Thermal vestige of the zero-temperature jamming transition

Abstract

When the packing fraction is increased sufficiently, loose particulates jam to form a rigid solid in which the constituents are no longer free to move. In typical granular materials and foams, the thermal energy is too small to produce structural rearrangements. In this zero-temperature (T = 0) limit, multiple diverging1,2,3,4,5,6,7,8 and vanishing2,9,10 length scales characterize the approach to a sharp jamming transition. However, because thermal motion becomes relevant when the particles are small enough, it is imperative to understand how these length scales evolve as the temperature is increased. Here we used both colloidal experiments and computer simulations to progress beyond the zero-temperature limit to track one of the key parameters—the overlap distance between neighbouring particles—which vanishes at the T = 0 jamming transition. We find that this structural feature retains a vestige of its T = 0 behaviour and evolves in an unusual manner, which has masked its appearance until now. It is evident as a function of packing fraction at fixed temperature, but not as a function of temperature at fixed packing fraction or pressure. Our results conclusively demonstrate that length scales associated with the T = 0 jamming transition persist in thermal systems, not only in simulations but also in laboratory experiments.

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Figure 1: Schematic jamming phase diagram.
Figure 2: Pair-correlation function g(r ) for the large particles at all experimental packing fractions.
Figure 3: Peak value of g(r), g1, measured from simulations.
Figure 4: Dynamics approaching the structural maximum.

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Acknowledgements

We thank T. Lubensky, D. Durian and K. Chen for discussions and a critical reading of the manuscript. We acknowledge the financial support of the Department of Energy and the National Science Foundation: DE-FG02-05ER46199 (A.J.L., N.X.), DE-FG02-03ER46088 (S.R.N., N.X.), the University of Chicago MRSEC DMR-0820054 (S.R.N., N.X.), DMR-080488 (A.G.Y.), and the PENN MRSEC DMR-0520020 (A.G.Y., A.J.L., Z.Z.). Z.Z. gratefully acknowledges partial support from Rhodia. Finally, we acknowledge the support of the Teraport computer cluster at the University of Chicago.

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Correspondence to Zexin Zhang or Ning Xu.

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This file contains Supplementary Methods, a Supplementary Discussion, Supplementary References and Supplementary Figures S1-S6 with Legends. (PDF 971 kb)

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Zhang, Z., Xu, N., Chen, D. et al. Thermal vestige of the zero-temperature jamming transition. Nature 459, 230–233 (2009). https://doi.org/10.1038/nature07998

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