A thermodynamic unification of jamming

Abstract

Fragile materials1 ranging from sand to fire retardant to toothpaste are able to exhibit both solid and fluid-like properties across the jamming transition. Unlike ordinary fusion, systems of grains, foams and colloids jam and cease to flow under conditions that still remain unknown. Here, we quantify jamming using a thermodynamic approach by accounting for the structural ageing and the shear-induced compressibility 2 of dry sand. Specifically, the jamming threshold is defined using a non-thermal temperature 3 that measures the 'fluffiness' of a granular mixture. The thermodynamic model, cast in terms of pressure, temperature and free volume, also successfully predicts the entropic data of five molecular glasses. Notably, the predicted configurational entropy averts the Kauzmann paradox 4 -an unresolved crisis where the configurational entropy becomes negative-entirely. Without any free parameters, the proposed equation-of-state also governs the mechanism of shear banding and the associated features of shear softening 5,6 and thickness invariance 2,7 . Despite their mundane appearance, granular materials exhibit a wide range of intriguing phenomena 8,9 . Dry sand, for instance, can deform readily 9 but can also jam abruptly, for example, as observed in the sudden stoppage of flow in an hourglass or a salt shaker. The abruptness of jamming refers to the narrow range of packing fractions 10 (0.62-0.64) under which the material no longer deforms. Molecular systems also exhibit similar jamming phenomena. For example, liquids such as wood glue become extremely viscous and resistant to flow when cooled within a narrow range of temperatures 11 (2-3 • C) below the freezing point. This jamming behaviour shared by both granular fluids and viscous liquids is astonishing 8,12,13 and suggestive of a common underlying mechanism, but thus far, a definitive theoretical connection remains unknown.Jamming was defined 14,15 as a means to unify all fragile systems 1 and has been qualitatively described using three independent variables: pressure, packing fraction and an effective temperature 13 . It is known, however, that granular packings are metastable: any perturbation in the magnitude or the direction of the applied stress will cause structural ageing 1,10 , during which particles rearrange through irreversible compaction. It is thus problematic to neglect ageing and assume, for example, that the temperature at which jamming occurs can be defined by pressure and packing fraction alone. Still, many studies of fragile systems neglect the implications of ageing, possibly because of the narrow range in the temperature and packing density of glassy and granular systems near structural arrest. Here, we present a new perspective on jamming that includes a connection to the glass transition of viscous liquids. The proposed equation-of-state (EOS) will introduce jamming as path-dependent states definable by the stationary observables pressure, packing density and shear rate. Recent shear flow experiments2 deduced the EOS of dense granu...

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