Characteristic temperatures of glassy behaviour in a simple liquid

A model for the metastable liquid in terms of holes present in the amorphous structure is considered using the classical density functional theory (DFT). For a one component Lennard-Jones liquid we obtain the temperature dependence of the free volume vf in the metastable state. A temperature T0, similar to that of the characteristic transition of the free volume theory, is identified by extrapolating vf(T) to zero. The Kauzmann temperature TK is also obtained here by extrapolating the entropy difference between the supercooled state and that of the crystal to zero. We compare the temperatures T0 and TK obtained in our model with other two characteristic temperatures for glassy behaviour, namely (a) the dynamic transition temperature Tc of the mode coupling theory (MCT) and (b) the glass transition temperature Tg which was obtained by Leonardo et al (2000 Phys. Rev. Lett. 84 6054) from studying the violation of the fluctuation–dissipation theorem. All the four temperatures, obtained from independent routes, are located with respect to the melting temperature Tm in a manner which is in agreement with experiments.

[1]  C. Alba-Simionesco,et al.  Effects of density and temperature on correlations between fragility and glassy properties , 2006 .

[2]  J. Dudowicz,et al.  The glass transition temperature of polymer melts. , 2005, The journal of physical chemistry. B.

[3]  Francesco Sciortino,et al.  Potential energy landscape description of supercooled liquids and glasses , 2005 .

[4]  C. Dasgupta.  Theoretical approaches to the glass transition in simple liquids , 2005 .

[5]  M. Shlesinger,et al.  Free-volume dynamics in glasses and supercooled liquids. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  C. Roland,et al.  Why liquids are fragile. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  S. Das.  Mode-coupling theory and the glass transition in supercooled liquids , 2004 .

[8]  A. Onuki,et al.  Sheared solid materials , 2004, cond-mat/0410151.

[9]  A. Granato,et al.  An interstitialcy theory of structural relaxation and related viscous flow of glasses. , 2004, Physical review letters.

[10]  Peter Harrowell,et al.  How reproducible are dynamic heterogeneities in a supercooled liquid? , 2004, Physical review letters.

[11]  D. Leporini,et al.  Role of the density in the crossover region of o-terphenyl and poly(vinyl acetate). , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  T. Munakata,et al.  Glass transition of hard sphere systems: molecular dynamics and density functional theory. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  S. Glotzer,et al.  What do we learn from the local geometry of glass-forming liquids? , 2002, Physical review letters.

[14]  Shankar P. Das,et al.  Stability of amorphous structures with voids , 2001, cond-mat/0103432.

[15]  M. A. Hoef,et al.  Free energy of the Lennard-Jones solid , 2000 .

[16]  G. Parisi,et al.  Off-equilibrium effective temperature in monatomic Lennard-Jones glass. , 2000, Physical review letters.

[17]  F. Sciortino,et al.  Thermodynamics of supercooled liquids in the inherent-structure formalism: a case study , 1999, cond-mat/9911062.

[18]  J. Bartoš,et al.  Free volume from the positron annihilation lifetime spectroscopy method and its relationships with the various microscopic and macroscopic dynamic properties of ortho-terphenyl , 1999 .

[19]  R. Yamamoto,et al.  Dynamics of highly supercooled liquids: Heterogeneity, rheology, and diffusion , 1998, cond-mat/9806207.

[20]  J. Langer,et al.  Dynamics of viscoplastic deformation in amorphous solids , 1997, cond-mat/9712114.

[21]  S. Glotzer,et al.  DYNAMICAL HETEROGENEITIES IN A SUPERCOOLED LENNARD-JONES LIQUID , 1997, cond-mat/9706075.

[22]  S. Nagel,et al.  Supercooled Liquids and Glasses , 1996 .

[23]  D. Henderson,et al.  Integral equation theory for Lennard‐Jones fluids: The bridge function and applications to pure fluids and mixtures , 1996 .

[24]  Marcus T. Cicerone,et al.  Relaxation of spatially heterogeneous dynamic domains in supercooled ortho‐terphenyl , 1995 .

[25]  F. Stillinger,et al.  A Topographic View of Supercooled Liquids and Glass Formation , 1995, Science.

[26]  C. Dasgupta.  Glass Transition in the Density Functional Theory of Freezing , 1992 .

[27]  Granato.  Interstitialcy model for condensed matter states of face-centered-cubic metals. , 1992, Physical review letters.

[28]  Y. Singh.  Density-functional theory of freezing and properties of the ordered phase , 1991 .

[29]  H. Löwen.  Elastic constants of the hard-sphere glass: a density functional approach , 1990 .

[30]  J. McCoy,et al.  Density functional theory of vacancies , 1990 .

[31]  Bengtzelius.  Theoretical calculations on liquid-glass transitions in Lennard-Jones systems. , 1986, Physical review. A, General physics.

[32]  M. Baus,et al.  The hard-sphere glass: metastability versus density of random close packing , 1986 .

[33]  U. Mohanty,et al.  A density functional-variational treatment of the hard sphere transition , 1985 .

[34]  Stoessel,et al.  Hard-sphere glass and the density-functional theory of aperiodic crystals. , 1985, Physical review letters.

[35]  W. Gotze,et al.  Dynamics of supercooled liquids and the glass transition , 1984 .

[36]  P. Tarazona,et al.  A density functional theory of melting , 1984 .

[37]  D. Oxtoby,et al.  A molecular theory of the solid–liquid interface. II. Study of bcc crystal–melt interfaces , 1982 .

[38]  Y. Hiwatari.  Free volumes and liquidlike clusters in soft‐core dense liquids and glasses , 1982 .

[39]  D. Oxtoby,et al.  A molecular theory for the solid–liquid interface , 1981 .

[40]  Gary S. Grest,et al.  Liquid-glass transition, a free-volume approach , 1979 .

[41]  D. J. Tildesley,et al.  Equation of state for the Lennard-Jones fluid , 1979 .

[42]  R. Evans.  The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids , 1979 .

[43]  M. Yussouff,et al.  First-principles order-parameter theory of freezing , 1979 .

[44]  N. Ogita,et al.  Fluctuating Free-Volume Analysis of the Soft-Core Model of High-Density Fluid States , 1978 .

[45]  Frans Spaepen,et al.  A microscopic mechanism for steady state inhomogeneous flow in metallic glasses , 1977 .

[46]  Charles H. Bennett,et al.  Serially Deposited Amorphous Aggregates of Hard Spheres , 1972 .

[47]  J. D. Bernal,et al.  The Bakerian Lecture, 1962 The structure of liquids , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[48]  Arthur K. Doolittle,et al.  Studies in Newtonian Flow. II. The Dependence of the Viscosity of Liquids on Free‐Space , 1951 .

[49]  W. Kauzmann.  The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures. , 1948 .

[50]  H. Eyring.  Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates , 1936 .