a fragile-to-strong liquid transition in water , 1999, Nature.

[25]  G. McKenna.  Glass dynamics: Diverging views on glass transition , 2008 .

[26]  J. Dyre.  The glass transition and elastic models of glass-forming liquids , 2006 .

[27]  David Chandler,et al.  Geometrical explanation and scaling of dynamical heterogeneities in glass forming systems. , 2002, Physical review letters.

[28]  J. P. Garrahan,et al.  Corresponding states of structural glass formers. , 2008, The journal of physical chemistry. B.

[29]  V. Dimitrov.  Breakdown of the Stokes-Einstein Relation in Supercooled Liquids , 2004 .

[30]  S. H. Chen,et al.  The fragile-to-strong dynamic crossover transition in confined water: nuclear magnetic resonance results. , 2006, The Journal of chemical physics.

[31]  R. Landel,et al.  The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids , 1955 .

[32]  H. Cummins,et al.  Light-scattering investigation of α and β relaxation near the liquid-glass transition of the molecular glass Salol , 1992 .

[33]  Chung-Yuan Mou,et al.  The violation of the Stokes–Einstein relation in supercooled water , 2006, Proceedings of the National Academy of Sciences.

[34]  G. Adam,et al.  On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids , 1965 .

[35]  J. Dyre,et al.  Little evidence for dynamic divergences in ultraviscous molecular liquids , 2008 .

[36]  Peter G Wolynes,et al.  Theory of structural glasses and supercooled liquids. , 2007, Annual review of physical chemistry.

[37]  J. P. Garrahan,et al.  Coarse-grained microscopic model of glass formers , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[38]  Quantitative theory of a time-correlation function in a one-component glass-forming liquid with anisotropic potential. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  H. Sillescu,et al.  Heterogeneity at the Glass Transition: Translational and Rotational Self-Diffusion , 1997 .

[40]  A. Heuer,et al.  Length Scale of Dynamic Heterogeneities at the Glass Transition Determined by Multidimensional Nuclear Magnetic Resonance , 1998 .

[41]  M D Ediger,et al.  Spatially heterogeneous dynamics in supercooled liquids. , 2003, Annual review of physical chemistry.

[42]  C. Angell,et al.  Formation of Glasses from Liquids and Biopolymers , 1995, Science.

[43]  I. Procaccia,et al.  Ergodicity and slowing down in glass-forming systems with soft potentials: no finite-temperature singularities. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  E. Donth.  The Glass Transition , 2001 .

[45]  I. Procaccia,et al.  Predictive Statistical Mechanics for Glass Forming Systems , 2009, 0905.3962.

[46]  Fumiko Yonezawa,et al.  Glass Transition , 1990, Int. J. High Perform. Comput. Appl..

[47]  J. Douglas,et al.  Obstruction model of the fractional Stokes Einstein relation in glass-forming liquids , 1998 .

[48]  S. Chong.  Connections of activated hopping processes with the breakdown of the Stokes-Einstein relation and with aspects of dynamical heterogeneities. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Pablo G. Debenedetti,et al.  Metastable Liquids: Concepts and Principles , 1996 .