Deliquescence and efflorescence of small particles.

We examine size-dependent deliquescence/efflorescence phase transformation for particles down to several nanometers in size. Thermodynamic properties of inorganic salt particles, coated with aqueous solution layers of varying thickness and surrounded by vapor, are analyzed. A thin layer criterion (TLC) is introduced to define a limiting deliquescence relative humidity (RH(D)) for small particles. This requires: (1) equality of chemical potentials between salt in an undissolved core, and thin adsorbed solution layer, and (2) equality of chemical potentials between water in the thin layer and vapor phase. The usual bulk deliquescence conditions are recovered in the limit of large dry particle size. Nanosize particles are found to deliquesce at relative humidity just below the RH(D) on crossing a nucleation barrier, located at a critical solution layer thickness. This barrier vanishes precisely at the RH(D) defined by the TLC. Concepts and methods from nucleation theory including the kinetic potential, self-consistent nucleation theory, nucleation theorems, and the Gibbs dividing surface provide theoretical foundation and point to unifying features of small particle deliquescence/efflorescence processes. These include common thermodynamic area constructions, useful for interpretation of small particle water uptake measurements, and a common free-energy surface, with constant RH cross sections describing deliquescence and efflorescence related through the nucleation theorem.