Ys. Djikaev et al., Theory of size dependent deliquescence of nanoparticles: Relation to heterogeneous nucleation and comparison with experiments, J PHYS CH B, 105(32), 2001, pp. 7708-7722
In this paper, we develop a thermodynamic theory for the deliquescence beha
vior of soluble crystals in an atmosphere of solvent vapor. In this endeavo
r, we have focused on studying possible free energy barriers that could imp
ede deliquescence. Our aim was to construct a theory general enough to trea
t both macroscopic and nanosized crystals. Toward this end, as a first atte
mpt, we focused on a theory capable of describing the qualitative features
of the results of recent experimental measurements, especially in the nanom
eter range where interfacial effects are bound to play a role. However, we
have also opted for simplicity, and with this in mind, the surface thermody
namics that we have used are of the simplest type, ignoring crystal shape,
rigorously defined dividing surfaces, curvature dependence of surface tensi
on, 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 tra
versed by the path of a deliquescing system. Analyses of these paths enable
us to define two types of deliquescence, "nucleate" and "activate", that o
ccur respectively with and without a free energy barrier. A most important
experimental behavioral feature that the theory cannot yet comfortably desc
ribe is the apparent existence, for nanosized and micron sized crystals, of
ranges of vapor saturation ratio within which there is a continuum of deli
quescent states such that a film of solution coexists in equilibrium with t
he core crystal. Within our thermodynamic theory, such coexistence can only
be achieved using draconian measures such as the choice of interfacial ten
sions that have an unphysical behavior. Because, in the case of micron size
d crystals, surface effects cannot be responsible for the coexistence of co
re and film, this together with the difficulty encountered in fashioning a
thermodynamic theory, incorporating surface phenomena, that allows such coe
xistence, suggests that apparent nonprompt deliquescence must be due to som
e other factor such as the state of the initial core crystals. The measurem
ents on small crystals involved (NH4)(2)SO4-H2O and NaCl-H2O systems and we
re performed using a tandem differential mobility analyzer. Aside from the
failure to predict continuous deliquescence, our first results are promisin
g, and a more sophisticated thermodynamic theory should provide a more thor
ough description of the observed features of deliquescence.