Diffusion-limited Cluster-cluster Aggregation Research Articles

Deep reinforcement learning for microstructural optimisation of silica aerogels

Silica aerogels are being extensively studied for aerospace and transportation applications due to their diverse multifunctional properties. While their microstructural features dictate their thermal, mechanical, and acoustic properties, their accurate characterisation remains challenging due to their nanoporous morphology and the stochastic nature of gelation. In this work, a deep reinforcement learning (DRL) framework is presented to optimise silica aerogel microstructures modelled with the diffusion-limited cluster–cluster aggregation (DLCA) algorithm. For faster computations, two environments consisting of DLCA surrogate models are tested with the DRL framework for inverse microstructure design. The DRL framework is shown to effectively optimise the microstructure morphology, wherein the error of the material properties achieved is dependent upon the complexity of the environment. However, in all cases, with adequate training of the DRL agent, material microstructures with desired properties can be achieved by the framework. Thus, the methodology provides a resource-efficient means to design aerogels, offering computational advantages over experimental iterations or direct numerical solutions.

Analysis of the microstructural connectivity and compressive behavior of particle aggregated silica aerogels

AbstractPorous media such as aerogels can exhibit unique properties including low thermal conductivity, low bulk density, and low sound velocity. However, the limited mechanical properties of aerogels restrict their widespread application. This study focuses on understanding the mechanical behavior of aggregated silica aerogels by investigating their microstructural connectivity and densification mechanisms under uniaxial compression. The interparticle connectivity is generated using the diffusion‐limited cluster–cluster aggregation (DLCA) algorithm, and the particle connections are modeled by beam elements that account for contact interaction. The mechanical response of representative volume elements (RVEs) is analyzed in both linear and nonlinear regimes while applying periodic boundary conditions. The model is correlated with experimental compression test data to validate the simulation results. With increasing compressive strain, load transitions between multiple backbone paths appear in the network structure. Thus, the simulation model provides insight into the compression process. Moreover, the simulation model enables the examination of the influence of various model parameters and facilitates the evaluation of the power–law relationship between the elasticity modulus and porosity of aerogels.

Aggregation-induced enhancements in aerosol absorption and scattering across the black-brown continuum

Global radiative forcing by carbonaceous aerosols is one of the largest sources of uncertainty in current climate models. The radiative impacts of brown carbon (BrC), a type of amorphous organic carbonaceous aerosol formed in biomass burning events, such as wildfires, remains poorly understood. Recently, the aggregation of spheres (monomers) of BrC was observed in wildfire smoke from various parts of the world. Aggregation could alter the optical properties and direct radiative forcing of BrC, yet very little is known about this phenomenon. This study improves upon the spectral optical properties of BrC aggregates observed in past field studies.We are motivated by the framework presented by Saleh et al. (2020) for the optical classification of carbonaceous particles across the black-brown continuum. Here, we simplify Saleh et al.'s BrC categorization into two sub-classes: dark brown carbon (d-BrC) and weakly-absorbing brown carbon (w-BrC). We calculate and compare the mass absorption cross-section (MAC), mass scattering cross-section (MSC), single scattering albedo (SSA), and asymmetry parameter (g) of d-BrC and w-BrC and determine their absorption and scattering enhancements due to aggregation. Polydisperse diffusion-limited cluster-cluster aggregation (p-DLCA) simulations generated 90 aggregates of varying monomer diameters, and discrete dipole approximation (DDA) was used to calculate optical properties of these aggregates at relevant refractive indices, monomer diameters, and incident wavelengths.We find that optical properties of BrC aggregates are more sensitive to the monomer number and mean diameter than to polydispersity. d-BrC has almost twice the MAC of w-BrC at 350 nm, but w-BrC has MSC values almost double that of d-BrC. Both MAC and MSC for both types of aerosol decrease with wavelength. Aggregation enhances optical properties, with smaller size parameters and lower imaginary part of the complex refractive index of aggregates resulting in stronger absorption and scattering.

Data‐driven inverse design and optimisation of silica aerogel model networks

AbstractSilica aerogels are highly porous ultralight materials with extremely low density and thermal conductivity. These exceptional properties of silica aerogels are often accounted to microstructure morphology, thus making them of keen research interest for analysing their structure‐property relationships. The classical approach for this involved the microstructure modelling of the silica aerogels with aggregation‐based modelling algorithm viz., diffusion‐limited cluster‐cluster aggregation (DLCA) and then performing finite element method (FEM) on the generated representative volume element (RVEs). However, the process often requires large computation time and resources.The objective of this work was thus to introduce an artificial intelligence approach based on neural networks and reinforcement learning to eliminate the necessity of generating and simulating 3D silica aerogel models for predicting their structural and mechanical properties. To this end for the forward prediction of the elastic modulus and fractal dimension of the silica aerogels from DLCA parameters, an artificial neural network was developed. Furthermore, to reverse engineer the material and perform inverse material design, a reinforcement learning framework was developed, that is shown to have learned to determine appropriate DLCA model parameters as actions for a desired fractal dimension and elastic modulus.

Colloidal Stability and Aggregation Mechanism in Aqueous Suspensions of TiO2 Nanoparticles Prepared by Sol-Gel Synthesis.

Understanding the colloidal stability and aggregation behavior of TiO2 nanoparticles in aqueous suspension is a prerequisite to tune supracolloidal structure formation. While the aggregation mechanism for dried TiO2 nanopowders is well documented, there is still work to be done to understand TiO2 nanoparticle aggregation in suspension. Therefore, this work focuses on the colloidal stability and aggregation mechanism of TiO2 nanoparticle aqueous suspensions prepared using a straightforward one-step sol-gel-based approach over a concentration range of 0.5-5 wt %. Fully crystalline nanoparticles consisting primarily of anatase were obtained. After assessing the colloidal stability of the as-prepared suspensions, small-angle X-ray scattering coupled with fractal analysis was carried out. This analysis showed, for the first time, how the TiO2 nanoparticle aggregation mechanism─predicted by the diffusion limited cluster-cluster aggregation (DLCA) and diffusion limited particle-cluster aggregation (DLA) theories─depends directly on the starting concentration in the aqueous suspensions. We found that concentrated suspensions favored DLA, while dilute suspensions tend to follow the DLCA mechanism. The effect of the aggregation mechanism on the aggregate shape is also discussed.

Predictive modeling and simulation of silica aerogels by using aggregation algorithms

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 their mechanical properties. The geometric structure of silica aerogels can be described by diffusion‐limited cluster‐cluster aggregation (DLCA) models.In this work, the DLCA method is implemented to model silica aerogel networks and investigate the influence of different input parameters, as for example, varying particle sizes on their fractal properties. The resulting model networks are characterized for their fractal properties and compared with the small angle X‐ray scattering (SAXS) results of silica aerogels. Furthermore, their mechanical properties are simulated using the finite element method. There, the effect of varying densities on their mechanical properties is examined. In addition, an artificial neural network (ANN) is trained based on the input parameters of the DLCA algorithm to predict the fractal properties of the silica aerogel model. By inverting the ANN it is possible to identify the necessary inputs to generate desired fractal morphologies with specific mechanical properties.

A Monte Carlo Simulation Study on: Deposition, Diffusion, and Aggregation

In this paper we present a Monte Carlo simulation program to implement a single model: deposition, diffusion, and aggregation (DDA). By using the simulation program, we show in the following that the DDA model generates a wide variety of fractal structures characteristic of different models such as diffusion-limited aggregation (DLA) or cluster-cluster aggregation (CCA), but such DLA and CCA models do not incorporate the possibility of cluster-mass dependent deposition. Starting from those kernels, aggregation laws to describe the interaction between free and deposited clusters were proposed and a simple cluster-mass dependent deposition law was employed. The simulation results are then discussed in the frame of the relative strength of parameters.

Disk-Ring Deposition in Drying a Sessile Nanofluid Droplet with Enhanced Marangoni Effect and Particle Surface Adsorption.

The present study is to explore the central particle deposition from drying a sessile nanofluid droplet experimentally and theoretically. Normally, a pinned colloidal droplet dries into a coffee-ring pattern as a result of moving the particles to a three-phase line by the radial direction capillary flow. However, the strong evaporation can generate the nonuniform temperature at the evaporating droplet interface and the droplet periphery temperature is higher than that close to the droplet centerline. The induced Marangoni flow would reversibly transport the particles at the periphery toward the centerline. We have thus designed the experiments to increase the droplet evaporation rate in vacuum conditions and accordingly to enhance the Marangoni effect. We have observed distinguishable disk deposition inside the outer coffee ring. A three-dimensional diffusion-limited cluster-cluster aggregation Monte Carlo model has been developed to simulate the deposition process. With modeling the Marangoni effect, particle adsorption at the liquid-air interface and particle aggregation behaviors, the formation of the disk pattern inside a coffee ring has been simulated. The qualitative agreement has been found in the comparison of local deposition distribution between the related experiment and simulation.

Three-dimensional tomography reveals distinct morphological and optical properties of soot aggregates from coal-fired residential stoves in China

Electron tomography (ET) is used to reconstruct the exact 3-dimensional morphologies of fractal-like soot aggregates sampled from a household heating stove commonly used in China. Conventional ET techniques suffer from “the missing wedge” problem caused by unreachable tilt angles, leading to noisy reconstructed tomograms. We overcame this problem by implementing a high-resolution object-edge identification method coupled with a novel voxel-filling algorithm to improve the reconstruction quality. Our reconstructed micron-length aggregates highlight the local non-idealities present throughout a particle's surface; these characteristics are almost impossible to account for in existing computational simulation exercises. Q-space analysis predicts the fractal dimension of our ET reconstructed aggregates to be in the range between 2.2 and 2.6, which deviates significantly from the universal value of 1.8 obtained using the widely adopted diffusion limited cluster-cluster aggregation (DLCA) model. The optical properties of our ET reconstructed aggregates are compared with those built with a DLCA model and equivalent spheres . The most striking optical characteristics of the ET reconstructed aggregates are their wavelength invariant mass absorption cross-sections of ~3.5 m2/g and single scattering albedo of ~0.5. The sample size investigated in this work is constrained by the extremely time-consuming object-edge identification process of electron tomography. This issue necessitates the development of more efficient computer vision algorithms for future research.

Modeling the formation of soil microaggregates

The functions of soils are intimately linked to its aggregated structure. Microaggregates formed during pedogenesis from a vast variety of mineral, organic, and biotic materials are the smallest conceivable compounds at the basis of soil structural hierarchy. Qualitative hypotheses and concepts on how aggregates form are quite elaborate, but the consistent quantitative application within a mechanistic and physically rigorous framework is still missing. This is partly caused by the fact that such an endeavor requires the combination of synergistic concepts on the transport of particles and their interactions affected by shape, size, and surface properties in aqueous suspension. Here we present a novel quantitative approach for the formation of soil microaggregates in silico that integrates diffusion-limited cluster-cluster aggregation with a probabilistic attachment following the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of particle interactions. To represent universal mineral shapes found in soils, we implemented spherical, plate-like as well as rod-like particle morphologies inspired by weathered silicates, secondary clay minerals and pedogenic iron oxides. In this way, we developed a model that produces an explicit three-dimensional structure of aggregates emerging from hetero- as well as homo-aggregation in response to the chemical milieu. We then exploited the 3D morphology to assess functional properties of aggregates exemplified with the water retention curve and pore size distribution.

Cluster–cluster aggregation with mobile impurities

We considered the diffusion-limited cluster–cluster aggregation (DLCA) model in the presence of inert template (mobile impurities) for the simulation of mesoporous materials obtained through sol–gel processes. A computer algorithm based on the off-lattice version of the two-dimensional DLCA model with moving impurities is introduced. If the density of monomers is large enough, a porous matrix results at the end of the aggregation mechanism. Impurities are removed at the final stage of the simulation, assuming that the porous structure is not altered as in some experiments. We are interested in the modification of the resulting porous structure due to the presence of moving inert impurities during aggregation. The resulting porous material consists of a homogeneous structure of interconnected fractal clusters. Such structure is characterized by computing the correlation length and the fractal dimension of these clusters. The numerical analysis of the pore size distribution reveals a strong dependence with the density and sizes of mobile impurities. Compared to the DLCA model, the curve distribution becomes bimodal when impurities are introduced, i.e., it appears a first maximum at small pore sizes (of the order of the monomer dimension), and a second maximum around the impurity size. For large monomer densities the amplitude of the peak around the impurity size becomes larger than the peak of the smallest pore size.

Numerical modeling of the gas-contributed thermal conductivity of aerogels

Due to the complex microstructure in aerogels and the intricate heat transfer mechanism of solid-gas coupling heat conduction, modeling of the gas-contributed thermal conductivity of this type of material is quite difficult. The present work introduces a novel numerical methodology for computing the gas-contributed thermal conductivity of aerogels by analyzing their microstructural characteristics and heat transfer mechanism of the thermal coupling between the gas phase and the solid backbone of the system. Specifically, structures of aerogels are reconstructed by an improved three-dimensional diffusion-limited cluster-cluster aggregation (DLCA) method, and the contribution of the solid-gas coupling heat transfer to the gas-contributed thermal conductivity of aerogels is quantified. The present numerical model is fully validated by the available experimental data for different aerogels with porosity ranging from 78% to 97.7%. The proposed numerical method is flexible and versatile because it is capable to account for both the geometrical and topological details of the aerogel structure.

Computer-generated mesoporous materials and associated structural characterization

This study aims to computationally generate and fully characterize realistic three-dimensional mesoporous materials. Notably, a new algorithm reproducing gas adsorption porosimetry was developed to calculate the specific surface area and pore size distribution of computer-generated structures. The diffusion-limited cluster-cluster aggregation (DLCCA) method was used to generate point-contact or surface-contact mesoporous structures made of monodisperse or polydisperse spherical particles. The generated structures were characterized in terms of particle overlapping distance, porosity, specific surface area, interfacial area concentration, pore size distribution, and average pore diameter. The different structures generated featured particle radius ranging from 2.5 to 40 nm, porosity between 35 and 95%, specific surface area varying from 35 to 550 m2/g, and average pore diameter between 3.5 and 125 nm. The specific surface area and pore size distribution of computer-generated mesoporous materials were in good agreement with experimental data reported for silica aerogels. Finally, widening the particle size distribution and increasing the particle overlapping were shown to strongly decrease the specific surface area and increase the average pore size of the mesoporous structures. The developed computational tools and methods can accelerate the discovery and optimization of mesoporous materials for a wide range of applications.

Aggregate shape determination via light scattering by aligned and randomly oriented polydisperse aggregates

We present calculations of light scattered by simulated aligned and randomly oriented fractal aggregates of touching spheres. The alignment by an applied electric field is in the direction yielding the minimum energy associated with the polarizability of the aggregate. This direction is also within a few degrees of the direction associated with the smallest inertial eigenvalue. Aggregates were generated to have a fractal dimension of 1.78 (characteristic of diffusion–limited cluster-cluster aggregation) and to simulate the range of aggregate sizes (30 to 2000) and size distributions for post-flame generated soot by a range of hydrocarbon fuels. More nearly monodisperse aggregates were also generated to simulate the size distributions obtained via mobility or mass classification. We show that a ratio of slopes computed from small angle light scattering intensities (Guinier plots) is related to the shape parameter A31, which is the ratio of the largest to the smallest principle radii of gyration of the inertia tensor. A geometric interpretation of the overall shape is presented based on the semi-axes of an ellipsoid. Results on the correlation between the maximum structure factor ratio {S(q)}a/ {S(q)}r for the monodisperse and polydisperse clusters and the average value of A31 indicate that light scattering measurements in the q range of fractal behavior would also be feasible for shape characterization. Our calculations indicate that light scattering measurements have a good potential for characterizing aggregate shape with an advantage of being more sensitive to shape than mobility measurements.

Kinetic percolation.

We demonstrate that kinetic aggregation forms superaggregates that have structures identical to static percolation aggregates, and these superaggregates appear as a separate phase in the size distribution. Diffusion limited cluster-cluster aggregation (DLCA) simulations were performed to yield fractal aggregates with a fractal dimension of 1.8 and superaggregates with a fractal dimension of D=2.5 composed of these DLCA supermonomers. When properly normalized to account for the DLCA fractal nature of their supermonomers, these superaggregates have the exact same monomer packing fraction, scaling law prefactor, and scaling law exponent (the fractal dimension) as percolation aggregates; these are necessary and sufficient conditions for same structure. The size distribution remains monomodal until these superaggregates form to alter the distribution. Thus the static percolation and the kinetic descriptions of gelation are now unified.

Numerical predictions of thermal conductivities for the silica aerogel and its composites

In the present paper, two kinds of microstructures are reconstructed for silica aerogels by diffusion-limited cluster-cluster aggregation (DLCA) method and open-cell structure generation method. The discrete ordinate method is adopted to solve radiative transfer equation, and the lattice Boltzmann method (LBM) is adopted to solve the conduction-radiation equation to predict the effective thermal conductivity considering the combined contribution of conduction and radiation. The partial bounce back scheme for thermal LBM is extended to consider the thermal contact resistance between two contact components with different thermal conductivity in aerogels. To validate the accuracy of the present model, some corresponding experimental measurements based on Hot Disk method are conducted. The results show that: the open-cell structure is more suitable for the real aerogel microstructure than DLCA structure; the effective thermal conductivity of the pure aerogel increases rapidly with temperature and is greatly suppressed if additives are doped; the Rosseland equation will over-predict the effective thermal conductivity of pure aerogels, especially at high temperature, but it can be applied for aerogel composites if the optical thickness assumption is satisfied; the thermal contact resistance in aerogels has a significant influence on their effective thermal conductivity, and a larger thermal contact resistance leads to a smaller effective thermal conductivity.

Scaling law, fractal analysis and rheological characteristics of physical gels cross-linked with sodium trimetaphosphate

The scaling behavior and fractal analysis of basil seed gum (BSG) cross-linked with sodium trimetaphosphate (STMP) have been investigated by rheological small amplitude oscillatory shear measurements. Storage modulus and critical strain (γo) of the gels exhibited power law relationships with BSG concentration. Based on the power-law exponent values, the fractal dimension (df) of gels was estimated using scaling models, revealed the weak-link regime of BSG. The df values lied well within the range of fractal dimension values (1.5–2.8) reported for protein gels. However, they slightly differed from df for diffusion-limited and reaction limited cluster-cluster aggregation processes. Stress sweep test was shown that STMP addition to BSG made a stronger gel than that of BSG lacking STMP. Mechanical spectrum of gels was also revealed that adding STMP can improve the elasticity of gels. BSG had a tan δ of >0.1, indicating paste-like weak gel, while tan δ of BSG-STMP has approached to 0.1 exhibited the character of a cross-linked network near to “true gel”. BSG-STMP was also recognized as a thermo-reversible physical gel, which gelation and thermal properties did not affect by STMP. Therefore, the scaling behavior can be applied for hydrocolloids gels to extract structural information through rheological measurements. Moreover, the rheological characteristics of BSG-STMP showed it can be used as a proper hydrogel in food and pharmaceutical applications.

Erratum: "Simulation on the aggregation process of spherical particle confined in a spherical shell"

The aggregation process of spherical particles confined in a spherical shell was studied by using a diffusion-limited cluster–cluster aggregation (DLCA) model. The influence of geometrical confinement and wetting-like properties of the spherical shell walls on the particle concentration profile, aggregate structure and aggregation kinetics had been explored. The results show that there will be either depletion or absorption particles near the shell walls depending on the wall properties. It is observed that there are four different types of density distribution which can be realized by modifying the property of the inner or outer spherical shell wall. In addition, the aggregate structure will become more compact in the confined spherical shell comparing to bulk system with the same particle volume fraction. The analysis on the aggregation kinetics indicates that geometrical confinement will promote the aggregation process by reducing the invalid movement of the small aggregates and by constraining the movement of those large aggregates. Due to the concave geometrical characteristic of the outer wall of the spherical shell, its effects on the aggregating kinetics and the structure of the formed aggregates are more evident than those of the inner wall. This study will provide some instructive information of controlling the density distribution of low-density porous polymer hollow spherical shells and helps to predict gel structures developed in confined geometries.

Simulation on the aggregation process of spherical particle confined in a spherical shell

The aggregation process of spherical particles confined in a spherical shell was studied by using a diffusion-limited cluster–cluster aggregation (DLCA) model. The influence of geometrical confinement and wetting-like properties of the spherical shell walls on the particle concentration profile, aggregate structure and aggregation kinetics had been explored. The results show that there will be either depletion or absorption particles near the shell walls depending on the wall properties. It is observed that there are four different types of density distribution which can be realized by modifying the property of the inner or outer spherical shell wall. In addition, the aggregate structure will become more compact in the confined spherical shell comparing to bulk system with the same particle volume fraction. The analysis on the aggregation kinetics indicates that geometrical confinement will promote the aggregation process by reducing the invalid movement of the small aggregates and by constraining the movement of those large aggregates. Due to the concave geometrical characteristic of the outer wall of the spherical shell, its effects on the aggregating kinetics and the structure of the formed aggregates are more evident than those of the inner wall. This study will provide some instructive information of controlling the density distribution of low-density porous polymer hollow spherical shells and helps to predict gel structures developed in confined geometries.

Choice of appropriate aggregation radius for the descriptions of different properties of the nanofluids

Nanofluids with suspensions containing nanoparticles, have been considered to have great potential in the application of energy conversion, chemical technology or heat transfer enhancement. Due to the high surface energy, nanoparticles in nanofluid tend to form large secondary aggregates. The aggregation and the size increase could lead to significant change in various physical properties of the suspension. It is well known that many kinds of equivalent radii can be potentially employed in the description of the particle aggregates, such as hydrodynamic radius (Rh), gyration radius (Rg) and smallest sphere enclosing radius (Rs) etc. However, in most of previous study, only hydrodynamic radius was used to study the effect of the aggregation on the properties of the nanofluids. Systematic study on the appropriate choice of the equivalent radii for the description of the different properties of the nanofluids, is rare. In this study, the three representative equivalent radii of nanoparticle aggregates, Rh, Rg and Rs, were studied. It was found that for both diffusion limited cluster–cluster aggregation (DLCA) and reaction limited cluster–cluster aggregation (RLCA), the general sequence is Rh<Rg<Rs. The three equivalent radii were correlated with each other by Monte Carlo method using an off-lattice cluster–cluster aggregation algorithm. The relationship is useful because hydrodynamic radius can be obtained experimentally from light scattering technique, while the other two are difficult to obtain experimentally. In our study, based on hydrodynamic radius obtained by DLS method, the other two equivalent radii were successfully obtained based on the proposed relationship. By comparing the experimental results with theoretical prediction, it was found that Rh, Rg and Rs showed the better accuracy when predicting viscosity, thermal conductivity and absorption coefficient, respectively. Based on these findings, in the last part, we propose a criterion for the choice of appropriate aggregation radii in predicting different physical properties of nanofluid. Our study is expected to provide a valuable guidance for the study of the effect of particle aggregation on the various properties of the nanofluids.