Cluster Aggregation Process Research Articles

Ag(Sn9-Sn9)]5- and [(η4-Sn9)Ag(η1-Sn9)]7-, as aggregates of spherical aromatic building blocks. Persistence of aromaticity upon cluster gathering.

Formation of cluster-based materials requires a fundamental understanding of the resulting cluster aggregation processes. The Sn94- Zintl-ion structure can be viewed as a building block featuring a spherical aromatic species, leading to a cluster gathering upon oxidative coupling and/or mediated by transition metals. Here, we evaluate the spherical aromatic properties of [Sn9-Sn9]6-, [Ag(Sn9-Sn9)]5- and [(η4-Sn9)Ag(η1-Sn9)]7-, as aggregates of two Sn9 building units held together via oxidative coupling and mediated by a Ag(I) transition metal center. Our results from magnetic criteria of aromaticity show that the inherent spherical aromatic characteristics of the parent Sn94- cluster are persistent in the overall aggregate where the enabled shielding cones ascribed to each Sn9 unit are able to interplay between them, leading to an overlap of the shielding regions. Hence, the two approaches for bringing cluster units together are able to retain the inherent spherical aromatic features for each Sn9 unit, leading to a cluster-based dimer where the parent properties remain. Thus, further cluster-based materials can be envisaged from aggregation upon oxidative coupling and/or mediated by transition metals, where the constituent building blocks retain their initial features, useful to guide the formation of more complex cluster-based aggregates.

Geochemistry and Geometrical Features of the Upper Cretaceous Vitulano Para-Autochthonous Karst Bauxites (Campania Region, Southern Italy): Constraints on Genesis and Deposition

In the Vitulano area, Upper Cretaceous bauxite bodies fill small depressions and karst cavities within Cretaceous shallow-water limestones. These bauxites were studied to understand the processes that led to their formation. Geochemical, mineralogical, and petrographic analyses were carried out on the bauxite samples, together with image analysis providing geometric parameters. The texture of Vitulano bauxite consists of ooids and sub-circular aggregates dispersed in a predominantly Ca-rich matrix. Ooids are generally formed by a single large core, often surrounded by an alternation of different aggregates of boehmite and Al-hematite reflecting different climate periods. The composition is dominated by the major elements Al2O3 and CaO with lower concentrations of Fe2O3 and SiO2. Boehmite, calcite, hematite, and anatase are the main mineralogical phases identified. Image analysis provided values of fractal dimension D that gives information on carbonate platform exposure times since it is linked to long-lasting sub-aerial events and diffusion-limited cluster aggregation processes. The tectonic evolution of the area played an important role in the genesis of the Vitulano bauxites since it favored the erosion, transport, and re-deposition of pre-existing bauxite material from the surrounding Campania bauxites. Based on this hypothesis, Vitulano bauxites are defined and classified as para-autochthonous, and this was supported by Eu/Eu* vs. Sm/Nd and Eu/Eu* vs. TiO2 Al2O3 indices displaying a similarity between Vitulano and the other Campania bauxites.

Factors influencing the structure of the complex-defects in AF2: RE3+ (A= Ca, Sr and Ba): A first-principles study

As aliovalent doping materials, RE3+ doped AF2 (A = Ca, Sr and Ba), which show not only high thermal conductivity and low nonlinear refractive index ascribed to fluorides, but also unique spectroscopic properties related to the RE3+ ions, are promising ultra-strong and ultra-fast laser crystal candidates. It is noted that the stability of the C3v complex-defect, in which Fi− compensates at the next-nearest interstitial site of RE3+, increases with the ratio of the lattice parameter to the dopant ionic radius. In this work, systematic first-principles calculations are performed to resolve factors influencing the structure of the RE-Fi monomers. The formation energy, the reorientation energy and the local structure of the monomers are obtained, and the Coulomb interaction and the sub-lattice distortion are quantified. It is concluded that the sub-lattice distortion determines the defect structure even though the Coulomb interaction is the fundamental basis for the complex-defect formation in aliovalent doping materials. On this basis, the cluster aggregation process in AF2: RE3+ are elucidated and the octahedral arrangement of the hexamer is specially explained. Our calculation results and analytical methods not only provide new insights for the defect formation mechanism in AF2: RE3+, but also guide the improvement of aliovalent doping materials.

HyCASTLE: A Hybrid ClAssification System based on Typicality, Labels and Entropy

Traditional supervised classification models aim to approximate the functional mapping between instance attributes and their class labels. These models, however, do not consider the interdependence between instances and global characteristics of data and thus often they lead to poor classification results. In this work, we present a novel hybrid classification model – named HyCASTLE – designed to solve the main shortcomings of hybrid models that employ topological information through clustering in order to improve classifiers performances: they make hypotheses on the underlying data distribution and do not consider the effect of noise. HyCASTLE utilises a non-parametric estimator to capture the underlying data distribution and creates entirely data-driven shape-free clusters. HyCASTLE then refines this cluster configuration using both data topology and available labels through an iterative cluster aggregation and separation process. We evaluated HyCASTLE performance on 37 datasets and compare it with both traditional and hybrid classification models. Our results show that HyCASTLE has comparable or better performance than the other models and results to be more resilient to class noise.

Influence of ionomer adsorption on agglomerate structures in high-solid catalyst inks

Because the agglomerate structures of carbon-black-supported platinum nanoparticles (Pt/C) in catalyst inks affect their productivity and performance, identifying the structural parameters that control the dispersion state and stability of Pt/C agglomerates is important. This study aimed to identify agglomerate structures of Pt/C in high-solidity catalyst inks by examining the rheological behavior, fractal dimension, and electrical conductivity of the inks. In inks containing 48–75% water, the amount of adsorbed ionomers decreased with decreasing water content, resulting in increases in the shear viscosity (η), storage modulus (G′), and electrical conductivity (Σ). The fractal dimension of the agglomerates (df) was 1.7–2.1, suggesting that Pt/C agglomerates form a rigid three-dimensional network via a diffusion-limited cluster aggregation process. Conversely, in inks containing 89% water, the amount of adsorbed ionomers increased, leading to the lowest values for η, G′, and Σ. The df value was 2.6, suggesting that Pt/C agglomerates formed a weak-link network via a reaction-limited cluster aggregation process, which was inhibited by the steric and electrostatic repulsion effects of the adsorbed ionomers. The results of this study demonstrate that agglomeration can be controlled through ionomer adsorption by Pt/C, leading to changes in the rheological behavior and stability of catalyst inks.

Cluster Assemblies Produced by Aggregation of Preformed Ag Clusters in Ionic Liquids.

Room-temperature ionic liquids (RTILs) can be used as electrosterical stabilizers for nanoparticles without adding stabilizing agents. However, the nanoparticle stability and its mechanisms are still in discussion. We deposited preformed 2 nm ±0.6 nm silver clusters into the ionic liquid C4MIM PF6 using in situ UV/vis absorption to monitor the deposition process. The time- and temperature-dependent cluster aggregation process was studied with ex situ UV/vis absorption spectroscopy analyzed with electrodynamic calculations using generalized Mie theory. On an atomistic level, the sample structure was investigated using EXAFS and a neural network based analysis of XANES. The combination of all methods shows that an aggregation of the original 2 nm clusters without coalescence takes place, which can be controlled or stopped by choosing an appropriate sample temperature. This approach allows the controlled production of chainlike cluster aggregates in RTIL, promising for a number of applications.

Carbon black networking in elastomers monitored by simultaneous rheological and dielectric investigations

The rheo-dielectric response of carbon black filled elastomer melts is investigated by dielectric relaxation spectroscopy in the frequency range from 0.1 Hz up to 10 MHz during oszillatory shearing in a plate–plate rheometer. Various concentrations and types of carbon blacks dispersed in a non-crosslinked EPDM melt are considered. It is demonstrated that during heat treatment at low strain amplitude a pronounced flocculation of filler particles takes place leading to a successive increase of the shear modulus and conductivity. Followed up by a strain sweep, the filler network breaks up and both quantities decrease simultaneously with increasing strain amplitude. Two relaxation times, obtained from a Cole–Cole fit of the dielectric spectra, are identified, which both decrease strongly with increasing flocculation time. This behaviour is analyzed in the frame of fractal network models, describing the effect of structural disorder of the conducting carbon black network on the diffusive charge transport. Significant deviations from the predictions of percolation theory are observed, which are traced back to a superimposed cluster–cluster aggregation process (CCA). During flocculation, a universal scaling behaviour holds between the conductivity and the corresponding high frequency relaxation time, which fits all the measured data. The scaling exponent agrees fairly well with the prediction obtained from CCA. It is demonstrated that the underlying basic mechanism is a change of the correlation length of the filler network, i.e. the size of the fractal heterogeneities. This decreases during flocculation due to the formation of additional conductive paths, making the system more homogeneous. An addition less pronounced effect is found from nanoscopic gaps between adjacent filler particles, which decrease during flocculation. The same universal scaling behaviour, as obtained for flocculation, is found for temperature-dependent dielectric measurements of the cured crosslinked systems, which are heated from room temperature up to 200 °C. Thereby, the conductivity decreases significantly and the relaxation time increases, indicating that the filler network breaks up randomly due to the thermal expansion of the rubber matrix.

Relationship between geometric parameters and compositional data: A new approach to karst bauxites exploration

Southern Italy karst bauxites occur in Apulia and Campania regions. In Apulia there are the autochthonous concentrations of Spinazzola (Murge) and San Giovanni Rotondo (Gargano), as well as the allochthonous Salento-type deposits. Typical Campania bauxites are those of the Matese Mts and in the Caserta area. During Cretaceous, both Apulia and Campania experienced sub-aerial carbonate exposures, which promoted bauxite accumulation.Southern Italy bauxite deposits share the same ooidic texture consisting of sub- circular aggregates dispersed in a fine-grained matrix. The ooids are mainly formed by a large core of Al-hematite surrounded by alternating layers of boehmite and Al-hematite reflecting dry and wet climate periods. The ooids of the allochthonous Salento-type bauxite consist of a large boehmite core surrounded by a thinner rim of Al-hematite.Image analysis, performed on these karst bauxites provided geometric data such as ooids circularity and aspect ratio, number of ooids and fractal dimension D. In the Southern Italy bauxite deposits significant correlations exist between the results of image analysis and compositional data. In the allochthonous Salento-type bauxites significant correlations between geometric features (number of ooids and aspect ratio) and some critical elements (Sc, Ni and REE) have been observed. In the autochthonous Apulian bauxites a significant correlation between Ni and circularity has been observed instead.The arrangement and the growth of the ooids can be described with a molecular diffusion pattern, and their growth can be described in terms of fractal geometry. The values of fractal dimension are different between Apulia and Campania bauxite deposits, this suggesting that during long-lasting sub-aerial events, the diffusion-limited cluster aggregation process may prevail over the simpler diffusion-limited one, which is responsible for ooids formation during time-limited exposure events.Image analysis and its integration with other analytical techniques provide interesting information about the genesis of bauxite deposits, and can therefore represent an innovative and useful tool for the exploration of bauxite ores.

Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents.

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a more unusual phase transition, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent τ in the range 2<τ(g)≤2.5. This pattern reveals a necessary condition for a hybrid transition in cluster aggregation processes, which is comparable to the power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.

From static micrographs to particle aggregation dynamics in three dimensions.

Studies on colloidal aggregation have brought forth theories on stability of colloidal gels and models for aggregation dynamics. Still, a complete link between developed frameworks and obtained laboratory observations has to be found. In this work, aggregates of silica nanoparticles (20 nm) are studied using diffusion limited cluster aggregation (DLCA) and reaction limited cluster aggregation (RLCA) models. These processes are driven by the probability of particles to aggregate upon collision. This probability of aggregation is one in the DLCA and close to zero in the RLCA process. We show how to study the probability of aggregation from static micrographs on the example of a silica nanoparticle gel at 9 wt%. The analysis includes common summary functions from spatial statistics, namely the empty space function and Ripley's K-function, as well as two newly developed summary functions for cluster analysis based on graph theory. One of the new cluster analysis functions is related to the clustering coefficient in communication networks and the other to the size of a cluster. All four topological summary statistics are used to quantitatively compare in plots and in a least-square approach experimental data to cluster aggregation simulations with decreasing probabilities of aggregation. We study scanning transmission electron micrographs and utilize the intensity-mass thickness relation present in such images to create comparable micrographs from three-dimensional simulations. Finally, a characterization of colloidal silica aggregates and simulated structures is obtained, which allows for an evaluation of the cluster aggregation process for different aggregation scenarios. As a result, we find that the RLCA process fits the experimental data better than the DLCA process.

Effects of oxygen addition in reactive cluster beam deposition of tungsten by magnetron sputtering with gas aggregation

In this work, we investigated the possibilities of tungsten and tungsten oxide nanoclusters generation by means of non-reactive and reactive magnetron sputtering with gas aggregation. It was found that in pure argon atmosphere, cluster aggregation proceeded in two regimes depending on argon pressure in the aggregation chamber. At the lower pressure, cluster generation was dominated by two-body collisions yielding larger clusters (about 5.5nm in diameter) at lower rate. At higher pressures, cluster generation was dominated by three-body collisions yielding smaller clusters (3–4nm in diameter) at higher rate. The small amount of oxygen admixture in the aggregation chamber had considerable influence on cluster aggregation process. At certain critical pressure, the presence of oxygen led to the raise of deposition rate and cluster size. Resulting clusters were composed mostly of tungsten trioxide. The oxygen pressure higher than critical led to the target poisoning and the decrease in the sputtering rate. Critical oxygen pressure decreased with increasing argon pressure, suggesting that cluster aggregation process was influenced by atomic oxygen species (namely, O− ion) generated by oxygen–argon collisions in the magnetron plasma.

A fast and accurate implementation of tunable algorithms used for generation of fractal-like aggregate models

In many branches of science experiments are expensive, require specialist equipment or are very time consuming. Studying the light scattering phenomenon by fractal aggregates can serve as an example. Light scattering simulations can overcome these problems and provide us with theoretical, additional data which complete our study. For this reason a fractal-like aggregate model as well as fast aggregation codes are needed. Until now various computer models, that try to mimic the physics behind this phenomenon, have been developed. However, their implementations are mostly based on a trial-and-error procedure. Such approach is very time consuming and the morphological parameters of resulting aggregates are not exact because the postconditions (e.g. the position error) cannot be very strict. In this paper we present a very fast and accurate implementation of a tunable aggregation algorithm based on the work of Filippov et al. (2000). Randomization is reduced to its necessary minimum (our technique can be more than 1000 times faster than standard algorithms) and the position of a new particle, or a cluster, is calculated with algebraic methods. Therefore, the postconditions can be extremely strict and the resulting errors negligible (e.g. the position error can be recognized as non-existent). In our paper two different methods, which are based on the particle–cluster (PC) and the cluster–cluster (CC) aggregation processes, are presented.

Molecular dynamics and kinetic study of carbon coagulation in the release wave of detonation products

We present a combined molecular dynamics and kinetic study of a carbon cluster aggregation process in thermodynamic conditions relevant for the detonation products of oxygen deficient explosives. Molecular dynamics simulations with the LCBOPII potential under gigapascal pressure and high temperatures indicate that (i) the cluster motion in the detonation gas is compatible with Brownian diffusion and (ii) the coalescence probability is 100% for two clusters entering the interaction cutoff distance. We used these results for a subsequent kinetic study with the Smoluchowski model, with realistic models applied for the physical parameters such as viscosity and cluster size. We found that purely aggregational kinetics yield too fast clustering, with moderate influence of the model parameters. In agreement with previous studies, the introduction of surface reactivity through a simple kinetic model is necessary to approach the clustering time scales suggested by experiments (1000 atoms after 100 ns, 10 000 atoms after 1 μs). However, these models fail to reach all experimental criteria simultaneously and more complex modelling of the surface process seems desirable to go beyond these current limitations.

Geometrical and Electrical Properties of Indium Tin Oxide Clusters in Ink Dispersions

The analysis of the TEM images of indium tin oxide (ITO) clusters in ink solutions deposited from ink dispersions reveals that their geometry arises from a diffusion limited cluster aggregation (DLCA) process. We model films of ITO clusters as built through deposition of DLCA clusters made of primary spherical nanoparticles of 13 nm in diameter. The deposition is then followed by a further compactification process that imitates sintering. We determine the conductivity of the sintered films by mapping the problem to that of the resistor network in which the contact regions between the touching spheres provide the dominant electric resistance. For a given volume fraction, conductivity of the sintered films is shown to be larger than that for the randomly packed spheres. However, the larger a typical radius of gyration of the clusters the smaller the enhancement. We also provide numerical tests for the routines used in the interpretation of the TEM images.

Cluster aggregation model for discontinuous percolation transitions

The evolution of the Erdos-Rényi (ER) network by adding edges is a basis model for irreversible kinetic aggregation phenomena. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel Kij approximately ij , where ij is the product of the sizes of two merging clusters. Here we study that when the giant cluster is discouraged to develop by a sublinear kernel Kij approximately (ij)omega with 0<or=omega<1/2 , the percolation transition (PT) is discontinuous. Such discontinuous PT can occur even when the ER dynamics evolves from proper initial conditions. The obtained evolutionary properties of the simple model sheds light on the origin of the discontinuous PT in other nonequilibrium kinetic systems.

Low Fractal Dimension Cluster-Dilute Soot Aggregates from a Premixed Flame

Using a novel morphology segregation technique, we observed minority populations ( approximately 3%) of submicron-sized, cluster-dilute fractal-like aggregates, formed in the soot-formation window (fuel-to-air equivalence ratio of 2.0-3.5) of a premixed flame, to have mass fractal dimensions between 1.2 and 1.51. Our observations disagree with previous observations of a universal mass fractal dimension of approximately 1.8 for fractal-like aerosol aggregates formed in the dilute-limit via three-dimensional diffusion-limited cluster aggregation processes. A hypothesis is presented to explain this observation. Subject to verification of this hypothesis, it may be possible to control the fractal dimension and associated properties of aggregates in the cluster-dilute limit through application of a static electric field during the aggregation process.

Kinetics of self-organization of polyampholyte nanoparticles in solutions

An appropriate composition of a binary solvent, water-ethanol, provides the necessary thermodynamic environment for the polyampholyte (gelatin) molecules to form self-assembled nano-clusters having fractal dimension, ≈ 2.6, in the bulk (3-D). The aggregation in the bulk of the solution appears to be an anomalous process and could be explained through Smoluchowski aggregation model. It gives a diffusion limited aggregation (DLA) type fractal dimension to the cluster in bulk, but shows extremely low polydispersity, which in fact is a signature of a slowly growing reaction limited cluster aggregation (RLA) process. Experimental results obtained from light scattering and electrophoresis experiments enable us to probe the kinetics of such growth processes.

Computer Simulation of Compressive Failure in Silica Aerogels

ABSTRACTHistorically, the low thermal conductivity of silica aerogels has made them of interest to the aerospace community for applications such as cryotank insulation. However, recent advances in the application of conformal polymer coatings to these gels have made them significantly stronger, and potentially useful as lightweight structural materials. In this work, we perform multiscale computer simulations to investigate the compressive strength and failure behavior of silica aerogels.The gels' nanostructure is simulated via the diffusion limited cluster aggregation (DLCA) process, which produces fractal aggregates that are structurally similar to experimentally observed gels. The largest distinct feature of the clusters is the so-called secondary particle, typically tens of nm in diameter, which is composed of primary particles of amorphous silica an order of magnitude smaller. The secondary particles are connected by amorphous silica bridges that are typically smaller in diameter than the particles they connect.We investigate compressive failure via the application of a uniaxial compressive strain to the DLCA clusters. In computing the energetics of the compression, the detailed structure of the secondary particles is ignored, and the interaction among secondary particles is described by a Morse pair potential parameterized such that the potential range is much smaller than the secondary particle size; an angular potential contribution is included in some of the simulations as well. The Morse and angular parameters are obtained by atomistic simulation of models of the interparticle bridges, with the compressive and bending behavior of these bridges modeled via molecular statics. We consider the energetics of compression and compressive failure, and compare qualitative features of low-and high-density gel failure.

Agglomeration Simulation of Chain-like Inclusions in Molten Steel Based on Fractal Cluster-Cluster Agglomeration Model

Based on the fractal cluster-cluster agglomeration (CCA) model, two-dimensional simulations of cluster aggregation process have beencarried out by varying initial particle number, particle size and sticking probability between clusters. Particle size and amount of seed particleshave small effects on the shape of clusters. Actual alumina clusters observed in tundish show the chain-like appearance and are very similar tothe simulatedagglomerated clusters with highstickingprobability.The agglomeration process of alumina chain-like clusters aroundimmersionnozzle in the tundish and RH process are plausibly controlled by the random collision process with high sticking probabilityvalues. [doi:10.2320/matertrans.MRA2007037](Received February 15, 2007; Accepted May 18, 2007; Published July 19, 2007)Keywords: fractal, fractal dimension, inclusion, chain-like inclusion, deoxidation, cluster-cluster aggregation

Nucleation, Growth, Fractal Aggregation, and Late-Stage Coarsening on Structural Development of Polymer Physical Gels

By using the time-resolved small-angle light scattering (TRSALS) technique, we present the real-time measurement of the physical gelation process for a crystalline polymer. To investigate the growth kinetics, a complete picture of the gel structural formation should be differentiated into the nucleation and growth of the microgels, the diffusive aggregation of the microgels, the percolation in cluster−cluster aggregation process, and the late-stage coarsening by the Ostwald ripening process. We propose some phenomenological functions to describe the hierarchical structure of the nucleation gels. The modeling of the late-stage gel structure could be built upon the following three relevant categories: the structure of the primary particle, the nonfractal local structure of a random packing of the nearest neighbors, and the fractal correlations between the particles constituting the aggregates. The model is able to reproduce the overall behavior of Hv and Vv scattering intensity distributions over the exper...