The structural origin of the hard-sphere glass transition in granular packing

Abstract

Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest is associated with the growth of a certain static order. Using granular packing as a model hard-sphere glass, we show the glass transition as a thermodynamic phase transition with a ‘hidden' polytetrahedral order. This polytetrahedral order is spatially correlated with the slow dynamics. It is geometrically frustrated and has a peculiar fractal dimension. Additionally, as the packing fraction increases, its growth follows an entropy-driven nucleation process, similar to that of the random first-order transition theory. Our study essentially identifies a long-sought-after structural glass order in hard-sphere glasses.

Origin of Noncubic Scaling Law in Disordered Granular Packing

“…3(c)], which suggests that these particles tend to aggregate to form regular triangles which can further lead to the formation of quasiregular tetrahedral structures [33,34]. In contrast to this, the distribution of  for   7,13 n  does not show a significant change apart from a slight change in the peak positions [ Fig.…”

“…4), which indicates that a local version of the same non-cubic law holds, suggesting that a low- packing with more liquid-like structure, i.e., smaller contact numbers, has an exponent d closer to 3. This subtle trend is hidden if one fits the global quantities  versus 13 R to obtain a single   In the following, we demonstrate that the exponent is closely related to the existence of contact neighbors as required by mechanical stability in granular packing [24,40,41], and is a phenomenon connected to jamming, instead of the fractal glass order as we set out to relate in the first place [34]. This finding is not totally surprising as we recall that even in the work which tried to relate the non-cubic exponent to a presumed fractal glass order in metallic glasses, the anomalous scaling is observed only far below the glass transition temperature, and the potential relationship to jamming is alluded [12].…”

“…The packing are prepared using three different methods, i.e., tapping, hopper deposition, and flow pulse, to obtain a broad range of global packing fractions  from 0.57 to 0.64 [34]. In tapping and flow pulse protocols,  is tuned by changing the tapping intensity or the flow velocity respectively, while in the hopper deposition protocol, particles gradually drain from a slowly lifting hopper and form a pile with 0.59  .…”

“…Therefore, such phenomenon is directly related to jamming phenomenon and might be universal near the jamming criticality [23,24]. In the experiment, we used synchrotron X-ray CT techniques to obtain the packing structures of packing with a wide range of packing fractions  [25][26][27][28][29][30][31][32][33][34] (see Supplemental Material [35]). In the following, we use the average particle diameter as a unit of length.…”

Ordering and dimensional crossovers in metallic glasses and liquids

“…A similar idea has been explored in granular materials; for example, Xia, et al found that polytetrahedra serve as structural elements to glassy order in hard-sphere particle glasses, forming a globally jammed fractal structure. 34 The mechanism for geometrical constraint in our systems may be similar to ideas in jamming or rigidity percolation. 35,36 IV.…”