Category: Dynamic arrest

Supercooled liquids are local equilibrium states where the features of glassy dynamics progressively emerge as we decrease the temperature. We have a broad understanding of what happens in a generic supercooled liquid: the dynamics become slow and highly heterogeneous, motion is gradually more cooperative, and some changes in the local spatial correlations occur accompanied by a reduction of the number of accessible configurations (the so-called configurational entropy). We have theoretical interpretations that emphasise one aspect or another of this phenomenological picture: some focus on the dynamical properties, others on the thermodynamical ones. Both schools of thought rely on intermediate concepts that vehiculate the message of the theories and link the microscopic constituents to the macroscopic relaxation behaviour: so-called dynamical facilitation relies on a hierarchy of excitations; thermodynamic theories have cooperatively rearranging regions as a critical ingredient for their description.

After many efforts by PhD student (and now Dr!) Levke Ortlieb, a quantitative analysis of how these concepts can be defined in practice at very low temperatures (where they should be more cogent) has just been published in Nature Communications, https://rdcu.be/dbtmK . The work, supervised by CP Royall and myself, leverages high-performance GPU molecular dynamics data produced by T Ingebrigtsen, from the Roskilde Glasss and Time group, and super-resolution colloidal experiments by J Hallett (Reading) to probe a supercooled regime well below conventional simulations. This allows us to revisit past definitions of excitations and cooperatively rearranging regions, to provide operative routes to measure these notions and compare one against the other. Furthermore, it allows us to show that the different theoretical approaches are sufficiently flexible to fit the data even in this low-temperature regime, making it difficult to rule out one or another mechanism. On the contrary, a complementarity between the two approaches appears to emerge: whether this is a physical or an epistemological reality is still yet to be investigated!

Full reference
Ortlieb, L., Ingebrigtsen, T.S., Hallett, J.E., Turci, F., Royall, C.P, Probing excitations and cooperatively rearranging regions in deeply supercooled liquids. Nat Commun 14, 2621 (2023). https://doi.org/10.1038/s41467-023-37793-2

Liquids are normally considered to be thermodynamically stable. However, rapidly cooled liquids attain a so-called metastable state — the supercooled or undercooled liquid. As we decrease the temperature, these liquids become more and more viscous and structural relaxation becomes slower and slower. One could naively infer that, as the slowing down proceeds, nothing happens in such systems since the motion of the constituents (atoms or molecules) is so severely hindered. Actually, the mystery of supercooled liquids resides precisely in the origin of such slowing down. Ultimately, this form of dynamic arrest leads to the formation of an amorphous solid, i.e. a solid that is not crystalline: we call this a glass.

This longstanding open problem in thermodynamics and statistical mechanics has prompted several theoretical approaches. These are inspired by different facets characterising glassy physics: glasses present a wide and heterogeneous distribution of relaxation timescales; glasses have signatures of reordering on very small lengths; glass-forming liquids display a reduction of the number of distinct configurations that the constituents can attain. Several conflicting theories have emerged over time, attempting to provide a unified picture.

We have just published a Perspective (a Featured Article in the Journal of Chemical Physics) retracing the connections existing between the theory of dynamical phase transitions and the structural and thermodynamical approaches to the glass transitions. We show that the theory of dynamical phase transitions allows us to identify metastable states in an operative sense. The glassy phenomenology can then be re-interpreted in an extended phase space. Here dynamical transitions between metastable states are coupled to structural features and configurational entropy reduction. This suggests a close relationship between microscopic structural arrangement, mesoscopic kinetic rules and thermodynamic phase transitions.

You can read the full Perspective here
C. Patrick Royall, Francesco Turci and Thomas Speck J. Chem. Phys. 153, 090901 (2020)

Last May, James Drewitt from the School of Earth Science here in Bristol asked me to have a look at his data on ver high pressure and temperature gallium. Used to my idealised particles in box, I thought that it would be interesting to look understand what information can reasonably emerge in this more realistic setting.

It turns out that gallium is a liquid with a number of noticeable physical characteristics: a melting point just above room temperature at ambient pressure conditions, high thermal conductivity and a strong tendency to undercooling, i.e. to remain disordered well below its melting temperature (which is even enhanced with respect to the bulk behaviour when small droplets of gallium as considered). To my surprise, it also appears that many of the tools that I have employed to study the structure of simple liquids are useful to understand how extreme pressure and temperatures affect this metallic liquid.

We have shown, for example, that as the pressure increases the liquid shows a preference to form local motifs of radically different nature in somewhat similar proportions, as opposed to what would happen in purely repulsive systems. This is interesting, as this competition between different forms of local order provides a mechanism for the enhanced stability in supercooled conditions. We also have found out that simplistic approaches to the modelling of the three dimensional structure of the liquid (such as naive Reverse Monte Carlo methods) overlook these changes in structure and are strongly biased by their initial guesses.

The reference to the full work, that combines new experimental evidence with a detailed numerical simulation analysis, is

James W. E. Drewitt, Francesco Turci, Benedict J. Heinen, Simon G. Macleod, Fei Qin, Annette K. Kleppe, and Oliver T. Lord, Phys. Rev. Lett. 124, 145501 (2020)

Computer simulations are very powerful: in the case of molecular dynamics, we can model the positions and velocities of atoms or molecules and observe the emergence of pattern and structures in situ, following each individual atom in its trajectory.

However, when we study supercooled liquids or glasses, it is hard to probe in computer simulations very low temperatures or very tightly packed systems, unless we opt for indirect and clever routes to glean some information on the low temperature behaviour. It would be great if one could directly take a very cold (or, similarly, very dense) liquid at equilibrium and see how the constituent particles are arranged.

This is precisely what James Hallett has managed to do during his stay in Bristol using super-resolution microscopy: this method can access the coordinates of equilibrium themal packings so dense that a direct simulation would never do. Thanks to James’s clever imaging, we have then carefully analysed the individual coordinates and trajectories of dense repulsive colloids and managed to clearly show how the local environment of these densely packed equilibrium systems changes as the density is increased.

We have found some notable features: as we take denser samples, the liquid becomes gradually richer in regions where particles are arranged into five-fold symmetric structures; those regions display reduced mobility compared to other regions of the sample; randomly selected domains of the system become more and more “similar to each other” as the density is increased, accompanied by the decrease in the number of distinct configurations the liquid can take, a quantity related to its so-called configurational entropy.

This work has just appeared in Nature Communications. Full text here:

James E. Hallett, Francesco Turci, and C. Patrick Royall. Nature Communications 9(1), 3272 (2018).

Hard spheres are one of the simplest model of fluid. When the density is increased, the motion is slowed down and non-trivial local arrangements of particles characteristic of the liquid emerge. We call these local structural motifs.

In hard spheres, special role is played by structures with pentagonal rings, such as icosahedra or pentagonal pyramids.

In collaboration with Pierre Ronceray (Princeton), to appear on the Journal of Chemical Physics, we have shown that if we study the cross-correlations between the variation of populations of different motifs we can understand more of the phase behaviour of this model liquid: for example, we can predict its propensity to form more motifs of a given type if an external field is applied; or, we can understand and classify different motifs that coexist in the liquid phase.

More details can be found in the JCP Editor’s Pick:

B. Carter, F. Turci, P. Ronceray, C.P. Royall, Structural Covariance in the Hard Sphere Fluid, The Journal of Chemical Physics 148, 204511 (2018); https://doi.org/10.1063/1.5024462