Cooperatively rearranging regions change shape near the mode-coupling crossover for colloidal liquids on a sphere

Abstract

The structure and dynamics of liquids on curved surfaces are often studied through the lens of frustration-based approaches to the glass transition. Competing glass transition theories, however, remain largely untested on such surfaces and moreover, studies hitherto have been entirely theoretical/numerical. Here we carry out single particle-resolved imaging of dynamics of bi-disperse colloidal liquids confined to the surface of a sphere. We find that mode-coupling theory well captures the slowing down of dynamics in the moderate to deeply supercooled regime. Strikingly, the morphology of cooperatively rearranging regions changed from string-like to compact near the mode-coupling crossover—a prediction unique to the random first-order theory of glasses. Further, we find that in the limit of strong curvature, Mermin–Wagner long-wavelength fluctuations are irrelevant and liquids on a sphere behave like three-dimensional liquids. A comparative evaluation of competing mechanisms is thus an essential step towards uncovering the true nature of the glass transition.

The energy landscapes of bidisperse particle assemblies on a sphere

“…The second key difference between the monodisperse and binary landscapes is that the binary landscapes are weakly funnelled with numerous deep minima, reminiscent of binary clusters 4 . This structure explains the diversity of stable states observed in experiments when prepared from a high temperature quench 14 , in simulations when relaxing to a local minimum from a random starting configuration 13 , and perhaps also the diverse packing arrangements of polydisperse epithelial cells in SphEMs 16 .…”

“…Interestingly, we find that a minority of small particles are able to passivate the topological defects necessary for spherical packings. Rather than destroying the global ordering 14 , we find that bidispersity is capable of stabilising highsymmetry structures relative to the monodisperse case. In contrast, a majority of small particles destabilises the global minima.…”

“…Separately, introducing size dispersity into the packing of particles is known to introduce severe frustration, leading to irregularly structured, glassy landscapes 4,[10][11][12] . The combined interactions of regular packing, spherical curvature, and bidispersity have recently began to be investigated, exhibiting extraordinarily diverse packing arrangements with multifunnel energy landscapes corresponding to alternative low-lying structures separated by high barriers [13][14][15] .…”

“…The principal effect of bidispersity is therefore not necessarily to disrupt low-energy regular packings, but rather create broken ergodicity in terms of low-lying minima separated by high barriers. This organisation explains the large range of highly defective structures observed in experimental and simulated systems, which may not be able to sample the lowest-energy structures on feasible time scales [13][14][15] . Probing these landscapes further, we study how the icosahedral order parameter and particle segregation change through the energy range of local minima.…”

Mixing-demixing transition and void formation in quasi-2D binary mixtures on a sphere

“…Confining particles to the surface of a sphere introduces several constraints to their placement that are absent in Euclidean (flat) space. Both the curvature and the topology of the sphere play a role in the way particles can be arranged on it-most prominently, no regular lattice can be fit onto its surface, as the topology of the sphere requires the presence of 12 pentagonal disclinations 8 , and introduces structural defects characterizing glassy fluids at large area fractions 9 . The compactness of the sphere also requires a careful treatment: instead of the straightforward thermodynamic limit, configurations of finite (small) numbers of particles become more relevant, and both the number of particles and the size of the sphere need to be considered as two independent parameters 10 .…”