When a body liquid water is heated under one atmospheric pressure, it starts to boil at 100C°. If we continue to add heat to the body, the entire water will eventually be converted into a vapor phase. If this vapor phase is cooled at the same pressure, it will start to condense, again, at 100C°. When the same process is repeated at a lower pressure, say at 0.1atm, the liquid phase will boil at 46C° and the vapor phase will condense at this temperature. The locus of the boiling temperature at various pressure then defines the boundary that separates the two phases. Essentially the same consideration applies to transition between solid and liquid phases, and that between solid and vapor phases.

This simplistic view, however, is not entirely accurate. For example, when impurities, such as dust particles, are carefully removed, pure vapor water can be compressed by several times of its density at saturation before it starts to condense. A cup of liquid water can be superheated in a microwave oven. The possible subsequent sudden boiling is a dangerous reminder of the reverse process.

Nucleation is an initial stage of the so-called first order phase transition, in which an embryo of a new and more stable phase forms in a metastable matrix phase. Its subsequent growth and coalescence with other similarly formed embryos lead to the eventual emergence of an macroscopic amount of the new phase. Nucleation plays a crucial role in various context ranging from global climate modeling to manufacturing processes, chemical/pharmaceutical industry and biological processes.

Experimental results of nucleation are correlated almost exclusively in terms of the so called classical nucleation theory, which relies on macroscopic thermodynamic quantities such as the bulk chemical potentials and the surface tension. Despite its predominant use in practice, classical theory suffers from many shortcomings. Its predictions of nucleation rate are usually in error by many orders of magnitude. The theory does not offer any information on the molecular level structure of the embryos involved in nucleation.

In contrast to assumptions in classical theory, distribution of molecules in multicomponent droplets may not be uniform, greatly affecting their reactivity in the atmosphere. Manufacturing of plastic foam takes advantage of bubble nucleation in liquid polymer supersaturated with gas phase species. Accurate knowledge of the rate of nucleation is important in controlling the physical properties of the foams. In crystal nucleation, polymorphism, defined as the ability of a material to crystallize in different structures, is an important issue as the functionality of the crystal, such as the optoelectrnic properties and the bio-availability of a drug, can depend strongly on the crystal structure.

In order to address the shortcomings of classical theory and to gain mechanistic insights into the nucleation process, we employ various machineries of statistical mechanics, including computer simulation and statistical mechanical density functional theory.