Dynamic criticality at the jamming transition

Abstract

We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, phi = phi_J). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near phi_J is divided in three different regimes separated by a characteristic temperature scale T*(phi) that vanishes quadratically with the distance to phi_J. While two of them, (T < T*(phi), phi > phi_J) and (T < T*(phi), phi < phi_J), are described by harmonic theories developed in the zero temperature limit, the third one for T > T*(phi) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T*(phi) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specifically-dedicated experiments.

18 pages; submitted to J. Chem. Phys. for "Special Topic Issue on the Glass Transition"

References in corpus (15)

• Theoretical perspective on the glass transition and amorphous materials
• Unified study of glass and jamming rheology in soft particle systems
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• The glass transition of dense fluids of hard and compressible spheres
• Critical scaling in linear response of frictionless granular packings near jamming
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Compressing nearly hard sphere fluids increases glass fragility
• Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
• Geometric interpretation of pre-vitrification in hard sphere liquids
• Unexpected drop of dynamical heterogeneities in colloidal suspensions approaching the jamming transition
• Growing length and time scales in a suspension of athermal particles
• A microscopic mean-field theory of the jamming transition
• Elementary Excitation Modes in a Granular Glass above Jamming
• Lower bound on the four-point dynamical susceptibility: Direct experimental test on a granular packing
• Can the jamming transition be described using equilibrium statistical mechanics?