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.
Highlights
The structure and dynamics of liquids on curved surfaces are often studied through the lens of frustration-based approaches to the glass transition
mode-coupling theory (MCT) is yet to be tested on such liquids on S2, and doing so opens the possibility of examining if the relaxation processes envisaged by the thermodynamic framework of the random first-order transition theory (RFOT) of glasses are at play[10]
Since MCT is a mean-field theory, the singularity predicted by this theory is only a crossover in finite dimensions and across this crossover RFOT anticipates a change in the shape of cooperatively rearranging regions (CRRs) from string-like to compact[11]
Summary
The structure and dynamics of liquids on curved surfaces are often studied through the lens of frustration-based approaches to the glass transition. It is only recently that numerical studies of a single-component liquid on a sphere, the simplest curved surface and denoted as S2, found that mode-coupling theory (MCT) can qualitatively capture the role of curvature on glassy dynamics[9]. Since MCT is a mean-field theory, the singularity predicted by this theory is only a crossover in finite dimensions and across this crossover RFOT anticipates a change in the shape of cooperatively rearranging regions (CRRs) from string-like to compact[11] This prediction, unique to RFOT, has been validated in simulations and experiments in Euclidean space[12,13,14,15,16]. Whether curving space fundamentally alters this scenario is not known
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