Generalized Kelvin equation and pseudospinodal in nucleation theory

Nucleation Rate of N2 and O2 in Cryogenic H2 and He

The homogeneous nucleation of N2 and O2 in cryogenic H2 and He is investigated by using classical molecular dynamics (MD) simulations. The nucleation kinetics of N2 and O2 clusters, including nucleation rate, critical cluster size, and cluster energy, are elucidated in H2 and He carrier gas at thermalization temperatures of 30-80 K and initial gas densities of 5.65 × 1024-2 × 1027 m-3. The energy released from the clusters during nucleation increases the system temperature by 77-138%, consistent with N2 nucleation experiments in supersonic nozzles and the mean-field kinetic nucleation theory. The nucleation rate derived by MD, Jsim, spans across 2.14 × 1029-5.25 × 1036 m-3 s-1 for both N2 and O2 under all conditions. The MD-obtained homogeneous nucleation rate is in agreement with predictions from the self-consistent classical nucleation theory (CNT) at low temperature (<70 K) but is 3-7 orders of magnitude faster than the CNT when temperature exceeds 70 K, consistent with the literature. Increasing temperature and decreasing concentration of the nucleating vapors leads to larger critical cluster sizes. The CNT underpredicts the critical cluster size at cryogenic temperatures below 60 K by 200-700%. The present MD methodology can be used for the direct determination of the nucleation rate and critical cluster size of N2 and O2 under cryogenic conditions, circumventing the assumptions inherent in CNT.

Formation free energy of an i-mer at spinodal

In statistical mechanics, the formation free energy of an i-mer can be understood as the Gibbs free energy change in a system consisting of pure monomers after and prior to the formation of the i-mer. For molecules interacting via Lennard-Jones potential, we have computed the formation free energy of a Stillinger i-mer [F. H. Stillinger, J. Chem. Phys. 38, 1486 (1963)] and a ten Wolde-Frenkel (tWF) [P. R. ten Wolde and D. Frenkel, J. Chem. Phys. 109, 9901 (1998)] i-mer at spinodal at reduced temperatures from 0.7 to 1.2. It turns out that the size of a critical Stillinger i-mer remains finite and its formation free energy is on the order of k_BT, and the size of a critical tWF i-mer remains finite and its formation free energy is even higher. This can be explained by Binder's theory [K. Binder, Phys. Rev. A 29, 341 (1984)] that for a system, when approaching spinodal, if the Ginzburg criterion is not satisfied, a gradual transition will take place from nucleation to spinodal decomposition, where the free-energy barrier height is on the order of k_BT.

Cluster Formation at Extreme Supersaturations: Nucleation versus Barrierless Transition

We study the process of cluster formation at extreme supersaturations and identify the temperature-supersaturation domain where evaporation can be neglected resulting in a barrierless process with kinetics dominated by the dimer formation. The cluster size distribution obeys the coalescence equation with the pressure-temperature-dependent association rate coefficients k_i, j. In view of the crucial role played by kinetics under these extreme conditions, the values of these coefficients calculated within the free molecular collision model are insufficient for the prediction of the nucleation rate and cluster distribution. An alternative is the use of k_i, j obtained from the ab initio calculations. We apply these considerations to the analysis of recent water nucleation experiments in the postnozzle flow of a Laval nozzle. Theoretical predictions of nucleation rate are in an excellent agreement with experiment. At the same time, there is a discrepancy in the densities of small clusters. The latter can be attributed to the difference in k_i, j extracted from the experimental data and those resulted from the ab initio calculations.

Correlation of Solubility with the Metastable Limit of Nucleation Using Gauge-Cell Monte Carlo Simulations

We present a novel simulation-based investigation of the nucleation of nanodroplets from solution and from vapor. Nucleation is difficult to measure or model accurately, and predicting when nucleation should occur remains an open problem. Of specific interest is the "metastable limit", the observed concentration at which nucleation occurs spontaneously, which cannot currently be estimated a priori. To investigate the nucleation process, we employ gauge-cell Monte Carlo simulations to target spontaneous nucleation and measure thermodynamic properties of the system at nucleation. Our results reveal a widespread correlation over 5 orders of magnitude of solubilities, in which the metastable limit depends exclusively on solubility and the number density of generated nuclei. This three-way correlation is independent of other parameters, including intermolecular interactions, temperature, molecular structure, system composition, and the structure of the formed nuclei. Our results have great potential to further the prediction of nucleation events using easily measurable solute properties alone and to open new doors for further investigation.

Laplace Pressure of Individual H2 Nanobubbles from Pressure-Addition Electrochemistry

The Young-Laplace equation is central to the thermodynamic description of liquids with highly curved interfaces, e.g., nanoscale droplets and their inverse, nanoscale bubbles. The equation relates the pressure difference across an interface to its surface tension and radius of curvature, but the validity in using the macroscopic surface tension for describing curved interfaces with radii smaller than tens of nanometers has been questioned. Here we present electrochemical measurement of Laplace pressures within single H₂ bubbles between 7 and 200 nm radius (corresponding, respectively, to between 200 and 7 atm). Our results demonstrate a linear relationship between a bubble's Laplace pressure and its reciprocal radius, verifying the classical thermodynamic description of H₂ nanobubbles as small as ∼10 nm.

Lifetime of metastable states in a Ginzburg-Landau system: Numerical simulations at large driving forces

We developed a "brute-force" simulation method and conducted numerical "experiments" on homogeneous nucleation in an isotropic system at large driving forces (not small supersaturations) using the stochastic Ginzburg-Landau approach. Interactions in the system are described by the asymmetric (no external field), athermal (temperature-independent driving force), tangential (simple phase diagram) Hamiltonian, which has two independent "drivers" of the phase transition: supersaturation and thermal noise. We obtained the probability distribution function of the lifetime of the metastable state and analyzed its mean value as a function of the supersaturation, noise strength, and volume. We also proved the nucleation theorem in the mean-field approximation. The results allowed us to find the thermodynamic properties of the barrier state and conclude that at large driving forces the fluctuating volumes are not independent.