Diffusion-limited Aggregation Research Articles

A solid-to-solid metallic conversion electrochemistry toward 91% zinc utilization for sustainable aqueous batteries.

The diffusion-limited aggregation (DLA) of metal ion (Mn+) during the repeated solid-to-liquid (StoL) plating and liquid-to-solid (LtoS) stripping processes intensifies fatal dendrite growth of the metallic anodes. Here, we report a new solid-to-solid (StoS) conversion electrochemistry to inhibit dendrites and improve the utilization ratio of metals. In this StoS strategy, reversible conversion reactions between sparingly soluble carbonates (Zn or Cu) and their corresponding metals have been identified at the electrode/electrolyte interface. Molecular dynamics simulations confirm the superiority of the StoS process with accelerated anion transport, which eliminates the DLA and dendrites in the conventional LtoS/StoL processes. As proof of concept, 2ZnCO3·3Zn(OH)2 exhibits a high zinc utilization of ca. 95.7% in the asymmetry cell and 91.3% in a 2ZnCO3·3Zn(OH)2 || Ni-based full cell with 80% capacity retention over 2000 cycles. Furthermore, the designed 1-Ah pouch cell device can operate stably with 500 cycles, delivering a satisfactory total energy density of 135 Wh kg−1.

Dendritic Self-assembled Structures from Therapeutic Charged Pentapeptides.

CRENKA [Cys-Arg-(NMe)Glu-Lys-Ala, where (NMe)Glu refers to N-methyl-Glu], an anti-cancer pentapeptide that induces prostate tumor necrosis and significant reduction in tumor growth, was engineered to increase the resistance to endogenous proteases of its parent peptide, CREKA (Cys-Arg-Glu-Lys-Ala). Considering their high tendency to aggregate, the self-assembly of CRENKA and CREKA into well-defined and ordered structures has been examined as a function of peptide concentration and pH. Spectroscopic studies and atomistic molecular dynamics simulations reveal significant differences between the secondary structures of CREKA and CRENKA. Thus, the restrictions imposed by the (NMe)Glu residue reduce the conformational variability of CRENKA with respect to CREKA, which significantly affects the formation of well-defined and ordered self-assembly morphologies. Aggregates with poorly defined morphology are obtained from solutions with low and moderate CREKA concentrations at pH 4, whereas well-defined dendritic microstructures with fractal geometry are obtained from CRENKA solutions with similar peptide concentrations at pH 4 and 7. The formation of dendritic structures is proposed to follow a two-step mechanism: (1) pseudo-spherical particles are pre-nucleated through a diffusion-limited aggregation process, pre-defining the dendritic geometry, and (2) such pre-nucleated structures coalesce by incorporating conformationally restrained CRENKA molecules from the solution to their surfaces, forming a continuous dendritic structure. Instead, no regular assembly is obtained from solutions with high peptide concentrations, as their dynamics is dominated by strong repulsive peptide-peptide electrostatic interactions, and from solutions at pH 10, in which the total peptide charge is zero. Overall, results demonstrate that dendritic structures are only obtained when the molecular charge of CRENKA, which is controlled through the pH, favors kinetics over thermodynamics during the self-assembly process.

Heterostructured Carbon Mesonetworks By Electrospinning

Thermodynamically stable dispersions of carbon nanotubes and graphene in water are prepared at high concentrations (6-17 % by weight) by scalable liquid phase exfoliation processing using polymerized ionic liquid (PIL) stabilizers (nanolatexes, nanoparticles). This stability emanates from stabilizers that are based on imidazolium moieties that provide strong binding to the sp2 surfaces of nanocarbons while exhibiting high solvation by water. These dispersions provide means to make advanced materials and coatings exhibiting ultra-high thermal conductivity, shear switchable rheo-optical fluids, and heterostructured and high specific surface area coatings. Such advanced coatings provide a platform for catalytic membranes and electrocatalytic electrodes derived by electrospinning and further extend the utility and potential of 2D materials. We demonstrate how nonwoven mats made by electrospinning can dimensionally grow beyond the inherent 1D fibers, intrinsic to electrospinning, to provide 2D- heterostructured networks. These networks are obtained by operating close to an instability boundary, the Rayleigh instability, where fluid (electrospinning) streams decompose into droplets. Two classes of such networks are demonstrated and discussed, wherein the carrier fluid is an aqueous solution of poly(vinyl alcohol), PVA:(i) The first is derived from aqueous graphene (2D) dispersions stabilized by 0D PIL nanolatexes (NLs) 20-30 nm in diameter. As the Plateau-Rayleigh instability is approached, the usual 1D fiber morphology transforms to (preserve) reveal the intrinsic 2D morphology of individual nanoplatelets that are connected by nanofibers.(ii) The second is derived from aqueous MWCNT (1D) dispersions stabilized by 0D NLs. As the Plateau-Rayleigh instability is approached, on drying a heterostructured 2D network is formed, where 0D (NL) + 1D (MWCNT) yields 2D networks. These 2D “microfilms” form from collapse of multiphase fluid menisci comprising aqueous PVA solution and NLs shed from MWCNT surfaces and are supported by mini-networks of MWCNTs.Morphology tuning, modulation of ionic and electrical conductivities, and directions for future applications are discussed. These examples provide bases for increasing network dimensionality using colloidal re-equilibration, rather than by diffusion-limited aggregation.

Growth of stationary Hastings–Levitov

We construct and study a stationary version of the Hastings-Levitov$(0)$ model. We prove that, unlike in the classical HL$(0)$ model, in the stationary case the size of particles attaching to the aggregate is tight, and therefore SHL$(0)$ is proposed as a potential candidate for a stationary off-lattice variant of Diffusion Limited Aggregation (DLA). The stationary setting, together with a geometric interpretation of the harmonic measure, yields new geometric results such as stabilization, finiteness of arms and arm size distribution. We show that, under appropriate scaling, arms in SHL$(0)$ converge to the graph of Brownian motion which has fractal dimension $3/2$. Moreover we show that trees with $n$ particles reach a height of order $n^{2/3}$, corresponding to a numerical prediction of Meakin from 1983 for the gyration radius of DLA growing on a long line segment.

Solvent effects on the rheology of fuel cell catalyst ink and the adsorption of ionomers on the particles

The solvent affects the morphology of ionomers, agglomeration structure, adsorption of ionomers on carbon or catalyst particles, and rheology in the proton exchange membrane fuel cell (PEMFC) ink, which are all related to the microstructure of catalyst inks. We investigated the link between the morphology of the ionomers or the fractal dimension (df) of graphitized carbon (GC) dispersion and the microstructure of the catalyst ink by solvent to change the morphology of the ionomers or df of GC dispersion. The nuclear magnetic resonance results showed relatively low mobility of the ionomer in ethylene glycol (EG), resulting in a weak interaction between the ionomer and EG. GC in water, EG, and n-propanol (nPA) form transition gels with a network structure by a diffusion-limited aggregation mechanism, with df of 1.76 ± 0.03, 1.95 ± 0.04, and 2.01 ± 0.06, respectively. Moreover, the addition of ionomers reduces the viscosity of inks due to the introduction of steric hindrance and an increase in electrostatic repulsion, transforming the ink from shear-thinning to Newtonian fluids. Further, the interaction between ionomer and particles in GC and graphitized-carbon-supported platinum (Pt/GC) inks is solvent-dependent, and nPA is more favorable than water and EG for ionomer adsorption on GC. These findings provide valuable insight into the internal interactions and microstructure of PEMFC catalyst inks.

A Computational Template for Three-Dimensional Modeling of the Vascular Scaffold of the Human Thyroid Gland.

We recently designed an innovative scaffold-bioreactor unit for the bioengineering of a three-dimensional (3D) bioartificial human thyroid gland or its miniaturized replica as a part of a microfluidic chip test system. This device is based on the evidence that the 3D geometry of the intraglandular stromal/vascular scaffold (SVS; i.e., the fibrous and vascular matrix) of mammalian viscera plays a key role in guiding growth and differentiation of in vitro seeded cells. Therefore, we initiated a research program focused on computer-aided reconstruction of the 2nd to 4th order intralobar arterial network (IAN) of the human thyroid gland as a reliable surrogate for its 3D SVS, to be used as an input for rapid prototyping of a biomaterial replica. To this end, we developed a computational template that works within the Mathematica environment, giving rise to a quasi-fractal growth of the IAN distribution, constrained within an approximation of the thyroid lobe shape as a closed surface. Starting from edge detection of planar images of real human thyroid lobes acquired by in vivo real-time ultrasonography, we performed data approximation of the lobar profiles based on splines and Bezier curves, providing 3D lobar shapes as geometric boundaries for vessel growth by a diffusion-limited aggregation model. Our numerical procedures allowed for a robust connection between development of lobar arterial trees and thyroid lobe shape, led to a vascular self-similarity consistent with that of a cadaveric lobar arterial cast, and reproduced arterial vessels in a proportion not statistically different from that described for the real human thyroid gland. We conclude that our algorithmic template offers a reliable reproduction of the extremely complex IAN of the adult human thyroid lobe, potentially useful as a computational guidance for bioprinting of thyroid lobe matrix replicas. In addition, due to the simplicity and limited number of morphometrical parameters required by our system, we predict its application to the design of a number of patient-tailored human bioartificial organs and organs-on-chip, including parenchymal viscera and bones. Impact statement The study introduces the computer simulation of the three-dimensional (3D) intrinsic vascular matrix of the human thyroid gland, offering a general concept applicable to a number of other human viscera. Indeed, it provides a flexible software tool for reproduction of a 3D surrogate of the organ's 3D stromal matrix, suitable for eventual 3D bioprinting with biomaterials, and recellularization with organ-specific stem cells/progenitors. The final expectation is the design of patient-tailored 3D organ's matrices upon clinical request.

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

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

Mesoscale Aggregation of Sulfur-Rich Asphaltenes: In Situ Microscopy and Coarse-Grained Molecular Simulation.

Asphaltene aggregation is critical to many natural and industrial processes, from groundwater contamination and remediation to petroleum utilization. Despite extensive research in the past few decades, the fundamental process of sulfur-rich asphaltene aggregation still remains not fully understood. In this work, we have investigated the particle-by-particle growth of aggregates formed with sulfur-rich asphaltene by a combined approach of in situ microscopy and molecular simulation. The experimental results show that aggregates assembled from sulfur-rich asphaltene have morphologies with time-dependent structural self-similarity, and their growth rates are aligned with a crossover behavior between classic reaction-limited aggregation and diffusion-limited aggregation. Although the particle size distribution predicted using the Smoluchowski equation deviates from the observations at the initial stage, it provides a reasonable prediction of aggregate size distribution at the later stage, even if the observed cluster coalescence has an important effect on the corresponding cluster size distribution. The simulation results show that aliphatic sulfur exerts nonmonotonic effects on asphaltene nanoaggregate formation depending on the asphaltene molecular structure. Specifically, aliphatic sulfur has a profound effect on the structure of rod-like nanoaggregates, especially when asphaltene molecules have small aromatic cores. Interactions between aliphatic sulfur and the side chain of neighboring molecules account for the repulsive forces that largely explain the polydispersity in the nanoaggregates and corresponding colloidal aggregates. These results can improve our current understanding of the complex process of sulfur-rich asphaltene aggregation and sheds light on designing efficient crude oil utilization and remediation technologies.

Brownian Tree‐Shaped Dendrites in Quasi‐2D Perovskite Films and Their Impact on Photovoltaic Performance (Adv. Mater. Interfaces 13/2022)

Dendrite Formation in Quasi-2D Perovskite Films for Solar Cells In article number 2102231, Fei Zheng, Kenneth P. Ghiggino, and co-workers report that Brownian tree-shaped dendrites that form in quasi-2D perovskite films are beneficial to perovskite solar cell performance. The dendrites are grown by the diffusion-limited aggregation of thicker Ruddlesden-Popper perovskite phase domains resulting in improved film morphology.

Peptide-Induced Fractal Assembly of Silver Nanoparticles for Visual Detection of Disease Biomarkers.

We report the peptide-programmed fractal assembly of silver nanoparticles (AgNPs) in a diffusion-limited aggregation (DLA) mode, and this change in morphology generates a significant color change. We show that peptides with specific repetitions of defined amino acids (i.e., arginine, histidine, or phenylalanine) can induce assembly and coalescence of the AgNPs (20 nm) into a hyperbranched structure (AgFSs) (∼2 μm). The dynamic process of this assembly was systematically investigated, and the extinction of the nanostructures can be modulated from 400 to 600 nm by varying the peptide sequences and molar ratio. According to this rationale, two strategies of SARS-CoV-2 detection were investigated. The activity of the main protease (Mpro) involved in SARS-CoV-2 was validated with a peptide substrate that can bridge the AgNPs after the proteolytic cleavage. A sub-nanomolar limit of detection (0.5 nM) and the capacity to distinguish by the naked eye in a wide concentration range (1.25-30 nM) were achieved. Next, a multichannel sensor-array based on multiplex peptides that can visually distinguish SARS-CoV-2 proteases from influenza proteases in doped human samples was investigated.

Finite dimension and particle heterogeneous DLAs.

We study heterogeneous Diffusion Limited Aggregates (DLAs) i.e. those formed by a mixture, in different proportions, of 4-legged and 2-legged particles. We fixed the total number of particles, let the proportions vary, and computed their finite dimension, a recent addition to the list of "fractal" dimensions. At one extreme, when all particles are 4-legged, the corresponding DLAs are complex, fractal structures whose appearance resembles very much that of the DLAs that occur in Nature. At the other extreme, when almost all particles are 2-legged, the DLAs lose much of their complexity and acquire long rectilinear stretches so that their appearance resembles more and more the structure of the underlying lattice. We expected the complexity in between would decrease monotonically, and this would be reflected in the finite dimension of the corresponding DLAs. However, the finite dimension first increases and then, when the proportion of 4-legged to 2-legged particles is about 30 to 70, starts decreasing. In the paper, we study and explain the mechanisms behind this unexpected, counter-intuitive behaviour.

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, Rm, with respect to the fractal dimension, df, and the fluid penetration depth, δ, have largely remained unexplored. Herein, we examine these aspects across a wide range of df'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 df 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 = Rm/Rg (where Rg is the radius of gyration of the cluster), this study reveals a monotonically increasing trend for β with increasing df. 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/Rg) approaches asymptotic constancy with respect to cluster size in contrast to a weak dependency of the form δ* ∼ (Rg/a)-(df-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.

Computational Complexity of Biased Diffusion-Limited Aggregation

Diffusion-Limited Aggregation (DLA) is a cluster growth model that consists of a set of particles that are sequentially aggregated over a two-dimensional grid. In this paper, we introduce a biased version of the DLA model, in which particles are limited to move in a subset of possible directions. We denote $k$-DLA the model where the particles move only in $k$ possible directions. We study the biased DLA model from the perspective of Computational Complexity, defining two decision problems The first problem is Prediction, whose input is a site of the grid $c$ and a sequence $S$ of walks, representing the trajectories of a set of particles. The question is whether a particle stops at site $c$ when sequence $S$ is realized. The second problem is Realization, where the input is a set of positions of the grid, $P$. The question is whether there exists a sequence $S$ that realizes $P$, i.e. all particles of $S$ exactly occupy the positions in $P$. Our aim is to classify the Prediciton and Realization problems for the different versions of DLA. We first show that Prediction is P-Complete for 2-DLA (thus for 3-DLA). Later, we show that Prediction can be solved much more efficiently for 1DLA. In fact, we show that in that case, the problem is NL-Complete. With respect to Realization, we show that restricted to 2DLA the problem is in P, while for 1DLA is in L.

Simulation of cellular-dendritic solidification structures of binary alloys in three-dimensional growth using a multiparticle diffusion-limited aggregation model

Abstract Solidification in binary alloy melts was simulated with two different three-dimensional models, that differ in the way the role of the solid/liquid interface energy on the solidification is expressed: either surface rearrangement or a surface curvature-dependent attachment probability was applied. In the melt, the simultaneous diffusion of all diffusing particles (atoms) was taken into account. Cellular –dendritic growth modes, as observed in practice, could be well simulated. The surface rearrangement model is essential for exhibiting details (as facetting) and the effect of the next-nearest neighbour interaction.

Modification of the RLA model for presenting a cluster system of a composite material with a fractal filler structure

The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP). As a result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.

The growth simulation of pine-needle like structure with diffusion-limited aggregation and oriented attachment.

A growth model combined with diffusion-limited aggregation (DLA) and oriented attachment (OA) is developed for deducing quantitative understanding of the growth process of pine-needle like structures. We define the completely random parameters for describing the realistic Brownian motion in DLA. The results indicate that the cluster by DLA changes from random branches to regular needles by the introduction of OA. And the cluster of DLA and OA has a fractal dimensionality of about 1.0 during the whole growth process. The maximum length of needels (Lmax) depends on the number of particles (Np). They satisfy the relation Lmax = aNpb (a and b are constant) over the whole range. The model has also been used to describe the formation of needles on a line, plane and sphere. The growth of needles has obvious steric hindrance from the outer needles. In particular, only one needle grows in the later period in the plane.

Effect of annealing temperature on the kinetics of aluminum-induced crystallization of amorphous silicon suboxide thin films

In this work, the kinetics of aluminum-induced crystallization (AIC) of non-stoichiometric silicon oxide a-SiO0.25 was investigated for the case of annealing at temperatures of 370, 385 and 400oC, as a result of which thin films of polycrystalline silicon were obtained. It is shown that, at low annealing temperatures, the surface morphology of the crystalline material is represented by dendritic structures corresponding to the growth model with diffusion-limited aggregation. In addition, with increasing annealing temperature, the nucleation density increases from 3 to 53 mm-2. From the Arrhenius plot, the activation energy of the a-SiO0.25 AIC was obtained for the first time and appeared to be 3.7± 0.4 eV. Keywords: aluminum-induced crystallization, silicon suboxide thin films, polycrystalline silicon, activation energy.

Про один підхід до формалізації процесу поширення інформації на основі агрегації, що обмежена дифузією

This article examines one of the approaches to the formalization of information dissemination processes based on the diffusion-limited aggregation model, using elements of cellular automata and their analogs. The model describes the dynamics of the information dissemination process without the influence of the mass media by taking into account the facts of information exchange that occurs during communication between participants of an arbitrary target audience. It is believed that the process is characterized by the property of self-similarity. An approach is proposed that makes it possible to study the dynamics of information dissemination processes, taking into account the attitude of the group members to each other and the attitude of the participants to the input information. As a result, an assessment of the effectiveness of the information dissemination process was obtained, which allows drawing conclusions regarding the success of information promotion measures. To demonstrate the processes of information dissemination modeled on the basis of the approach, the results of numerical experiments are presented, in which the implementation of the information exchange procedure for each person is limited to three members of the target group.

ИССЛЕДОВАНИЕ ЗАКОНОМЕРНОСТЕЙ ПРОЦЕССА ХИМИЧЕСКОГО ОСАЖДЕНИЯ ДИСУЛЬФИДА МОЛИБДЕНА ИЗ ГАЗОВОЙ ФАЗЫ В СИСТЕМЕ MO(CO)6-C2H6S2

In this article, the influence of the temperature and composition of the gas in the reactor on the morphology, structure, and composition of thin films deposited using the new sulfur-containing reagent C2H6S2 was studied. The existence of horizontal layers and their deformation, confirmed by X-ray diffraction and Raman scattering, suggest that vertical dendrites grow from horizontal layers that bend due to deformation, which is very similar to the growth of vertical nanoleaves. However, the transition from vertical dendritic growth at low temperature and high deposition rates to vertical sheet growth at high temperature or lower deposition rates suggests that the formation mechanism can be described by a diffusion-limited aggregation model. The results of experimental studies have shown that vertical dendrites are the main morphology of films deposited at low pressure in the reactor, while at a relatively high pressure it is possible to grow a monolayer in a reasonable time. The probability of formation of layers consisting of dendrites or flat fragments strongly depends on both the deposition temperature and the composition of the reaction gas mixture in the reactor.

Self-Organized Fractal Structures on Plasma-Exposed Silver Surface.

Planar fractal microstructure is observed on the silver film treated by positive corona discharge for the first time. Due to the abundant positive ions driven by the electrical field of positive polarity, surface modification is mainly induced by the plasma oxidation effect, resulting in a large scale of dendritic pattern with self-similarity and hierarchy. In contrast, negative ions dominate the plasma-film interaction under negative corona discharge condition, leading to a different surface morphology without fractal characteristics. A growth model based on the modified diffusion-limited aggregation (DLA) theory is proposed to describe the formation of the dendritic fractal structure, whilst the physics behind is attributed to the electric field directed diffusion of the positive ions around the surface roughness. Numerical simulation verifies the high density of the hot spot in the dendritic pattern, which may enable potential applications in fractal photonic metamaterials.