Fractal-like Aggregates: Relation between Morphology and Physical Properties

Conformations of a highly expressed Z19 α-zein studied with AlphaFold2 and MD simulations

α-zeins are amphiphilic maize seed storage proteins with material properties suitable for a multitude of applications e.g., in renewable plastics, foods, therapeutics and additive manufacturing (3D-printing). To exploit their full potential, molecular-level insights are essential. The difficulties in experimental atomic-resolution characterization of α-zeins have resulted in a diversity of published molecular models. However, deep-learning α-zein models are largely unexplored. Therefore, this work studies an AlphaFold2 (AF2) model of a highly expressed α-zein using molecular dynamics (MD) simulations. The sequence of the α-zein cZ19C2 gave a loosely packed AF2 model with 7 α-helical segments connected by turns/loops. Compact tertiary structure was limited to a C-terminal bundle of three α-helices, each showing notable agreement with a published consensus sequence. Aiming to chart possible α-zein conformations in practically relevant solvents, rather than the native solid-state, the AF2 model was subjected to MD simulations in water/ethanol mixtures with varying ethanol concentrations. Despite giving structurally diverse endpoints, the simulations showed several patterns: In water and low ethanol concentrations, the model rapidly formed compact globular structures, largely preserving the C-terminal bundle. At ≥ 50 mol% ethanol, extended conformations prevailed, consistent with previous SAXS studies. Tertiary structure was partially stabilized in water and low ethanol concentrations, but was disrupted in ≥ 50 mol% ethanol. Aggregated results indicated minor increases in helicity with ethanol concentration. β-sheet content was consistently low (∼1%) across all conditions. Beyond structural dynamics, the rapid formation of branched α-zein aggregates in aqueous environments was highlighted. Furthermore, aqueous simulations revealed favorable interactions between the protein and the crosslinking agent glycidyl methacrylate (GMA). The proximity of GMA epoxide carbons and side chain hydroxyl oxygens simultaneously suggested accessible reactive sites in compact α-zein conformations and pre-reaction geometries for methacrylation. The findings may assist in expanding the applications of these technologically significant proteins, e.g., by guiding chemical modifications.

Aggregation and breakage dynamics of alumina particles under shear by coupled Computational Fluid Dynamics - Discrete Element Method

HYPOTHESIS

Shear affects simultaneous aggregation and fragmentation of fine particles. Understanding the effect of shear on the dynamics of particle aggregation and break-up is important to predict aggregate size and structure. It is hypothesized that there is a transition from pure breakage of large aggregates to regimes where restructuring and aggregation also play a role as aggregates become smaller.

SIMULATIONS

Here, aggregation and fragmentation dynamics of alumina particles are investigated under laminar shear flow using Discrete Element Method (DEM) coupled with Computational Fluid Dynamics (CFD). The effect of the shear rate on the aggregation and breakage rates is quantified accounting for particle-particle and particle-fluid interactions.

FINDINGS

High shear rates promote the formation of small, compact aggregates. The collision efficiency decreases with increasing shear rate following a power law for shear rates higher than 1250 s-1. The transition from the pure breakage limit to the region dominated by breakage and restructuring has been observed for the first time. The breakage rate decreases significantly as the transition occurs upon decreasing aggregate size. CFD-DEM-derived collision efficiency and breakage rate equations are proposed that can be readily employed in detailed population balance equation models for industrial particle process design.

Simultaneous Inversion of Particle Size Distribution, Thermal Accommodation Coefficient, and Temperature of In-Flame Soot Aggregates Using Laser-Induced Incandescence

Measuring the size distribution and temperature of high-temperature dispersed particles, particularly in-flame soot, holds paramount importance across various industries. Laser-induced incandescence (LII) stands out as a potent non-contact diagnostic technology for in-flame soot, although its effectiveness is hindered by uncertainties associated with pre-determined thermal properties. To tackle this challenge, our study proposes a multi-parameter inversion strategy-simultaneous inversion of particle size distribution, thermal accommodation coefficient, and initial temperature of in-flame soot aggregates using time-resolved LII signals. Analyzing the responses of different heat transfer sub-models to temperature rise demonstrates the necessity of incorporating sublimation and thermionic emission for accurately reproducing LII signals of high-temperature dispersed particles. Consequently, we selected a particular LII model for the multi-parameter inversion strategy. Our research reveals that LII-based particle sizing is sensitive to biases in the initial temperature of particles (equivalent to the flame temperature), underscoring the need for the proposed multi-parameter inversion strategy. Numerical results obtained at two typical flame temperatures, 1100 K and 1700 K, illustrate that selecting an appropriate laser fluence enables the simultaneous inversion of particle size distribution, thermal accommodation coefficient, and initial particle temperatures of soot aggregates with high accuracy and confidence using the LII technique.

Zero-shot learning of aerosol optical properties with graph neural networks

Black carbon (BC), a strongly absorbing aerosol sourced from combustion, is an important short-lived climate forcer. BC's complex morphology contributes to uncertainty in its direct climate radiative effects, as current methods to accurately calculate the optical properties of these aerosols are too computationally expensive to be used online in models or for observational retrievals. Here we demonstrate that a Graph Neural Network (GNN) trained to predict the optical properties of numerically-generated BC fractal aggregates can accurately generalize to arbitrarily shaped particles, including much larger ([Formula: see text]) aggregates than in the training dataset. This zero-shot learning approach could be used to estimate single particle optical properties of realistically-shaped aerosol and cloud particles for inclusion in radiative transfer codes for atmospheric models and remote sensing inversions. In addition, GNN's can be used to gain physical intuition on the relationship between small-scale interactions (here of the spheres' positions and interactions) and large-scale properties (here of the radiative properties of aerosols).

Agglomeration of Spray-Dried Milk Powder in a Spray Fluidized Bed: A Morphological Modeling

The type of solid substrate plays a critical role in determining the kinetics of the spray fluidized bed (SFB) agglomeration process. In the case of porous (also soft) primary particles (PPs), droplet aging is due to imbibition and drying. The surface properties of the substrate also change due to imbibition. The focus of the present work is to simulate the agglomeration of the spray-dried milk powder using the Monte Carlo (MC) method coupled with a drying-imbibition model. In order to extract the morphology of the formed agglomerates, an aggregation model is employed. Further, this aggregation model is employed to predict the number of positions on the PPs (later agglomerates) for droplet deposition; previously, the ‘concept of positions’ was used. The transient growth of different milk powders (whole and skim) is depicted using the enhanced MC model. The enhancement in the droplet deposition model had a prominent influence on the overall kinetics of agglomeration. As expected, this enhanced MC model predicted that the agglomeration rate of skim milk powder is higher than that of whole milk powder.

Relationship Between the Mobility of Aggregates and Fluid Penetration Depth Across a Range of Fractal Dimensions Using Stokesian Dynamics

The hydrodynamic behavior of fractal aggregates plays an important role in various applications in industry and the environment, and has been a topic of interest over the past several decades. Despite this, crucial aspects such as the relationship of the mobility radius, R_m, with respect to the fractal dimension, d_f, and the fluid penetration depth, δ, have largely remained unexplored. Herein, we examine these aspects across a wide range of d_f's through a Stokesian dynamics approach. It takes into account all orders of monomer-monomer interactions to construct the resistance matrix for the entire cluster, which is assumed to be rigid. Statistical fractals created using algorithms such as diffusion limited aggregation (DLA), cluster-cluster aggregation (CCA), tunable Monte Carlo algorithm, and a deterministic Vicsek fractal, with d_f varying from 1.76 to 3, and the number of monomers ranging from 20 to 10 240 are considered. While confirming the expected asymptotic cluster-size independence of the hydrodynamic ratio, β = R_m/R_g (where R_g is the radius of gyration of the cluster), this study reveals a monotonically increasing trend for β with increasing d_f. The decay of the fluid velocity within the aggregate is quantified via the concept of penetration depth (δ). Analysis shows that the dimensionless penetration depth (δ* = δ/R_g) approaches asymptotic constancy with respect to cluster size in contrast to a weak dependency of the form δ* ∼ (R_g/a)^{-(d_f - 1)/2}, predicted by the mean-field theory (a being the monomer radius). Furthermore, the penetration depth is found to decrease rapidly, in an exponential manner, with increasing β. This establishes a quantitative relationship between the resistance experienced by the cluster and the degree of penetration of fluid into it. The implications of these results are further discussed.

Laser-induced incandescence for non-soot nanoparticles: recent trends and current challenges

Laser-induced incandescence (LII) is a widely used combustion diagnostic for in situ measurements of soot primary particle sizes and volume fractions in flames, exhaust gases, and the atmosphere. Increasingly, however, it is applied to characterize engineered nanomaterials, driven by the increasing industrial relevance of these materials and the fundamental scientific insights that may be obtained from these measurements. This review describes the state of the art as well as open research challenges and new opportunities that arise from LII measurements on non-soot nanoparticles. An overview of the basic LII model, along with statistical techniques for inferring quantities-of-interest and associated uncertainties is provided, with a review of the application of LII to various classes of materials, including elemental particles, oxide and nitride materials, and non-soot carbonaceous materials, and core-shell particles. The paper concludes with a discussion of combined and complementary diagnostics, and an outlook of future research.

Mass fractal dimension from 2D-microscopy images via an aggregation model with variable compactness

Microscopy-image analysis provides precious information on size and structure of colloidal aggregates and agglomerates. The structure of colloids is often characterized using the mass fractal dimension d_f , which is different from the two-dimensional fractal dimension d_p that can be computed from microscopy-images. In this work we propose to use a recent morphological aggregation model to find a relationship between 2D image fractal dimension and 3D mass fractal dimension of aggregates and agglomerates. Our case study is represented by scanning transmission electron microscopy-images of boehmite colloidal suspensions. The behaviour of the computed d_f at different acid and base concentration shows a fair agreement with the results of Small Angle X-Ray Scattering and with the literature, enabling to use the d_f vs d_p relationship to study the impact of the composition of the colloidal suspension on the density of colloidal aggregates and agglomerates. This article is protected by copyright. All rights reserved.

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.

A Fast and Improved Tunable Aggregation Model for Stochastic Simulation of Spray Fluidized Bed Agglomeration

Agglomeration in spray fluidized bed (SFB) is a particle growth process that improves powder properties in the chemical, pharmaceutical, and food industries. In order to analyze the underlying mechanisms behind the generation of SFB agglomerates, modeling of the growth process is essential. Morphology plays an imperative role in understanding product behavior. In the present work, the sequential tunable algorithm developed in previous studies to generate monodisperse SFB agglomerates is improved and extended to polydisperse primary particles. The improved algorithm can completely retain the given input fractal properties (fractal dimension and prefactor) for polydisperse agglomerates (with normally distributed radii of primary particles having a standard deviation of 10% from the mean value). Other morphological properties strongly agreed with the experimental SFB agglomerates. Furthermore, this tunable aggregation model is integrated into the Monte Carlo (MC) simulation. The kinetics of the overall agglomeration at various operating conditions, like binder concentration and inlet fluidized gas temperature, are investigated. The present model accurately predicts the morphological descriptors of SFB agglomerates and the overall kinetics under various operating parameters.

Aggregation affects optical properties and photothermal heating of gold nanospheres

Laser heating of gold nanospheres (GNS) is increasingly prevalent in biomedical applications due to tunable optical properties that determine heating efficiency. Although many geometric parameters (i.e. size, morphology) can affect optical properties of individual GNS and their heating, no specific studies of how GNS aggregation affects heating have been carried out. We posit here that aggregation, which can occur within some biological systems, will significantly impact the optical and therefore heating properties of GNS. To address this, we employed discrete dipole approximation (DDA) simulations, Ultraviolet-Visible spectroscopy (UV-Vis) and laser calorimetry on GNS primary particles with diameters (5, 16, 30 nm) and their aggregates that contain 2 to 30 GNS particles. DDA shows that aggregation can reduce the extinction cross-section on a per particle basis by 17-28%. Experimental measurement by UV-Vis and laser calorimetry on aggregates also show up to a 25% reduction in extinction coefficient and significantly lower heating (~ 10%) compared to dispersed GNS. In addition, comparison of select aggregates shows even larger extinction cross section drops in sparse vs. dense aggregates. This work shows that GNS aggregation can change optical properties and reduce heating and provides a new framework for exploring this effect during laser heating of nanomaterial solutions.

Simultaneous determination of primary particle size distribution and thermal accommodation coefficient of soot aggregates using low-fluence LII

For the ill-posed inverse problem of LII-based nanoparticle size measurement, recovered primary particle size distribution (PPSD) is sensitive to the uncertainty of LII model parameters. In the absence of reliable prior knowledge, the thermal accommodation coefficient (TAC) and fractal-dependent shielding factor are often required to be inferred simultaneously with the PPSD. In the simplified LII model for low fluence regime, TAC and fractal-dependent shielding factor are combined to define a new fractal-dependent TAC. The present study theoretically verified the feasibility of inferring PPSD and fractal-dependent TAC from the normalized LII signals. Moreover, the inversion is independent of prior knowledge of most full LII model parameters, which is attributed to low laser fluence, normalized signal, and fractal-dependent TAC.

Effects of phase transformation on the ultraviolet optical properties of alumina clusters in aircraft plumes

Alumina particles experience phase transition as an undercooling process along the plume, during which the liquid alumina clusters transform into multiphase, and then into α phase. The phase transformation model was built by an improved diffusion limited aggregation (DLA) algorithm with monomers of stratified structure. The effects of phase transformation on the ultraviolet optical characteristics of alumina clusters were studied using the superposition T-matrix method (STMM). We found that the alumina clusters in phase transition had completely different optical properties compared with the fixed phase ones. Forward scattering, absorption efficiency and asymmetry parameter gradually decreased, whereas backward scattering, scattering efficiency, and single-scattering albedo gradually increased during the phase transformation process. Besides, multiphase alumina clusters were compared with the other two equivalent models, including the sphere model approximated by equivalent volume sphere (EVS) and the equivalent surface sphere (ESS) approaches and single-phase cluster model approximated by Maxwell-Garnett (MG) and Bruggeman (BR) approaches. Generally speaking, the optical properties of the single-phase cluster approximated by MG and BR approaches were relatively close to those of the real multiphase alumina cluster. Whereas the spheres approximated by EVS and ESS had great deviations, especially when the number of monomers in the cluster was 20, the relative error of scattering efficiency calculated by ESS was up to 52%. Therefore, approximate approaches for multiphase clusters should be chosen cautiously. Our results give further the understanding of the optical properties of alumina clusters. As the phase states are usually closely related to the plume radiation and burning process, these kinds of researches will be helpful to aircraft detection, identification, and other related fields.

Monte Carlo Aggregation Code (MCAC) Part 1: Fundamentals

The application of Monte Carlo methods to simulate the agglomeration of suspended nanoparticles is currently limited to specific agglomeration regimes with reduced accuracy in terms of the particle's physical residence time. The definition of specific particles persistent distance, its corresponding time step and subsequent probabilities for particle displacements may improve the accuracy of this method. To solve these issues, a new persistent distance and its corresponding time step based on Langevin dynamics simulations are introduced. Additionally, a probability of particle displacements, not restricted to a specific agglomeration regime, is introduced. All the modifications are validated by comparison with Langevin dynamics simulations. Finally, the above mentioned modifications considerably improve the accuracy of Monte Carlo methods to predict the dynamics and agglomeration of suspended nanoparticles.

Sedimentation of Fractal Aggregates in Shear-Thinning Fluids

Solid–liquid separation is a key unit operation in the wastewater treatment, generally consisting of coagulation and flocculation steps to promote aggregation and increase the particle size, followed by sedimentation, where the particles settle due to the effect of gravity. The sedimentation efficiency is related to the hydrodynamic behavior of the suspended particles that, in turn, depends on the aggregate morphology. In addition, the non-Newtonian rheology of sludges strongly affects the drag coefficient of the suspended particles, leading to deviations from the known settling behavior in Newtonian fluids. In this work, we use direct numerical simulations to study the hydrodynamic drag of fractal-shaped particles suspended in a shear-thinning fluid modeled by the power-law constitutive equation. The fluid dynamics governing equations are solved for an applied force with different orientations uniformly distributed over the unit sphere. The resulting particle velocities are interpolated to compute the aggregate dynamics and the drag correction coefficient. A remarkable effect of the detailed microstructure of the aggregate on the sedimentation process is observed. The orientational dynamics shows a rich behavior characterized by steady-state, bistable, and periodic regimes. In qualitative agreement with spherical particles, shear-thinning increases the drag correction coefficient. Elongated aggregates sediment more slowly than sphere-like particles, with a lower terminal velocity as the aspect ratio increases.

Rheology of a Dilute Suspension of Aggregates in Shear-Thinning Fluids

The prediction of the viscosity of suspensions is of fundamental importance in several fields. Most of the available studies have been focused on particles with simple shapes, for example, spheres or spheroids. In this work, we study the viscosity of a dilute suspension of fractal-shape aggregates suspended in a shear-thinning fluid by direct numerical simulations. The suspending fluid is modeled by the power-law constitutive equation. For each morphology, a map of particle angular velocities is obtained by solving the governing equations for several particle orientations. The map is used to integrate the kinematic equation for the orientation vectors and reconstruct the aggregate orientational dynamics. The intrinsic viscosity is computed by a homogenization procedure along the particle orbits. In agreement with previous results on Newtonian suspensions, the intrinsic viscosity, averaged over different initial orientations and aggregate morphologies characterized by the same fractal parameters, decreases by increasing the fractal dimension, that is, from rod-like to spherical-like aggregates. Shear-thinning further reduces the intrinsic viscosity showing a linear dependence with the flow index in the investigated range. The intrinsic viscosity can be properly scaled with respect to the number of primary particles and the flow index to obtain a single curve as a function of the fractal dimension.

Heating ability of magnetic nanoparticles with cubic and combined anisotropy

The low frequency hysteresis loops and specific absorption rate (SAR) of assemblies of magnetite nanoparticles with cubic anisotropy are calculated in the diameter range of D = 20-60 nm taking into account both thermal fluctuations of the particle magnetic moments and strong magneto-dipole interaction in assemblies of fractal-like clusters of nanoparticles. Similar calculations are also performed for assemblies of slightly elongated magnetite nanoparticles having combined magnetic anisotropy. A substantial dependence of the SAR on the nanoparticle diameter is obtained for all cases investigated. Due to the influence of the magneto-dipole interaction, the SAR of fractal clusters of nanoparticles decreases considerably in comparison with that for weakly interacting nanoparticles. However, the ability of magnetic nanoparticle assemblies to generate heat can be improved if the nanoparticles are covered by nonmagnetic shells of appreciable thickness.

Sensitivity analysis of morphology on radiative properties of soot aerosols

Absorption cross section (Cabs), scattering cross section (Csca) and asymmetry parameter (ASY) of soot particles in different atmospheric aging status were investigated under fixed equivalent volume radius (RV) using the numerically exact multiple-sphere T-matrix method. The radiative properties of soot particles would be largely diverse in different aging status even RV is fixed. However, there are many insensitive parameters under different aging status. The Cabs and ASY is insensitive to monomers number (Ns) when Ns is larger than a threshold value. For bare and thinly coated soot aggregates, Cabs is insensitive to fractal dimension (Df) when the RV is small, where the relative errors of Cabs for different Df are within 2.5%. However, the effects of Df is obvious for large soot due to the shielding effects of large monomers, and the relative errors for different Df can reach to 18% for bare soot. For thinly coated soot, the changes of ASY with soot volume fraction (fsoot) is small due to the little changes of the fractal structure when the RV is fixed. In addition, for thickly coated soot, ASY is insensitive to Ns due to the unchanged overall spherical structure. Our results give a further understanding of the influences of morphology on radiative properties. It may be helpful for model selection and model simplification.

Approximate Bayesian computation techniques for optical characterization of nanoparticle clusters

Characterization of nanoparticle aggregates from observed scattered light leads to a highly complex inverse problem. Even the forward model is so complex that it prohibits the use of classical likelihood-based inference methods. In this study, we compare four so-called likelihood-free methods based on approximate Bayesian computation (ABC) that requires only numeric simulation of the forward model without the need of evaluating a likelihood. In particular, rejection, Markov chain Monte Carlo, population Monte Carlo, and adaptive population Monte Carlo (APMC) are compared in terms of accuracy. In the current model, we assume that the nanoparticle aggregates are mutually well separated and made up of particles of same size. Filippov's particle-cluster algorithm is used to generate aggregates, and discrete dipole approximation is used to estimate scattering behavior. It is found that the APMC algorithm is superior to others in terms of time and acceptance rates, although all algorithms produce similar posterior distributions. Using ABC techniques and utilizing unpolarized light experiments at 266 nm wavelength, characterization of soot aggregates is performed with less than 2 nm deviation in nanoparticle radius and 3-4 deviation in number of nanoparticles forming the monodisperse aggregates. Promising results are also observed for the polydisperse aggregate with log-normal particle size distribution.

Interaction Effects in Assembly of Magnetic Nanoparticles

A specific absorption rate of a dilute assembly of various random clusters of iron oxide nanoparticles in alternating magnetic field has been calculated using Landau-Lifshitz stochastic equation. This approach simultaneously takes into account both the presence of thermal fluctuations of the nanoparticle magnetic moments and magneto-dipole interaction between the nanoparticles of the clusters. It is shown that for usual 3D clusters, the intensity of the magneto-dipole interaction is determined mainly by the cluster packing density η = N _p V/V _cl , where N _p is the average number of the particles in the cluster, V is the nanoparticle volume, and V _cl is the cluster volume. The area of the low frequency hysteresis loop and the assembly-specific absorption rate have been found to be considerably reduced when the packing density of the clusters increases in the range of 0.005 ≤ η < 0.4. The dependence of the specific absorption rate on the mean nanoparticle diameter is retained with an increase of η, but becomes less pronounced. For fractal clusters of nanoparticles, which arise in biological media, in addition to a considerable reduction of the absorption rate, the absorption maximum is shifted to smaller particle diameters. It is found also that the specific absorption rate of fractal clusters increases appreciably with an increase of the thickness of nonmagnetic shells at the nanoparticle surfaces.

Anthropogenic iron oxide aerosols enhance atmospheric heating

Combustion-induced carbonaceous aerosols, particularly black carbon (BC) and brown carbon (BrC), have been largely considered as the only significant anthropogenic contributors to shortwave atmospheric heating. Natural iron oxide (FeO_x) has been recognized as an important contributor, but the potential contribution of anthropogenic FeO_x is unknown. In this study, we quantify the abundance of FeO_x over East Asia through aircraft measurements using a modified single-particle soot photometer. The majority of airborne FeO_x particles in the continental outflows are of anthropogenic origin in the form of aggregated magnetite nanoparticles. The shortwave absorbing powers (P_abs) attributable to FeO_x and to BC are calculated on the basis of their size-resolved mass concentrations and the mean P_abs(FeO_x)/P_abs(BC) ratio in the continental outflows is estimated to be at least 4–7%. We demonstrate that in addition to carbonaceous aerosols the aggregate of magnetite nanoparticles is a significant anthropogenic contributor to shortwave atmospheric heating.

Iron oxide nanoparticles contribute to shortwave absorption in the form of desert dust. Moteki et al. show that iron oxide particles of anthropogenic origin, potentially from motor vehicles and blast furnaces, also contribute to atmospheric heating over East Asia.

Quantifying intra- and extracellular aggregation of iron oxide nanoparticles and its influence on specific absorption rate

A promising route to cancer treatment is hyperthermia, facilitated by superparamagnetic iron oxide nanoparticles (SPIONs). After exposure to an alternating external magnetic field, SPIONs generate heat, quantified by their specific absorption rate (SAR, in W g(-1) Fe). However, without surface functionalization, commercially available, high SAR SPIONs (EMG 308, Ferrotec, USA) aggregate in aqueous suspensions; this has been shown to reduce SAR. Further reduction in SAR has been observed for SPIONs in suspensions containing cells, but the origin of this further reduction has not been made clear. Here, we use image analysis methods to quantify the structures of SPION aggregates in the extra- and intracellular milieu of LNCaP cell suspensions. We couple image characterization with nanoparticle tracking analysis and SAR measurements of SPION aggregates in cell-free suspensions, to better quantify the influence of cellular uptake on SPION aggregates and ultimately its influence on SAR. We find that in both the intra- and extracellular milieu, SPION aggregates are well-described by a quasifractal model, with most aggregates having fractal dimensions in the 1.6-2.2 range. Intracellular aggregates are found to be significantly larger than extracellular aggregates and are commonly composed of more than 10(3) primary SPION particles (hence they are "superaggregates"). By using high salt concentrations to generate such superaggregates and measuring the SAR of suspensions, we confirm that it is the formation of superaggregates in the intracellular milieu that negatively impacts SAR, reducing it from above 200 W g(-1) Fe for aggregates composed of fewer than 50 primary particles to below 50 W g(-1) for superaggregates. While the underlying physical mechanism by which aggregation leads to reduction in SAR remains to be determined, the methods developed in this study provide insight into how cellular uptake influences the extent of SPION aggregation, and enable estimation of the reduction of SAR brought about via uptake induced aggregation.

Fractality à la carte: a general particle aggregation model

In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters’ fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

Accounting for biological aggregation in heating and imaging of magnetic nanoparticles

Aggregation is a known consequence of nanoparticle use in biology and medicine; however, nanoparticle characterization is typically performed under the pretext of well-dispersed, aqueous conditions. Here, we systematically characterize the effects of aggregation on the alternating magnetic field induced heating and magnetic resonance (MR) imaging performance of iron oxide nanoparticles (IONPs) in non-ideal biological systems. Specifically, the behavior of IONP aggregates composed of ~10 nm primary particles, but with aggregate hydrodynamic sizes ranging from 50 nm to 700 nm, was characterized in phosphate buffered saline and fetal bovine serum suspensions, as well as in gels and cells. We demonstrate up to a 50% reduction in heating, linked to the extent of aggregation. To quantify aggregate morphology, we used a combination of hydrodynamic radii distribution, intrinsic viscosity, and electron microscopy measurements to describe the aggregates as quasifractal entities with fractal dimensions in the 1.8-2.0 range. Importantly, we are able to correlate the observed decrease in magnetic field induced heating with a corresponding decrease in longitudinal relaxation rate (R1) in MR imaging, irrespective of the extent of aggregation. Finally, we show in vivo proof-of-principle use of this powerful new imaging method, providing a critical tool for predicting heating in clinical cancer hyperthermia.

Absorption and scattering of light from ensembles of randomly oriented aggregates

This paper presents one approach to the absorption and scattering of light from aggregates of primary particles. The primary particles are sphere-like and small compared to the wavelength, whereas the aggregate can be large compared to the wavelength. This situation applies to when soot particles formed in flames are measured using methods based on laser light. The method presented in this work, called generalized Rayleigh-Debye-Gans, leads to closed-form expressions for the scattered intensity and the absorbed power of an ensemble of aggregates with random positions and orientations. The expressions ensure a fast and accurate numerical evaluation of the scattering and absorption from ensembles of aggregates. The numerical results are compared with the ones obtained from the T-matrix method and the discrete dipole approximation method.