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 diverging and vanishing 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.

The jamming scenario—an introduction and outlook

“…This maximum is interpreted as a thermal vestige of the zero-temperature jamming transition. Corroborating simulations show [64] that the divergence in g 1 ∼ 1/(φ − φ c ) for soft repulsive spheres at the zero-temperature jamming transition is softened to a maximum at nonzero temperature. The maximum in g 1 decreases in height and shifts to higher density with increasing temperature.…”

“…The peak is a vestige of that T = 0 transition where the first peak of g(r) is a δ-function. Figure reproduced from [65].…”

“…There is also a local maximum in g 1 at φ ≈ 0.74, above which no changes in the coordination and geometrical features of Voronoi cells are observed. This secondary maximum at nonzero kinetic energy due to airflowinduced interactions, may correspond to the finite-temperature vestige [64] of the divergence in the height of the first peak of g(r) at the zero-temperature transition discussed below.…”

“…Experiments on a two-dimensional bidisperse system of NIPA particles by Zhang, et al [64], measured the pair correlation function as a function of density at essentially fixed, nonzero temperature. The system exhibits a maximum in the height of the first peak of the pair correlation, g 1 -see Fig.…”

Measurement of Correlations between Low-Frequency Vibrational Modes and Particle Rearrangements in Quasi-Two-Dimensional Colloidal Glasses

“…0031-9007=11=107(10)=108301 (5) 108301-1 Ó 2011 American Physical Society soft tail [15], enabling particles to be packed at a high concentration. A binary mixture of microgel particles, with diameters of 1 and 1:4 m and with a large or small particle number ratio of 0.7, was loaded between two glass cover slips to create a colloidal monolayer.…”