Diffusion-limited Cluster Aggregation Research Articles

Simulations on the gelling process of particle suspension systems forin-situpreparing porous materials in a capillary

The gelling process of particle suspension in a capillary which is crucial for in-situ preparing small size foam products has been simulated with an off-lattice diffusion limited cluster aggregation (DLCA) model by the three-dimensional Monte Carlo simulations. The effects of the model parameters, such as the interaction between capillary wall and particles, particle volume fraction, capillary size etc. on the density distribution of the system have been fully explored. And the aggregation kinetics process over a broad range of volume fractions and interactions have also been discussed. The results show that the geometric constraint of capillary can be analogous to a weak repulsive interaction between capillary wall and particles. And we found that as the capillary size or particle volume fraction increase, particle concentration distribution will be more uniform with other parameters constant. Porous network with relatively uniform density distribution can be also obtained through controlling the interaction between capillary wall and particles. In addition, by analyzing the aggregation kinetics process, we found that the attraction of capillary wall dramatically reduces the probability of gelation in the small-scale capillary. The obtained results will be of great importance in controlling the density distribution of porous materials prepared by in-situ methods.

Generic model for tunable colloidal aggregation in multidirectional fields.

Based on Brownian Dynamics computer simulations in two dimensions we investigate aggregation scenarios of colloidal particles with directional interactions induced by multiple external fields. To this end we propose a model which allows continuous change in the particle interactions from point-dipole-like to patchy-like (with four patches). We show that, as a result of this change, the non-equilibrium aggregation occurring at low densities and temperatures transforms from conventional diffusion-limited cluster aggregation (DLCA) to slippery DLCA involving rotating bonds; this is accompanied by a pronounced change of the underlying lattice structure of the aggregates from square-like to hexagonal ordering. Increasing the temperature we find a transformation to a fluid phase, consistent with results of a simple mean-field density functional theory.

Multi-scale simulation of the tensile properties of fiber-reinforced silica aerogel composites

A new multi-scale model is proposed to investigate the relationship between the mechanical properties and microstructure of fiber-reinforced silica aerogel composites. The multi-scale model consists of the aerogel model in nanometers and the composite model in micrometers. The aerogel model is generated to represent the cluster structure of silica aerogels based on a modified diffusion-limited cluster aggregation (DLCA) algorithm, in which the size-dependent interactions between the primary particles are obtained from theoretical derivations. A continuum damage constitutive model is established to represent the behavior of the silica aerogel matrix in the composite by implementing the aerogel model with the discrete element method (DEM). After that, a modified embedded element technique (EET) is proposed to generate the finite element (FE) model of the silica aerogel composite with curve fibers. This multi-scale model is used to investigate the tensile behavior of fiber-reinforced silica aerogel composites, while a comparison with experimental results is presented. The numerical results show that the primary particle size has a significant effect on the Young׳s modulus and the tensile strength of the composites. Moreover, our present model is employed to explore the relationship between the mechanical properties of the composite and the fiber characteristics, including the fiber volume fraction, length and curvature. The predictions indicate that the characteristics of the reinforcing fibers are significant for the mechanical properties of silica aerogel composites. The present multi-scale model can be extended to study the mechanical properties of other aerogel composites.

A Coarse-Grained Model for Polyglutamine Aggregation Modulated by Amphipathic Flanking Sequences

The aggregation of proteins with expanded polyglutamine (polyQ) tracts is directly relevant to the formation of neuronal intranuclear inclusions in Huntington’s disease. In vitro studies have uncovered the effects of flanking sequences as modulators of the driving forces and mechanisms of polyQ aggregation in sequence segments associated with HD. Specifically, a seventeen-residue amphipathic stretch (N17) that is directly N-terminal to the polyQ tract in huntingtin decreases the overall solubility, destabilizes nonfibrillar aggregates, and accelerates fibril formation. Published results from atomistic simulations showed that the N17 module reduces the frequency of intermolecular association. Our reanalysis of these simulation results demonstrates that the N17 module also reduces interchain entanglements between polyQ domains. These two effects, which are observed on the smallest lengthscales, are incorporated into phenomenological pair potentials and used in coarse-grained Brownian dynamics simulations to investigate their impact on large-scale aggregation. We analyze the results from Brownian dynamics simulations using the framework of diffusion-limited cluster aggregation. When entanglements prevail, which is true in the absence of N17, small spherical clusters and large linear aggregates form on distinct timescales, in accord with in vitro experiments. Conversely, when entanglements are quenched and a barrier to intermolecular associations is introduced, both of which are attributable to N17, the timescales for forming small species and large linear aggregates become similar. Therefore, the combination of a reduction of interchain entanglements through homopolymeric polyQ and barriers to intermolecular associations appears to be sufficient for providing a minimalist phenomenological rationalization of in vitro observations regarding the effects of N17 on polyQ aggregation.

Self-assembly of phosphorous containing oligomers: morphological features and pH-sensitiveness in suspension.

Methacrylamide-based oligomers bearing phosphonate pending groups at the end of a long alkyl chain and originating from undecylenic acid synthons were subjected to direct oligomer dissolution. Size improvement towards much smaller objects was reached using the nanoprecipitation method: the oligomers were first dissolved in an organic solvent, and then precipitated in water using a syringe pump. Dynamic light scattering (DLS) showed phosphorous containing monomodal and quite narrow-sized self-assemblies in water with hydrodynamic diameters (DH) ranging from 80 to 280 nm (depending on the oligomer system). Direct visualization using transmission electron microscopy (TEM) and atomic force microscopy (AFM) showed filled and almost individual particles with spherical shape. They were considerably shrunk, suggesting the highly swollen character of the self-assemblies in suspension. Morphological information on the multi-scale self-assembled structures was complementarily obtained using static light scattering (SLS). Thus, at a low length-scale, highly segregated sub-units having sharp boundaries surrounded by water (Porod behaviour) were observed, whereas at a high length-scale random non-compact organization of these sub-units via weak interactions was found, forming a chaplet-like structure (Gaussian behaviour). Furthermore, the pH-sensitiveness of the suspensions obtained after the nanoprecipitation method was studied. Particularly, at pH = 12, the characteristic size drastically increased within few hours from typically ∼280 nm to 2 μm due to electrostatic repulsion between deprotonated hydroxyl groups. At longer times, the observed peculiar behaviour corresponded to the model of diffusion-limited cluster aggregation (DLCA) where the particles stuck easily together upon contact [continuation of the article by C. Bouilhac, C. Travelet, A. Graillot, S. Monge, R. Borsali and J.-J. Robin, Polym. Chem., 2014, 5, 2756-2767].

Automated Determination of Aggregate Primary Particle Size Distribution by TEM Image Analysis: Application to Soot

In many applications, nanoparticles appear to be in an aggregated form. Thus, a complete description of their morphology involves an analysis of their size at different scales, from the aggregate size to the primary particle size. In this study, we present an automated method for the determination of the primary particle size distribution. It is based on an image-processing algorithm operating Euclidian distance mapping leading to a function that contains information about aggregates morphology. This algorithm is first applied to virtual aggregates with point contact between spheres, generated by diffusion limited cluster aggregation code. It shows that obtained functions can be used to retrieve the parameters of the primary particle diameter size distribution. However, it also demonstrates that overlapping or necking effects between primary spheres can have an impact on the shape of the function. The analysis is also performed on real soot images generated by ethylene diffusion flame and civil aviation e...

Colloidal aggregation and dynamics in anisotropic fluids.

We present experiments and numerical simulations to investigate the collective behavior of submicrometer-sized particles immersed in a nematic micellar solution. We use latex spheres with diameters ranging from 190 to 780 nm and study their aggregation properties due to the interplay of the various colloidal forces at work in the system. We found that the morphology of aggregates strongly depends on the particle size, with evidence for two distinct regimes: the biggest inclusions clump together within minutes into either compact clusters or V-like structures that are completely consistent with attractive elastic interactions. On the contrary, the smallest particles form chains elongated along the nematic axis, within comparable timescales. In this regime, Monte Carlo simulations, based on a modified diffusion-limited cluster aggregation model, strongly suggest that the anisotropic rotational Brownian motion of the clusters combined with short-range depletion interactions dominate the system coarsening; elastic interactions no longer prevail. The simulations reproduce the sharp transition between the two regimes on increasing the particle size. We provide reasonable estimates to interpret our data and propose a likely scenario for colloidal aggregation. These results emphasize the growing importance of the diffusion of species at suboptical-wavelength scales and raise a number of fundamental issues.

Population Balance Modeling of Aggregation and Coalescence in Colloidal Systems

A complex interplay between aggregation and coalescence occurs in many colloidal polymeric systems and determines the morphology of the final clusters of primary particles. To describe this process, a 2D population balance equation (PBE) based on cluster mass and fractal dimension is solved, employing a discretization method based on Gaussian basis functions. To prove the general reliability of the model and to show its potential, parametric simulations are performed employing both diffusion‐limited‐cluster aggregation (DLCA) and reaction‐limited‐cluster‐aggregation (RLCA) kernels and different coalescence rates. It turns out that in both DLCA and RLCA regimes, a faster coalescence leads to smaller sized and more compact clusters, whereas a slow coalescence promotes the formation of highly reactive fractals, resulting in larger aggregates.

Tuning the nanopore structure and separation behavior of hybrid organosilica membranes

The exceptional hydrothermal- and solvent stability of organically linked silica makes it a promising candidate material for molecular separation membranes. Tailoring towards specific separation properties however requires precise control over the pore structure. Here we show that this can be achieved by adjusting the acid-to-Si ratio immediately before the onset of physical drying of the 1,2-bis(triethoxysilyl)ethane-based polymeric colloidal sols. This procedure provides uniform coating conditions and results in defect-free films. The structure development is investigated with in-situ Small-Angle X-ray Scattering, both in a solvent and during film drying. Acid-catalyzed colloidal growth in a solvent is governed by diffusion-limited cluster aggregation for all studied acid concentrations. Upon solvent evaporation, micropores (<2nm) are formed at low acid concentrations (H+:Si⩽0.1). This can be explained by compressive capillary forces exerted by the receding pore liquid. At H+:Si=1, reaction-limited cluster aggregation is observed during drying, followed by the formation of pores >2nm. The compressive forces are balanced by a network strengthened by ongoing condensation reactions, and by the positive charge on the hybrid organosilica. This results in a larger pore size under more acidic conditions. The permselectivity of the supported membranes correlates with the pore structure of the unsupported materials. Thus, the adaptability of the pore structure allows a wider applicability of organosilica membranes in energy-efficient industrial molecular separations.

Examination of the regime controlling sol–gel based colloidal silica aggregation

The behavior of the size distribution of colloidal silica during aggregation was studied. The effecting parameters including: pH, temperature, colloidal concentration, and electrolyte concentration were altered to elucidate the nature of the aggregation kinetic regime. Size distribution was measured by Dynamic Light Scattering monitoring the progress of the reaction.We found clear evidences for a mixed regime of both diffusion limited and reaction limited cluster aggregation. In addition, using computer simulations, we compared the empirical behavior to the theory. This enabled us unveiling the empirical kernel of the system for the first time. The empirical kernel shows a curiosity arousing difference with the classical kernel.

Barycentric fixed-mass method for multifractal analysis

We present a method to estimate the multifractal spectrum of point distributions. The method incorporates two motivated criteria (barycentric pivot point selection and nonoverlapping coverage) in order to reduce edge effects, improve precision, and reduce computation time. Implementation of the method on synthetic benchmarks demonstrates the superior performance of the proposed method compared with existing alternatives routinely used in the literature. Finally, we use the method to estimate the multifractal properties of the widely studied growth process of diffusion-limited aggregation (DLA) and compare our results with recent and earlier studies. Our tests support the conclusion of a genuine but weak multifractality of the central core of DLA clusters, with D(q) decreasing from 1.75±0.01 for q=-10 to 1.65±0.01 for q =+10.

Effects of Aggregate Structure on the Dissolution Kinetics of Citrate-Stabilized Silver Nanoparticles

Aggregation and dissolution kinetics are important environmental properties of silver nanoparticles (AgNPs), and characterization of the interplay between these two processes is critical to understanding the environmental fate, transport, and biological impacts of AgNPs. Time-resolved dynamic light scattering was employed to measure the aggregation kinetics of AgNPs over a range of monovalent electrolyte (NaCl) concentrations. The fractal dimensions (Df) obtained from aggregation kinetics and static light scattering were found to be dependent on the aggregation mechanism and, in accord with expectation, varied from 1.7 for diffusion-limited cluster aggregation to 2.3 for reaction-limited cluster aggregation. An aggregation-dissolution model, in which the proportion of accessible reactive sites on primary particles as well as the aggregate size and Df are assumed to be key determinants of reactivity, is found to provide an excellent description of the decline of normalized rate of dissolution of AgNPs during aggregation for different NaCl concentrations. This model also provides fundamental insights into the factors accounting for the observed change in rate of dissolution of AgNPs on injection into seawater thereby facilitating improved prediction of the likely toxicity of AgNPs in the marine environment.

Ca2+ and Cu2+ Induced Aggregation of Variably Charged Soil Particles: A Comparative Study

The different surface reactions of metal ions with variably charged soil particles can considerably influence the particle interactions, which will further influence soil particle aggregation, sedimentation, dispersion, and transportation. This paper presents a study of the aggregation kinetics of variably charged soil colloidal particles at different Ca2+ and Cu2+ concentrations by using dynamic light scattering (DLS) and then investigating the formed aggregates structures by static light scattering (SLS). From the comparison of the experimental results, we found Cu2+ adsorption‐induced aggregation was much faster than Ca2+ adsorption‐induced aggregation. An aggregation process referred to as “attraction‐diffusion‐limited cluster aggregation” (ADLCA) was observed in the Cu2+ adsorption‐induced aggregation of the soil particles, resulting from electrostatic attraction forces between oppositely charged particles. The fractal dimensions of the Cu2+ specific adsorption‐induced aggregation were much higher than those of the Ca2+ electrostatic adsorption‐induced aggregation, irrespective of whether aggregation for the former was by the ADLCA, diffusion‐limited cluster aggregation (DLCA), or an ADLCA + DLCA process. Also, the ADLCA process led to the lowest fractal dimension, the DLCA process led to the highest fractal dimension, and the ADLCA + DLCA process led to an intermediate moderate fractal dimension, which shows the complexity of interactions between variably charged particles interactions when specific adsorption occurs at a particle surface. The above observations were well explained by analysis of the net interaction forces between particles in suspension.

Lacunarity and multifractal analysis of the large DLA mass distribution

We show the methodology used to analyze fractal and mass-multifractal properties of very large Diffusion-Limited Aggregation (DLA) clusters with a maximum of 109 particles for 2D aggregates and 108 particles for 3D clusters, to support our main result; the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects. In order to estimate lacunarity measures for large DLA clusters, we develop a variant of the gliding-box algorithm which reduces the computer time needed to obtain experimental results. We show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters. Lacunarity analysis shows, provided we study small clusters mass distributions, data which might be interpreted as two different values of fractal dimensions while the cluster grows; however, this effect tends to vanish when the cluster size increases further, in such a way that monofractality is achieved. The outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior (Vicsek et al., 1990 [13]) detected for DLA clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena, since the scaling behavior of our DLA clusters space corresponds to monofractal objects, being this situation remarkably noticeable in the limit of very large clusters.

Spectral and angular light-scattering from silica fractal aggregates

This work applies a new model based on the discrete dipole approximation to simulate the scattering of coherent broadband light from fixed and randomly oriented silica fractal aggregates. Two classes of aggregate morphology are considered; the standard aggregate with a single fractal dimension and superaggregates with two dimensions, both of which are generated from a Diffusion-Limited Cluster-Aggregation model. Light scattering from these aggregates is simulated over the short wave infrared to ultraviolet spectral range. We find features in the distribution of the spectral and angular scattered-intensities that do not disappear after orientation averaging and are seen for both types of aggregates. The important role played by the wavelength in q-space analysis is observed and we report the utility of a spectral q-space analysis for multi-dimensional objects like superaggregates with spectrally dependent refractive index.

Deposition of Aggregated Nanoparticles — A Theoretical and Experimental Study on the Effect of Aggregation State on the Affinity between Nanoparticles and a Collector Surface

Theoretical and experimental approaches were employed to study the effect of aggregation on the affinity between nanoparticles (NPs) and a flat surface that is quantified by the attachment efficiency. Computer simulations were used to generate virtual aggregates formed via either diffusion limited cluster aggregation or reaction limited cluster aggregation. The colloidal interactions between the simulated aggregates and a flat surface were evaluated based on the surface element integration approach. It was found that the strength of colloidal interaction for the aggregated NPs was on the same order of magnitude as those for the primary particles and was significantly weaker than that for an equivalent sphere defined by the gyration radius of the aggregate. The results from the deposition experiments using quartz crystal microbalance suggested that the attachment efficiencies (unfavorable deposition) for aggregated NPs were higher at the initial stage but later became similar to that of the primary NPs when equilibrium deposition was reached. The high initial affinity was postulated to be attributable to secondary minimum deposition. These results suggest that it is the size of the primary particles, not that of the aggregates, that determines the strength of the colloidal interaction between the aggregate and an environmental surface.

Discontinuous percolation in diffusion-limited cluster aggregation

Recently, the diffusion-limited cluster aggregation (DLCA) model was restudied as a real-world example of showing discontinuous percolation transitions (PTs). Because a larger cluster is less mobile in Brownian motion, it comes into contact with other clusters less frequently. Thus, the formation of a giant cluster is suppressed in the DLCA process. All clusters grow continuously with respect to time, but the largest cluster grows drastically with respect to the number of cluster merging events. Here, we study the discontinuous PT occurring in the DLCA model in more general dimensions such as two, three, and four dimensions. PTs are also studied for a generalized velocity, which scales with cluster size s as vs ∝ sη. For Brownian motion of hard spheres in three dimensions, the mean relative speed scales as s−1/2 and the collision rate σvs scales as ∼s1/6. We find numerically that the PT type changes from discontinuous to continuous as η crosses over a tricritical point ηc ≈ 1.2 (in two dimensions), ηc ≈ 0.8 (in three dimensions), and ηc ≈ 0.4 (in four dimensions). We illustrate the root of this crossover behavior from the perspective of the heterogeneity of cluster size distribution. Finally, we study the reaction-limited cluster aggregation (RLCA) model in the Brownian process, in which cluster merging takes place with finite probability r. We find that the PTs in two and three dimensions are discontinuous even for small r such as r = 10−3, but are continuous in four dimensions.

Fractal Self-Assembly of Single-Stranded DNA on Hydrophobic Self-Assembled Monolayers

The self-assembled structures possess superior stability, biocompatibility and mechanical strength, and their study can provide insight into the use of creating novel biomaterials. Atomic force microscopy (AFM) images of single-stranded DNA (ssDNA) nanostructures show that well-ordered organization, high homogeneity, and molecular dimensions fractal-shaped fibers formed on a gold substrate covered with self-assembled monolayers (SAMs) of 1-hexadecanethiol (HDT). The nanoscaled architectures of ssDNA on HDT/Au changed remarkably following the process of diffusion-limited cluster aggregation (DLA) over time. The ssDNA fibers prefer to form on hydrophobic SAMs instead of hydrophilic SAMs, and the ssDNA has to have complementary regions in their sequences. This method might not be used only for the construction of fractal patterns, but also for the design and fabrication of functional DNA-based, self-assembled materials that exhibit self-similarity at multiple length scales.

The fractal hologram and elucidation of the structure of liposomal carriers in aqueous and biological media

The present study deals with the physicochemical characterization (size, polydispersity, ζ-potential) of dipalmitoylphosphatidylcholine (DPPC) liposomes and DPPC:cholesterol (chol) (9:1 molar ratio) liposomes, and the determination of their fractal dimension (mass fractal (df) and surface fractal (ds)), in an aqueous (HPLC grade water) and in a biological (fetal bovine serum – FBS) medium. Dynamic, static and electrophoretic light scattering and fluorescence spectroscopy are used as experimental techniques to elucidate the structure and physicochemical parameters of liposomes in an ageing study in two different media, as well as their structural response in changes in concentration and temperature. The extended DLVO theory would be the tool to explain the phenomenology of the colloidal behavior in these systems and of their aggregation process. The fractal dimensionality of DPPC liposomes was decreased while for DPPC:cholesterol (9:1) it remained unaffected in the two dispersion media. The structure of the liposomal systems, the process kinetics, and the fractal dimension are consistent with the diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) models. On the contrary, hydrodynamic radius (Rh) was found to be stable during the variations of colloidal system conditions, especially due to concentration changes. Finally, we suggest that this study can be a rational road map to design advanced Drug Delivery nano Systems (aDDnSs) with improved pharmacokinetic profile which could be considered as crucial for their effectiveness.

Electrocoagulation versus chemical coagulation: Coagulation/flocculation mechanisms and resulting floc characteristics

Electrocoagulation (EC) and chemical coagulation (CC) are employed in water treatment for particle removal. Although both are used for similar purposes, they differ in their dosing method – in EC the coagulant is added by electrolytic oxidation of an appropriate anode material, while in CC dissolution of a chemical coagulant is used. These different methods in fact induce different chemical environments, which should impact coagulation/flocculation mechanisms and subsequent floc formation. Hence, the process implications when choosing which to apply should be significant. This study elucidates differences in coagulation/flocculation mechanisms in EC versus CC and their subsequent effect on floc growth kinetics and structural evolution. A buffered kaolin suspension served as a representative solution that underwent EC and CC by applying aluminum via additive dosing regime in batch mode. In EC an aluminum anode generated the active species while in CC, commercial alum was used. Aluminum equivalent doses were applied, at initial pH values of 5, 6.5 and 8, while samples were taken over pre-determined time intervals, and analyzed for pH, particle size distribution, ζ potential, and structural properties. EC generated fragile flocs, compared to CC, over a wider pH range, at a substantially higher growth rate, that were prone to restructuring and compaction. The results suggest that the flocculation mechanism governing EC in sweep floc conditions is of Diffusion Limited Cluster Aggregation (DCLA) nature, versus a Reaction Limited Cluster Aggregation (RLCA) type in CC. The implications of these differences are discussed.