On aggregate structures in a rod-like haematite particle suspension by means of Brownian dynamics simulations

We have investigated aggregation phenomena in a suspension composed of rod-like haematite particles by means of Brownian dynamics simulations. The magnetic moment of the haematite particles lies normal to the particle axis direction and therefore the present Brownian dynamics method takes into account the spin rotational Brownian motion about the particle axis. We have investigated the influence of the magnetic particle–field and particle–particle interactions, the shear rate and the volumetric fraction of particles on the particle aggregation phenomena. Snapshots of aggregate structures are used for a qualitative discussion and the cluster size distribution, radial distribution function and the orientational correlation functions of the direction of particle axis and magnetic moment are the focus for a quantitative discussion. The significant formation of raft-like clusters is found to occur at a magnetic particle–particle interaction strength much larger than that required for a magnetic spherical particle suspension. This is because the rotational Brownian motion has a significant influence on the formation of clusters in a suspension of rod-like particles with a large aspect ratio. An applied magnetic field enhances the formation of raft-like clusters. A shear flow does not have a significant influence on the internal structure of the clusters, but influences the cluster size distribution of the raft-like clusters.     

Formation mechanisms of colloidal silica via sodium silicate

Colloidal silica is formed by titrating active silicic acid into a heated KOH with seed solution. The colloidal silica formation mechanisms are investigated by sampling the heated solution during titration. In the initial stage, the added seeds were dissolved. This might due to the dilution of seed concentration, the addition of potassium hydroxide (KOH) and the heating at 100°C. Homogenous nucleation and surface growth occur simultaneously in the second stage of colloidal silica formation. Homogenous nucleation is more important when the seed concentration is relatively low. On the other hand, surface growth plays an important role when the seed concentration is increased. In the middle seed concentration, the seed particles grow up and some new small particles are born by the homogenous nucleation process to form a bimodal size distribution product. As the titrating volume of active silicic acid exceeds a specific value in the last stage the particle size increases rapidly and the particle number decreases, which may be caused by the aggregation of particles. The intervals between each stage were varied with the seed concentration. Increasing the seed concentration led to the formation of uniform particle size colloidal silica.     

Pattern phenomena in an rf discharge dusty plasma system

Various dust patterns are observed in an rf discharge dusty plasma system. According to the dust growth process from small to large in size, the formation of different dust patterns can be divided into two stages: the small-particle stage (or dust cloud stage), and the large-particle stage (or dust crystal stage). The evolution relations between different dust patterns with gas pressure changing are investigated. Dust voids, dust acoustic waves and strong turbulence modes are presented at the small-particle stage. The self-organized dust lattices and dust clusters are investigated at the large-particle stage. The static structure of a dust lattice is characterized by means of the pair correlation function. Dust clusters formed by particles with different numbers and the regular evolution of the clusters with gas pressure are also investigated. The packing sequences of dust clusters are verified through two-dimensional confined molecular dynamics simulations.     

Dynamic Scaling of Ramified Clusters Formed on Liquid Surfaces

A comprehensive simulation model -- deposition, diffusion, rotation, reaction and aggregation model is presented to simulate the formation processes of ramified clusters on liquid surfaces, where clusters can disuse and rotate easily. The mobility （including diffusion and rotation） of clusters is related to its mass, which is given by Dm = Dos^-γD and θm = θos^-γθ, respectively. The influence of the reaction probability on the kinetics and structure formation is included in the simulation model. We concentrate on revealing dynamic scaling during ramified cluster formation. For this purpose, the time evolution of the cluster density and the weight-average cluster size as well as the cluster-size distribution scaling function at different time are determined for various conditions. The dependence of the cluster density on the deposition flux and time-dependence of fractal dimension are also investigated. The obtained results are helpful in understanding the formation of clusters or thin film growth on liquid surfaces.     

Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal dimension of DLA clusters taking two limits, of vanishingly small probe particle size and of infinitely large size of a DLA cluster. We generate 1000 DLA clusters consisting of 50 million particles each, using an off-lattice killing-free algorithm developed in the early work. The introduced method leads to unprecedented accuracy in the estimation of the fractal dimension. We discuss the variation of the probability distribution function with the size of probing particles.     

Kinetic Monte Carlo simulations of Au clusters on Si(111)-7 × 7 surface

Self-assembled growth of Au nanoclusters on the Si(111)-7 × 7 surface has been studied using kinetic Monte Carlo simulations. A model considering various atomic processes of deposition, adsorption, diffusion, nucleation, and aggregation is introduced, and the main energetic parameters are optimized based on the experimental results. The evolution of surface morphology during Au growth is simulated in real time, from which the atomic behaviors of Au could be really captured. Most of Au atoms diffuse on the substrate in the very early stage of growth, and Au clusters nucleate and grow with the increasing coverage. The competition among various atomic processes results in the distinct distribution of Au clusters under different coverages. The growth conditions are further optimized, showing that the higher uniformity of Au clusters would be obtained at a low deposition rate and an optimal substrate temperature of about 380 K.     

Effect of the size of nanoparticles on the properties of a capacitive high-frequency discharge

The properties of a capacitive HF discharge with growing nanoparticles are studied with the use of kinetic PIC-MCC simulation. At the initial stage of growth, the nanoparticles are shown to be localized at the interface between the near-electrode layer and quasi-neutral plasma, where the rate of ionization by electron impact has the maximum value. At the beginning of formation of particles, plasma parameters change rapidly and a transition between the capacitive and spatial discharge burning modes is observed for a certain critical size of the particles. If the growth of the dust particles continues, their distribution over the discharge becomes more uniform and the steady-state parameters of the gas-discharge plasma hardly change.     

Active transport and cluster formation on 2D networks

We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.     

Cluster dynamics and cluster size distributions in systems of self-propelled particles

Systems of self-propelled particles (SPP) interacting by a velocity alignment mechanism in the presence of noise exhibit rich clustering dynamics. Often, clusters are responsible for the distribution of (local) information in these systems. Here, we investigate the properties of individual clusters in SPP systems, in particular the asymmetric spreading behavior of clusters with respect to their direction of motion. In addition, we formulate a Smoluchowski-type kinetic model to describe the evolution of the cluster size distribution (CSD). This model predicts the emergence of steady-state CSDs in SPP systems. We test our theoretical predictions in simulations of SPP with nematic interactions and find that our simple kinetic model reproduces qualitatively the transition to aggregation observed in simulations.     

Kinetics of isothermal homogeneous-condensation processes

Isothermal condensation of supersaturated vapors of various substances and formation of lampblack particles by isothermal decomposition of hydrocarbon (acetylene) molecules is investigated by analytic methods. Expressions that differ generally from the classical ones are obtained, on the basis of the quasichemical model of cluster particles, for the quasi-equilibrium and stationary distribution functions of the cluster sizes, as well as for the rates of formation of clusters having critical dimensions. Analytic expressions describing the time evolution of the degree of supersaturation and of the size distribution function of condensed cluster particles are obtained for the case when the system goes over from the supersaturated state to thermodynamic equilibrium. Equations for the principal characteristics of lampblack formation, viz., the characteristic time and the average size and density of the lampblack particles, are obtained with allowance for the properties of the formation and dissociation (evaporation) of small lampblack cluster particles.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 189–219, 1984.     

Internally consistent verification of mean-field models for aggregation using large-scale molecular dynamics

The underlying atomistic mechanisms that govern vacancy aggregation in crystalline silicon are probed using a parametrically consistent, two-scale approach. The essential ingredient in this framework is a direct, quantitative comparison between the predictions of atomistic and continuum simulations for the transient size distribution of vacancy clusters. The former is carried out with parallel molecular dynamics simulation of a silicon system containing 215?000 atoms and 1000 vacancies. The continuum model is based on a sequence of coupled Master equations and is parametrized based on the same empirical potential used to perform the atomistic aggregation simulation. An excellent representation of the cluster size distribution can be obtained with consistent parameters only if the relevant physical mechanisms are captured correctly. The inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Finally, the continuum model is used to investigate cluster evolution for longer times, which are relevant for process simulation of defect-optimized silicon substrates for microelectronic device fabrication.     

Colloidal aggregation with sedimentation: computer simulations

A computer model for colloidal aggregation is presented that considers both the Brownian motion and the gravitational drift experienced by the colloidal particles and clusters. It is shown that the aggregation crosses over from diffusion-limited aggregation to another type with a higher cluster fractal dimension, a speeding up followed by a slowing down of the aggregation rate, an algebraically decaying cluster size distribution, and a higher concentration required for gelation. Although these findings are in accordance with the experimental results, some interpretations are different.     

Observation of a universal aggregation mechanism and a possible phase transition in Au sputtered by swift heavy ions

Two exponents delta for the size distribution of n-atom clusters, Y(n) approximately n{-delta}, have been found in Au clusters sputtered from embedded Au nanoparticles under swift heavy ion irradiation. For small clusters, below 12.5 nm in size, delta has been found to be 3/2, which can be rationalized as occurring from a steady state aggregation process with size independent aggregation. For larger clusters, a delta value of 7/2 is suggested, which might come from a dynamical transition to another steady state where aggregation and evaporation rates are size dependent. In the present case, the observed decay exponents do not support any possibility of a thermodynamic liquid-gas-type phase transition taking place, resulting in cluster formation.     

Flocculation and percolation in reversible cluster-cluster aggregation

Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (t_e). t_e is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is d_f=2.0 and the size distribution has a power law decay with exponent τ=1.5. At larger values of t_e transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension d_f=2.7 and the power law exponent of the size distribution is τ=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction.     

Enhancement Factor in the Light Backscattered by Fractal Aggregated Media

We investigate the phenomenon of the enhanced backscattering of light from soft sediments of fractal clusters. The clusters consist of spherical PMMA particles with the diameter of 0.4 μ, aggregated in aqueous solutions of NaCl. We found that the kinetics of aggregation, which determines the average cluster size in sediments, is controlled by the salt concentration and that the sediments are mutually self-similar media. In comparison to uniform random media, specific features for the enhancement peaks are revealed. It is found that the peak line-shape reflects the particularities of the density of scatterers in a fractal-like medium. It is shown experimentally that the enhancement factor in the light backscattered by fractal aggregated media is sensitive to the average cluster size. On this basis, we suggest a possible way to distinguish between mutually self-similar media.     

Two-dimensional magnetic cluster growth with a power-law interaction

A two-dimensional cluster model in which the morphology of clusters depends on power-law magnetic interactions that decay with distance r as a r^−α law is introduced. The growth algorithm is a generalization of diffusion-limited aggregation (DLA) model. The particles with spin degree diffuse on a square lattice and each spin is allowed to flip under a Monte Carlo probability. The simulation shows that, for the antiferromagnetic coupling, the spins of the particles in clusters tend to be oriented alternately. For the ferromagnetic coupling, however, the spin distribution depends on the exponent α: for large value of α, domains with different sizes are observed in the clusters; while for small α, during the earlier stage of the growth process, the clusters exhibit approximately antiferromagnetic structure, then, in subsequent growth of the outer part of the clusters, the spin states of all particles are similar. The magnetization and system energy of the clusters as well as their evolutions with the growth parameters are also studied in detail.     

范德华作用和静电作用下的二元粒子自组装

采用简单粗粒化粒子模型,通过郎之万动力学模拟研究了具有范德华作用和静电作用的二元粒子自组装．研究发现,通过改变粒子尺寸和粒子间作用强度,二元粒子能够自发形成各种聚集结构,如球 形、堆叠层状与管状结构．利用两亲性分子或两嵌段聚合物自组装理论,解释了二元粒子聚集结构的形成规律．当向溶液中加入反电荷离子时,模拟表明粒子聚集结构在相图中的分布出现了明显偏移．     

Simulation of the early stage of binary alloy decomposition,based on the free energy density functional method

Based on the free energy density functional method, the early stage of decomposition of a onedimensional binary alloy corresponding to the approximation of regular solutions has been simulated. In the simulation, Gaussian composition fluctuations caused by the initial alloy state are taken into account. The calculation is performed using the block approach implying discretization of the extensive solution volume into independent fragments for each of which the decomposition process is calculated, and then a joint analysis of the formed second phase segregations is performed. It was possible to trace all stages of solid solution decomposition: nucleation, growth, and coalescence (initial stage). The time dependences of the main phase distribution characteristics are calculated: the average size and concentration of the second phase particles, their size distribution function, and the nucleation rate of the second phase particles (clusters). Cluster trajectories in the size–composition space are constructed for the cases of growth and dissolution.     

Diffusion and aggregation of Ag n -clusters ( n =2-9) on HOPG probed by fs-two-photon-photoemission

The diffusion and aggregation of preformed Ag_n-clusters ( n = 2-9) deposited onto a highly oriented pyrolytic graphite (HOPG) substrate is studied by two-photon-photoemission (2PPE). The sample is irradiated with ultrashort laser pulse pairs and the kinetic energy of the emitted photoelectrons is analyzed in a magnetic bottle type time-of-flight spectrometer. During annealing of the sample from 100 K up to room temperature, nanoparticles are formed on the surface by diffusion and aggregation of the silver clusters. A steep increase of the total photoelectron yield at a sample temperature of about 150 K is explained by the excitation of plasmons in the silver nanoparticles. From the kinetic energy distribution of the photoelectrons we deduce a strong variation of the work function of the sample during the formation of the nanoparticles, which is attributed to a quantum size effect.     

引出口的几何参数对团簇形成影响的DSMC研究

利用直接模拟蒙特卡洛方法(DSMC),模拟了气体凝聚团簇源的引出口尺寸和中心位置不同的条件下,Cu团簇的尺寸分布以及模拟了随着时间的增长,腔内团簇数目的变化.模拟结果表明:引出口的直径越大,产生大团簇的比例越小;在引出口的直径相同的情况下,引出口的中心位置偏离坐标原点比在原点产生的大团簇的比例要大;随着时间的增长,腔内团簇数目先变多后变少.