On the rigidity of amorphous solids

M. Wyart

    Research output: Contribution to journalArticle

    Abstract

    We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work, we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the "boson peak" in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.

    Original languageEnglish (US)
    Pages (from-to)1-96
    Number of pages96
    JournalAnnales de Physique
    Volume30
    Issue number3
    DOIs
    StatePublished - 2005

    Fingerprint

    jamming
    rigidity
    glass
    vibration mode
    thresholds
    geometry
    bulk modulus
    coordination number
    scaling laws
    modulus of elasticity
    plane waves
    bosons
    assembly
    transport properties
    breakdown
    silicon dioxide
    shear
    low frequencies
    scaling
    causes

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    On the rigidity of amorphous solids. / Wyart, M.

    In: Annales de Physique, Vol. 30, No. 3, 2005, p. 1-96.

    Research output: Contribution to journalArticle

    Wyart, M. / On the rigidity of amorphous solids. In: Annales de Physique. 2005 ; Vol. 30, No. 3. pp. 1-96.
    @article{836b6e5cc43348e0a79e090221f3dcad,
    title = "On the rigidity of amorphous solids",
    abstract = "We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work, we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the {"}boson peak{"} in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.",
    author = "M. Wyart",
    year = "2005",
    doi = "10.1051/anphys:2006003",
    language = "English (US)",
    volume = "30",
    pages = "1--96",
    journal = "European Physical Journal H",
    issn = "2102-6459",
    publisher = "Springer Verlag",
    number = "3",

    }

    TY - JOUR

    T1 - On the rigidity of amorphous solids

    AU - Wyart, M.

    PY - 2005

    Y1 - 2005

    N2 - We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work, we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the "boson peak" in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.

    AB - We poorly understand the properties of amorphous systems at small length scales, where a continuous elastic description breaks down. This is apparent when one considers their vibrational and transport properties, or the way forces propagate in these solids. Little is known about the microscopic cause of their rigidity. Recently it has been observed numerically that an assembly of elastic particles has a critical behavior near the jamming threshold where the pressure vanishes. At the transition such a system does not behave as a continuous medium at any length scales. When this system is compressed, scaling is observed for the elastic moduli, the coordination number, but also for the density of vibrational modes. In the present work, we derive theoretically these results, and show that they apply to various systems such as granular matter and silica, but also to colloidal glasses. In particular we show that: (i) these systems present a large excess of vibrational modes at low frequency in comparison with normal solids, called the "boson peak" in the glass literature. The corresponding modes are very different from plane waves, and their frequency is related to the system coordination; (ii) rigidity is a non-local property of the packing geometry, characterized by a length scale which can be large. For elastic particles this length diverges near the jamming transition; (iii) for repulsive systems the shear modulus can be much smaller than the bulk modulus. We compute the corresponding scaling laws near the jamming threshold. Finally, we discuss the implications of these results for the glass transition, the transport, and the geometry of the random close packing.

    UR - http://www.scopus.com/inward/record.url?scp=33646390110&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=33646390110&partnerID=8YFLogxK

    U2 - 10.1051/anphys:2006003

    DO - 10.1051/anphys:2006003

    M3 - Article

    VL - 30

    SP - 1

    EP - 96

    JO - European Physical Journal H

    JF - European Physical Journal H

    SN - 2102-6459

    IS - 3

    ER -