Edwards statistical mechanics for jammed granular matter

Baule, Adrian; Morone, Flaviano; Herrmann, Hans J.; Makse, Hernán A.

doi:10.1103/revmodphys.90.015006

Title: Edwards statistical mechanics for jammed granular matter

Journal Article · Thu Mar 08 00:00:00 EST 2018 · Reviews of Modern Physics

DOI:https://doi.org/10.1103/revmodphys.90.015006· OSTI ID:1541410

Baule, Adrian ^[1]; Morone, Flaviano ^[2]; Herrmann, Hans J. ^[3]; Makse, Hernán A. ^[2]

Queen Mary Univ. of London (United Kingdom). School of Mathematical Sciences
City College of New York, NY (United States). Levich Inst. Physics Dept.
ETH Zürich (Switzerland). Computational Physics for Engineering Materials. Inst. for Building Materials

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter—one of the very few generalizations of Gibbs-Boltzmann statistical mechanics to out-of-equilibrium matter—has garnered an extraordinary amount of attention by both theorists and experimentalists. Its importance stems from the fact that jammed states of matter are ubiquitous in nature appearing in a broad range of granular and soft materials such as colloids, emulsions, glasses, and biomatter. Indeed, despite being one of the simplest states of matter—primarily governed by the steric interactions between the constitutive particles—a theoretical understanding based on first principles has proved exceedingly challenging. Here a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble is reviewed. The construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems, is discussed. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to nonspherical shapes such as dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse, and polydisperse particles in any dimensions is discussed providing insight into a unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards ensemble of metastable jammed states and metastability in spin glasses is established. This highlights the fact that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin glasses.

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Research Organization:: City College of New York, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-03ER15458

OSTI ID:: 1541410

Alternate ID(s):: OSTI ID: 1424822

Journal Information:: Reviews of Modern Physics, Vol. 90, Issue 1; ISSN 0034-6861

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 106 works

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