Phenomenological model of melting in Lennard-Jones clusters

Extensive molecular-dynamics simulations were coupled to infinitely fast quenches by steepest descent in order to obtain more information on the melting transition of small clusters with 12 to 14 atoms interacting via Lennard-Jones potentials. A procedure is devised to measure the fraction of times f that the high-energy local minima of the potential-energy surface are accessed during a long trajectory. The computer experiment shows that f depends on temperature and presents a sigmoid shape. The temperature at which f is valued, (1/2 is identified with the cluster melting temperature $T_m$. This is a new criterion that can be framed into a phenomenological description of melting in clusters. The theoretical model is based on a mapping of the segments of a copolymer with the short-time excursions of the cluster among the high-energy local minima. Melting in this pseudopolymer is characterized by the S-shaped behavior of f as a function of temperature. In small clusters the slope of f at $T_m$ is moderately high, the width of the transition region being ≊0.3$T_m$. The 12- and 13-atom clusters melt at 0.24ε and 0.3ε. The 14-atom cluster evaporates before melting.