Diffusion-limited Cluster Aggregation Research Articles

New Insights into the Formation of Aggregates of Bidisperse Nano- and Microplastics in Water Based on the Analysis of In Situ Microscopy and Molecular Simulation.

Microplastics (MPs) and nanoplastics (NPs) in water pose a global threat to human health and the environment. To develop efficient removal strategies, it is crucial to understand how these particles behave as they aggregate. However, our knowledge of the process of aggregate formation from primary particles of different sizes is limited. In this study, we analyzed the growth kinetics and structures of aggregates formed by polystyrene MPs in mono- and bidisperse systems using in situ microscopy and image analysis. Our findings show that the scaling behavior of aggregate growth remains unaffected by the primary particle size distribution, but it does delay the onset of rapid aggregation. We also performed a structural analysis that reveals the power law dependence of aggregate fractal dimension (df) in both mono- and bidisperse systems, with mean df consistent with diffusion-limited cluster aggregation (DLCA) aggregates. Our results also suggest that the df of aggregates is insensitive to the shape anisotropy. We simulated molecular forces driving aggregation of polystyrene NPs of different sizes under high ionic strength conditions. These conditions represent salt concentration in ocean water and wastewater, where the DLVO theory does not apply. Our simulation results show that the aggregation tendency of the NPs increases with the ionic strength. The increase in the aggregation is caused by the depletion of clusters of ions from the NPs surface.

Modeling Colloidal Particle Aggregation Using Cluster Aggregation with Multiple Particle Interactions.

In this study, we investigate the aggregation dynamics of colloidal silica by generating simulated structures and comparing them to experimental data gathered through scanning transmission electron microscopy (STEM). More specifically, diffusion-limited cluster aggregation and reaction-limited cluster aggregation models with different functions for the probability of particles sticking upon contact were used. Aside from using a constant sticking probability, the sticking probability was allowed to depend on the masses of the colliding clusters and on the number of particles close to the collision between clusters. The different models of the sticking probability were evaluated based on the goodness-of-fit of spatial summary statistics. Furthermore, the models were compared to the experimental data by calculating the structures' fractal dimension and mass transport properties from simulations of flow and diffusion. The sticking probability, depending on the interaction with multiple particles close to the collision site, led to structures most similar to the STEM data.

Fractal analysis on Ag2O thin film using a data-driven approach

The synthesis of fractal Ag oxide (Ag2O) on the surface of Ag thin film has been achieved at room temperature by using Synchrotron X-ray irradiation. We have performed an automated quantitative analysis of a batch of 1879 fractal Ag2O patterns in a scanning electron microscopy (SEM) image within a radius of 2000 mm outward from the center of the X-ray beam. The morphology is similar to that of the diffusion-limited cluster aggregation (DLCA) model. The fractal dimension (D) of Ag2O is between 1.7 and 1.5 from the center to the edge. The area distribution density of fractal Ag2O follows a quadratic function with radius R. It is found that the branches’ number of fractal Ag2O is a key factor affecting the fractal dimension. The more branches the fractal has, the greater the D is. This is the first time that Ag fractal has been investigated by combining automated data analysis methods with batch experimental data. This data-driven approach provides a new research perspective for rationally regulating materials’ fractal morphology and performance.

Fractal simulation of hydrophobic flocculation fragmentation and reconstruction of coal particles

Based on a diffusion limited cluster aggregation model, this study analyzed the fragmentation and reconstruction of flocs during the hydrophobic flocculation process of coal particles. The flocs gyration radius and gyration fractal dimension calculated by the program characterize the geometric size and spatial structure of the coal particle flocs, respectively. With advancing step length, the distributions of gyration radius first increased and then decreased and finally basically stabilized at approximately 1.70 ± 0.2, indicating that the reconstruction of flocs is reversible in geometric size. However, the gyration fractal dimensions first decreased and then increased and finally stabilized at 1.49, 1.63, 1.60 and 1.51 with increasing step length, showing variability. This indicated that the spatial structure of the flocs is irreversible. The above conclusions of the simulation analysis were confirmed by the floc particle size distribution curves and the image analysis of surface fractal dimensions. The study clarifies the morphological changes and fragmentation-reconstruction changes of flocs and improves the hydrophobic flocculation mechanism of coal particles.

Monitoring effects of hydrodynamic cavitation pretreatment of sodium oleate on the aggregation of fine diaspore particles through small-angle laser scattering

Hydrodynamic cavitation (HC) enhanced fine particle aggregation could be largely due to the generation of tiny bubbles and their role in bridging particles. However, the lack of adequate characterizations of aggregates severally limits our further understanding of the associated aggregation behaviors. In this study, the aggregation of fine diaspore particles was comparatively investigated in sodium oleate (NaOl) solutions with and without HC pretreatment through the small-angle laser scattering (SALS) technique in a shear-induced aggregation (SIA) system. Results showed that HC pretreatment caused the formation of bulk nanobubbles (BNBs), which significantly modified the particle interactions and thereby modified the size and mass fractal dimension (Df) of aggregates under different SIA conditions. Although HC pretreatment did not noticeably alter the gradual change trend of aggregate size and structure characteristics under specific variables, BNBs bridging facilitated the aggregation process towards the diffusion-limited cluster aggregation model, resulting in the formation of larger but looser aggregates. This effect was more pronounced under relatively high NaOl concentrations. Apart from BNBs, the aggregation was also affected by cavitation bubbles formed during shear cavitation, which was more significant under high stirring intensity conditions (i.e., 1800 rpm) than the low stirring intensity conditions (i.e., 600 rpm).

Effects of microstructure and moisture content on the radiative properties of porous films for radiative cooling

Global warming is a major concern, and active cooling technology, which consumes substantial energy, contributes to global warming. Radiative cooling (RC) is a form of passive cooling. An optically selective porous film can provide cost-effective and efficient radiative cooling. This study aims to investigate the theoretical effects of the structural parameters on the cooling performance of porous films. An improved diffusion-limited cluster aggregation (DLCA) algorithm is established to reproduce porous structures with moisture content. A combination of discrete dipole approximation and Monte Carlo method was employed to predict the structure-related solar reflectance and “sky window” emissivity. An optimal design of a porous RC film was developed. The results demonstrate that the BaSO4 porous film can achieve high solar reflectance (∼ 97%), high “sky window” emissivity (∼ 99%), and a net cooling power of 102 W/m2 during the day. In particular, the effect of moisture content on the cooling performance of the porous RC film was analyzed. Moisture content enhances the cooling performance at night but decreases it during the daytime. The results provide guidance for designing optically selective porous films for radiative cooling.

Small angle X-ray scattering of particle growth and structure in spray flame synthesis

Customized metal oxide nanoparticles are on increasing demand due to their high specific surface area coupled with their material properties. Spray flame synthesis (SFS) is able to produce such particles in high quantity and purity. However, the turbulent flame including droplets is a complex system. The analysis of the product is challenging due to the broad size distribution of the aggregated primary particles. Thus, this study combines small angle X-ray scattering (SAXS) with transmission electron microscopy (TEM) in order to gain valuable information about primary particle sizes and fractal properties. Insights about the particle formation is obtained by comparing the SAXS data of titanium oxide and iron oxide particles produced with a variety of precursors in different concentrations using two burner setups. Remarkably, all presented systems show a size distribution of the primary particle with two size fractions. The differences in the sizes and consequences for the gained information about the fractal dimensions are discussed in detail. This includes the overlap of scattering information and resolution limits. All particle structures include small particles of 5–8 nm pointing to a gas-to-particle pathway. The large particle fraction ranges from 35 to 320 nm depending on precursor composition and concentration. Their formation is likely linked to hydrolysis reactions of the precursor in spray droplets. For the aggregates, the fractal dimension of mass with values 1.6–1.8 point to diffusion-limited cluster aggregation which is typical for flame-made products. The evaluation of in situ studies with synchrotron radiation confirms the gas-to-particle pathway.

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.

Toward a Realistic Model of Diffusion-Limited Aggregation: Rotation, Size-Dependent Diffusivities, and Settling.

In this Brownian dynamics simulation study on the formation of aggregates made of spherical particles, we build on the well-established diffusion-limited cluster aggregation (DLCA) model. We include rotational effects, allow diffusivities to be size-dependent as is physically relevant, and incorporate settling under gravity. We numerically characterize the growth dynamics of aggregates and find that their radius of gyration, R g, grows approximately as R g ∼ t 1.02 for classical DLCA but slows to an approximate growth rate of R g ∼ t 0.71 when diffusivity is size-dependent. We also analyze the fractal structure of the resulting aggregates and find that their fractal dimension, d, decreases from d ≈ 1.8 for classical DLCA to d ≈ 1.7 when size-dependent rotational diffusion is included. The addition of settling effects further reduces the fractal dimension observed to d ≈ 1.6 and appears to result in aggregates with a vertical extent marginally smaller than their horizontal extent.

Evaluation of properties and structural transitions of Poly (2-acrylamido-2-methyl-1-propanesulfonic acid-co-acrylonitrile) / β-Galactosidase complex coacervates: effects of pH and aging

The coacervates of the Poly (2-acrylamido-2-methyl-1-propanesulfonic acid-co-acrylonitrile) / β-Galactosidase complex are characterized using several techniques (Turbidimetry, dynamic and static light scattering (DLS / SLS), optical microscopy, image dynamic light scattering (IDLS), and ultra-small angles light scattering (USALS)). Turbidity and SLS were used to accurately determine the critical pHs of complex formation (pHc, pHϕ1, pHopt, and pHϕ2), DLS was used to probe the microscopic structure of coacervate droplets rich in proteins and polyelectrolytes in liquid-liquid phase separation, and IDLS and USALS have been introduced to better understand, during aging, the topology of the network formed of materials based on fractals in the dense phase. Observations of the architecture, the spatial inhomogeneity, and the size distributions of liquid complex coacervate droplets and fractal solid precipitates, were performed by optical microscopy. The pair-distance distribution function, P(r), presented in this review, is a new methodology of calculus for determining with precision the radius of gyration Rg of droplets coacervates. These techniques show that aging improves the stability of swollen condensates, the growth of the coacervate droplets is due to the attractive electrostatic interactions within the complex and does not undergo Ostwald ripening, except for the case of pHopt and having fractal dimensions Df generated by diffusion-limited cluster aggregation (DLCA).

All-day effective radiative cooling by optically selective and thermally insulating mesoporous materials

Due to serious solar absorption and poor thermal insulation on the cold side, current daytime radiative cooling falls far short of the theoretical potential. The mesoporous film can be used for both thermal insulation and optical selection. In this study, the radiative properties of infrared transparent mesoporous materials are investigated. The Diffusion Limited Cluster Aggregation algorithm is employed to reproduce the micro-structures of the mesoporous materials. The structure-dependent normal hemispherical transmittance is predicted by the combination of discrete dipole approximation and Monte Carlo method. The effects of material type and structure characteristics (particle size, volume fraction and cover thickness) on the infrared transmittance and all-day radiative cooling performance are quantified. The results show that the polyethylene (PE) aerogel achieves the best thermal insulation performance and good spectral selectivity. It can work as a thermally insulating barrier and an infrared transparent window for the radiative cooling surface. By integrating with PE aerogel, the radiative cooling surface can enable the passive cooling up to 13 K below the ambient temperature during the day and 15 K below the ambient temperature during the night at a wind speed of 2.8 m/s. This work provides an optimal design of optically selective and thermally insulating mesoporous materials in passive all-day radiative cooling applications.

A semi-empirical correction for the Rayleigh-Debye-Gans approximation for fractal aggregates based on phasor analysis: Application to soot particles

The Rayleigh Debye-Gans approximation for Fractal Aggregates (RDG-FA) is commonly used for the evaluation of the radiative properties of fractal aggregates of nanometer-scale nearly spherical particles as soot particles. The cost of its simplicity, however, is the precision of the aggregate cross sections when the refractive index deviates from unity and when the aggregate’s spheres, or monomers, are not sufficiently small compared to the wavelength. While correction factors have been highlighted before, their physical origin is not clear and no universal correction factors are proposed. The present study develops an approach based on phasor analysis of the aggregate’s internal electric field rigorously determined by the discrete dipole approximation. Aggregates representative of the Diffusion Limited Cluster Aggregation (DLCA) regime having a fractal dimension of Df=1.78 are considered as representative of a soot aggregate. The results reveal that correction factors to the RDG-FA for forward scattering (A) and the absorption cross section (h) are due to a competition between internal-field hot-spots caused by point contact between the spherical monomers and a decrease of the field amplitude as the field propagates through the aggregate. Both phenomena are neglected in the RDF-FA by definition. The absorption phenomenon explains the aggregate-size dependence of A and h. These effects are then studied as the aggregate size varies according to the number of monomers Nm ranging from 10 to 1000, as the monomer radius varies from Rm=5nm - 30nm, and as the wavelength varies from λ=266nm - 1064nm. Both constant and wavelength dependent refractive indices for organic, graphitic, and amorphous soot are considered. Finally, a semi-empirical model is proposed intended to correct the RDG-FA theory based on the analysis.

Grand canonical Monte Carlo simulations of hydrogen adsorption in carbon aerogels

Hydrogen storage plays a fundamental role in the future hydrogen energy system, and carbon aerogel is one of the most potential hydrogen storage materials because of its high gravimetric and volumetric density on hydrogen adsorption. In this paper, the amorphous structure of carbon, obtained by a numerical simulation process by using the molecular dynamic and Monte Carlo methods, as well as the primary unit method, was intercepted as a sphere structure for numerical annealing to build a carbon nanosphere, which serves as the basic unit to reconstruct the carbon aerogel's skeleton by the Diffusion Limited Cluster Aggregation (DLCA) method. The hydrogen adsorption in carbon aerogel was simulated by using the self-coding parallel grand canonical Monte Carlo (GCMC) method. The influences of particle diameter, density, temperature, pressure, and specific surface area on the hydrogen adsorbing capacity in carbon aerogel were analyzed in detail. The results showed that the carbon aerogel's hydrogen storage capacity with a specific surface area of 2680 m2/g could reach 4.52 wt % at 77 K and 3.0 MPa.

Physiochemical Changes to TTCF Ensilication Investigated Using Time-Resolved SAXS

Successful eradication or control of prevailing infectious diseases is linked to vaccine efficacy, stability, and distribution. The majority of protein-based vaccines are transported at fridge (2–8 °C) temperatures, cold chain, to retain potency. However, this has been shown to be problematic. Proteins are inherently susceptible to thermal fluctuations, occurring during transportation, causing them to denature. This leads to ineffective vaccines and an increase in vaccine-preventable diseases, especially in low-income countries. Our research utilises silica to preserve vaccines at room temperature, removing the need for cold chain logistics. The methodology is based upon sol–gel chemistry in which soluble silica is employed to encapsulate and ensilicate vaccine proteins. This yields a protein-loaded silica nanoparticle powder which is stored at room temperature and subsequently released using a fast chemical process. We have previously shown that tetanus toxin C fragment (TTCF) ensilication is a diffusion-limited cluster aggregation (DLCA)-based process using time-resolved small-angle x-ray scattering (SAXS). Here, we present our expanded investigation on the modularity of this system to further the understanding of ensilication via time-resolved SAXS. Our results show that variations in the ensilication process could prove useful in the transition from batch to in-flow manufacturing of ensilicated nanoparticles.

Fractal dimension of diffusion-limited aggregation clusters grown on spherical surfaces.

In this work we study the fractal properties of diffusion-limited aggregation (DLA) clusters grown on spherical surfaces. Diffusion-limited aggregation clusters, or DLA trees, are highly branched fractal clusters formed by the adhesion of particles. In two-dimensional media, DLA clusters have a fractal dimension D_{f}=1.70 in the continuous limit. In some physical systems, the existence of characteristic lengths leads us to model them as discrete systems. Such characteristic lengths may result also from limitations in measuring instruments, for example, the resolution of biomedical imaging systems. We simulate clusters for different particle sizes and examine the influence of discretization by exploring the systems in terms of the relationship between the particle size r and the radius of the sphere R. We also study the effect of stereographic projection on the fractal properties of DLA clusters. Both discretization and projection alter the fractal dimension of DLA clusters grown on curved surfaces and must be considered in the interpretation of photographic biomedical images.

Analysis of the fractal properties of silica aerogels using diffusion‐limited aggregation

AbstractSilica aerogels are highly porous solids with very low densities and thermal conductivities. Their high porosity results in a fractal morphology which has a strong influence on mechanical properties. In this work, the diffusion‐limited cluster aggregation (DLCA) method is implemented to model silica aerogel aggregates. A preliminary model based on this approach demonstrates good agreement with experimental data [1]. The influence on the fractal properties of different input parameters as for example the particle size is investigated. Moreover, the resulting geometries are compared to fractal features of silica aerogels determined by experimental data from small angle X‐ray scattering (SAXS). The mechanical response of these aggregation models is analyzed by a finite element analysis (FEA) for the generated representative volume elements (RVE). The effect of varying densities on the mechanical properties, for e.g., Young's modulus, is further elucidated.

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.

Heat conduction mechanism in silica aerogel skeleton

In order to study the specific heat conduction process of silica aerogels, a three-dimensional random fractal skeleton model of aerogels was generated by using the diffusion-limited cluster aggregation (DLCA) method to simulate the gel process. Based on the idea of finite volume method, a numerical model of heat conduction in porous framework was established and verified. The three-dimensional temperature field and apparent thermal conductivity of the skeleton were calculated. The results show that when the initial particle concentration is 0.0764 ~ 0.191, the fractal dimension range of the skeleton model is 2.0 ~ 2.45, which is consistent with the measured value. However, in the plane perpendicular to the heat flow direction, the particle temperature is not exactly the same, which can be approximately described by normal distribution. The apparent thermal conductivity of the skeleton is three orders of magnitude lower than that of the bulk material, which can be attributed to its open form network structure.

Ensilicated tetanus antigen retains immunogenicity: in vivo study and time-resolved SAXS characterization

Our recently developed ensilication approach can physically stabilize proteins in silica without use of a pre-formed particle matrix. Stabilisation is done by tailor fitting individual proteins with a silica coat using a modified sol-gel process. Biopharmaceuticals, e.g. liquid-formulated vaccines with adjuvants, frequently have poor thermal stability; heating and/or freezing impairs their potency. As a result, there is an increase in the prevalence of vaccine-preventable diseases in low-income countries even when there are means to combat them. One of the root causes lies in the problematic vaccine ‘cold chain’ distribution. We believe that ensilication can improve vaccine availability by enabling transportation without refrigeration. Here, we show that ensilication stabilizes tetanus toxin C fragment (TTCF), a component of the tetanus toxoid present in the diphtheria, tetanus and pertussis (DTP) vaccine. Experimental in vivo immunization data show that the ensilicated material can be stored, transported at ambient temperatures, and even heat-treated without compromising the immunogenic properties of TTCF. To further our understanding of the ensilication process and its protective effect on proteins, we have also studied the formation of TTCF-silica nanoparticles via time-resolved Small Angle X-ray Scattering (SAXS). Our results reveal ensilication to be a staged diffusion-limited cluster aggregation (DLCA) type reaction. An early stage (tens of seconds) in which individual proteins are coated with silica is followed by a subsequent stage (several minutes) in which the protein-containing silica nanoparticles aggregate into larger clusters. Our results suggest that we could utilize this technology for vaccines, therapeutics or other biopharmaceuticals that are not compatible with lyophilization.

Morphological characterization of particles emitted from monopolar electrosurgical pencils

Monopolar electrosurgical pencils are used extensively in surgical operations. With such pencils, electric current passes to the tissue, and as such, electrosurgical pencil operation generates a significant amount of thermal energy, which in turn leads to the generation of electrosurgical smoke (ES). The health risks of ES are dependent on the size distributions as well as the morphologies of the produced particles. To better characterize such particles, in this study we utilized (1) differential mobility analysis with a condensation particle counter (DMA-CPC), (2) an aerodynamic particle spectrometer (APS), (3) DMA-transmission electron microscopy analysis (DMA-TEM), and (4) DMA-aerosol particle mass analysis (DMA-APM) to examine the size distribution and morphologies of particles produced during simulated operation of an electrosurgical pencil (Neptune E-SEP, Stryker Corporation) on bovine, porcine, and ovine tissue. We find that under a variety of operating conditions, ES particles are broadly distributed, with a mode mobility diameter in the 150–200 nm size range, and concentrations well above background levels in the 50 nm–5 μm size range. We also find that the “cut” mode of monopolar electrosurgical pencil operation generates higher particle concentrations than the “coagulate” mode, and that increasing the maximum applied power from 20 W to 50 W also increases ES particle concentrations. TEM images of mobility selected particles reveal both spherical particles and fractal-like agglomerates in ES; these different particle types are produced under the same operation conditions leading to an externally-mixed, morphologically-complex aerosol. Quantitative analysis of the agglomerate images revealed that agglomerates have an average fractal dimension near 1.93 and that they are structurally similar to agglomerates expected from a diffusion limited cluster aggregation growth mechanism. Despite the presence of both spheres and agglomerates, DMA-APM analysis reveals that all particles have effective densities in the 1000–2000 kg m−3 range, suggesting that they likely contain inorganic components. Finally, we determined that the collection efficiency of the ES capture suction unit attached to the electrosurgical pencil was >95% for particles in the 50–400 nm mobility diameter range.