Diffusion Coefficients Of Clusters Research Articles

Preparation of a Stable Superhydrophobic Mortar Surface Using a One-Step Method.

Research efforts have intensified on developing superhydrophobic surfaces on concrete structures to limit the damage caused by the natural porosity and hydrophilicity of cementitious materials. However, the feasibility idea is impeded by the complex preparation process and weak adhesion/stability performance. Therefore, superhydrophobic coatings were rapidly prepared on mortar surfaces by a straightforward and effective one-step method using zinc oxide (ZnO) modified with stearic acid and epoxy resin. The microstructure, physical/chemical properties, hydrophobic properties, and stability of the coatings were systematically investigated. The experimental results showed that the water contact angle of the samples reached a maximum value of 164.2° and a sliding angle of 4.6° when the stearic acid content was 0.5 g. The water absorption of the coated superhydrophobic mortar was reduced by approximately 61% compared to that of ordinary mortar, and neither particulate pollutants nor liquid pollutants could contaminate the superhydrophobic mortar. The coating maintained a superhydrophobic state and exhibited good physical durability after sandpaper abrasion, tape peeling, and high-temperature resistance tests. The water cluster diffusion coefficient on surface of the ordinary coating was 0.1645 × 10-4 and 0.0328 × 10-4 cm2/s on surface of the modified coating after molecular dynamics simulation.

Version 4.0 of code Java for 3D simulation of the CCA model

This paper presents a new version Java code for the three-dimensional simulation of Cluster–Cluster Aggregation (CCA) model to replace the previous version. Many redundant traverses of clusters-list in the program were totally avoided, so that the consumed simulation time is significantly reduced. In order to show the aggregation process in a more intuitive way, we have labeled different clusters with varied colors. Besides, a new function is added for outputting the particle’s coordinates of aggregates in file to benefit coupling our model with other models. New version program summaryProgram Title: CCA v04Program Files doi:http://dx.doi.org10.17632/zwz37tvjny.1Licensing provisions: Apache-2.0Programming language: JavaJournal reference of previous version: Computer Physics Communications 207 (2016) 547–548Does the new version supersede the previous version?: YesNature of problem: The previous program for CCA model can be optimized for yielding better operation efficiency and visualization effects. Besides, it can be extended for coupling with other models by adding some new functions.Solution method: Some redundant traverses of the clusters-list for updating an important variable were removed technically. Furthermore, displaying different clusters with distinct colors can benefit to the effectiveness of visualization. We have also introduced a new function for outputting the aggregated clusters, so that this model can be easily coupled with other models.Reasons for the new version:1. In the previous versions [1–3], the global variable of Dmax, which means the maximum diffusion coefficient of clusters, is supposed to be calculated when aggregation occurs. In fact, this variable is critical to determine whether the currently selected cluster carries out diffusion or not. In the previous version, we had to traverse the clusters-list to update Dmax, even though it may keep unchanged after a round of aggregation. But, we have explored that it is not necessary to traverse all clusters, if we compare the previous variable of Dmax with the diffusion coefficient of the new cluster, which is formed by aggregating two clusters. In the case of the new one is larger, Dmax will be updated to it; otherwise, Dmax keep unchanged. Obviously, removing redundant traverses can enhance algorithm efficiency, and the time complexity of the algorithm is closely related to the loop in it. As a result, the new version of code can greatly cut down the simulation time, in contrast to the previous codes.2. The old versions paint all particles with same color, which does not help to identify different clusters. In order to show the visualization of the 3D aggregate process in different states intuitively, we introduce labeling different clusters with different colors. Consequently, the particles belong to one cluster are painted with the same color.3. A new function is added to record intermediate or final state of clusters so that it can be used for further research when using other relevant models.Summary of revisions:1. Reduce unnecessary traverses of the clusters-list for speeding up simulation.2. Paint clusters with different colors to pursuit better visualization effects.3. Add a new function of exporting the coordinates of clusters to a text file for benefiting other models.Additional comments:To test the optimization effects offered by the new version of code, we have carried out a comparison experimentto measure the simulation time with different initial particles, by using the new and the previous version 3.0 of code. In the experiments, we set concentration C to 0.01, diffusion exponent γ to 0, sticking probability exponent σ to 1, the sticking probability P1 to 0.1, absolute temperature T to 298 K, and the side length L of cube was respectively set to 30, 40, 50, 60, 70 and 80 to yield different initial particles, as the number of particles N can be calculated by the formula N=C∗L3 [1]. To avoid the influences of hardware and software, we use Monte Carlo steps (MCS) as our simulation time [4–6]. As shown in Fig. 1, the slope coefficient caused by this new version of code is about 1.3813, it is close to line complexity, as for the previous version, it is 1.5703, larger than the new one. It is obvious the new one has a faster running speed than the previous one. More importantly, the reduction of simulation time becomes more obvious when the number of simulated particles is getting larger.The changed visualization of our program is shownin Fig. 2. We can clearly see how much clusters in simulation system, and how they distribute. And the button “save” marked red in Fig. 2 can help realize our new function by exporting the particle coordinates to a text file, which also store the related initial conditions.AcknowledgmentsThis work was partially supported by “National Natural Science Foundation of China (Nos. 41271292, 61303038)”.

Mobility of large clusters on a semiconductor surface: Kinetic Monte Carlo simulation results

The mobility of clusters on a semiconductor surface for various values of cluster size is studied as a function of temperature by kinetic Monte Carlo method. The cluster resides on the surface of a square grid. Kinetic processes such as the diffusion of single particles on the surface, their attachment and detachment to/from clusters, diffusion of particles along cluster edges are considered. The clusters considered in this study consist of 150–6000 atoms per cluster on average. A statistical probability of motion to each direction is assigned to each particle where a particle with four nearest neighbors is assumed to be immobile. The mobility of a cluster is found from the root mean square displacement of the center of mass of the cluster as a function of time. It is found that the diffusion coefficient of clusters goes as D = A(T)Nα where N is the average number of particles in the cluster, A(T) is a temperature-dependent constant and α is a parameter with a value of about –0.64 < α < –0.75. The value of α is found to be independent of cluster sizes and temperature values (170–220 K) considered in this study. As the diffusion along the perimeter of the cluster becomes prohibitive, the exponent approaches a value of –0.5. The diffusion coefficient is found to change by one order of magnitude as a function of cluster size.

Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters.

Nanoparticle dynamics impact a wide range of biological transport processes and applications in nanomedicine and natural resource engineering. Differential dynamic microscopy (DDM) was recently developed to quantify the dynamics of submicron particles in solutions from fluctuations of intensity in optical micrographs. Differential dynamic microscopy is well established for monodisperse particle populations, but has not been applied to solutions containing weakly scattering polydisperse biological nanoparticles. Here we use bright-field DDM (BDDM) to measure the dynamics of protein-rich liquid clusters, whose size ranges from tens to hundreds of nanometers and whose total volume fraction is less than 10(-5). With solutions of two proteins, hemoglobin A and lysozyme, we evaluate the cluster diffusion coefficients from the dependence of the diffusive relaxation time on the scattering wave vector. We establish that for weakly scattering populations, an optimal thickness of the sample chamber exists at which the BDDM signal is maximized at the smallest sample volume. The average cluster diffusion coefficient measured using BDDM is consistently lower than that obtained from dynamic light scattering at a scattering angle of 90°. This apparent discrepancy is due to Mie scattering from the polydisperse cluster population, in which larger clusters preferentially scatter more light in the forward direction.

Cluster diffusion on two-dimensional surface with immobile impurities

We study diffusion of a two-dimensional cluster on a two-dimensional surface with immobile impurities. We perform a kinetic Monte Carlo simulation using a simple square lattice model. In our model, not only atoms forming an edge of two-dimensional cluster but also atoms in the cluster, which is neighboring impurities in the cluster, are able to evaporate. The cluster diffusion coefficient in the system with a high impurity concentration is larger than that with no impurities.

Relaxation Process and Dynamical Heterogeneities in Chemical Gels: Critical Behavior of Self-Overlap and Its Fluctuation

We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.

Dynamic Imaging Analysis of SERS-Active Nanoparticle Clusters in Suspension.

A novel wide-field approach for the real-time Surface Enhanced Raman Scattering (SERS) imaging of multiple silver nanoparticle clusters suspended in solution is described. This method enables direct correlation of the SERS activity of a single nanoparticle aggregate and its size through measurement of the cluster diffusion coefficient and can also be performed in a high-throughput basis. As a first demonstration, we investigate the salt-induced aggregation of silver nanoparticles in the presence of a reporter tag molecule, which has a high affinity for the nanoparticle surface. In addition to tracking individual particles, direct comparison of Rayleigh and SERS videos of the same colloid solution enabled measurement of the fraction of individual clusters that are SERS active and the dependence of this value on the relative concentration of the tag molecule. Furthermore, given the ability to also rapidly profile any nonuniformity in particle size distributions, we expect this approach will not only provide a new tool for the fundamental understanding of SERS but also significantly contribute to the development of an array of emerging nanoparticle-enhanced biomolecule and imaging detection platforms.

Self-diffusion dynamic behavior of atomic clusters on Re(0 0 0 1) surface

Using molecular dynamics simulations and a modified analytic embedded atom potential, the self-diffusion dynamics of rhenium atomic clusters up to seven atoms on Re(0 0 0 1) surface have been studied in the temperature ranges from 600 K to 1900 K. The simulation time varies from 20 ns to 200 ns according to the cluster sizes and the temperature. The heptamer and trimer are more stable comparing to other neighboring non-compact clusters. The diffusion coefficients of clusters are derived from the mean square displacement of cluster's mass-center, and diffusion prefactors D 0 and activation energies E a are derived from the Arrhenius relation. It is found that the Arrhenius relation of the adatom can be divided into two parts at different temperature range. The activation energy of clusters increases with the increasing of the atom number in clusters. The prefactor of the heptamer is 2–3 orders of magnitude higher than a usual prefactor because of a large number of nonequivalent diffusion processes. The trimer and heptamer are the nuclei at different temperature range according to the nucleation theory.

Energetics and self-diffusion behavior of Zr atomic clusters on a Zr(0 0 0 1) surface

Using a molecular dynamics method and a modified analytic embedded atom potential, the energetic and the self-diffusion dynamics of Zr atomic clusters up to eight atoms on α-Zr(0001) surface have been studied. The simulation temperature ranges from 300 to 1100K and the simulation time varies from 20 to 40ns. It’s found that the heptamer and trimer are more stable comparing to other neighboring non-compact clusters. The diffusion coefficients of clusters are derived from the mean square displacement of cluster’s mass-center and the present diffusion coefficients for clusters exhibit an Arrhenius behavior. The Arrhenius relation of the single adatom can be divided into two parts in different temperature range because of their different diffusion mechanisms. The migration energies of clusters increase with increasing the number of atoms in cluster. The differences of the prefactors also come from the diverse diffusion mechanisms. On the facet of 60nm, the heptamer can be the nuclei in the crystal growth below 370K.

Effect of atomic diagonal motion on cluster diffusion coefficient and its scaling behavior

Abstract The effect of atomic diagonal motion on the cluster diffusion and its size dependence is simulated by kinetic Monte Carlo method. The diffusion coefficient D(N) of a cluster with size N satisfies a power law D(N)∝N−α, where the scaling exponent α decreases with the increase of additive diagonal motion barrier Ed. When Ed is very small, the cluster diffusion is dominantly controlled by periphery diffusion mechanism and α is found to be about 1.5. On the contrary, when Ed is very large, the cluster diffusion is mainly controlled by the correlation evaporation and condensation (CEC) mechanism and α approaches 1.0. Furthermore, a threshold Edt∼0.4E0 (E0 is the diffusion barrier for a free adatom), corresponding to the transition of different dominant mechanisms for the cluster diffusion, is found existing in the relationship between D and Ed. When Ed Edt, the CEC mechanism is more important, and D is nearly independent of Ed. Additionally, the temperature dependent of D is found to be D∼ exp (− E a k B T ) and the active energy Ea is found to ∼1.42E0.

Monte Carlo simulation of the effect of atomic diagonal transition on cluster diffusion

The effect of atomic diagonal transition on the cluster diffusion and its size dependence is simulated by kinetic Monte Carlo method. The thresholds of atomic diagonal transition barriers Edt are found to be 0.2eV and 0.4eV, corresponding to with and without evaporation and condensation mechanism, respectively. The results indicate that the cluster diffusion is controlled primarily by the atomic diagonal transition and the cluster diffusion coefficient D decreases drastically with increasing Ed when Ed Edt and the relationship between D and N changes into D∝N-1.08±0.027.

Ordering of Fractal Clusters in Crystallizing Lysozyme Solutions

The cluster formation in nucleating hen egg white lysozyme−NaCl solutions was studied by simultaneous static and dynamic light scattering. Angular dependence measurements of the total scattered intensity and of the average cluster diffusion coefficient revealed the appearance of pronounced structure factor peaks at the initial nucleation stages. Such peaks are characteristic for the ordering often observed in highly concentrated colloidal suspensions. Free-energy minimizations of 4−60 particles, that adequately model the lysozyme monomer, were performed by using the effective interaction potentials described in previous work (Soumpasis; Georgalis Biophys. J. 1997, 72, 2770). Both experiment and computations show formation of clusters with fractal morphology, compatible with the findings of the present and previous works.

EFFECT OF LOCAL DIFFUSION COEFFICIENT VARIATION ON SUBMONOLAYER GROWTH

In this article Au was deposited on PVF(Polyviny formal) film which was kept at 253 K to grow Au submonolayer film. It is found that there are special areas whose morphology differs from other's experiment in which metal was deposited on single crystal. In these areas especially big clusters were found and they were surrounded by empty bands. Our deduction that this is caused by variation of local coefficient is proved by a modified DDA(Deposition-Diffusion-Aggregation) model which includes edge diffusion. We also argue that the relationship between cluster diffusion coefficient DS, and particles numbers S which the cluster contains should be exponential for Au cluster on PVF film instead of power-dependent in original DDA model.

Late-stage coarsening of adlayers by dynamic cluster coalescence

We consider the late stages of adlayer coarsening when this process is dominated by cluster diffusion and coalescence. The growth rate of the average cluster size can be directly related to the cluster diffusion coefficient of individual clusters. The distribution of cluster sizes and the spatial correlations between clusters are examined as a function of coverage and cluster diffusion rate using Monte Carlo simulations. We also show how the Smoluchowski equation can give an approximate closed-form solution for the cluster size distribution during coarsening by coalescence. The coarsening of adlayers by cluster coalescence in a model that includes local inter-cluster interactions is also examined.

Cluster diffusivity: Structure, correlation, and scaling

We have investigated the diffusion of clusters on a triangular lattice using Monte Carlo simulations. A cluster is defined as a two-dimensional collection of particles which are connected to each other, either directly or indirectly through other particles in the cluster, by nearest-neighbor bonds. Each particle is allowed to hop, with probability αδb/2/(α−δb/2+αδb/2), to a vacant nearest-neighbor site with the constraint that the hop does not break the cluster. The change in the number of bonds is given by δb. The equilibrium clusters are correlated animals with structure controlled by the parameter α. We show that the diffusion coefficient of a cluster can be decomposed into two factors. One is a measure of the weighted length of the ‘‘active’’ perimeter and the other is a measure of the correlation between pairs of steps taken by the cluster during its walk. The perimeter measure is asymptotically proportional to cluster size N, as anticipated for ramified animals, but it crosses over to N1/2 dependence for smaller compact clusters with α&amp;gt;1. Our focus is on the accurate determination of the size and structure dependence of the correlation factor, which is more sensitive to statistical fluctuations. As a result, we describe the scaling of the cluster diffusion coefficient with cluster size.

Annihilation of deformation-produced vacancy clusters in alkali halides at room temperature

The aging of plastically deformed crystals of NaCl and KCl at room temperature for a long time results in a bulk density increase as evidenced by thermal gradient flotation measurements. The effect is explained by the annihilation of deformation-induced clusters on dislocations. No density variation was found in LiF and NaF crystals. A model has been suggested for the formation of vacancy clusters by disrupture of unrelaxed dislocation dipoles. From the model it follows that cluster size and mobility should decrease in the homologic row of alkali halides, which is consistent with experimental evidence. The cluster diffusion coefficient has been estimated to be 10 −16 cm 2s −1 at room temperature.

The translational friction coefficient and time dependent cluster size distribution of three dimensional cluster–cluster aggregationa),b)

The diffusion coefficient of clusters 𝒟 formed by cluster–cluster aggregation is computed according to the Kirkwood–Riseman Theory. In three dimensions one finds 𝒟 proportional to sγ where s is the number of particles in the cluster and γ=−0.544±0.014. This relationship is employed to simulate the time evolution of the cluster size distribution Ns(t) which is found to exhibit simple scaling behavior Ns(t) ∼s−2g(s/tz) with z∼1.1.

Diffusion-limited aggregation in three dimensions: Results from a new cluster-cluster aggregation model

Diffusion-limited aggregation has been investigated using three-dimensional lattice models in which both particles and clusters can move and stick together. The final state consists of a single cluster or network of occupied lattice sites with a fractal dimensionality of about 1.75. Two versions of the model have been investigated. In Model 1, the cluster diffusion coefficient is independent of cluster size, and in Model 2, only the smallest clusters are allowed to “diffuse.” Both models give final states which are identical within the accuracy of the simulations. However, the cluster size dispersion at intermediate stages is distinctly different for Model 1 and Model 2. The results taken together with more extensive simulations in two dimensions indicate that a fractal dimensionality of ≈ 1.75 will be obtained for all versions of the model in which the diffusion coefficient of small clusters is equal to or greater than the diffusion coefficient for larger clusters. A number of the geometric properties which characterize final state and intermediate clusters are analyzed. Some of these properties should be amenable to measurement in real systems. The results of the simulations are in good agreement with measurements of the fractal dimensionality of metal particle aggregates.

Formation of Fractal Clusters and Networks by Irreversible Diffusion-Limited Aggregation

A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion coefficient is either size independent or inversely proportional to number of particles (mass) give very similar results. In the limit of low concentration and large system size both models lead to structures with a fractal (Hausdorff) dimensionality of about 1.45-1.5 in two-dimensional lattice-based simulations.

On the diffusion of clusters of hard rods

It is shown that the diffusion coefficient of clusters of hard rods in one dimension is exactly independent of the number of rods comprising the cluster. An expression for the autocorrelation function of the velocity of the cluster centre of mass is obtained from a simple stochastic model, and asymptotically for large clusters from the exact autocorrelation function. Neither approximate nor exact velocity autocorrelation function decays exponentially for any size of cluster.