Dynamics of aggregation－annihilation process with cluster removals

We have studied the kinetic behaviours of irreversible aggregation－annihilation models with cluster removals. In the models, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible annihilation reaction occurs simultaneously between two different species; meanwhile, the clusters of large size are gradually removed from the system. In a mean-field limit, we obtain the general solutions of the cluster-mass distributions for the cases with an arbitrary removal probability. We found that the cluster-mass distribution of either species satisfies a generalized or modified scaling form. The results also indicate that the evolution behaviours of the systems depend strongly on the details of the reaction events.     

Kinetics of an n-Species Aggregation Chain Model with Complete Annihilation

The kinetic behavior of an n-species (n ≥ 3) aggregation-annihilation chain reaction model is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species, and an irreversible complete annihilation reaction occurs only between two species with adjacent number. Based on the rnean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions of the clustermass distributions for the system. The results show that the kinetic behavior of the system not only depends crucially on the ratio of the aggregation rate I to the annihilation rate J, but also has relation with the initial concentration of each species and the species number's odevity. We find that the cluster-mass distribution of each species obeys always a scaling law. The scaling exponents may strongly depend on the reaction rates for most cases, however, for the case in which the ratio of the aggregation rate to the annihilation rate is equal to a certain value, the scaling exponents are only dependent on the initial concentrations of the reactants.     

Particle aggregation versus cluster aggregation in high dimensions

We distinguish two different types of irreversible aggregation-accretion of individual particles and successive aggregation of clusters of comparable size. In aggregation of particles which follow trajectories of fractal dimensionD ₁, we show that physical limits on the aggregation rate impose a lower bound on the fractal dimensionD ₀ of the aggregate. Ind-dimensional space,D ₀{d–D}₁ + 1. Thus aggregation of ballistic particles, withD ₁ = 1, is not fractal. By contrast, cluster aggregates appear to attain a finite, limitingD ₀ in high dimensions. We present a soluble model with this property, and argue that it should agree with Sutherland's binary aggregation model in high dimensions. For this model,D ₀ depends continuously on a parameter; the exponent is not universal.     

On anomalous diffusion of fractal clusters under certain realistic physical conditions

Summary Diffusion of a fractal cluster of dimensiond _f in a three-dimensional space is investigated. The diffusion process is assumed to be modelled by a standard parabolic diffusion equation, although a more general case represented by the Fokker-Planck-Kolmogoroff equation is also introduced. The mean-square displacement of the cluster mass centre is analysed and its anomalous behaviour is presented and critically discussed. The results obtained can be applied to describe some effects which may occur during the diffusion-limited cluster-cluster aggregation process, especially when the viscosity of the solvent is changed in time and/or a directed transport of clusters is present in the system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Correlation and anticorrelation of fractal aggregates. A model for «spinodal-type» aggregation

Summary We present a simple phenomenological model, based on mass conservation arguments, in order to describe aggregation in dense solutions. It has been previously shown that fordiffusion-limited processes scattered intensity distributions exhibit a peak atq≠0 which grows in time and moves to smaller and smallerq vectors. According to the model, each aggregate is surrounded by a depletion region whose size depends on the aggregation kinetics. The form factor for such a cluster should satisfy local mass conservation and hence exhibit a pronounced depression atq=0. the initial stages of aggregation, when the clusters are far apart, are accounted on the basis of a form factor alone. The model shows good agreement with the data and also explains the experimental evidence that the peak does not appear inreaction-limited conditions. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Kerr effect from fractal aggregates of polystyrene microspheres

Summary We study the slow aggregation of aqueous suspensions of optically isotropic microspheres by means of transient electric birefringence. Aggregating clusters exhibit large Kerr constants, and consequently we provide direct experimental evidence that the clusters do posses form anisotropy. From the birefringence relaxation time we derive information on the average cluster size and on the size distribution, and determine their evolution during the aggregation process. Static and dynamic light scattering data confirm the validity of the transient electric birefringence results. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Spatial fluctuations in reaction-diffusion systems: A model for exponential growth

The spatial fluctuations in an exactly soluble model for the irreversible aggregation of clusters are treated. The model is characterized byrate constants K _ij =i+j for the clustering of ani- and aj-mer, anddiffusion constants D _j =D. It is assumed thatD1 (reaction-limited aggregation). Explicit expressions for the correlation functions at equal and at different times are calculated. The equal-time correlation functions show scaling behavior in the scaling limit. The correlation length remains finite ast, and the fluctuations becomelarge at large times (tt _D ) inany dimension. The crossover timet _D , at which the mean field theory (Smoluchowski's equation) breaks down, is given byt _D InD. These exact results imply that the upper critical dimension of this model isd _c= and, hence, that there isno unique upper critical dimension in models for the irreversible aggregation of clusters.     

Scaling Behavior of an Aggregation-Migration Model

We study the kinetic behavior of a two-species aggregation-migration model in which an irreversible aggregation occurs between any two clusters of the same species and a reversible migration occurs simultaneously between two different species. For a simple model with constant aggregation rates and with the migration rates K_A(i;j)=K'_A(i;j) ∝ij^v₁ and K_B(i;j)=K'_B(i;j) ∝ij^v₂, we find that the evolution behavior of the system depends crucially on the values of the indexes v₁ and v₂. The aggregate size distribution of either species obeys a conventional scaling law for most cases. Moreover, we also generalize the two-species system to the multi-species case and analyze its kinetic behavior under the symmetrical conditions.     

N-body study of anisotropic membrane inclusions: Membrane mediated interactions and ordered aggregation

We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes. Received 30 July 1999 and Received in final form 8 September 1999     

Acetone: isomerization and aggregation

The advanced experimental and theoretical techniques enable us to obtain information on the rearrangement of atoms or molecules in a reaction nowadays. As an example, we report on our research work on acetone isomerization and aggregation to give an insight into the reaction pathways, the products and their structures, and the growth regularity of aggregation. The evidences on the structural change of acetone and the stability of acetone clusters are found by a laser ionization mass spectrometer and the results are interpreted from theoretical analysis based on the DFT/B3LYP method. Various isomerization channels of acetone have been established and the optimal structures of the neutral clusters (CH₃COCH₃)_n and the protonated acetone clusters (CH₃COCH₃)_nH⁺ for n=1–7 have been determined.     

Effects of the System Temperature on Dust Cluster Formation in Plasma

Effects of the system temperature on dust aggregation in plasmas are investigated using two‐dimensional molecular dynamics simulations. It is shown that as the system temperature increases, the boundary of the clusters becomes gradually irregular (i.e., deviating from sphere‐like), and the cluster system gradually changes from solid to liquid and finally to gas state. The mean square displacement, mean nearest‐neighbor distance in the clusters, cluster size and coupling parameter of the system are obtained and the properties of the system structure and dynamics are investigated. The time τ needed for reaching equilibrium for different temperatures is obtained. It is shown that τ firstly decreases and then increases with the temperature, indicating that there is an optimum temperature allowing a dust aggregation to reach an equilibrium state most rapidly. The simulation results agree qualitatively with the experimental observations. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The valence band of free K clusters studied by photoelectron and Auger spectroscopies

The valence states of free neutral potassium clusters produced by a gas aggregation source were probed by synchrotron radiation based photoelectron spectroscopy. The first ionization energy (IE) of the clusters was determined to be 10% larger than the work function of bulk potassium. Using electrostatic concepts and the IE, the mean size of the clusters was estimated to be ≈2000 atoms. Further information about the valence band was provided by investigation of the Auger process initiated by the ionization of the 3p level with a subsequent emission of an Auger electron from the valence band (M_2,3VV). Plasmon satellites were observed in Auger spectra of free metal clusters.     

Self-focusing dynamics in monopolarly charged suspensions

The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power-law to sublogarithmic cluster growth at a characteristic time and cluster size. For larger times the suspension is usually called stable, although aggregation still proceeds slowly. In this regime the size distribution evolves towards a universal scaling form, independent of any parameter included in the theory. The relative width falls off to a universal value sigma(infinity)(r) approximately 0.2017 that is much smaller than in the uncharged case. We conjecture that sigma(infinity)(r) is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.     

Control of island morphology by dynamic coalescence of soft-landed clusters

The deposition of preformed clusters on surfaces has been established as a new way for growing nano-suctures on surfaces. It has been shown that supported island morphology relies on the dynamics of clusters, during the growth, giving rise to shapes from compact to ramified types. This paper identifies and discusses, in the case of antimony cluster deposits, several processes responsible for the non-equilibrium island shapes: limited kinetic cluster aggregation, size dependent coalescence, “wetting-like behavior” of antimony clusters on antimony islands. Using successive predetermined cluster sizes during the deposition process to synthesize polymorphic structure involves the interplay of those mechanisms. Received 1st December 2000     

Molecular simulation of LiCl aqueous solutions

Non-primitive LiCl aqueous electrolyte solutions were studied at 1.0, 5.0 and 10.0 M concentrations by molecular dynamics simulations. It was observed that the ion hydration structure is progressively lost with increasing concentration. The ions are aggregated in small clusters at C = 1.0 M. However, at this concentration, two large clusters were detected that are an initial step in an aggregation process. At C = 5.0 M, the highly unstable ion clustering seems to correspond to an intermediary state between low concentration states with poor aggregation and states where the ions are highly aggregated, as observed at C = 10.0 M where almost all the ions are clustered in one cluster. This cluster does not present a crystal-like structure. The high solubility of LiCl in aqueous solutions can consequently be explained as a result of the large radii difference between the anion and the cation that results in the instability of the ionic aggregates, which makes the formation of crystal seeds difficult.     

Colloidal aggregation with sedimentation: concentration effects

The results of computer models for colloidal aggregation, that consider both Brownian motion and gravitational drift experienced by the colloidal particles and clusters, are extended to include concentrations spanning three orders of magnitude. In previous publications and for a high colloidal concentration, it was obtained that the aggregation crosses over from diffusion-limited colloidal aggregation (DLCA) to another regime with a higher cluster fractal dimension and a speeding up followed by a slowing down of the aggregation rate. In the present work we show, as the concentration is decreased, that we can still cross over to a similar regime during the course of the aggregation, as long as the height of the sample is increased accordingly. Among the differences between the mentioned new regimes for a high and a low colloidal concentration, the cluster fractal dimension is higher for the high concentration case and lowers its value as the concentration is decreased, presumably reaching for low enough concentrations a fixed value above the DLCA value. It is also obtained the fractal dimension of the sediments, arising from the settling clusters that reach the bottom and continue a 2D-like diffusive motion and aggregation, on the floor of the container. For these clusters we now see two and sometimes three regimes, depending on concentration and sedimentation strength, with their corresponding fractal dimensions. The first two coming from the crossover already mentioned, that took place in the bulk of the sample before the cluster deposition, while the third arises from the two-dimensional aggregation on the floor of the container. For these bottom clusters we also obtain their dynamical behavior and aggregation rate.Received: 7 January 2004, Published online: 25 March 2004PACS: 61.43.Hv Fractals; macroscopic aggregates (including diffusion-limited aggregates) - 82.70.Dd Colloids - 05.10.Ln Monte Carlo methods     

Effects of Monomer Size Distribution on the fractal dimensionality of diffusion-limited aggregates

Computer simulations of diffusion-limited aggregation (DLA) for monomers to investigate the effects of size and of lognormal distribution on the fractal dimensionality of the aggregates were conducted on a two-dimensional lattice. The results show the DLA clusters posses multifractal characteristics. For clusters consisting of monodisperse monomers, the bifurcation point on the graph of the pair correlation function (PCF) for each cluster is located right at the monomers size under investigation The textural dimension (D_f1) has a stable value of about 1.65, whereas the structural dimension (D_f2) decreased with increase in monomer size. For the cases with monomers in log-normal distributions, the textural dimension is around 1.67; however, the structural dimension decreases with increasing polydispersity of monomer size.     

基于幂次相互作用的二维磁性团簇耦合能研究

在扩散限制凝聚模型基础上,采用Monte Carlo方法模拟了磁耦合作用随粒子间距离幂次变化的磁性粒子动力学凝聚过程.重点研究了在不同幂指数α值下团簇在生长过程中,即随着粒子数N的增加,团簇平均耦合能E_c(N)的演化过程.模拟结果表明:对于α≥5时,E_c(N)随着粒子数N的增加变化较小;当α=2时,E关键词： 扩散限制凝聚模型 幂次相互作用 耦合能