In 1948, chemist Walter Kauzmann published experimental data that could point to the existence of an "ideal glass": a hypothetical fourth state of matter in which a solid, despite having an amorphous structure, is in thermodynamic equilibrium. Using computer simulations, a team led by Innsbruck physicist Gerhard Jung has now observed for the first time a "Kauzmann transition" from a liquid to an ideal glass.
In the physical sense, glass is not limited to familiar window glass; it forms whenever a liquid is cooled so quickly that it cannot crystallize. As a result, glass has an amorphous structure-that is, its "building blocks" are not arranged regularly as in crystals. At the same time, however, glass is similarly resistant to deformation as a crystalline solid.
What happens during the glass transition?
Exactly what glass is remains one of the major unsolved questions in condensed-matter physics. For example, it is unclear whether the transition from liquid to the glassy state is a genuine thermodynamic phase transition between two distinct states of matter, or a purely dynamical phenomenon in which the liquid merely deforms extremely slowly.
A hypothetical fourth state of matter-alongside gas, liquid, and crystalline solid-has been predicted by several theoretical approaches and is referred to as the "ideal glass." Experimental or numerical confirmation has not been possible so far, however, since obtaining an ideal glass would require cooling the corresponding liquid infinitely slowly without crystallizing.
First-ever computer simulation down to absolute zero
A team of physicists led by Gerhard Jung from the Department of Theoretical Physics has now succeeded in computationally modeling the cooling of a two-dimensional liquid in such a way that it reaches the ideal glass state.
The key was the combination of different numerical methods, because conventional computer simulations hit a hard limit for this task: they calculate how particles move step by step under the influence of the forces acting on them. Calculations of this kind can only represent a limited time span, even if repeated millions of times.
Only the integration of three different statistical methods enabled the research team to cool the temperature of a model system all the way down to absolute zero. "We show that it is fundamentally possible to model ideal glasses and to test theories of the glass transition. That was not clear before and is therefore extremely positive news," emphasizes study author Gerhard Jung.
Order that doesn't meet the eye
With the help of the simulation, the researchers were able to investigate the properties of an ideal glass directly for the first time. They observed that the number of possible particle configurations becomes extremely small at low temperatures. This is unusual for amorphous structures, which are typically characterized by countless different, equivalent configurations-unlike a crystal, which has one clearly prescribed structure. In the ideal glass, however, this diversity shrinks almost completely.
In the end, only a tiny number of configurations remain available to the system: an order that still looks disordered to the human eye, but can be defined almost as unambiguously as that of a crystal.
The arrangement of the particles in the ideal glass appears disordered, but actually follows a unique order. (Visualization created with Ovito 2.9.0)
The modeling in the study focused on very small systems, with a maximum of 77 particles. However, the authors were able to show that, as system size increases, the temperature at which the ideal glass forms approaches absolute zero. It can therefore be concluded that in two-dimensional materials with a large number of particles, no glass transition can be observed, because absolute zero would be reached before that point-a result that is consistent with theoretical arguments and previous numerical estimates.
From the second to the third dimension
With this publication, the authors are one step closer to describing the glass transition-one of the most interesting problems in solid-state theory, according to Nobel laureate Philip W. Anderson. The next step is to extend and apply the developed methodology. For example, the calculations should be applied to three-dimensional systems, where a transition temperature above absolute zero is expected even for large systems.
"To finally answer the question of the glass transition, however, it is necessary to apply the algorithm to significantly larger systems. How that can be achieved is still an open question," explains Gerhard Jung. "But the truly decisive message of our work is that it is fundamentally possible to develop structures that we can bring into thermodynamic equilibrium at arbitrarily low temperatures," says Jung.
Publication: Numerical investigation of the equilibrium Kauzmann transition in a two-dimensional atomistic glass. Gerhard Jung, Misaki Ozawa, Giulio Biroli, Ludovic Berthier. Proc. Natl. Acad. Sci. U.S.A. 123 (34) e2612355123. DOI: doi.org/10.1073/pnas.2612355123
