A glass is (broadly speaking) mostly composed of particles that very slowly move due to surrounding cages formed by the disordered structure of the liquid. A way to study the glass transition is to actually freeze-in a subset of the particles and observe how this induces changes to the slow relaxation and how this relates to the emergence of local order.
The freezing-in procedure (also called pinning) has a secondary important effect: the pinned liquid has a “simplified” configurational space, as many configurations become forbidden. The number of available configurations (and hence the configurational entropy of the liquid) is therefore reduced by the simple pinning procedure and if a thermodynamic origin of dynamical arrest is to be surmised, such a reduction would be a necessity.
Some years ago, Ian Williams designed a novel, clever way to pin large two-dimensional colloidal supercooled liquids. In an article recently accepted in the Journal of Physics: Condensed Matter we have shown that the technique allows us to observe the crossover from a free-flowing liquid to a pinned glass and that this is accompanied by very limited structural changes. However, if we map the configurational entropy of the experiments with the entropy measured from model numerical simulations, we do observe that accounting for the fraction of pinned particles leads to a reduction in the estimated configurational entropy.
I. Williams, F. Turci et al. (2018) Experimental determination of configurational entropy in a two-dimensional liquid under random pinning, J. Phys.: Condens. Matter in press https://doi.org/10.1088/1361-648X/aaa869
I have recently been given the opportunity to study the segmentation of 3D data. The group of Dr. C. Hammond of the School of Physiology, Pharmacology and Neuroscience in Bristol studies malformation in tissues of Zebrafish a model organism which can be genetically manipulated relatively easily .
A major task is to identify bone malformation or osteoarthritis. Hammond’s group manages to image hundreds of Zebrafish in three dimensions so that bone structures can be visualised. Identifying bone deformations in the spine, for example, is key to associate them to specific genetic marker. To do so, a quantitative analysis of the structure of the individual vertebrae is necessary.
It turned out that it is possible to do this via image analysis techniques that are publicly available in Python: the key libraries that I employed are scipy. ndimage and scikit-image. Identifying the vertebrae in 3d means to perform a segmentation of volumes and surfaces in 3d images.
An example of the vertebrae, individually resolved, can be visualised in 3d here below:
We just published on the Journal of Chemical Physics the experimental and computer simulation work of a Ioatzin Rios de Anda (PhD student in the Royall group) on kinetically arrested crystalline phases in colloidal binary mixtures.
Despite slightly different conditions (presence/absence of confinement or polydispersity in the particle sizes) the experiments and simulations match in the fundamental message of the work: when we have two species rather different in sizes, crystallisation of the bigger species can occur before the reordering of the smaller species, forming long-lived kinetically arrested structures (interstitial solid solutions), characterised by a high density of imperfections and vacancies. This shows how challenging the formation of a well ordered binary crystal is and, on the other hand, how they can potentially be considered for the realisation of partially ordered porous matrices.
We have just published in the Journal of Chemical Physics the simulation work of a brilliant former master student of the School of Physics at the University of Bristol (Thomas Jenkinson) on the local structural changes occurring during ageing in two atomistic glass formers with Lennard-Jones interactions (the Kob-Andersen and Wahnström mixtures).
We find some expected results (local order steadily increases as the out-of-equilibrium liquid ages) and some more surprising ones (for example, the rate at which such increase occurs changes weakly for temperatures above the apparent dynamical divergence of viscosities, T0). We also investigate the effect of transient deep quenches, finding very moderate traces of so-called rejuvenation.
The reference to the work is J. Chem. Phys. 147, 054501, (2017).
One central piece of the problem of dynamic arrest is whether the phenomenology of slow relaxation, increasing dynamical length scales, mild (or dramatic) structural changes are somewhat related to the existence of a zero entropy amorphous state emerging at a non-zero temperature.
A comprehensive theory would need on the one hand to take into account of the well established phenomenon of dynamical heterogeneities, i.e. the non-homogenous patterns of diffusion that emerge together with the glassy dynamics itself; on the other hand, it should also rationalise the many findings that point (for several model systems) to a dramatic reduction of the so-called configurational entropy as one approaches a finite temperature (sometimes termed Kauzmann temperature) at which also the relaxation times appear to diverge.
In our recent work (Physical Review X 7, 031028) Thomas Speck, C. Patrick Royall and I discuss a unified scenario that combines dynamical aspects to structural ones in order to sample very low energy and entropy states, employing dynamical large deviations.
We find that the equilibrium supercooled liquid competes with a secondary metastable amorphous liquid rich in long-lived structural motifs, hidden in the tails of probability distributions in trajectory space. We also show that sampling the tails of such probabilities at a single moderate temperature allows us to retrieve the thermodynamic properties of the ordinary liquid in much wider range of temperatures, down to very low temperatures. We can then draw a diagram for the stable and metastable phase, pointing towards critical-like fluctuations in the region where the Kauzmann temperature is normally located, and allowing us to review currently proposed scenarios from an alternative point of view, rooted in the large deviation theory of metastability.
When installing software on an High Performance Computing unit, additional packages are often handled by the module package.
To have a list of all the modules available it is sufficient to type
Often one then retrieves a very long list of possible modules, in alphabetic order. This is not very convenient if one is looking for a particular feature and dos not really know how it has been categorised.
One may think that grep would suffice to filter the results. This is almost true: in order to use grep first one needs to reformat the result of module avail with the -t option into a single column, redirect the standard error output (labelled by 2 in Bash) to the standard output (labelled by 1, so that the redirection is 2>&1) and then pipe it with grep.
For example, if we want to search for all the modules containing “python” in their name we would type:
module avail -t 2>&1 | grep -i python
and eventually just write a convenient script named modsearch in our ~/bin :
module avail -t 2>&1 | grep -i $1
so that in the future we will just have to type
Rattachai Pinchaipat is a crafty experimentalist (PhD student in Bristol) that I have had the pleasure to work with within a Bristol-Mainz collaboration aimed at demonstrating in experiments the existence of phase transitions in trajectory space for supercooled liquids. Our work is going to appear in Physical Review Letters. Here is the preprint.
In Mainz, preliminary simulations on hard spheres in trajectory space (by Matteo Campo) have sampled the tails of the probability distribution of time-integrated structural observables and predicted long non-gaussian tails (signature of a phase transition). In experiments, Rattachai managed to find an analogous signature via subsampling the trajectories of a rather large system.
The result demonstrates that the dynamical heterogeneities that characterise fragile glass forming liquids can be read as the coexistence, in trajectory space, of different long-lived (metastable) stationary states: some are structure-less, while others show the presence of extraordinary extended and long-lived motifs. Crucially, the phase transition between the two states is not accessible in current experiments, and could eventually never be accessible, if it is always buried in the tails of the probability distribution.
But this is another story… (actually, this story).
Our work on curved space and frustration with Gilles Tarjus at the Université Pierre et Marie Curie in Paris is
going to appear published in Physical Review Letters, 118, 215501.
In it, we provide a test of one of the competing theories for the origins of the glass transition: this is geometric frustration, i.e. the idea that the slowing down observed in glass forming liquids goes hand in hand with the formation of particular non-cristalline geometric motifs, that increase in size as the liquids are cooled.
We test this on the most favourable ground for the theory, which is a curved manifold. We do this for the first time in three dimensions, observing the structural evolution of a glass former on the surface of a sphere embedded in four dimensions (This is a funny space to work in. A beautiful way to visualise such a hypersurface is to use the so-called two-ball construction, see image above, which nicely matches with the vision of the universe that Dante and his teacher Brunetto Latini had).
What we find is that geometrical motifs become gradually unfrustrated as the curvature increases (which is compatible with the basic assumptions of geometric frustration) and ordered phases (with some tricky defects, that we discuss in the Supplemental Material) spontaneously form for low enough temperatures. However, the size of the domains in such motifs is tightly coupled with the slowing down only for very strong curvatures, making geometric frustration just one of the mechanisms that eventually play a role in realistic glass-forming fluids (that exist in our ordinary Euclidean space).
During an invited talk at the University of Bath on May 3rd 2017, I have had the chance to discuss the work that we have done in Bristol on binary crystals and binary mixtures.
The story, that you can find in the following slides, discusses experimental and numerical aspects in the formation and dissolution of binary crystals:
- The routes to the formation interstitial solid solution (work with I. Rios de Anda).
- The role of compositional frustration (work with P. Crowther), published here.
- The emergence of dynamical transition under mechanical deformation of the crystals (work with E. Brillaux).
Disordered systems under confinement may show very specific properties, such as enhanced density fluctuations or flow instabilities.
Azaima Razali (Bristol) and Christopher Fullerton (Bath, now in Montpellier) have performed experiments and simulations on the effect of extreme confinement in colloidal gels and their work (to which I have the pleasure to add my contribution) has just been published in Soft Matter.
The notable result is that while gelation is often employed in bulk systems in order to slow down sedimentation, in strongly confined systems the opposite appears to be true, with sedimentation facilitated by the formation of a percolating network.
The full article can be found here: