Understanding the ideal glass transition: lessons from an equilibrium study of hard disks in a channel

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
M J Godfrey, M A Moore

Abstract

We use an exact transfer-matrix approach to compute the equilibrium properties of a system of hard disks of diameter σ confined to a two-dimensional channel of width 1.95σ at constant longitudinal applied force. At this channel width, which is sufficient for next-nearest-neighbor disks to interact, the system is known to have a great many jammed states. Our calculations show that the longitudinal force (pressure) extrapolates to infinity at a well-defined packing fraction ϕ(K) that is less than the maximum possible ϕ(max), the latter corresponding to a buckled crystal. In this quasi-one-dimensional problem there is no question of there being any real divergence of the pressure at ϕ(K). We give arguments that this avoided phase transition is a structural feature, the remnant in our narrow channel system of the hexatic to crystal transition, but that it has the phenomenology of the (avoided) ideal glass transition. We identify a length scale ξ̃(3) as our equivalent of the penetration length for amorphous order: In the channel system, it reaches a maximum value of around 15σ at ϕ(K), which is larger than the penetration lengths that have been reported for three-dimensional systems. It is argued that the α-relaxation time would app...Continue Reading

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Citations

Apr 14, 2017·Soft Matter·Lin FuPatrick Charbonneau
Mar 27, 2018·Soft Matter·Yi Hu, Patrick Charbonneau
Dec 15, 2016·Physical Review. E·Péter GurinGerardo Odriozola
Apr 10, 2017·The Journal of Chemical Physics·Péter GurinEnrique Velasco
Jun 17, 2018·Physical Review. E·Péter GurinEnrique Velasco
Jan 23, 2020·Physical Review. E·Yuri Martínez-Ratón, Enrique Velasco
Jun 16, 2018·Physical Review Letters·C L HicksM A Moore
Apr 15, 2016·Physical Review. E·J F RobinsonM A Moore
May 17, 2017·Physical Review. E·Péter GurinSzabolcs Varga
Apr 27, 2016·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Miguel González-PintoEnrique Velasco
Nov 21, 2020·Physical Review. E·Yuxiao ZhangM A Moore
Jan 21, 2021·Physical Review. E·Eric R Weeks, Keely Criddle
Oct 23, 2020·The Journal of Chemical Physics·V M Pergamenshchik

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