Abstract
Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states. The traditional understanding of glasses includes their thermodynamic metastability with respect to crystals. However, here we present specific examples of interactions that eliminate the possibilities of crystalline and quasicrystalline phases, while creating mechanically stable amorphous glasses down to absolute zero temperature. We show that this can be accomplished by introducing a new ideal state of matter called a “perfect glass”. A perfect glass represents a soft-interaction analog of the maximally random jammed (MRJ) packings of hard particles. These latter states can be regarded as the epitome of a glass since they are out of equilibrium, maximally disordered, hyperuniform, mechanically rigid with infinite bulk and shear moduli, and can never crystallize due to configuration-space trapping. Our model perfect glass utilizes two-, three-, and four-body soft interactions while simultaneously retaining the salient attributes of the MRJ state. These models constitute a theoretical proof of concept for perfect glasses and broaden our fundamental understanding of glass physics. A novel feature of equilibrium systems of identical particles interacting with the perfect-glass potential at positive temperature is that they have a non-relativistic speed of sound that is infinite.
Highlights
Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states
Perfect glasses obtained in this way can be regarded as glasses produced by an infinitely rapid quench from infinite temperature to zero temperature because the random initial configuration is equivalent to the infinite-temperature state, and an energy minimization process may be thought of as evolving the system to a state of zero temperature
We will restrict ourselves to α ≥ 1 because, as we will see, this places a lower bound on the rigidity of a perfect glass and is consistent with the maximally random jammed (MRJ) nature of g2(r) S(k)
Summary
Rapid cooling of liquids below a certain temperature range can result in a transition to glassy states. Here we present specific examples of interactions that eliminate the possibilities of crystalline and quasicrystalline phases, while creating mechanically stable amorphous glasses down to absolute zero temperature We show that this can be accomplished by introducing a new ideal state of matter called a “perfect glass”. One resolution of this well-known paradox is to assume that supercooled liquids at the Kauzmann temperature must undergo a thermodynamic phase transition to “ideal glasses”. The perfect glass paradigm does not even allow this to occur because ordered states (for all temperatures) are completely banished
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
