Temperature dependent energies of formation for hydrogen-bonded water clusters using a modified mndo and a statistical mechanics approach

Employing a modified MNDO treatment, the hydrogen-bond energies of large water clusters are computed. Considering a statistical mechanical treatment in association with the computed results, an expression of temperature dependent formation energy for water clusters to treat varying conditions of temperature and ambient humidities is introduced. Encouragingly, predicted formation energies (energies of formation) are found to be well correlated with the classical theory of capillarity approximation for the Gibbs free energy change. Based on the predicted energies of formation, stability of water clusters is discussed as a function of cluster size.     

Heterogeneous condensation of the Lennard-Jones vapor onto a nanoscale seed particle

The heterogeneous condensation of a Lennard-Jones vapor onto a nanoscale seed particle is studied using molecular dynamics simulations. Measuring the nucleation rate and the height of the free energy barrier using the mean first passage time method shows that the presence of a weakly interacting seed has little effect on the work of forming very small cluster embryos but accelerates the rate by lowering the barrier for larger clusters. We suggest that this results from a competition between the energetic and entropic features of cluster formation in the bulk and at the heterogeneity. As the interaction is increased, the free energy of formation is reduced for all cluster sizes. We also develop a simple phenomenological model of film formation on a small seed that captures the general features of the nucleation process for small heterogeneities. A comparison of our simulation results with the model shows that heterogeneous classical nucleation theory provides a good estimate of the critical size of the film but significantly overestimates the size of the barrier.     

Molecular Dynamics Studies of the Kinetics of Phase Changes in Clusters II: Crystal Nucleation from Molten (RbCl)256 and (RbCl)500 Clusters

Molecular dynamics computer simulations have been carried out to study the effects of cluster size and temperature on the nucleation rate of rubidium chloride clusters in the temperature range of 500-650 K. Clusters with 256 and 500 RbCl molecules have been studied and the results are compared with those obtained from 108 molecule clusters. The melting point (MP) of the clusters was observed to increase with the size of the clusters and can be described by a linear equation MP=997-405 N^−1/3, where N is the number of molecules in the cluster. The nucleation rate is found to decrease with increasing cluster size or increasing nucleation temperature. Both classical nucleation theory and diffuse interface theory are used to interpret our observed results.     

A kinetic model for nonisothermic homogeneous nucleation

A model for isothermal homogeneous nucleation is proposed that improves the classical model. A quasiequilibrium distribution of clusters was calculated on a basis of the Frenkel’-Lothe-Pound theory. The dependence of the free energy of clusters on their size was represented by an interpolation formula relating the free energy of dimers and large clusters to which a notion of macroscopic surface tension is applicable. The nucleation rate and the dependence of the cluster temperature on their size were calculated by balance equations describing the heating of from a cluster due to the condensation of monomers and its cooling due to collisions with an ambient gas. It is shown that the nucleation rate in excess buffer gas is higher than for the pure condensing gas by approximately two orders of magnitude. The model adequately describes the experimental data for the nucleation of methanol supersaturated vapor.     

Reaction of niobium and tantalum neutral clusters with low pressure, unsaturated hydrocarbons in a pickup cell: from dehydrogenation to Met-Car formation

Neutral niobium and tantalum clusters (Nbn and Tan) are generated by laser ablation and supersonic expansion into a vacuum and are reacted in a pickup cell with various low pressure (approximately 1 mTorr) unsaturated hydrocarbons (acetylene, ethylene, propylene, 1-butene, 1,3-butadiene, benzene, and toluene) under nearly single collision conditions. The bare metal clusters and their reaction products are ionized by a 193 nm laser and detected by a time of flight mass spectrometer. Partially and fully dehydrogenated products are observed for small (nor=m) neutral metal clusters, respectively, with m ranging from 2 to 5 depending on the particular hydrocarbon. In addition to primary, single collision products, sequential addition products that are usually fully dehydrogenated are also observed. With toluene used as the reactant gas, carbon loss products are observed, among which Nb8C12 and Ta8C12 are particularly abundant, indicating that the Met-Car molecule M8C12 can be formed from the neutral metal cluster upon two collisions with toluene molecules. The dehydrogenation results for low pressure reactions are compared with those available from previous studies employing flow tube (high pressure) reactors. Low pressure and high pressure cluster ion reactions are also compared with the present neutral metal cluster reactions. Reactions of unsaturated hydrocarbons and metal surfaces are discussed in terms of the present neutral cluster results.     

Anion photoelectron spectroscopy and density functional investigation of vanadium carbide clusters

The influence of source conditions on vanadium-carbon cluster formation in a methane-vanadium plasma is explored and analyzed by photoelectron spectroscopy, revealing that the metal-carbon ratio has substantial influence over the cluster products. Experiments that employ large methane content produce carbon-rich mono- and divanadium carbides. The carbon-rich clusters show a preference for the formation of cyclic neutral and linear ionic structures. When the methane concentration is decreased, VmCn clusters are formed with m = 1-4 and n = 2-8. The photoelectron spectra of clusters formed under these conditions are indicative of a three-dimensional network. We have measured a significantly lower vertical electron affinity for the VC2, V2C3, and V4C6 clusters compared with proximate species. Interestingly, the VC2 species is a proposed building block of the M8C12 Met-Car cluster, and the 2,3 and 4,6 clusters correspond to the 1/4 and 1/2 Met-Car cages, respectively. This correlation is taken as evidence of their importance in the formation of the larger Met-Car species. These results are supported by density functional theory (DFT) calculations carried out at the PBE/GGA level.     

Molecular Dynamics Studies of the Kinetics of Phase Changes in Clusters IV： Crystal Nucleation from Molten （NaCl）256 and （NaCl）500 Clusters

Molecular dynamics computer simulation based on the Born-Mayer-Huggins potential function has been carried out to study the effects of duster size and temperature on the nucleation rate of sodium chloride dusters in the temperature range of 580 K to 630 K. Clusters with 256 and 500 NaCl molecules have been studied and the results have been compared with those obtained from 108 molecule dusters. The melting point (MP) of the clusters were observed to increase with the size of the clusters and can be well described by a linear equation MP =1107(37)-1229(23)N^-1/3(N is the number of molecules in the duster).The nucleation rate was found to decrease with increasing the duster size or temperature. Various nucleation theories have been used to interpret the nucleation rates obtained from this molecular dynamics simulation. It is possible to use a constant diffuse interface thickness to interpret the nucleation rate from the diffuse interface theory in the temperature range of this study. However, the interfacinl free energy estimated from classical nucleation theory and diffuse interface theory increases too fast with increasing the temperature while that from Gran-Gunton theory does not change with changing temperatures.The sizes of critical nuclei estimated from all the theories are smaller than those estimated from our simulations.     

Recent developments in the kinetic theory of nucleation

A review of recent progress in the kinetics of nucleation is presented. In the conventional approach to the kinetic theory of nucleation, it is necessary to know the free energy of formation of a new-phase particle as a function of its independent variables at least for near-critical particles. Thus the conventional kinetic theory of nucleation is based on the thermodynamics of the process. The thermodynamics of nucleation can be examined by using various approaches, such as the capillarity approximation, density functional theory, and molecular simulation, each of which has its own advantages and drawbacks. Relatively recently a new approach to the kinetics of nucleation was proposed [Ruckenstein E, Nowakowski B. J Colloid Interface Sci 1990;137:583; Nowakowski B, Ruckenstein E. J Chem Phys 1991;94:8487], which is based on molecular interactions and does not employ the traditional thermodynamics, thus avoiding such a controversial notion as the surface tension of tiny clusters involved in nucleation. In the new kinetic theory the rate of emission of molecules by a new-phase particle is determined with the help of a mean first passage time analysis. This time is calculated by solving the single-molecule master equation for the probability distribution function of a surface layer molecule moving in a potential field created by the rest of the cluster. The new theory was developed for both liquid-to-solid and vapor-to-liquid phase transitions. In the former case the single-molecule master equation is the Fokker-Planck equation in the phase space which can be reduced to the Smoluchowski equation owing to the hierarchy of characteristic time scales. In the latter case, the starting master equation is a Fokker-Planck equation for the probability distribution function of a surface layer molecule with respect to both its energy and phase coordinates. Unlike the case of liquid-to-solid nucleation, this Fokker-Planck equation cannot be reduced to the Smoluchowski equation, but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.     

Formation mechanism of critical nucleus during nucleation process of liquid metal sodium

To deeply understand the formation mechanism of a critical nucleus during the nucleation process of liquid metal sodium, a system consisting of 10 000 Na atoms has been simulated by using molecular dynamics method. The evolutions of nuclei are traced directly, adopting the cluster-type index method. It is found that the energies of clusters and their geometrical constraints interplay to form the favorable microstructures during the nucleation process. The nucleus can be formed through many different pathways, and the critical size of the nucleus would be different for each pathway. It is also found that the critical nucleus is nonspherical and may include some metastable structures. Furthermore, the size of the cluster and its internal structure both play a crucial role in determining whether it is a critical nucleus, and this is in agreement with the simulations by computing the free energy of the Lennard-Jones system [D. Moroni, P. R. ten Wolde, and P. G. Bolhuis, Phys. Rev. Lett. 94, 235703 (2005)].     

Growth of PtRu Clusters on Ru(0001)‐Supported Monolayer Graphene Films

We report on results of a detailed scanning tunnelling microscopy study on the formation, size and size distribution, and internal structure of small bimetallic PtRu clusters on a graphene monolayer film supported on a Ru(0001) substrate. These clusters, with sizes around ～15 (Ru) or ～40 (Pt) atoms per cluster at the lowest coverage, are interesting model systems for the catalytic behaviour of small metal PtRu particles, for example for application in electrocatalytic oxidation reactions. The clusters were generated by sequential deposition of the two metals at room temperature. The data reveal a distinct influence of the deposition sequence on the cluster formation process, with Ru pre‐deposition followed by Pt deposition leading to predominantly bimetallic clusters, possibly with a core–shell‐type structure, while the reverse sequence results in co‐existent mono‐ and bimetallic clusters, where the latter are likely to intermix at the interface. The observations are related to the nucleation process of the respective metals on the templated surface, and the 2D growth behaviour of the two metals.     

Insights into the early stages of metal nanoparticle formation via first-principle calculations: the roles of citrate and water

The early stages of silver nanoparticle formation in the presence of citrate and water have been investigated via first-principle theoretical calculations. Our study revealed that the charge density of the clusters is a key factor determining the selectivity among various growth pathways. An optimal charge density appears to control the selection between neutral and charged species in cluster growth; partially positively charged clusters are thermodynamically preferred and can serve as seeds for further growth. They interact favorably with both the solvent, leading to their solubility, and the citrate. The solvent (water) plays an important role in cluster growth both on the energetics of reactions including highly charged clusters and on the geometry of the resulting silver structures by preventing the formation of asymmetric ones (a structure directing action). Contrary to the common belief we found, from an energetic viewpoint, that growth of small clusters is not blocked by the citrate. Citrate, by acting as a reducing agent, opens up new channels for cluster growth involving highly charged species. By regulating the cluster charge, cluster-cluster associations may be promoted by the citrate, providing a new mechanistic interpretation for the effect of citrate concentration on nanoparticle size substantially different from the classic nucleation theory. From the citrate-silver and water-silver cluster interactions, linear free energy relationships have been retrieved that provide insights into metal nanoparticle growth mechanisms.     

Heterogeneous multicomponent nucleation theorems for the analysis of nanoclusters

In this paper we present a new form of the nucleation theorems applicable to heterogeneous nucleation. These heterogeneous nucleation theorems allow, for the first time, direct determination of properties of nanoclusters formed on pre-existing particles from measured heterogeneous nucleation probabilities. The theorems can be used to analyze the size (first theorem) and the energetics (second theorem) of heterogeneous clusters independent of any specific nucleation model. We apply the first theorem to the study of small water and n-propanol clusters formed at the surface of 8 nm silver particles. According to the experiments the size of the two-component critical clusters is found to be below 90 molecules, and only less than 20 molecules for pure water, less than 300 molecules for pure n-propanol. These values are drastically smaller than the ones predicted by the classical nucleation theory, which clearly indicates that the nucleating clusters are too small to be quantitatively described using a macroscopic theory.     

Structural Evolution of Boron Clusters on Ag(111) Surfaces – From Atomic Chains to Triangular Sheets with Hexagonal Holes

Unlike graphene and other 2D materials, borophene is 2D polymorphic with diverse hexagonal holes (HHs)-triangles ratios and the concentrations of HHs are highly substrate dependent. Here, we systematically explored the evolution of boron cluster on Ag(111) surface, B_N@Ag(111) (N=1∼36), to understand the nucleation of 2D boron sheet on metal surface. Our calculation showed that, with the size increasing, the structures of most stable B_N clusters undergo an evolution from compact triangular lattice, such as double-chains or triple-chains, to the ones with mixed triangular-hexagonal lattices. The first single-HH appears at N=12 and the first double-HH appears at N=27. The stability of large B_N clusters with mixed structures is derived from the charge transfer between triangular lattice and the HHs, as well as between the substrates and the B_N clusters. Our results provide a deep understanding on the formation of small boron clusters in the initial nucleation stage of borophene growth.     

Computer simulation of selective aggregation in binary colloids

The morphology of clusters formed by selective aggregation of binary colloids is studied in a two-dimensional Monte Carlo simulation for a large range of number fractions (200:1, 100:1, 10:1, 2:1). We find remarkable similarity in morphology to those observed in experiments, from the formation of closed "micelles" to large branched clusters. Quantitative studies of the fractal dimension, kinetics, and cluster size distribution are also carried out and compared with diffusion-limited cluster aggregation and reaction-limited cluster aggregation models.