Deliquescence of small particles

Abstract

The deliquescence of particles smaller than 100 nm in diameter from crystalline form to liquid droplets involves both solvation effects and surface energies. Here we study this phenomenon for the case of salt particles of initial dry diameters from 8 to 100 nm that are exposed to humid conditions from 45 to 95% relative humidity. With a simple thermodynamic equilibrium model for three soluble species (sodium chloride, ammonium sulfate, and a soluble organic compound), we show that the role of surface tension is to increase the relative humidity at which particles will deliquesce. For example, 15 nm dry diameter sodium chloride particles deliquesce at 83%, an 8% increase over the 75% deliquescence relative humidity for supermicron droplets and bulk solution. Many soluble species in air above 45% relative humidity are wetted with multiple layers of water molecules such that the relevant interface is that between the partially dissolved salt crystal and a saturated salt solution rather than between the dry crystal and air. Since surface tensions for this solid/liquid interface are not well known, a range of values have been used from the literature, yielding consistent results. While the existence of unstable equilibria during deliquescence of the system precludes complete experimental verification of the predicted behavior with measurements, a recent experiment suggests indirect agreement with the change in predicted deliquescence relative humidity.