We analyze peculiarities of phase transitions in small systems. We focus on the formation of a tiny liquid drop in a small N, V, T system, and develop an “extended modified liquid drop” model, which incorporates the effect of the fluctuations relevant for small systems. We compare the predictions for the p−v isotherms and the density profiles with the results of Monte-Carlo simulations of a Lennard-Jones system, and Density Functional Theory.

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function of two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.

A theory is developed for the deliquescence of small particles that incorporates the effect of surface phenomena on the deliquescence process. The theory is based on rudimentary surface thermodynamics since we are primarily interested in the orders of magnitude of the various effects. Applying the theory to a generic crystal with properties similar to NaCl, in water vapor, we find that the surface tension has a significant effect for crystals with a radius smaller than 10−5 cm. We suggest an experiment for the determination of the surface tension of soluble crystals that utilizes the deliquescence of these small particles. Serendipitously, such an experiment has just been performed by another group of authors. The qualitative analysis of this experiment should eventually be accompanied by a further development of the rigorous thermodynamic theory of solid surfaces.

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.

A molecular theory of the rate of homogeneous vapor phase nucleation is formulated. The ultimate goal is a theory that contains no ad hoc assumptions or arbitrary parameters having magnitudes that must be assigned in an ad hoc manner. The centerpiece of the theory is a defined cluster denoted as the n/v-Stillinger cluster, a hybrid that combines the original Stillinger cluster and the more recent n/v cluster. The Stillinger component assures that redundancy is avoided in the characterization of the cluster and the n/v component makes the Monte Carlo simulation of the free energy of the cluster relatively simple, and also allows dynamics to weight the importance of a cluster to the nucleation rate process. In the companion paper (paper II), dealing with the application of the theory to argon vapor, it is shown that the avoidance of redundancy is of primary importance to the non ad hoc nature of the theory. The theory provides a standard against which subtle inconsistencies in earlier theories, both molecular and phenomenological, are revealed, and should provide guidance for the development of necessary, useful, future phenomenological theories. Earlier theories are described in sufficient detail to allow a clear discussion of such inconsistencies. This is not just a review, since the illustration of important connections and relationships, not carefully examined in the past, forms one of the major goals of the exposition. A fairly general theory for the nucleation rate is given and some of the parameters entering the theory are discussed. This paper provides the basis for its application to argon vapor in paper II.