Nucleation and Molecular clustering about ions

Vapor nucleation on a wettable nanoparticle carrying a non-central discrete electric charge

We have studied thermodynamics of vapor nucleation on a spherical wettable dielectric nanoparticle carrying a discrete electric charge located at a certain distance from the particle center. New general equations for the chemical potential of a condensate molecule in the droplet around the particle, the work of the droplet formation and the droplet shape as functions of the effective radius of condensate film, and the value of an electric charge and its location with respect to the particle center have been derived analytically. These equations take into account both the effects of the non-central electric field and the disjoining pressure in the thin liquid film forming the droplet. Under the assumption of small distortion of the droplet shape in the axisymmetric electric field of non-central discrete charge from the spherical one, these equations have been simultaneously solved analytically. The obtained explicit formulas for the condensate chemical potential, the work of droplet formation, and the droplet shape have been numerically investigated for the case of the charge adsorbed below and above the surface of the particle. It has been shown that the effect of the electric field of non-central charge reveals itself in decreasing the maximum value of the condensate chemical potential in the droplet and shifting it away from the particle surface. As a result, the threshold value of the vapor supersaturation for barrierless nucleation and the activation barrier for barrier nucleation on the charged nanosized nuclei diminish in comparison with nucleation on nuclei with central charge. The effect is larger for smaller nuclei. It decreases with increase in the dielectric constant of the nuclei in the case of charge location below the particle surface.

Monte Carlo tests of nucleation concepts in the lattice gas model

The conventional theory of homogeneous and heterogeneous nucleation in a supersaturated vapor is tested by Monte Carlo simulations of the lattice gas (Ising) model with nearest-neighbor attractive interactions on the simple cubic lattice. The theory considers the nucleation process as a slow (quasistatic) cluster (droplet) growth over a free energy barrier ΔF(*), constructed in terms of a balance of surface and bulk term of a critical droplet of radius R(*), implying that the rates of droplet growth and shrinking essentially balance each other for droplet radius R=R(*). For heterogeneous nucleation at surfaces, the barrier is reduced by a factor depending on the contact angle. Using the definition of physical clusters based on the Fortuin-Kasteleyn mapping, the time dependence of the cluster size distribution is studied for quenching experiments in the kinetic Ising model and the cluster size ℓ(*) where the cluster growth rate changes sign is estimated. These studies of nucleation kinetics are compared to studies where the relation between cluster size and supersaturation is estimated from equilibrium simulations of phase coexistence between droplet and vapor in the canonical ensemble. The chemical potential is estimated from a lattice version of the Widom particle insertion method. For large droplets it is shown that the physical clusters have a volume consistent with the estimates from the lever rule. Geometrical clusters (defined such that each site belonging to the cluster is occupied and has at least one occupied neighbor site) yield valid results only for temperatures less than 60% of the critical temperature, where the cluster shape is nonspherical. We show how the chemical potential can be used to numerically estimate ΔF(*) also for nonspherical cluster shapes.

Heterogeneous nucleation at a wall near a wetting transition: a Monte Carlo test of the classical theory

While for a slightly supersaturated vapor the free energy barrier ΔF(hom)(*), which needs to be overcome in a homogeneous nucleation event, may be extremely large, nucleation is typically much easier at the walls of the container in which the vapor is located. While no nucleation barrier exists if the walls are wet, for incomplete wetting of the walls, described via a nonzero contact angle Θ, classical theory predicts that nucleation happens through sphere-cap-shaped droplets attracted to the wall, and their formation energy is ΔF(het)(*) = ΔF(hom)(*)f(Θ), with f(Θ) = (1-cosΘ)(2)(2+cosΘ)/4. This prediction is tested through simulations for the simple cubic lattice gas model with nearest-neighbor interactions. The attractive wall is described in terms of a local 'surface field', leading to a critical wetting transition. The variation of the contact angle with the strength of the surface field is determined by using thermodynamic integration methods to obtain the wall free energies which enter Young's equation. Obtaining the chemical potential as a function of the density for a system with periodic boundary conditions (and no walls), the droplet free energy of a spherical droplet in the bulk is obtained for a wide range of droplet radii. Similarly, ΔF(het)(*) is obtained for a system with two parallel walls. We find that the classical theory is fairly accurate if a line tension correction for the contact angle is taken into account.

Hydrocarbon nucleation and aerosol formation in Neptune's atmosphere

Photodissociation of methane at high altitude levels in Neptune's atmosphere leads to the production of complex hydrocarbon species such as acetylene (C2H2), ethane (C2H6), methylacetylene (CH3C2H), propane (C3H8), diacetylene (C4H2), and butane (C4H8). These gases diffuse to the lower stratosphere where temperatures are low enough to initiate condensation. Particle formation may not occur readily, however, as the vapor species become supersaturated. We present a theoretical analysis of particle formation mechanisms at conditions relevant to Neptune's troposphere and stratosphere and show that hydrocarbon nucleation is very inefficient under Neptunian conditions: saturation ratios much greater than unity are required for aerosol formation by either homogeneous, heterogeneous, or ion-induced nucleation. Homogeneous nucleation will not be important for any of the hydrocarbon species considered; however, both heterogeneous and ion-induced nucleation should be possible on Neptune for most of the above species. The relative effectiveness of heterogeneous and ion-induced nucleation depends on the physical and thermodynamic properties of the particular species, the abundance of the condensable species, the temperature at which the vapor becomes supersaturated, and the number and type of condensation nuclei or ions available. Typical saturation ratios required for observable particle formation rates on Neptune range from approximately 3 for heterogeneous nucleation of methane in the upper troposphere to greater than 1000 for heterogeneous nucleation of methylacetylene, diacetylene, and butane in the lower stratosphere. Thus, methane clouds may form slightly above, and stratospheric hazes far below, their saturation levels. When used in conjunction with the results of detailed models of atmospheric photochemistry, our nucleation models place realistic constraints on the altitude levels at which we expect hydrocarbon hazes or clouds to form on Neptune.