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

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 ψ₆^l and ψ₆^g, 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 ω_BP shifts towards a lower frequency and the intensity of the boson peak D(ω_BP)/ω_BP 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 ω_BP/D(ω_BP), the shear modulus G, and the basin curvature S_IS 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.