Session L8: Jamming at Nonzero Temperature and Stress

Simple scaling of the glass transition temperature with pressure

Zero-temperature packings of frictionless spheres have been used as a starting point for understanding granular materials, foams, colloids and even glass-forming liquids. Such packings exhibit a jamming transition, known as Point J, with increasing packing fraction. This symposium presents recent work that explores the implications of Point J for systems at nonzero temperature, shear stress, or friction. In this talk, I present results that push beyond zero temperature to explore the connection between Point J and the glass transition. We performed molecular dynamics simulations of several three-dimensional models of glass-forming liquids, and measured the relaxation time from the intermediate scattering function along several trajectories to the glass transition, such as lowering temperature at fixed packing fraction, or raising pressure at fixed temperature. Along each trajectory, we extrapolated the relaxation time using the form $\tau={\rm exp}(A/(T-T_0)^{\alpha})$ or $\tau={\rm exp}(A/(p^r-p^r_0)^{\alpha})$, depending on whether temperature or pressure was varied, where $p^r$ is the contribution to the pressure from repulsive forces, only. Here, $A$, $\alpha$, $T_0$ and $p^r_0$ are fit parameters. We find that $T_0$ is linear in the repulsive contribution to the pressure, $p^r$: $T_0=vp^r$. The fit parameter $v$ is approximately $0.035v_0=(0.37\sigma)^3$, independent of potential, where $v_0$ is the average volume per particle and $\sigma$ is the diameter of the particle. This linear scaling of $T_0$ with $p^r$ holds very well at low $p^r$, which corresponds to the vicinity of Point J in purely repulsive systems where jamming transition at T=0 exists. This suggests that Point J marks the onset of a nonzero value of the glass transition temperature, $T_0$. Experimental data for glycerol (K. Z. Win and N. Menon, Phys. Rev. E 73, 040501 (2006)) also show that $T_0$ is linear in pressure, with a prefactor of 0.04$\times$ the molecular volume.   

Critical Scaling of Shear Viscosity At the Jamming Transition

I review the assumptions behind a scaling theory of the jamming transition for shear driven non-equilibrium steady states of a granular medium. Scaling predictions are compared against data from numerical simulations for a simple two dimensional model of frictionless soft core interacting disks with overdamped dynamics. Methods are discussed to accurately measure the critical jamming density and the critical exponents describing the jamming transition. \\[4pt] Work carried out in collaboration with Peter Olsson, Department of Physics, Ume{\aa} University.   

Rigidity vs. Glass transition of a granular system close to Jamming

``Jamming'' is associated with two rather different notions, not always well distinguished in the literature. One, the glass transition, is that of dynamical arrest and the divergence of the structural relaxation time, the second, the proper jamming transition, is the appearance of mechanical rigidity. Both may in principle be different. In the past few years we have investigated the dynamics of a bi-disperse monolayer of disks under two different mechanical forcing i.e. cyclic shear and horizontal vibrations. (i) In the first case, one observes the so-called cage effect: at short times, any given particle is trapped in a confined area by its neighbors until the particle has managed to leave its cage and is able to diffuse through the sample by successive cage jumps [1]. Such features are reminiscent of what is observed in colloidal suspension, super-cooled liquids or other glass formers, close to the glass transition. In the present case, we have shown that cage jumps organize in clusters which avalanche in a facilitation like process to build up long term dynamical heterogeneities [2,3]. (ii) In the second case, the quench protocol produces very dense configurations with structural relaxation time much larger than the experimental time scales. One observes that long-time correlations, accompanied by the growth of spatial correlations are maximal at a volume fraction , where a snapshot of the displacement field reveals the existence of a super-diffusive motion organized in channel currents meandering between blobs of blocked particles [4,5]. We will discuss these results focusing on the distinction between the glass and jamming transitions also underlying the key role of friction in granular media as opposed to other glass formers. \\[4pt] [1] G. Marty, O. Dauchot, PRL 94, 015701 (2005). \\[0pt] [2] O. Dauchot, G. Marty, G. Biroli, PRL 95, 265701 (2005). \\[0pt] [3] R. Candelier, O. Dauchot, G. Biroli, arXiv 0811.0201. \\[0pt] [4] F. Lechenault, O. Dauchot, G. Biroli and J. P. Bouchaud, EPL, 83 46003 (2008). \\[0pt] [5] F. Lechenault, O. Dauchot, G. Biroli and J. P. Bouchaud, EPL, 83 46002 (2008).   

Measurement of growing dynamical length scale on approach to jamming in granular systems

The flow of granular materials is of widespread practical and fundamental interest. One challenge to understanding and controlling behavior is that the response is nonlinear, with a forcing threshold below which the medium is static. Furthermore, just above threshold the response may be intermittent even though the forcing is steady. Two familiar examples are avalanches on a heap and clogging in a silo. Another example is dynamical heterogeneities for systems brought close to jamming, where intermediate-time motion is correlated in the form of intermitted string-like swirls. Here this will be illustrated with experiments on air-driven beads, where jamming is approached by lowering the effective temperature, as well as by experiments on rapid heap flow, where jamming is approached as a function of depth from the free surface. Use of novel statistical quantities and optical spectroscopies reveal a growing dynamical length scale on approach to jamming. Collaborators: Adam Abate, Hiroaki Katsuragi, Aaron Keys, Sharon Glotzer.