Phases, Phase Changes, and the Thermodynamics of Small Systems

Abstract

The thermodynamics of small systems seems strange, even bizarre, at first encounter, especially if one’s thinking is locked to the concepts traditionally presented in texts and courses on thermodynamics of conventional bulk systems. Perhaps the most striking aspect shows itself in the thermodynamics of phase changes. Atomic and molecular clusters exhibit a variety of phase-like forms and phase changes that differ from those of bulk matter. It is possible to relate some — but not all—of these to corresponding phases and phase transitions of bulk matter. Clusters are attractive vehicles for studying phases and phase changes because they are susceptible to the analytic and computational methods applicable to small systems. Moreover they open the way to study size dependence of phase characteristics, even to quite large systems. Among the properties that distinguish phases and phase changes of small systems are bands of temperature and pressure within which two or more phase-like forms may coexist — not just curves of coexistence. This coexistence is dynamic, like that of coexisting chemical isomers. Moreover clusters may exhibit phase-like forms that do not exist for bulk matter. These properties of existence and coexistence are the consequence of the small differences between the free energies of clusters in different phase-like forms. Theory predicts that the bands of coexistence should have sharp boundaries, due to the disappearance of local stability of each phase-like form, implying that, in the bulk limit, the two branches of the spinodals should have sharp limits of temperature and pressure. One necessary condition that a species of cluster exhibit a particular phase is that such clusters must reside in the corresponding region of configuration and phase space long enough to establish equilibrium-like properties characteristic of that phase.