Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies

Abstract

Two-dimensional disordered granular assemblies composed of 2048 polydispersed frictionless disks are simulated using the discrete element method. The height of the first peak of the pair correlation function, g1, the local and global bond orientational parameters ψ6l and ψ6g, and the fluctuations of these parameters decrease with increasing polydispersity s, implying the transition from a polycrystalline state to an amorphous state in the system. As s increases, the peak position of the boson peak ωBP shifts towards a lower frequency and the intensity of the boson peak D(ωBP)/ωBP increases, indicating that the position and the strength of the boson peak are controlled by the polydispersity of the system. Moreover, the inverse of the boson peak intensity ωBP/D(ωBP), the shear modulus G, and the basin curvature SIS all have a similar dependence on s, implying that the s dependence of the vibrational density of states at low frequencies likely originates from the s dependence of the basin curvature.