- Force distribution affects vibrational properties in hard-sphere glasses
- Proceedings of the National Academy of Sciences of the United States of America
- Volume | Issue number
- 111 | 48
- Pages (from-to)
- Number of pages
- Document type
- Faculty of Science (FNWI)
- Institute for Theoretical Physics Amsterdam (ITFA)
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)∼fθe, the force distribution of such pairs and ϕc 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)∼ω2+a, and decaying above ω* as D(ω)∼ω−a where a=(1−θe)/(3+θe) and ω is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with〈δR2〉∼1/μ∼(ϕc−ϕ)κ, where κ=2−2/(3+θe), and (iii) continuum elasticity breaks down on a scale ℓc∼1/√δz∼(ϕc−ϕ)−b, where b=(1+θe)/(6+2θe) and δz=z−2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that θe≈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.
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