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Abstract
Grains, foams and colloids can behave as liquids or solids. Their flow is difficult to predict, often jamming. Such systems are far from equilibrium but there may now be a thermodynamic framework for granular media. 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 compressibility2 of dry sand. Specifically, the jamming threshold is defined using a non-thermal temperature3 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 paradox4—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 softening5,6 and thickness invariance2,7.Cite this article
Lu, K., Brodsky, E. & Kavehpour, H. A thermodynamic unification of jamming. Nature Phys 4, 404–407 (2008). https://doi.org/10.1038/nphys934 