Fractal Clusters Research Articles

Simulation of the Structure of Dust Fractal Clusters in Protoplanetary Gas–Dust Disks

Simulation of the Structure of Dust Fractal Clusters in Protoplanetary Gas–Dust Disks

Yield stress behavior of colloidal gels with embedded active particles

The yield stress behavior of colloidal gels with embedded active particles is studied with three experiments: start-up of steady shear, oscillatory strain amplitude sweep, and creep testing. Activity is generated by Janus particles with a platinum hemisphere; these particles undergo self-diffusiophoretic and self-electrophoretic motion in hydrogen peroxide solutions. The free particle active motion of the Janus colloids is consistent with an active energy of 25 times thermal energy at the highest hydrogen peroxide concentration studied. Consistent with prior work, the gels with embedded active particles display enhanced microdynamics and a reduction in linear viscoelastic moduli. Furthermore, at the activity levels studied, the yield stress decreases by as much as threefold for gels with an active-to-passive particle ratio of only 1:1200. We additionally find the yield strain is independent of activity. The significant reduction in yield stress at a very low active-to-passive particle ratio is modeled by combining the theory of how activity changes the spring constant of interparticle bonds in the gel with an argument that the number of active fractal clusters in the gel—rather than the number of active particles—drives the activity-induced softening of rheological properties. We estimate that 1 in 40 fractal clusters in the gel is active due to the presence of an active particle. This approach explains how an extremely small fraction of active particles causes a substantial change in both linear and nonlinear rheological properties. The results and modeling are potentially useful for the creation of gels with multistate mechanical properties.

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.

Rheological investigation of supramolecular physical gels in water/dimethylsulfoxide mixtures by lysine derivatives

AbstractTwo derivatives of lysine were synthesized by acylating the Nα with dodecanoic acid starting from commercial precursors in which the Nε was already acylated by the benzoyloxycarbonyl or o‐chloro‐benzoyloxycarbonyl group. Both derivatives self‐assembled in dimethylsulfoxide/water mixtures (above 40% v/v water) leading to solid‐like formulations. The rheological properties were studied as a function of gelator concentration and solvent composition. From stress sweep experiments it was assumed that the gels consisted of jammed suspensions of mesoscopic clusters formed by self‐assembly processes similar to those at the origin of crystallization. The temporal variation of storage and loss moduli was monitored immediately after mixing over times between 20 and 120 min using isothermal oscillatory rheological experiments. Experimental curves were satisfactorily depicted using previously reported semi‐empirical equations. Both transient evolution and stationary values were consistent with the representation of gels as resulting from the formation, one‐dimensional growth and dynamic arrest of fractal clusters (with fractal dimension between 1.6 and 2.0). The presence of a chlorine atom within the aromatic ring of one of the lysine derivatives induced a significant increase of the gelation time scale and a decrease of rheological moduli. © 2021 Society of Chemical Industry

Gold nanoparticles obtained by ns-pulsed laser ablation in liquids (ns-PLAL) are arranged in the form of fractal clusters

Gold nanoparticles (AuNPs), synthesized by ns-pulsed laser ablation in liquid (ns-PLAL) in the absence of any capping agents, are potential model systems to study the interactions with biological structures unencumbered by interference from the presence of stabilizers and capping agents. However, several aspects of the physics behind these AuNPs solutions deserve a detailed investigation. The structure in solution of ns-PLAL-synthesized AuNPs was investigated in solution by means of small-angle X-ray scattering (SAXS) and dynamic light scattering (DLS). Furthermore, the (dried) NPs have been examined using TEM. The analysis of the SAXS curve shows the presence of a large number of small aggregates with a fractal structure stabilized by strong long-range repulsive interactions. Fitting of the SAXS curve to a suitable “fractal model” allows the estimation of the features of the fractal including the fractal dimension d = 1.9. The latter allows to estimate the fraction of light scattered by fractals of different sizes and thus permits a fair comparison between the DLS and TEM data. Here, a stable abundant population of fractal clusters is reported reflecting a mechanism where primary AuNPs (size 7.6 nm) are forced to aggregate forming clusters during the collapse of the cavitation bubble. When these clusters are released in the aqueous phase, their large negative charge builds up repulsive interactions that prevent cluster-cluster aggregation imparting colloidal stability.

Holographic characterization and tracking of colloidal dimers in the effective-sphere approximation.

An in-line hologram of a colloidal sphere can be analyzed with the Lorenz-Mie theory of light scattering to measure the sphere's three-dimensional position with nanometer-scale precision while also measuring its diameter and refractive index with part-per-thousand precision. Applying the same technique to aspherical or inhomogeneous particles yields measurements of the position, diameter and refractive index of an effective sphere that represents an average over the particle's geometry and composition. This effective-sphere interpretation has been applied successfully to porous, dimpled and coated spheres, as well as to fractal clusters of nanoparticles, all of whose inhomogeneities appear on length scales smaller than the wavelength of light. Here, we combine numerical and experimental studies to investigate effective-sphere characterization of symmetric dimers of micrometer-scale spheres, a class of aspherical objects that appear commonly in real-world dispersions. Our studies demonstrate that the effective-sphere interpretation usefully distinguishes small colloidal clusters in holographic characterization studies of monodisperse colloidal spheres. The effective-sphere estimate for a dimer's axial position closely follows the ground truth for its center of mass. Trends in the effective-sphere diameter and refractive index, furthermore, can be used to measure a dimer's three-dimensional orientation. When applied to colloidal dimers transported in a Poiseuille flow, the estimated orientation distribution is consistent with expectations for Brownian particles undergoing Jeffery orbits.

Ячеистый беспорядок наноглобул желатина

The surface topology of thin polymer films obtained on glass from micellar solutions of gelatin samples in a mixture of isooctane – water – (bis-2-ethylhexyl) sodium sulfosuccinate (AOT) with a variation in the average molecular weight M of the polymer and a constant molar ratio [H2O]/[AOT] = 40, has been studied using electron microscopy. It is shown that solutions with an initial gelatin concentration corresponding to the gelation threshold form films with a characteristic structure: polymer nanoglobuls are located in the cells of the physical network of macromolecules-the internal percolation cluster of particles. At the same time, with a decrease in M, the average size of the globules decreases and the degree of their polydisperity increases. The same changes are observed for network cells in which local density – density correlations weaken. The ratio of average cell sizes to nanoglobuls is independent of M due to the universal fractal cluster structure of the films.

Dynamic Destruction as Analogs of Critical Phenomena in Metal Samples with Various Geometries within a Wide Ranges of Amplitude–Time Characteristics of External Action

The quantitative characteristics of the products of dispersion and the cascade of dissipative structures arising in metals under shock-wave loading are determined. The fractal dimension df and the Hurst exponent H (standardized range of dissipative structures) of the cascade of hydrodynamic modes, the roughness of the fracture surface, and the dispersion products are determined. Destructive processes occurring in loaded samples are numerically simulated using the Lagrangian technique TIM 3D [1, 2]. It is shown that a cascade of dissipative structures at different scale–temporal levels (nanolevel, mesolevel I, mesolevel II, and macrolevel) is a fractal cluster, and it is a percolation cluster on the threshold of a macrofracture, when there is connectivity in the system of dissipative structures [1, 2]. The self-similarity of dissipative structures is due to the self-organization in nonequilibrium systems; and the dynamic fracture and dispersion processes are examples of scale invariance. The scale invariance of the dissipative structures indicates the nonequilibrium system has reached a critical state.

Tuning the Hierarchical Structure and Resilience of Resilin-like Polypeptide Hydrogels Using Graphene Oxide.

Resilin-like polypeptides (RLPs) are an important class of intrinsically disordered multistimuli-responsive bioelastomers. The nanostructure of RLPs in solution has been extensively studied in the past few years, from dilute to molecular crowding conditions, and with the addition of rigid biopolymers. Modification of the hierarchical network structure of RLP hydrogels using graphene oxide (GO) as an additive is a burgeoning prospect for their application in the bioelectronic and biomedical fields. In this work, we systemically study the influence of incorporating GO into RLP (Rec1) hydrogels for tuning their physicochemical properties and understanding the gel-cell interactions. The nature of GO interaction with the Rec1 hydrogel is deduced from the change in structure and properties. Contrast-matching small-angle and ultra-small-angle neutron-scattering techniques were used to investigate the network structure of the Rec1 hydrogel and how this structure is modified in the presence of GO. Incorporation of GO in the Rec1 hydrogel matrix results in an increase in the micromechanical resilience, equilibrium water swelling ratio, micropore size, cross-linked domain size; with a decrease in the cross-link density, mass fractal cluster size, local compressive elastic modulus, and cell inert characteristics. These property combinations achieved with the addition of GO further open up the available structure-property design window for RLP applications.

CONTACT PROCESS ON FRACTAL CLUSTERS SIMULATED BY GENERALIZED DIFFUSION-LIMITED AGGREGATION (g-DLA) MODEL

The spread of infectious disease, virus epidemic, fashion, religion and rumors is strongly affected by the nearest neighbor hence underlying morphologies of the colonies are crucial. Likewise, the morphology of naturally grown patterns ranges from fractal to compact with lacunarity. We analyze the contact process on the fractal clusters simulated by generalized Diffusion-limited Aggregation (g-DLA) model. In g-DLA model, randomly walking particle is added to the cluster with sticking probability [Formula: see text] depending on the local density of occupied sites in the neighborhood of radius [Formula: see text] from the center of active site. It takes values [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) for highly dense, moderately dense and sparsely occupied regions, respectively. The corresponding morphology varies from fractal to compact as [Formula: see text] varies from [Formula: see text] to [Formula: see text]. Interestingly, the contact process on the g-DLA clusters shows clear transition from active phase to absorbing phase and the exponent values fall between 1-d and 2-d in directed percolation (DP) universality class. The local persistence exponents at transition are studied and are found to be much smaller than that for 1-d and 2-d DP cases. We conjecture that infection in the fractal cluster does not easily reach far-flung or remote areas at the periphery of the cluster.

Супрамолекулярный механизм влияния поликарбоксилатных суперпластификаторов на управляемое твердение строительных нанокомпозитов

Introduction. The use of modifying nano-additives in the production of binding building materials is one of the most effective ways to control the technological parameters of concrete by conducting good control of the rheological characteristics reliability. Plasticizing additives increase the water-holding capacity of building compositions, which leads to the dispersed nanosystems stability. This article is focused on examining the physical and chemical mechanisms of the supramolecular effects of polycarboxylate ethers on technological and rheological characteristics of cement nanobinders. Methods and materials. This study describes controlled hardening processes of concrete nanocompositions with demanded technological characteristics in the presence of highly effective plasticizers. Moreover, this paper carries out the analysis of the innovative trends in regulating the consistency of building nanocomposites with the use of new comb-like polycarboxylate esters, which as superplasticizers allow to purposefully influence the kinetics of structure formation of cement nanocomposites. Results. Electrostatic and steric repulsion mechanisms, as well as the dispersing effects of innovative and traditional plasticizing nanoparticles, affect the adsorption and diffusion layers of the hydrated cement nanobinders ultrastructure. The most effective plasticizing properties are shown by comb-like polycarboxylate esters (CPE) with a linear chain molecular weight of ≈12000 g/mol and a length of side branches which correspond to a molecular weight of ≈750 g/mol. The supramolecular mechanism of nanosteric van der Waals repulsive forces begins to be detected at a distance of ≈11 nm, and the elasticity of the lateral branches of innovative CPE is ≈ 5 nm. Individual segments of CPE macromolecules enter the diffuse layer of dispersed nanosystems due to lateral interactions of anions of functional groups, hydrophobic fragments, etc.; they enhance the plasticizing effect of cement binders in concrete nanocompositions. Discussion. When using superplasticizing CPE, the density of concrete nanocomposites can be increased by reducing the amount of water mass to the cement mass ratio to the optimal 0.3; at the same time, technological pumpability and reliability control of the joint hardening kinetics with fillers are preserved within the framework of the technological problems system solutionsconcept. Supramolecular interaction of «anchoring» functional groups of polyacrylic acid containing solid phase cations of cement microparticles, fractal clusters of calcium hydrosilicates and simultaneous steric stabilization of polyethylene glycol radicals give the necessary rheological characteristics to construction nanocompositions and allow the construction of high-strength 55÷80 MPa building materials. Conclusions. The branched comb-like nanostructure of polycarboxylate esters exhibits effective technological characteristics of superplasticizers for concrete, building mortars and dry building mixes

Кластерний аналіз фрактальної розмірності мозочка людини

The cerebellum is a multifractal that includes several fractal clusters that correspond to different components of the cerebellar tissue: white matter and layers of the cortex. A fractal analysis (pixel dilation method in one of the author's modifications) was used to determine the complexity of spatial organization and the degree of filling of space with different components of cerebellar tissue. The purpose of the study was to determine clusters of fractal dimension of various components of human cerebellar tissue according to magnetic resonance imaging. Material and methods. The study was performed on digital T2 weighted images of magnetic resonance images of 30 patients (15 men and 15 women) who did not have pathological changes of the brain. Fractal analysis was performed using the pixel dilation method. The fractal dimension of cerebellar tissue for its components in the range of brightness values from 0 to 255 was determined. The difference in fractal dimension increase at different parts of the brightness range was calculated. Results and discussion. The study showed that the increase in fractal dimension is not gradual and has four zones of the most pronounced increase in values: 70-80, 85-90, 95-105 and 110-120. These areas can be separated into distinct clusters that correspond to the main components of the cerebellar tissue. The first cluster with the most intense increase of fractal dimension corresponds to the white matter of the cerebellum, which has the biggest density and the lowest values of brightness, the second – the granular layer of the cortex, the third – the molecular layer of the cortex. The fourth, least pronounced cluster corresponds to the pixels of the image with the highest brightness level, which correspond to the meninges. Conclusion. Three clusters of fractal dimension values corresponding to the main components of cerebellar tissue and average brightness values corresponding to them were determined: cerebellar white matter (70.684±0.473), granular layer of cortex (84.263±0.475), and molecular layer of cortex (96.263±0.449). The absence of certain clusters present in intact tissue and the presence of additional, pathological clusters may be criteria for diagnosing of the cerebellum using fractal analysis of magnetic resonance imaging of the brain

Reaction Rate Governs the Viscoelasticity and Nanostructure of Folded Protein Hydrogels.

Hydrogels constructed from folded protein domains are of increasing interest as resilient and responsive biomaterials, but their optimization for applications requires time-consuming and costly molecular design. Here, we explore a complementary approach to control their properties by examining the influence of crosslinking rate on the structure and viscoelastic response of a model hydrogel constructed from photochemically crosslinked bovine serum albumin (BSA). Gelation is observed to follow a heterogeneous nucleation pathway in which BSA monomers crosslink into compact nuclei that grow into fractal percolated networks. Both the viscoelastic response probed by shear rheology and the nanostructure probed by small-angle X-ray scattering (SAXS) are shown to depend on the photochemical crosslinking reaction rate, with increased reaction rates corresponding to higher viscoelastic moduli, lower fractal dimension, and higher fractal cluster size. Reaction rate-dependent changes are shown to be consistent with a transition between diffusion- and rate-limited assembly, and the corresponding changes to viscoelastic response are proposed to arise from the presence of nonfractal depletion regions, as confirmed by SAXS. This controllable nanostructure and viscoelasticity constitute a potential route for the precise control of hydrogel properties, without the need for molecular modification.

Deformation Relief of the Surface as a Characteristic of Fatigue Damage of Clad Aluminum Alloys. Part 1. Deformation Relief Evolution Under Cyclic Loading

The formation and evolution of a deformation relief on the surface of a clad aluminum alloy are examined under cyclic loading. The deformation relief originates on the surface of a clad layer in the form of local plastic strain regions with higher roughness, which characterizes the fatigue damage of the material. Saturation (relative surface area covered with the deformation relief) is a two-dimensional property of the deformation relief, while plastic surface strain is its threedimensional characteristic. The deformation relief can be registered with a contactless interference profilometer. Deformation relief saturation vs number of load cycles relations were plotted. Those relations are established to be similar above a certain level of maximum cycle stresses.The plastic surface strain grows linearly with saturation; the relation possesses two linear sections irrespective of active cycle stresses. The deformation relief examination as an aggregate of fractal clusters demonstrated that the power relation between the total perimeter and area of those clusters was revealed. The two sections of that relation were chosen, and with a certain area of clusters, the exponent is shown to drop from 1.53 to 1.00. Its decrease is indicative of the fractality loss by the deformation relief clusters. The change in the clad layer damage mechanism is established to occur at the deformation relief saturation within 0.22–0.25. At such a saturation level, initial fatigue cracks originate, while fractal relief evolution and plastic surface strain behavior of a clad layer are changed.

Reconstructing the fractal clusters of detonation nanodiamonds from small-angle X-ray scattering

Detonation nanodiamonds (DND) form fractal-like aggregates composed of polydisperse DND particles. We present a novel methodology for the visualisation and characterisation of fractal clusters of DND from one-dimensional small-angle X-ray scattering (SAXS) intensity. The fractal nature and polydispersity of DND are modelled by combining a diffusion-limited aggregation (DLA) process implemented in Monte Carlo simulations with the distribution of DND sizes measured from high-resolution transmission electron microscopy. The radius of gyration (42–44 nm), aggregation number (850–1150), and the maximum dimension (226–242 nm) of DND fractal clusters were obtained from the fitting of the synchrotron-based SAXS data (q∼0.11–4.75 1/nm) measured for two samples of commercialized DND powders by the developed theoretical model.

Modeling fractal aggregates of polydisperse particles with tunable dimension

A generalized non-kinetic off-lattice algorithm to construct stochastic fractal clusters of polydisperse particles with tunable cluster parameters including dimension, is presented. The model based on a hierarchical procedure extends the previous studies in this area to the general case of the cluster-cluster aggregation and, in contrast to the previous kinetic models, makes it possible to generate clusters with a continuous change in the structure, in particular, covering the full range of natural mass fractal dimensions between one and three. An example of the morphological study of numerically generated clusters based on the correlation analysis in both direct and reciprocal spaces is given. In the latter case, it is demonstrated that the use of the developed fast algorithm gives an accurate and self-consistent description of the small-angle scattering data.

Ag nanoparticle decorated Sb2O3 thin film: synthesis, characterizations and application

The property modifications in a thin film when its surface undergoes a nanoparticle decoration process in addition to its surface nanostructuring are investigated this paper. In specific, it describes the property modifications of antimony trioxide and its annealed variant, when their surface is decorated with Ag nanoparticles. Along with the modifications brought to the thin films, the morphology variations or agglomeration effects happening to Ag nanoparticles through/after this decoration process is also discussed here. We observe a mutual tuning of morphology as well as properties of thin film and nanoparticles. A fractal like cluster formation of Ag nanoparticle on the surface of nanostructured Sb2O3 thin film was witnessed. Whereas on the surfaces of Sb2O3 (annealed) thin film and glass plate, clustering of Ag nanoparticle is found to be different. On annealed Sb2O3 thin film surface, instead of forming fractal clusters most of the Ag nanoparticles fill in the voids between the thorns like structure of the film. The surface modification highly influences the optical absorption as well as the hydrophilicity of antimony trioxide samples. Due to the introduction of Ag nanoparticle, the absorption of Sb2O3 thin film in the visible region increased. All the synthesized films have roughness coefficient >1 and all are hydrophilic in nature. Nano structured Sb2O3 thin film is extremely hydrophilic and they become hydrophilic due to the introduction of Ag nanoparticle. The filling of Ag nanoparticles in the voids between the thorn structures might have prevented the water droplet penetration into these voids. Consequently, a partial wetting occurs on the film surface. High SERS efficiency factor (EF) and good reproducibility of Ag/Sb2O3/Glass make it a good candidate for SERS application.

Mechanical and Self-Healing Behavior of Matrix-Free Polymer Nanocomposites Constructed via Grafted Graphene Nanosheets.

Through molecular dynamics (MD) simulation, the structure and mechanical properties of matrix-free polymer nanocomposites (PNCs) constructed via polymer-grafted graphene nanosheets are studied. The dispersion of graphene sheets is characterized by the radial distribution function (RDF) between graphene sheets. We observe that a longer polymer chain length Lg leads to a relatively better dispersion state attributed to the formation of a better brick-mud structure, effectively screening the van der Waals interactions between sheets. By tuning the interaction strength εend-end between end functional groups of grafted chains, we construct physical networks with various robustness characterized by the formation of the fractal clusters at high εend-end values. The effects of εend-end and Lg on the mechanical properties are examined, and the enhancement of the stress-strain behavior is observed with the increase of εend-end and Lg. Structural evolution during deformation is quantified by calculating the orientation of the graphene sheets and their distribution, the stress decomposition, and the size of the clusters formed between end groups and their distribution. Then, we briefly study the effects of time and temperature on the self-healing behavior of these unique PNCs in the rubbery state. Lastly, the self-healing kinetics is quantitatively analyzed. In general, this work can provide some rational guidelines to design and fabricate matrix-free PNCs with both excellent mechanical and self-healing properties.

Fractality and the small-world property of generalised (u, v)-flowers

• We generalise ( u, v )-flowers by introducing probabilities into u and v . • Small-world property provides different values of different fractal dimensions. • Value of fractal cluster dimension reflects the behaviour of the mean path length. • Value of fractal box dimension reflects the behaviour of the diameter of the graph. So-called ( u, v )-flowers are recursive networks which produce self-similar structures with fractality or the small-world property. This paper generalises ( u, v )-flowers by introducing probabilities into the realisations of u and v , which enables the study of intermediate states between small and non-small worlds in fractal networks. We obtain the analytical relation between the diameter of the graph L and the graph size N , L ∼ N 1 / d L , and the degree distribution with a power-law form. We show that the difference between the fractal cluster d c and the fractal box d b dimensions reflects different behaviour of the mean path length 〈 l 〉 and L. There seems to be an apparent contradiction between fractality and the small-world property. However, the small-world property can be reconciled with fractality of the graph by size-dependent fractal dimensions where d b shows a size-dependent increase with an upper limit d L . The invariance and equivalence of d c , d b and d L are maintained only when both 〈 l 〉 and L are subject to the same non-small-world behaviour. Our investigation provides useful information for interpreting empirical fractal data and basic tools for studying the various dynamics that occur in networks.

Formation of CrxCyOz Coatings under Laser Treatment of Chromium Carbide Ceramics

The effect of the pulsed laser irradiation in air on Cr23C6 ceramic with Cr3C2 and Cr7C3 additives has been studied. It is established that the main process occurring in the zone of laser radiation is the melting of the ceramic surface of chromium carbide and the formation of a crater. This process is accompanied by the ejection of melt droplets from the crater zone and the dissociation of chromium carbides. As a result, the crater area is enriched in such ablation products as Cr, C, CO, and CO2. Reduction of hydrogen in the crater zone and neighboring areas leads to slowing down of the rate of oxidation processes, and the presence of ablation products such as Cr and C atoms promotes the process of synthesis of oxycarbides CrxCyOz (x ≈ 0.3–0.8, y ≈ 0.03–0.3, z ≈ 0.61–0.26) in the gas phase. Emission of the newly formed products of ablation from the crater and their distribution to the neighboring areas is accompanied by coagulation of nanoparticles into clusters. Depending on the length of flight of nanoclusters through different temperature zones and temperature of the deposition surface, oxycarbides with different morphology are formed: from islets (like fractal clusters) to film ones. The deposited ablation products are characterized by the signs of particle size “separation.” This makes it possible to create films of a given type and purpose. The passage of particles of different sizes through a gaseous medium containing oxygen is accompanied by the oxidation of oxycarbides to Cr2O3.