The effect of a finite number of monomers available for aggregation at nucleation and micellization in a fixed volume

Confinement Effects in Droplet Formation on a Solid Particle

Formation of a droplet around a spherical solid particle in supersaturated vapor is considered. The number and stability of equilibrium solutions in a closed small system are studied in the canonical ensemble in comparison to an open system in the grand canonical ensemble. Depending on the system's parameters, two modes exist in the canonical ensemble: the first one with only one solution and the second one with three solutions; the presence of the third solution is due to confinement. The analysis is conducted first on a macroscopic thermodynamic level of description, and then the results are supported by studies within two versions of classical density functional theory: the square-gradient approximation with the Carnahan-Starling equation of state for hard spheres on a completely wettable particle and the random-phase approximation with the fundamental measure theory on a poorly wettable particle. In the latter case, a solution breaking the spherical symmetry is observed at a small total number of molecules.

Gas–liquid transition of van der Waals fluid confined in fluctuating nano-space

Gas–liquid transition is generally a complex process, which involves nucleation of droplets and their growth by evaporation–condensation or collision–coalescence processes. Here, we focus on a microscopic system in which there is only one liquid droplet at most. In this case, we can develop an equilibrium theory for the formation of the droplet in the gas phase using the classical nucleation theory. We use the van der Waals fluid model with surface tension and calculate the size fluctuation of the droplet for various confinement conditions, NVT (in which the volume V of the system is fixed), NPT (in which the pressure P of the system is fixed), and NBT (in which the system is confined in a nano-bubble immersed in a host liquid, where both V and P can fluctuate). We show that in the NBT system, the size flexibility along with space confinement induces a wealth of properties that are not found in NVT and NPT. It exhibits richer phase behaviors: a stable droplet appears and coexists with the pure gas phase and/or pure liquid phase. When compared to the NVT system, the NBT system shows not only the oscillatory fluctuation between the two stable states but also a large fluctuation in the total volume and the pressure.

On the thermodynamics of curved interfaces and the nucleation of hard spheres in a finite system

We determine, for hard spheres, the Helmholtz free energy of a liquid that contains a solid cluster as a function of the size of the solid cluster by means of the formalism of the thermodynamics of curved interfaces. This is done at the constant total number of particles, volume, and temperature. We show that under certain conditions, one may have several local minima in the free energy profile, one for the homogeneous liquid and others for the spherical, cylindrical, and planar solid clusters surrounded by liquid. The variation of the interfacial free energy with the radius of the solid cluster and the distance between equimolar and tension surfaces are inputs from simulation results of nucleation studies. This is possible because stable solid clusters in the canonical ensemble become critical in the isothermal-isobaric ensemble. At each local minimum, we find no difference in chemical potential between the phases. At local maxima, we also find equal chemical potential, albeit in this case the nucleus is unstable. Moreover, the theory allows us to describe the stable solid clusters found in simulations. Therefore, we can use it for any combination of the total number of particles, volume, and global density as long as a minimum in the Helmholtz free energy occurs. We also study under which conditions the absolute minimum in the free energy corresponds to a homogeneous liquid or to a heterogeneous system having either spherical, cylindrical, or planar geometry. This work shows that the thermodynamics of curved interfaces at equilibrium can be used to describe nucleation.

A review of efflorescence kinetics studies on atmospherically relevant particles

The efflorescence transitions of aerosol particles have been intensively investigated due to their critical impacts on global climate and atmospheric chemistry. In the present study, we present a critical review of efflorescence kinetics focusing on three key issues: the efflorescence relative humidity (ERH) and the influence factors for aerosol ERH (e.g. particle sizes, and temperature); efflorescence processes of mixed aerosols, concerning the effect of coexisting inorganic and organic components on the efflorescence of inorganic salts; homogeneous and heterogeneous nucleation rates of pure and mixed aerosols. Among the previous studies, there are significant discrepancies for measured aerosol ERH under even the same conditions. Moreover, the interactions between organic and inorganic components remain largely unclear, causing efflorescence transition behaviours and chemical composition evolutions of certain mixed systems to be debatable. Thus, it is important to better understand efflorescence to gain insights into the physicochemical properties and characterize observed efflorescence characteristics of atmospheric particles, as well as guide further studies on aerosol hygroscopicity and reactivity.

Kinetic broadening of size distribution in terms of natural versus invariant variables

We study theoretically the size distributions of nanoparticles (islands, droplets, nanowires) whose time evolution obeys the kinetic rate equations with size-dependent condensation and evaporation rates. Different effects are studied which contribute to the size distribution broadening, including kinetic fluctuations, evaporation, nucleation delay, and size-dependent growth rates. Under rather general assumptions, an analytic form of the size distribution is obtained in terms of the natural variable s which equals the number of monomers in the nanoparticle. Green's function of the continuum rate equation is shown to be Gaussian, with the size-dependent variance. We consider particular examples of the size distributions in either linear growth systems (at a constant supersaturation) or classical nucleation theory with pumping (at a time-dependent supersaturation) and compare the spectrum broadening in terms of s versus the invariant variable ρ for which the regular growth rate is size independent. For the growth rate scaling with s as s^{α} (with the growth index α between 0 and 1), the size distribution broadens for larger α in terms of s, while it narrows with α if presented in terms of ρ. We establish the conditions for obtaining a time-invariant size distribution over a given variable for different growth laws. This result applies for a wide range of systems and shows how the growth method can be optimized to narrow the size distribution over a required variable, for example, the volume, surface area, radius or length of a nanoparticle. An analysis of some concrete growth systems is presented from the viewpoint of the obtained results.