Diffusion-limited Aggregation Growth Research Articles

Different types of phase separation in binary monolayers of long chain alkyltrichlorosilanes on silicon oxide

In the present work, we studied the growth and morphology of binary monolayers made with triacontyltrichlorosilane (C30H61SiCl3) as the long chain and hexadecyltrichlorosilane (C16H33SiCl3), octadecyltrichlorosilane (C18H37SiCl3) or eicosyltrichlorosilane (C20H41SiCl3) as the short chain according to the deposition conditions on silicon oxide, using mainly atomic force microscopy, ellipsometry, and contact angle measurements. We distinguished three types of different phase separation. Besides the classical phase separation by islands of long chains in a surrounding phase of shorter molecules, we observed a separation involving dendritic “filaments” of long chains in a shorter chain phase, regardless of the couple of molecules studied. A third sort of phase separation also appears in the case of triacontyltrichlorosilane with octadecyltrichlorosilane or eicosyltrichlorosilane: formation of “holes”, i.e. islands of the shorter molecule in a surrounding phase of long chains. We obtained “hole” and “filament” type phase separation only by working below a critical temperature, which depends on the molecule length. Moreover, the level of ambient relative humidity was shown to have an impact on “hole” versus “filament” phase separation types. We then showed that for phase separation by islands or holes the composition of binary monolayers (RSAM) prepared at low humidity (18% RH) is almost the same as that of the silanisation solution (Rsol). Conversely, for SAMs prepared at high humidity (45% RH) RSAM is always lower than Rsol whatever the type of phase separation by islands or holes. Moreover, concerning phase separation with C30 filaments we observed that RSAM is independent from both the nature of the short molecule and the humidity conditions. Considering a diffusion limited aggregation growth model, we found that at high humidity the monolayer growth is mainly driven by the diffusion coefficient, while at low humidity the deposition rate from solution is the leading parameter of the growth. The efficiency of phase separation is also addressed.

Nanowire directed diffusion limited aggregation growth of nanoparticles

A binary solution of germanium nanoparticles and nanowires was drop cast on a silicon oxide surface. We investigated the dynamic behavior of the drop drying, successfully verifying the Diffusion Limited Aggregation growth mediated by nanowire attractors. The directed growth of nanostructures could be useful in view of device design.

Fractal analysis of Xylella fastidiosa biofilm formation

We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

Abnormal Stability in Growth of Diffusion-Limited Aggregation

An abnormal and unsteady growth of an isotropic cluster in diffusion-limited aggregation (DLA) is observed in stability analyses. Macroscopic fluctuation due to the delay of transition from a dendritic tip to a tip-splitting growth induces the anisotropy of DLA. An asymptotic deformation factor e ∞ = 0.0888 is obtained from large DLA clusters. A symmetric oval model proposed from the dual-stability growth of DLA gives an asymptotic fractal dimension of 1.7112 using e ∞ . The correspondence of this model to the box dimension is excellent.

Tourmaline nodules from Capo Bianco aplite (Elba Island, Italy): an example of diffusion limited aggregation growth in a magmatic system

The morphology of tourmaline nodules occurring in the Capo Bianco aplite (Elba Island, Italy) is studied. Outcrop features indicate that tourmaline nodules are the product of magmatic crystallization, as they are aligned along flow fields developed within the magmatic hosting mass. Mesoscopic observations indicate that nodule morphologies are very variable, from rounded to dendritic. Morphometric analyses show that tourmaline nodules are fractals and that fractal dimension quantifies their degree of irregularity. Numerical simulations of nodule growth are performed by using a Diffusion-Limited Aggregation process. The presence in natural samples of nodules with different morphologies is explained by considering a chaotic magmatic system characterized by a complex interplay between growth rate in different dynamical regions, latent heat of crystallization, and local convection dynamics. It is suggested that higher growth rates correspond to growth of tourmaline nodules in dynamical regions where the transfer of nutrients is very efficient. In such conditions, the latent heat released by the growing nodule is high, inducing strong local convection dynamics, destabilizing the nodule interface, and promoting the formation of dendritic morphologies. On the contrary, the growth of nodules in dynamical regions characterized by weak transfer of nutrients is inhibited leading to weak local convection dynamics and, consequently, to the formation of rounded morphologies.

STRUCTURE AND MORPHOLOGICAL STUDIES OF CdSe NANOCRYSTALS

Nanocrystalline thin films of CdSe have been synthesized from an acidic solution containing CdSO 4 and SeO 2 by a cathodic electrodeposition technique under galvanostatic condition. The crystal structure and morphology have been investigated by Grazing angle X-Ray Diffraction (GXRD), Transmission Electron Microscopy (TEM) and optical microscopic measurement. The X-Ray and TEM diffraction patterns of the deposit reveal a bimodal size distribution with the presence of cubic (zinc blende) phase in the deposit. The particle sizes have been estimated from GXRD measurement found to be 4 nm to 6 nm, comparable to that obtained from TEM analysis. A Branched Fractal Pattern (BFP) in CdSe nanocrystals has been observed by optical microscopy, suggesting a diffusion-limited aggregation growth mechanism with fractal dimension 1.69 ± 0.04.

Initial stages of WO 3 growth on silicon substrates

Ultrathin films (5 nm, 10 nm and 20 nm effective thickness) of WO 3 have been deposited in high vacuum (10 − 6 Torr) onto single crystal Si(100) substrates and studied with X-ray diffraction, atomic force microscopy, scanning tunneling microscopy and spectroscopy. The experiments have been carried out on “as-deposited” thin films or after 1 h post-deposition annealing at various temperatures (ranging from 300 °C to 500 °C). A size induced increase of the amorphous to crystalline (monoclinic) phase transition has been observed for the 5 nm and 10 nm films, with a critical crystallite size of 25 ± 5 nm and a critical temperature of 345 ± 5 °C. All the experimental evidences show that, upon annealing, there is a diffusion limited aggregation growth of WO 3 that forms large flat two-dimensional islands composed by aggregates of individual crystallites approximately uniform in size and shape. These islands are isolated in the 5 nm thin films, are connected in the 10 nm case and form a uniform patchwork in the 20 nm thin films. Scanning tunneling spectroscopy shows the opening of a large surface band gap (2.7 eV) in the 500 °C annealed films and the significant presence of in gap states for thin films prepared with a lower (below 400 °C) annealing temperature. These findings are discussed in view of the optimization of the best morphological, structural and electronic parameters to fabricate WO 3 gas sensing devices at the sub-micrometer length scale.

A Production Method for Aligned Nanowires on Arbitrary Materials

AbstractWe present a method that allows us to produce aligned metallic nanowires on almost any material. This method recently enabled us to produce interconnected platinum nanowire networks on polymeric Nafion® or gold nanowires on Teflon AF. We will explain the principle of this method by means of a reference material, the so called layered transition metal dichalcogenides (TMDC) crystals. The method is based on producing cracks in thin films as templates, using large sticking coefficient differences and long diffusion lengths. The underlying mechanism that forms the template cracks is mechanical stress. In the case of the TMDC crystals this stress is introduced in the substrate by an electronic interaction between the metal used for the nanowires and the TMDC-crystal. The large difference in the condensation coefficient is an immanent property of layered crystals for many different adsorbates. Obtained by cleavage along a so called “Van-der-Waals-gap”, surfaces of such crystals are atomically flat over hundreds of microns. As a consequence of their layered character the surfaces have no reconstruction and almost no step edges or other defects, which is the basis for the long diffusion length. In contrast, the rare defects have a very high sticking coefficient and act as excellent nucleation centers. Therefore, after metal evaporation on such surfaces in UHV, various structures can be formed in a self organized processes. We observed, e.g., clusters in fractal or geometric arrangements or large nanowire networks on the surfaces [1]. In order to understand, why the different structures form, a systematic study of the growth parameters, (nucleation, diffusion length, evaporated metal, influence of the substrate-crystal), is necessary. Therefore, we first carried out diffusion studies on these surfaces. We could show that in extreme cases (Cu on metallic TaS2) diffusion length of more than 50νm could be observed combined with a nucleation probability of almost zero. This is evident from a growth mode showing similarities with the DLA (Diffusion Limited Aggregation) growth process. In contrast, metal diffusion (Cu) on the geometrically similar surfaces on the semiconducting (WSe2) surface shows much a shorter diffusion length and no DLA growth. We suggest a model to explain the different diffusion behavior as a key to understand the different self organized structures. Learning from the TMDC crystals, we show the application on technological more important materials.

New Indices of Structure Formation in Clusters of Non-Metallic Inclusions.

Computer simulations have been conducted to investigate the cluster formation process. Clusters can be expressed with some indices, including new ones. Growth of diffusion-limited aggregation (DLA) and ballistic aggregation (BA) are characterized by their indices, for example, cluster diameter, fractal dimension (D), density distribution along radius and so on. As the consequences of comparison between the both types of clusters, BA seems to be more harmful than DLA. Particle jump length (L) affects the cluster formation. When L is situated middle between DLA and BA, values of D, cluster diameter and cluster shape are also intermediate. From the fact that these new indices have great influence on structure formation, we can get possibility to identify the process which the clusters are generated in.

HAUSDORFF DIMENSION AND SCALING NATURE OF ANISOTROPY DIFFUSION DLA CLUSTER

In this paper,the effect of the anisotropy diffusion on the growth of diffusion-limited aggregation(DLA) clusters is discussed.Our computer simulation results verify that DLA clusters grown with anisotropic diffusion rules have a striking overall diamond shape.A new anisotropic diffusion equation of particles is derived.The Hausdorff dimension of a two-dimensional DLA cluster in the anisotropic diffusion is calculated.The results show that the effective angle βeff=min(βix,βiy).In addition,the generalized dimension Dq of the anisotropic diffusion DLA is also discussed and an expression of the generalized dimension Dq is obtained using the modified wedge model.

Universality and Scale Invariant Dynamics in Laplacian Fractal Growth

The individuation of the scale invariant dynamics in Laplacian fractal growth processes, like diffusion-limited aggregation (DLA), is an important problem whose solution would clarify some crucial issues concerning the origin of fractal properties and the identification of universality classes for such models. Here, we develop a real space renormalization group scheme to study the dynamic evolution of DLA in a restricted space of relevant parameters. In particular, we investigate the effect of a sticking probability P s and an effective noise reduction parameter S. The renormalization equations flow towards an attractive fixed point corresponding to the scale invariant DLA dynamics ([Formula: see text], S*≃2.0). The existence of a non-trivial fixed point value for S, shows that noise is spontaneously generated by the DLA growth process, and that screening, which is at the origin of fractal properties, persists at all scales.

Diffusion-limited aggregation as a growth process statistically invariant under an infinitesimal affine transformation of mass and multiple spatial coordinates

This work has two major results. First, it proposes a model of diffusion-limited aggregation (DLA) that accounts for the diversity of mass dependence exponents of four characteristic lengths: radius of gyration, major and minor asymmetry axes, and width of active growth zone. Second, it uses the agreement of model predictions with simulation data to show that the invariance of DLA growth probability under an infinitesimal affine transformation of mass and several growth zone spatial coordinates is consistent with the results of simulation data, to a high degree of approximation, in the range of aggregate mass from 200 to 50 000 for the first three of the above characteristic lengths, and in the range 1100\char21{}440 000 for the active zone width.

Diffusion-limited aggregation with Eden growth surface kinetics

Abstract The diffusion-limited aggregation (DLA) model has been generalized to include homogeneous Eden growth surface kinetics. On-lattice simulations are compared with theory in the deterministic zero-noise limit. As the cluster grows, for a fixed value of the surface kinetics parameter Γ, there is a crossover from compact Eden growth to dendritic DLA growth. Larger Eden clusters are obtained at larger values of Γ. A theoretical analysis based on conformal mapping techniques provides a good description of this behaviour.

Tip lengths and whiskering in noise-reduced diffusion-limited aggregation

The authors examine the nature of the tunable family of patterns obtained from the discrete eta -DLA model in the deterministic zero-noise limit. The eta -DLA model is a variant of the standard diffusion-limited aggregation (DLA) model in which the DLA growth probabilities are raised to the power eta . The observed morphologies, which range from compact Eden clusters for eta =0 through to sharp needle-like clusters with increasing eta , can be characterized by a sequence of step lengths in a stable staircase structure proceeding back from the tip. Side-branch whiskers, which are found on the triangular lattice but not on the square lattice, occur closer to the tip as eta is increased. Beyond a value eta c, whiskers are found immediately behind the tip. They derive the length of the exposed tip as a function of eta using a stationary contour approximation and conformal mapping methods. A theoretical estimate for eta c is derived by refining this approach to incorporate the possible shielding of surface sites by aggregate sites. Their theoretical results are in excellent agreement with the numerical results on both lattices.

The potential distribution around growing fractal clusters

THE process of diffusion-limited aggregation (DLA) is a common means by which clusters grow from their constituent particles, as exemplified by the formation of soot and the aggregation of colloids in solution. DLA growth is a probabilistic process which results in the formation of fractal (self-similar) clusters. It is controlled by the harmonic measure (the gradient of the electrostatic potential) around the cluster's boundary. Here we show that interactive computer graphics can provide new insight into this potential distribution. We find that points of highest and lowest growth probability can lie unexpectedly close together, and that the lowest growth probabilities may lie very far from the initial seed. Our illustrations also reveal the prevalence of 'fjords' in which the pattern of equipotential lines involves a 'mainstream' with almost parallel walls. We suggest that an understanding of the low values of the harmonic measure will provide new understanding of the growth mechanism itself.