Although phase transformations in nanosystems exhibit characteristic features of first order phase transitions, a rigorous interpretation of experimental and simulation data represents a fundamental problem. Phase transitions are well understood and classified at the thermodynamic limit of infinite systems based on non-analyticities of the thermodynamic potentials. In small systems, the thermodynamic limit concept is not applicable. The thermodynamic potentials are analytical and the system behavior depends on the statistico-mechanical ensemble employed. Thus, the basic notions of phase equilibrium and criticality in nanosystems are to be clearly defined. In this work, we study the phase behavior of a LJ fluid confined to a localized harmonic potential that bears characteristic features of Bose-Einstein condensation of cold gases in magnetic traps. The difference between the canonical ensemble (CE) and the grand canonical ensemble (GCE) is elucidated. We show that the concept of the mesoscopic canonical ensemble (MCE) [1,2] provides a rigorous framework for .the description and molecular simulations of nanophases confined by rigid and soft walls.

[1].A.V. Neimark and A. Vishnyakov, J. Chem. Phys., 2005, v. 122, 234108. [2].A.V. Neimark and A. Vishnyakov, J. Phys. Chem. B, Published on Web 04/21/2006.