Scaling structure of the growth-probability distribution in diffusion-limited aggregation processes

Noble metal nanodendrites: growth mechanisms, synthesis strategies and applications

Inorganic nanodendrites (NDs) have become a kind of advanced nanomaterials with broad application prospects because of their unique branched architecture. The structural characteristics of nanodendrites include highly branched morphology, abundant tips/edges and high-index crystal planes, and a high atomic utilization rate, which give them great potential for usage in the fields of electrocatalysis, sensing, and therapeutics. Therefore, the rational design and controlled synthesis of inorganic (especially noble metals) nanodendrites have attracted widespread attention nowadays. The development of synthesis strategies and characterization methodology provides unprecedented opportunities for the preparation of abundant nanodendrites with interesting crystallographic structures, morphologies, and application performances. In this review, we systematically summarize the formation mechanisms of noble metal nanodendrites reported in recent years, with a special focus on surfactant-mediated mechanisms. Some typical examples obtained by innovative synthetic methods are then highlighted and recent advances in the application of noble metal nanodendrites are carefully discussed. Finally, we conclude and present the prospects for the future development of nanodendrites. This review helps to deeply understand the synthesis and application of noble metal nanodendrites and may provide some inspiration to develop novel functional nanomaterials (especially electrocatalysts) with enhanced performance.

Quantitative investigation of the formation and growth of palladium fractal nanocrystals by liquid-cell transmission electron microscopy

Liquid-cell transmission electron microscopy reveals the early formation stage of fractal nanocrystals and the effects of supersaturation on their growth dynamics.

Growth rate distribution of NH4Cl dendrite and its scaling structure

Scaling structure of the growth rate distribution on the interface of a dendritic pattern is investigated. The distribution is evaluated for an NH4Cl quasi-two-dimensional crystal by numerically solving the Laplace equation with the boundary condition taking account of the surface tension effect. It is found that the distribution has multifractality and the surface tension effect is almost ineffective in the unscreened large growth region. The values of the minimum singular exponent and the fractal dimension are smaller than those for the diffusion-limited aggregation pattern. The Makarov's theorem, the information dimension equals one, and the Turkevich-Scher conjecture between the fractal dimension and the minimum singularity exponent hold.

Multifractal analysis of the branch structure of diffusion-limited aggregates

We examine the branch structure of radial diffusion-limited aggregation (DLA) clusters for evidence of multifractality. The lacunarity of DLA clusters is measured and the generalized dimensions D(q) of their mass distribution is estimated using the sandbox method. We find that the global n-fold symmetry of the aggregates can induce anomalous scaling behavior into these measurements. However, negating the effects of this symmetry, standard scaling is recovered.

Multifractal analysis of human retinal vessels

In this paper, it is shown that vascular structures of the human retina represent geometrical multifractals, characterized by a hierarchy of exponents rather then a single fractal dimension. A number of retinal images from the STARE database are analyzed, corresponding to both normal and pathological states of the retina. In all studied cases, a clearly multifractal behavior is observed, where capacity dimension is always found to be larger then the information dimension, which is in turn always larger then the correlation dimension, all the three being significantly lower then the diffusion limited aggregation (DLA) fractal dimension. We also observe a tendency of images corresponding to the pathological states of the retina to have lower generalized dimensions and a shifted spectrum range, in comparison with the normal cases.

Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles, and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through the Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e., it can be analyzed in terms of its f(alpha) multifractal spectrum. For low dipolar strengths, the f(alpha) spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing the dipolar strength both the minimal local growth exponent alpha(min) and the information dimension D(1) decrease, while the fractal dimension remains the same.

Multifractal structure of the harmonic measure of diffusion-limited aggregates

The method of iterated conformal maps allows one to study the harmonic measure of diffusion-limited aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of the measure in the deepest fjords that were hitherto screened away from any numerical probing. We resolve probabilities as small as 10(-35), and present an accurate determination of the generalized dimensions and the spectrum of singularities. We show that the generalized dimensions D(q) are infinite for q<q*, where q* is of the order of -0.2. In the language of f(alpha) this means that alpha(max) is finite. The f(alpha) curve loses analyticity (the phenomenon of "phase transition") at alpha(max) and a finite value of f(alpha(max)). We consider the geometric structure of the regions that support the lowest parts of the harmonic measure, and thus offer an explanation for the phase transition, rationalizing the value of q* and f(alpha(max)). We thus offer a satisfactory physical picture of the scaling properties of this multifractal measure.

Thermodynamic formalism of the harmonic measure of diffusion limited aggregates: phase transition

We study the nature of the phase transition in the multifractal formalism of the harmonic measure of diffusion limited aggregates. Contrary to previous work that relied on random walk simulations or ad hoc models to estimate the low probability events of deep fjord penetration, we employ the method of iterated conformal maps to obtain an accurate computation of the probability of the rarest events. We resolve probabilities as small as 10(-35). We show that the generalized dimensions D(q) are infinite for q<q*, where q* = -0.18+/-0.04. In the language of f(alpha) this means that alpha(max) is finite. We present a converged f(alpha) curve.

Left-sided multifractality in a binary random multiplicative cascade

In this paper we study a binary random multiplicative cascade. Specifically, the cascade is used to produce and study left-sided multifractal random measures. Extensive numerical simulations of the random cascade process were undertaken and f(alpha) spectra obtained and compared with the analytical results. We believe that this model and approach can serve as a simple and fundamental tool in the analysis and understanding of physical systems possessing an underlying multiplicative structure.