Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 Statistical physics of liquids
- 2 The freezing transition
- 3 Crystal nucleation
- 4 The supercooled liquid
- 5 Dynamics of collective modes
- 6 Nonlinear fluctuating hydrodynamics
- 7 Renormalization of the dynamics
- 8 The ergodic–nonergodic transition
- 9 The nonequilibrium dynamics
- 10 The thermodynamic transition scenario
- References
- Index
10 - The thermodynamic transition scenario
Published online by Cambridge University Press: 07 September 2011
- Frontmatter
- Contents
- Preface
- Acknowledgements
- 1 Statistical physics of liquids
- 2 The freezing transition
- 3 Crystal nucleation
- 4 The supercooled liquid
- 5 Dynamics of collective modes
- 6 Nonlinear fluctuating hydrodynamics
- 7 Renormalization of the dynamics
- 8 The ergodic–nonergodic transition
- 9 The nonequilibrium dynamics
- 10 The thermodynamic transition scenario
- References
- Index
Summary
In Chapter 4 we introduced the Kauzmann temperature TK as a possible limiting temperature for the existence of the supercooled liquid phase. The original hypothesis due to Kauzmann proposes eventual crystallization in the supercooled liquid at very low temperatures as a possible way out of the paradoxical situation in which the entropy of the disordered state becomes less than that of the crystal. Another possible explanation of the Kauzmann paradox could be that the simple extrapolation of the high-temperature result to very low temperature is not correct and the entropy difference between supercooled liquid and crystal remains finite down to very low temperature (Donev et al., 2006; Langer, 2006a, 2006b, 2007), finally going to zero only near T = 0. Either of these resolutions, however, leaves us with no understanding of the dramatic slowing down and associated phenomenology of the supercooled region above Tg. The difference of the entropy of the supercooled liquid from that of the solid having only vibrational motion around a frozen structure represents the entropy due to large-scale motion and is identified with the configurational entropy Sc of the liquid. The rapid disappearance of the configurational entropy of the disordered liquid or the so-called “entropy crisis” poses an important question that is essential for our understanding of the physics of the glass-transition phenomena and the divergence of the relaxation time at Tg. Apart from having a characteristic large viscosity, the supercooled liquid shows a discontinuity in specific heat cp at Tg due to freezing of the translational degrees of freedom in the liquid.
- Type
- Chapter
- Information
- Statistical Physics of Liquids at Freezing and Beyond , pp. 486 - 539Publisher: Cambridge University PressPrint publication year: 2011