Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session T7: Structural and Mechanical Properties of Jammed Amorphous Materials |
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Sponsoring Units: GSNP Chair: Bulbul Chakraborty, Brandeis University Room: Ballroom C3 |
Wednesday, March 23, 2011 2:30PM - 3:06PM |
T7.00001: Length scale of dynamic heterogeneity and its relation to time scales in a glass-forming liquid Invited Speaker: The role of the length scale of dynamic heterogeneity in the enormous increase in the relaxation times of glass-forming liquids upon supercooling has received much attention recently. Using molecular dynamics simulations and finite-size scaling for a realistic glass-forming liquid, we establish that the growth of dynamic heterogeneity with decreasing temperature is governed by a growing dynamic length scale. We also perform a computational study of a four-point structure factor, defined from spatial correlations of mobility, for the same liquid and show that estimates of the dynamic correlation length and susceptibility obtained from this study are consistent with the results of the finite-size scaling analysis. However, the observed dependence of the simultaneously growing time scale of the long-time $\alpha$-relaxation on system size does not exhibit the same scaling behavior as the dynamic heterogeneity: this time scale is instead determined, for all studied system sizes and temperatures, by the configurational entropy, in accordance with the Adam-Gibbs relation. We also investigate the dependence of the time scale of the short-time $\beta$-relaxation on temperature and system size. A finite-size scaling analysis of this dependence reveals the existence of a length scale that grows as the temperature is reduced. Surprisingly, the temperature dependence of this length scale is found to be identical to that of the length scale that governs the growth of dynamic heterogeneity at the $\alpha$-relaxation time scale. This result suggests a close connection between short-time dynamics and dynamic heterogeneity at time scales of the order of the $\alpha$-relaxation time. [Preview Abstract] |
Wednesday, March 23, 2011 3:06PM - 3:42PM |
T7.00002: Point-to-Set as a measure of Correlations during Unjamming in Granular Systems Invited Speaker: There is evidence indicating that the unjamming of frictionless, soft grain packings occurs at a critrical point, however, no correlation function associated with a diverging, static length scale has been identified. To better understand the nature of this transition, we consider the soft grain packing problem as a constraint satisfaction problem [1]. Jammed configurations are mechanically stable packings with non-zero pressure. Contact forces on each grain therefore satisfy the equations of mechanical equilibrium, which are a set of local constraints, as well as a global constraint from the pressure. In general when jammed, there are more contact forces than constraints, so that an ensemble of force networks exists [2] which satisfy the constraints. These force networks make up a high-dimensional solution space that shrinks to a point at the unjamming transition, suggesting that the unjamming transition can be considered an entropy vanishing transition. We explore a new type of ``point-to-set'' correlation function which has been used to identify non-obvious length scales in other constraint satisfaction problems [3], and show that it exhibits a diverging length scale. We compare and contrast this length scale with the well established ``isostatic length'' of Wyart et. al [4].\\[4pt] [1] F. Krzakala and J. Kurchan, PRE 76, 021122 (2007)\\[0pt] [2] J.H. Snoeijer et. al, PRE 70, 061306 (2004)\\[0pt] [3] A. Montanari and G. Semerjain, Journal of Stat. Phys, 125, 1 (2006)\\[0pt] [4] M. Wyart et. al, PRE 72, 051306 (2005) [Preview Abstract] |
Wednesday, March 23, 2011 3:42PM - 4:18PM |
T7.00003: Protocol Dependence in Jammed Particulate Media: Statistics of the Density Landscape Invited Speaker: The density at which hard-sphere fluids jam into amorphous solids depends strongly on the compression protocol. Extremely fast quenching protocols bring each initial point in configuration space to the closest basin-maximum on the density landscape. In contrast, slower quench protocols allow the system to relax and explore configuration space. The protocol-dependence of the density, other structural quantities, and mechanical properties depends strongly on statistical features of the landscape. In this talk, I describe calculations of the the basin volumes associated with jammed hard sphere packings, and the critical quench rate $\Gamma^*$ above which the probabilities for obtaining jammed packings are determined by their basin volumes. Basin volumes are exponentially distributed; thus, for $\Gamma > \Gamma^*$, so are jammed packing probabilities. We discuss the implications of this result on the statistical mechanics of jammed systems. [Preview Abstract] |
Wednesday, March 23, 2011 4:18PM - 4:54PM |
T7.00004: Vibrational modes identify soft spots in a sheared model glass Invited Speaker: Both solids and fluids can flow under applied stress. In crystalline solids, flow occurs via particle rearrangements controlled by a population of dislocations, while in fluids, particle rearrangements occur everywhere throughout the material. In disordered solids, flow generally occurs via localized rearrangements, but no one has been able to identify a population of flow defects, analogous to dislocations, that are structurally different from the rest of the system and more susceptible to flow. It has therefore remained unclear whether a solid-like or fluid-like description is more appropriate for describing flow in such systems. By analyzing the low-energy vibrational modes in a model glass, we have identified a population of structural ``soft spots'' and have shown that particle rearrangements are initiated at these spots. Thus, these spots serve as good candidates for flow defects. We analyze statistical and structural features of the spots and find that the density of spots decreases with increasing packing fraction and that the population of spots changes slowly compared to the time between particle rearrangements. These results support a solid-like description of flow controlled by a population of localized flow defects in glassy materials. [Preview Abstract] |
Wednesday, March 23, 2011 4:54PM - 5:30PM |
T7.00005: Jamming Mechanisms and Density Dependence of Dynamic Heterogeneities in a Kinetically-Constrained Model Invited Speaker: Experiments on granular [1] and colloidal [2] systems show steady growth in dynamic heterogeneities as the relaxation time increases with increasing density. In glass-forming liquids, however, the scale of heterogeneities remains modest even as the relaxation time increases by more than ten orders of magnitude with decreasing temperature [3]. This difference may be attributed to the far greater dynamic range measurable in glass-forming liquids [2]. We introduce a simple lattice model [4] which suggests that this difference signals a fundamental distinction between jamming due to an increase in particle density as opposed to jamming by lowering the temperature, or the strength of external driving forces. The recently proposed spiral model [5] has a kinetic constraint that breaks its ergodicity at a critical density smaller than 1. We add to it relaxation mechanisms that mimic the effect of temperature and non-equilibrium driving. This enables us to explore its jamming phase-diagram and study unjamming by temperature or driving above the critical density, which we relate to the random close packing density in particulate systems. We separate the effects of density, temperature and driving and show that jamming resulting from increasing density gives rise to dynamic heterogeneity that grows unboundedly. Whereas decreasing temperature or driving eventually leads to a saturation of the dynamic correlation length even though the relaxation time diverges. \\[4pt] [1] A.R. Abate and D.J. Durian, Phys. Rev. E 76, 021306 (2007).\\[0pt] [2] G. Brambilla et al., Phys. Rev. Lett. 102, 085703 (2009).\\[0pt] [3] C. Dalle-Ferrier et al., Phys. Rev. E 76, 041510 (2007).\\[0pt] [4] Y. Shokef, A.J. Liu, Europhys. Lett. 90, 26005 (2010).\\[0pt] [5] C. Toninelli, G. Biroli, D.S. Fisher, Phys. Rev. Lett. 98, 129602 (2007). [Preview Abstract] |
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