Anomalous temperature dependence in phase transitions via ballistic coalescence

Abstract: We study kinetics of phase transitions within a single component Lennard-Jones model. For low enough particle densities disconnected clusters form that can move ballistically in an inviscid vapor background. The clusters undergo sticky collisions, thereby forming larger aggregates, which can be of fractal nature at ultra cold temperatures. As the temperature is varied, the exponent of the algebraic growth of average cluster mass changes, exhibiting pronounced nonmonotonic character. We capture this anomalous behavior, in two and three space dimensions, within a ballistic aggregation theory. We show that the scope of the theory is much broader than the typically considered case where cluster motions are uncorrelated. An analysis of the theory shows that ballistic aggregation can even occur exponentially fast. This is in sharp contrast with the conventional algebraic picture, regarding passive matter phase transitions. We discuss scenario where such explosive growth can be realized. In addition, our results are widely relevant in understanding structure and growth in aerosols, cosmic dust and other aggregation processes.