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 microscopic kinetics of ubiquitous solid-solid phase transitions remain poorly understood. Here, by using single-particle-resolution video microscopy of colloidal films of diameter-tunable microspheres, we show that transitions between square and triangular lattices occur via a two-step diffusive nucleation pathway involving liquid nuclei. The nucleation pathway is favoured over the direct one-step nucleation because the energy of the solid/liquid interface is lower than that between solid phases. We also observed that nucleation precursors are particle-swapping loops rather than newly generated structural defects, and that coherent and incoherent facets of the evolving nuclei exhibit different energies and growth rates that can markedly alter the nucleation kinetics. Our findings suggest that an intermediate liquid should exist in the nucleation processes of solid-solid transitions of most metals and alloys, and provide guidance for better control of the kinetics of the transition and for future refinements of solid-solid transition theory.

The rheology near jamming of a suspension of soft colloidal spheres is studied using a custom microfluidic rheometer that provides stress versus strain rate over many decades. We find nonNewtonian behavior below the jamming concentration and yield stress behavior above it. The data may be collapsed onto two branches with critical scaling exponents that agree with expectations based on Hertzian contacts and viscous drag. These results support the conclusion that jamming is similar to a critical phase transition, but with interaction-dependent exponents.

We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.PACS numbers: 63. 63.50 Lm, 82.70 Dd Crystalline solids are all alike in their vibrational properties at low frequencies; every disordered solid is disordered in its own way. Disordered solids nonetheless exhibit common low-frequency vibrational properties that are completely unlike those of crystals, which are dominated by sound modes. Disordered atomic or molecular solids generically exhibit a "boson peak," where many more modes appear than expected for sound. The excess modes of the boson peak are believed to be responsible for the unusual behavior of the heat capacity and thermal conductivity at low-to-intermediate temperatures in disordered solids [2].It has been proposed that a zero-temperature jamming transition may provide a framework for understanding this unexpected commonality [3]. For frictionless, idealized spheres this jamming transition lies at the threshold of mechanical stability, known as the isostatic point [3,4]. As a result of this coincidence, the vibrational behavior of the marginally jammed solid at densities just above the jamming transition is fundamentally different from that of ordinary elastic solids [5][6][7][8]. A new class of lowfrequency vibrational modes arises because the system is at the threshold of mechanical stability [10]; these modes give rise to a divergent boson peak at zero frequency [5]. As the system is compressed beyond the jamming transition, the boson peak shrinks in height and shifts upwards in frequency [5]. Generalizations of the idealized sphere model suggest that the boson peaks of a wide class of disordered solids may arise from proximity to the jamming transition [9][10][11][12]. Moreover, the jamming scenario predicts that systems with larger constituents such as colloids should also have boson peaks.Colloidal glasses offer signal advantages over atomic or molecular disordered solids because colloids can be tracked by video microscopy. Vibrational behavior has been explored in hard-sphere colloids [13] and vibrated granular packings [14], but difficulties with statistics [13] or micro-cracks [14] were encountered. In contrast, we use deformable, thermosensitive hydrogel particles to tune the packing fraction in situ. Our experiments show unambiguously that the commonality in vibrational properties observed in atomic and molecular glas...

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