Melting,freezing and other peculiarities in small systems

The theory of solid-liquid phase changes in small systems implies that such systems may—but need not—exhibit sharp but unequal freezing and melting temperatures. The origin of this conclusion is reviewed and its implications for the theory of first-order phase transitions in bulk matter are discussed. The logical separation is made of the two temperatures as limits of stable existence, each of its own ‘phase’; and the convergence, with increasing size of cluster, of the observable coexistence to a sharp transition temperature is discussed. The equilibrium ratios of concentrations for such a coexistence are discontinuous functions of temperature at the limits of stability. The possibility of observing coexisting forms in equilibrium depends on there being a time scale separability, who validity lies outside the realm of thermodynamics. It is conjectured that spinodals are the loci of the same kind of locally stable states responsible for coexisting solid and liquid forms of clusters, and that the limits of spinodals are the points of discontinuity in the equilibrium concentration ratios, the chemical ‘equilibrium constants’.