Force distribution affects vibrational properties in hard-sphere glasses.

ABSTRACT: 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(?(e)), the force distribution of such pairs and ?(c) the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ?*, rising up to it as D(?) ~ ?(2+a), and decaying above ?* as D(?) ~ ?(-a) where a = (1 - ?(e))/(3 + ?(e)) and ? is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with ??R²? ~ 1/? ~ (?(c) - ?)(?), where ? = 2 - 2/(3 + ?(e)), and (iii) continuum elasticity breaks down on a scale ?(c) ~ 1/?(?z) ~ (?(c) - ?)(-b), where b = (1 + ?(e))/(6 + 2?(e)) and ?z = z - 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that ?(e) ? 0.41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to ? ? 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.

SUBMITTER: DeGiuli E 

PROVIDER: S-EPMC4260553 | biostudies-literature | 2014 Dec

REPOSITORIES: biostudies-literature