Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

Abstract

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0

10 pages, 9 figures, submitted to PRE

References in corpus (7)

• Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity
• Glassy behaviour in a simple topological model
• Statistical Mechanics of the Glass Transition in One-Component Liquids with Anisotropic Potential
• Ageing and Relaxation in Glass Forming Systems
• Mechanical Properties of Glass Forming Systems
• Dynamics of Triangulations
• A Topological Glass

Cited by in corpus (23)

• Theoretical perspective on the glass transition and amorphous materials
• The role of local structure in dynamical arrest
• The glass transition of dense fluids of hard and compressible spheres
• A brief critique of the Adam-Gibbs entropy model
• Ultra-fast quenching of binary colloidal suspensions in an external magnetic field
• Strong geometric frustration in model glassformers
• Locally favoured structures and dynamic length scales in a simple glass-former
• Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System
• Does the configurational entropy of polydisperse particles exist?
• Scaling Theory for Steady State Plastic Flows in Amorphous Solids
• Experimental Determination of Configurational Entropy in a Two-Dimensional Liquid under Random Pinning
• Correlation between crystalline order and vitrification in colloidal monolayers
• A Theory of Localized Excitations in Supercooled Liquids
• Recasting a model atomistic glassformer as a system of icosahedra
• Ageing and Relaxation in Glass Forming Systems
• The Effective Temperature in Elasto-Plasticity of Amorphous Solids
• Quantitative Theory of a Time-Correlation Function in a One-Component Glass-Forming Liquid with Anisotropic Potential
• Predictive Statistical Mechanics for Glass Forming Systems
• Quantitative Theory of a Relaxation Function in a Glass-Forming System
• Statistical Mechanics of Glass Formation in Molecular Liquids with OTP as an Example
• Structure in Sheared Supercooled Liquids: Dynamical Rearrangements of an Effective System of Icosahedra
• Yielding of a Model Glassformer: an Interpretation with an Effective System of Icosahedra
• Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model