Scaling laws in fragmentation kinetics

We analyze scaling laws in fragmentation kinetics for mass and velocities of debris and report a new scaling quantity which we call “shattering degree”. To check the universality of the scaling laws, we investigate collisions of clusters comprised of atoms or elementary blocks with very different interaction potentials. Namely, we study Lennard-Jones (L-J), Tersoff and modified L-J potentials and the force associated with Johnson–Kendall–Roberts (JKR) model. They include short, middle and long-ranged inter-particle interactions and also include descriptions for both inter-atomic and macroscopic adhesive bodies interactions. We perform comprehensive molecular dynamics simulations and observe scaling laws for all four potentials for the debris size and velocity distribution. Additionally, we reveal a universal scaling for the shattering degree, which quantifies the fraction of monomers (atoms or elementary blocks) in debris; it holds true for all potentials. We classify the collisions by the outcome and develop a statistical theory, which provides a qualitative explanation for the observed scaling behavior.