Normal Modes and Density of States of Disordered Colloidal Solids

Kaya, Deniz; Green, N. L.; Maloney, Craig; Islam, Mohammad F.

doi:10.1126/science.1187988

Cited by 101 publications

(161 citation statements)

References 30 publications

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“…20 it was observed that contact-opening excitations in packings are marginally stable, so that the bounds 14 and 15 are satisfied with equality, with numerical values γ ≈ 0:4, θ ℓ ≈ 0:17, and θ e ≈ 0:44. Saturation of [15] was recently proven for certain dynamics (38). Assuming such marginal stability, it follows that θ f = θ ℓ < θ e and the exponent θ e can be determined from θ e = 2θ f =ð1 − θ f Þ ≈ 0:41, a value consistent with the direct measurement 0.44.…”

Section: Hard Spheressupporting

confidence: 60%

“…These two sets of results yield a stability constraint on the microscopic structure of hard-sphere glasses, which in practice appears to lie very close to saturation (6,7,12). Such marginal stability implies the abundance of very soft elastic modes, as confirmed empirically (6,7,(12)(13)(14)(15)(16), and fixes the scaling behavior of elasticity as jamming is approached (7). In particular the particles' mean-squared displacement was predicted to follow hδR 2 i ∼ ðϕ c − ϕÞ κ with κ = 1:5 (7) instead of the naive κ = 2, which would hold in a crystal: Particles in the glass fluctuate much more than the size of their cage (defined as the typical distance between particles), due to the presence of collective soft modes.…”

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confidence: 92%

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Force distribution affects vibrational properties in hard-sphere glasses

DeGiuli

Lerner

Brito

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

121

166

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We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting P(f ) ∼ f θe , the force distribution of such pairs and ϕ c the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ω*, rising up to it as D(ω) ∼ ω 2+a , and decaying above ω* as D(ω) ∼ ω −a where a = (1 − θ e )=(3 + θ e ) and ω is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with 〈δR 2 〉 ∼ 1=μ ∼ (ϕ c − ϕ) κ , where κ = 2 − 2=(3 + θ e ), and (iii) continuum elasticity breaks down on a scale ℓ c ∼ 1= ffiffiffiffiffi δz p ∼ (ϕ c − ϕ) −b , where b = (1 + θ e )=(6 + 2θ e ) and δz = z − 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that θ e ≈ 0:41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to κ ≈ 1:41, a ≈ 0:17, and b ≈ 0:21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d = ∞, whereas some observations differ, as rationalized by the present approach.colloids | glass transition | marginal stability | boson peak | jamming T he emergence of rigidity near the glass transition is a fundamental and highly debated topic in condensed matter and is perhaps most surprising in hard-sphere glasses where rigidity is purely entropic in nature. The rapid growth of relaxation time around a packing fraction ϕ g ≈ 0:58 suggests that metastable states have appeared in the free-energy landscape, and that activation above barriers is required for the system to flow (1). This scenario is presumably what mode-coupling theory captures (2, 3) and can be rationalized via density functional theory (4) and via the replica method (5). Recently a real-space description of mechanical stability and elasticity in hard-sphere glasses has been proposed (6, 7), which is most easily tested at large pressure, deep in the glass phase. It is based on two results. First, in elastic networks and athermal packings of soft spheres (8-10), mechanical stability is controlled by the mean number of contacts per particle, or coordination z (as already discussed by Maxwell in ref. 11), and the applied compressive strain e (10). As one may intuitively expect, increasing coordination is stabilizing, whereas increasing pressure at fixed coordination is destabilizing. Second, within a long-lived metastable state the vibrational free energy of a hard-sphere system can be approximated as a sum of local interaction terms between pairs of colliding particles, which are said to be in contact. On a time scale that contains many...

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Section: Hard Spheressupporting

confidence: 60%

mentioning

confidence: 92%

Force distribution affects vibrational properties in hard-sphere glasses

DeGiuli

Lerner

Brito

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

121

166

View full text Add to dashboard Cite

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“…The work is made possible by recently developed covariance matrix techniques that have led to the measurement of vibrational modes in thermal colloids from microscopy experiments [9][10][11]. The colloidal glasses are composed of thermosensitive microgel particles which readily permit in situ variation of the sample packing fraction.…”

Section: Recommended Citationmentioning

confidence: 99%

“…The measured displacement covariance matrix [9][10][11]19] was employed to extract vibrational modes of the shadow colloidal system, which shares the same geometric configuration and interactions of the experimental colloidal system, but is undamped. A displacement covariance matrix is constructed by calculating the equal-time covariance of displacements between each particle pair for each direction.…”

Section: Recommended Citationmentioning

confidence: 99%

Measurement of Correlations between Low-Frequency Vibrational Modes and Particle Rearrangements in Quasi-Two-Dimensional Colloidal Glasses

et al. 2011

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We investigate correlations between low-frequency vibrational modes and rearrangements in twodimensional colloidal glasses composed of thermosensitive microgel particles which readily permit variation of sample packing fraction. At each packing fraction, the particle displacement covariance matrix is measured and used to extract the vibrational spectrum of the "shadow" colloidal glass (i.e., the particle network with the same geometry and interactions as the sample colloid but absent damping). Rearrangements are induced by successive, small reductions in packing fraction. The experimental results suggest that low-frequency quasi-localized phonon modes in colloidal glasses, i.e., modes that present low energy barriers for system rearrangements, are spatially correlated with rearrangements in this thermal system.

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“…However, instead of a pure drop of g(ω) at higher frequencies, a typical "boson peak" can develop in disordered systems [39], the origin of which is still under debate [40]. In our example of a two-dimensional disordered solid, the curve for g(ω) in Fig.…”

Section: Figmentioning

confidence: 99%

Tunable dynamic response of magnetic gels: Impact of structural properties and magnetic fields

et al. 2014

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Ferrogels and magnetic elastomers feature mechanical properties that can be reversibly tuned from outside through magnetic fields. Here we concentrate on the question how their dynamic response can be adjusted. The influence of three factors on the dynamic behavior is demonstrated using appropriate minimal models: first, the orientational memory imprinted into one class of the materials during their synthesis; second, the structural arrangement of the magnetic particles in the materials; and third, the strength of an external magnetic field. To illustrate the latter point, structural data are extracted from a real experimental sample and analyzed. Understanding how internal structural properties and external influences impact the dominant dynamical properties helps to design materials that optimize the requested behavior.

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Normal Modes and Density of States of Disordered Colloidal Solids

Cited by 101 publications

References 30 publications

Force distribution affects vibrational properties in hard-sphere glasses

Force distribution affects vibrational properties in hard-sphere glasses

Measurement of Correlations between Low-Frequency Vibrational Modes and Particle Rearrangements in Quasi-Two-Dimensional Colloidal Glasses

Tunable dynamic response of magnetic gels: Impact of structural properties and magnetic fields

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