Theory of Size Dependent Deliquescence of Nanoparticles:  Relation to Heterogeneous Nucleation and Comparison with Experiments

Abstract

In this paper, we develop a thermodynamic theory for the deliquescence behavior of soluble crystals in an atmosphere of solvent vapor. In this endeavor, we have focused on studying possible free energy barriers that could impede deliquescence. Our aim was to construct a theory general enough to treat both macroscopic and nanosized crystals. Toward this end, as a first attempt, we focused on a theory capable of describing the qualitative features of the results of recent experimental measurements, especially in the nanometer range where interfacial effects are bound to play a role. However, we have also opted for simplicity, and with this in mind, the surface thermodynamics that we have used are of the simplest type, ignoring crystal shape, rigorously defined dividing surfaces, curvature dependence of surface tension, and the presence of surface excess (adsorption). We do however include the effects of “disjoining pressure”. Nevertheless, we are able to describe several of the observed features and to calculate free energy surfaces traversed by the path of a deliquescing system. Analyses of these paths enable us to define two types of deliquescence, “nucleate” and “activate”, that occur respectively with and without a free energy barrier. A most important experimental behavioral feature that the theory cannot yet comfortably describe is the apparent existence, for nanosized and micron sized crystals, of ranges of vapor saturation ratio within which there is a continuum of deliquescent states such that a film of solution coexists in equilibrium with the core crystal. Within our thermodynamic theory, such coexistence can only be achieved using draconian measures such as the choice of interfacial tensions that have an unphysical behavior. Because, in the case of micron sized crystals, surface effects cannot be responsible for the coexistence of core and film, this together with the difficulty encountered in fashioning a thermodynamic theory, incorporating surface phenomena, that allows such coexistence, suggests that apparent nonprompt deliquescence must be due to some other factor such as the state of the initial core crystals. The measurements on small crystals involved (NH4)2SO4−H2O and NaCl−H2O systems and were performed using a tandem differential mobility analyzer. Aside from the failure to predict continuous deliquescence, our first results are promising, and a more sophisticated thermodynamic theory should provide a more thorough description of the observed features of deliquescence.

Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres

“…A saddle point associated with a pure liquid critical cluster leads to the liquid free-energy basin, which is then separated from the △-crystal basin by a ridge on the free-energy surface, so nucleation requires the crossing of two barriers. Accounting for the disjoining pressure [37,38] associated with the thin wetting layer and the strain energy of the lattice [15], the CNT introduces a saddle point on the free-energy surface with a liquid-△-solid critical cluster leading directly to the crystal phase, as observed in our simulations, but the valley floor approaching this saddle point, and hence the precritical fluctuations, grows along the △-solid axis. In our simulation results, the early stages of nucleation are characterized by the formation of pure liquidlike clusters, which is at odds with CNT.…”

Hygroscopicity of organic compounds from biomass burning and their influence on the water uptake of mixed organic ammonium sulfate aerosols

“…In addition, it has been reported that water-soluble organic compounds from biomass burning, i.e., mono-and carboxylic acids, levoglucosan, and humic acid were quite abundant in the find mode (D p < 1.1 µm) (Robert et al, 2003;Rissler et al, 2006;Vestin et al, 2007;Agarwal et al, 2010;Claey et al, 2010). Also, different effects of particles size (in the submicron size range) on the hygroscopic growth factors and deliquescence behavior of aerosol are reported in the literature (Hämer et al, 2000;Mirabel et al, 2000;Djikaev et al, 2001;Russell and Ming, 2002;Robert et al, 2003;Biskos et al, 2006a, b), especially for particles smaller than 100 nm in the diameter. For example, Biskos et al (2006a, b) observed that the deliquescence and efflorescence of ammonium sulfate nanoparticles (6-60 nm) are similar to their larger-particle counterparts.…”

Nanosize Effect on the Deliquescence and the Efflorescence of Sodium Chloride Particles

“…Russell and Ming (2002) predict a DRH of 87% for a dry 10-nm NaCl particle. In parallel work, rather than providing results of the dependence of DRH on particle size, Djikaev et al (2001) address a theory for prompt versus nonprompt deliquescence in the nanosize regime to follow up on the measurements of Hämeri et al (2001). We are aware of no theoretical studies regarding the nanosize effect on the ERH of NaCl particles.…”