Analyzing the liquid state of two-dimensional dust clusters: The instantaneous normal mode approach

Abstract

The liquid state and the freezing transition of finite two-dimensional dust systems are studied using the instantaneous normal mode (INM) analysis. This technique measures the instantaneous unstable modes of a cluster configuration and relates them to the liquid properties of the system. Here, the INM analysis has been applied to experiments on laser-heated dust clusters. From the experiments, diffusion constants and melting temperatures for clusters of different size have been derived. The INM diffusion constants have been compared to those derived from other standard approaches. The scatter of the diffusion constant retrieved by the INM is smaller than that retrieved by other methods, allowing a more reliable determination of melting temperatures. Moreover, the behavior of double-well and escape modes, which reflect certain topological properties of unstable modes, correlates very well with the behavior of the diffusion constant. Further, the dynamic nature of the unstable modes has been determined as mostly shearlike. Finally, the INM results on the experiments are checked against those from Langevin simulations.