Nucleation in Gas–Liquid Transitions

The dynamic processes that lead to the formation of a new phase in pure fluids and multicomponent mixtures have become a lively area of research in physical chemistry in the past 15 years (1, 2). This burst of attention is driven by the recognition of the central role of the dynamics of phase transitions in atmospheric chemistry, chemical engineering, and material processing. However, few undergraduate chemistry students have the opportunity to develop a clear understanding of what really happens in a system undergoing a phase transition. Conventional curricula in universities and colleges limit most classroom discussions to the analysis of equilibrium phase diagrams and the thermodynamic conditions for phase coexistence. Unfortunately, this knowledge is not enough to explain such fascinating phenomena as the formation of clouds or salt crystals. Most of the phase transitions that we observe in nature or that are induced during technological processes occur under nonequilibrium conditions. Water at atmospheric pressure, for example, can easily be supercooled below its freezing point of 0 °C without crystallizing. Similarly, most liquids can be superheated tens or hundreds of degrees above their boiling points and gases can be compressed much beyond their equilibrium pressures (supersaturated) before they condense into a liquid (3). In all these cases, a minor perturbation in the system, such as a vibration, a crack on the walls of the container, or the presence of impurities, can trigger the formation of the stable phase. A superheated liquid and a supersaturated gas are examples of what we call “metastable states”, and the range of temperatures and pressures under which these states can be observed depends on factors such as the chemical composition of the system and the characteristics of the container. For pure water at atmospheric pressure, this range extends up to 280 °C for the superheated liquid and down to 41 °C for supercooled states (3). The existence of metastable states that persist over long periods of time can be explained if we assume that their decay toward the stable phase requires surmounting a free-energy barrier between the metastable state and the stable phase (4). In a supersaturated gas, for example, the phase change is initiated by the formation of density fluctuations in various parts of the system. These fluctuations can be thought of as liquid droplets of different sizes that can act as nuclei for the formation of the new phase. However, small droplets will tend to disappear owing to the high free-energy cost of creating the gas–liquid interface. Only nuclei larger than a critical size will grow, since the energetic advantage of creating a larger volume of the more stable phase overcomes the surface freeenergy cost. The time that it takes for the phase transition to occur is determined by the time it takes for these critical nuclei to appear, and this in turn depends on the free-energy cost for their formation. The higher the cost, the longer the lifetime of the metastable state. Metastable states evolve to a stable phase by nucleation of droplets in supersaturated vapors and superheated crystals, by nucleation of bubbles in superheated liquids, and by nucleation of small crystallites in supercooled liquids. In all these cases, the kinetics of the phase transition is essentially determined by the free energy that needs to be invested to generate a critical nucleus. This “work of formation” defines the height of the free energy barrier that lies between shrinking and growing sections of the stable phase. The size of this barrier depends strongly on temperature and pressure, which explains why different metastable states evolve at different rates. Supercooled water at 2 °C can be kept without crystallizing for several days, whereas ice will appear in seconds at 30 °C. In general, the height of the barrier to nucleation decreases as we move away from the coexistence state. The process of nucleation of a new phase in the midst of a metastable state has been the subject of diverse experimental and theoretical studies, as well as the center of interest of novel computer simulations (1). This paper presents an overview of some of the most relevant approaches in these areas, with emphasis on the nucleation of fluid phases (liquids and gases). It will illustrate most of the fundamental aspects of nucleation in the particular case of nucleation of a pure liquid from its metastable vapor, and then extend these ideas to other systems of practical interest. Although most of the discussion concerns homogeneous nucleation (5, 6 ), a brief description of aspects of heterogeneous nucleation involving impurities and surfaces is also presented (3, 4 ).