Off-Lattice Monte-Carlo Approach for Studying Nucleation and Evaporation Phenomena at the Molecular Scale

Droplet nucleation and evaporation are ubiquitous in nature and many technological applications, such as phase-change cooling and boiling heat transfer. So far, the description of these phenomena at the molecular scale has posed challenges for modelling with most of the models being implemented on a lattice. Here, we propose an off-lattice Monte-Carlo approach combined with a grid that can be used for the investigation of droplet formation and evaporation. We provide the details of the model, its implementation as Python code, and results illustrating its dependence on various parameters. The method can be easily extended for any force-field (e.g., coarse-grained, all-atom models, and external fields, such as gravity and electric field). Thus, we anticipate that the proposed model will offer opportunities for a wide range of studies in various research areas involving droplet formation and evaporation and will also form the basis for further method developments for the molecular modelling of such phenomena.

Nucleation of Ga droplets self-assembly on GaAs(111)A substrates

We investigated the nucleation of Ga droplets on singular GaAs(111)A substrates in the view of their use as the seeds for the self-assembled droplet epitaxial quantum dots. A small critical cluster size of 1–2 atoms characterizes the droplet nucleation. Low values of the Hopkins-Skellam index (as low as 0.35) demonstrate a high degree of a spatial order of the droplet ensemble. Around $$350\,^{\circ }\hbox {C}$$ 350 ∘ C the droplet size distribution becomes bimodal. We attribute this observation to the interplay between the local environment and the limitation to the adatom surface diffusion introduced by the Ehrlich–Schwöbel barrier at the terrace edges.

Atmospheric Turbulence May Promote Cloud Droplet Formation

Turbulence causes local variations in relative humidity, which can push particles past a critical saturation threshold for droplet nucleation.

Modeling of Al and Ga Droplet Nucleation during Droplet Epitaxy or Droplet Etching

The temperature dependent density of Al and Ga droplets deposited on AlGaAs with molecular beam epitaxy is studied theoretically. Such droplets are important for applications in quantum information technology and can be functionalized e.g., by droplet epitaxy or droplet etching for the self-assembled generation of quantum emitters. After an estimation based on a scaling analysis, the droplet densities are simulated using first a mean-field rate model and second a kinetic Monte Carlo (KMC) simulation basing on an atomistic representation of the mobile adatoms. The modeling of droplet nucleation with a very high surface activity of the adatoms and ultra-low droplet densities down to 5 × 106 cm−2 is highly demanding in particular for the KMC simulation. Both models consider two material related model parameters, the energy barrier ES for surface diffusion of free adatoms and the energy barrier EE for escape of atoms from droplets. The rate model quantitatively reproduces the droplet densities with ES = 0.19 eV, EE = 1.71 eV for Al droplets and ES = 0.115 eV for Ga droplets. For Ga, the values of EE are temperature dependent indicating the relevance of additional processes. Interestingly, the critical nucleus size depends on deposition time, which conflicts with the assumptions of the scaling model. Using a multiscale KMC algorithm to substantially shorten the computation times, Al droplets up to 460 °C on a 7500 × 7500 simulation field and Ga droplets up to 550 °C are simulated. The results show a very good agreement with the experiments using ES = 0.19 eV, EE = 1.44 eV for Al, and ES = 0.115 eV, EE = 1.24 eV (T≤ 300 °C) or EE = 1.24 + 0.06 (T[°C] − 300)/100 eV (T>300 °C) for Ga. The deviating EE is attributed to a re-nucleation effect that is not considered in the mean-field assumption of the rate model.

Nucleation of Ga Droplets Self-Assembly on GaAs(111)A Substrates

We investigated the nucleation of Ga droplets on exact GaAs(111)A substrates in the view of their use as the seeds for the self-assembly droplet epitaxial quantum dots. A small critical cluster size of 1-2 atoms characterizes the droplet nucleation. Low values of the Hopkins-Skellam index (as low as 0.35) demonstrate a high degree of a spatial order of the droplet ensemble. Around 350 °C the droplet size distribution becomes bimodal. We attribute this observation to the interplay between the local environment and the limitation to the adatom surface diffusion introduced by the Ehrlich-Schwöbel barrier at the terrace edges.

Study on droplet nucleation position and jumping on structured hydrophobic surface using the lattice Boltzmann method

In this study, droplet nucleation and jumping on the conical microstructure surface is simulated using the Lattice Boltzmann Method (LBM). The nucleation and jumping laws of the droplet on the surface are summarized. The numerical results suggest that the height and the gap of the conical microstructure exhibit a significant influence on the nucleation position of the droplet. When the ratio of height to the gap of the microstructure(H/D) is small, the droplet tends to nucleate at the bottom of the structure. Otherwise, the droplet tends to nucleate towards the side of the structure. The droplet grown in the side nucleation mode possesses better hydrophobicity than that of the droplet grown in the bottom nucleation mode and the droplet jumping becomes easier. Apart from the coalescence of the droplets jumping out of the surface, jumping of individual droplets may also occur under certain conditions. The ratio of the clearance to the width of the conical microstructure(D/F) depends on the jumping mode of the droplet. The simulation results indicate that when the D/F ratio is greater than 1.2, the coalescence jump of droplets is likely to occur. On the contrary, the individual jump of droplets is easy to occur.

Droplet nucleation in miniemulsion thiol–ene step photopolymerization

Reaction parameters, such as droplet size, initiator solubility and monomer solubility, which are important in favouring droplet nucleation in a miniemulsion thiol–ene step polymerization are reviewed.