Diffusion-limited Aggregation Process Research Articles

Small-Angle Neutron Scattering Study of Natural Aquatic Nanocolloids

We examine the potential of small-angle neutron scattering (SANS) as a quantitative tool for studying nanostructure and length scales in natural freshwater aquatic colloidal dispersions (river water, river bed sediments, agricultural field drainage and slurry). Our results show that natural aquatic colloids are generally fractal with 3D network-type structures. None of these structures are consistent with diffusion-limited (DLCA) or reaction-limited (RLCA) particleparticle aggregation processes. The results also suggest three characteristic length scales: one ca. 3-10 nm, which we identify with "primary particle" sizes, another of ca. 20-50 nm suggestive of small aggregates, and the last ca. 50-200 nm which we postulate arises from transient networks of the aggregates. The role of organic matter in mediating colloid structure in aquatic dispersions was examined by neutron contrast variation and by measuring samples both before and after treatment with hydrogen peroxide. The results suggest that the aggregate network structure is mediated by organic matter.

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.

Intergrowth mechanism of silicon nanowires and silver dendrites

The intergrowth mechanism of silicon nanowires and silver dendrites formed by electroless metal deposition has been investigated by scanning electron microscopy. A self-assembled localized microscopic electrochemical cell model can adequately describe the self-organized Si nanowires growth. Using these in situ prepared Si nanowire arrays as templates, a diffusion-limited aggregation process is proposed to explain the formation of the silver dendritic nanostructures.

Synthetic melanin films: Assembling mechanisms, scaling behavior, and structural properties

In this work we report on the surface characterization of melanin thin films prepared using both water-based and organic solvent-based melanin syntheses. Atomic force microscopy (AFM) analysis of these films suggests that the organic solvent synthesis provides relatively planar basic melanin structures; these basic structures generate surface steps with height in the range of 2–3nm and small tendency to form larger aggregates. The scaling properties obtained from the AFM data were used to infer the assembling mechanisms of these thin films which depend on the solvent used for melanin synthesis. The behavior observed in organic solvent-based melanin suggests a diffusion-limited aggregation process. Thus films with good adhesion to the substrate and smoother morphologies than water-prepared melanin films are obtained. Electronic structure calculations using a conductorlike screening model were also performed in order to elucidate the microscopic processes of thin film formation. Our results suggest that the agglomerates observed in hydrated samples originate from reaction with water at specific locations on the surface most likely defects on the planar structure.

Spatial embedding of neuronal trees modeled by diffusive growth

The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees based on diffusion-limited aggregation process. The model reproduces diverse neuronal shapes (i.e., granule cells, Purkinje cells, the basal and apical dendrites of pyramidal cells, and the axonal trees of interneurons) by changing only the size of the growth area, the time span of pruning, and the spatial concentration of ‘neurotrophic particles’. Moreover, the presented model shows how competition between neurons can affect the shape of the dendritic trees. The model reveals that the creation of complex (but reproducible) dendrite-like trees does not require precise guidance or an intrinsic plan of the dendrite geometry. Instead, basic environmental factors and the simple rules of diffusive growth adequately account for the spatial embedding of different types of dendrites observed in the cortex. An example demonstrating the broad applicability of the algorithm to model diverse types of tree structures is also presented.

Self-assembled growth and green emission of gold nanowhiskers

Unique structured Au nanowhiskers were fabricated via electroless metal deposition on Si wafer in KAuCl4–HF solution. A self-assembled localized microscopic electrochemical cell model and a diffusion-limited aggregation process are associated with the formation of Au nanowhiskers. A green photoluminescence (PL) band was recorded. Spectral analyses suggest the green PL arises from the radiative recombination of sp-band electrons with d-band holes in the Au nanowhiskers and its intensity enhancement is due to local electric field connected with the Au particle plasmons oscillation. A red PL band was also observed from long-time etched Si substrates and proposed to be related to Si nanocrystals in the surface layer of etched Si wafer. Its stability was considered to be owing to the formation of stable Si–Au bonds on the surfaces of Si nanocrystals.

Self-organized synthesis of micrometer scale silver disks by electroless metal deposition on Si-incorporated diamond-like carbon films

Via electroless metal deposition, we have successfully synthesized micrometer scale silver disks with perfectly hexagonal structure on Si-incorporated diamond-like carbon (Si-DLC) films and discussed their growth mechanism in terms of self-assembled localized microscopic electrochemical cell model and diffusion-limited aggregation process. The self-assembled electrochemical reaction automatically ceases by exhausting all the Si nanocrystalline clusters on the surface of the amorphous carbon matrix. The growth of silver disks on Si-DLC films follows Volmer–Weber growth mechanism and the rate of nucleation is slow. The disks have a fcc crystal structure with (1 1 1) stacking faults lying parallel to the (1 1 1) surface and extending across entire disk.

Self-organized synthesis of silver dendritic nanostructures via an electroless metal deposition method

Unique silver dendritic nanostructures, with stems, branches, and leaves, were synthesized with self-organization via a simple electroless metal deposition method in a conventional autoclave containing aqueous HF and AgNO3 solution. Their growth mechanisms are discussed in detail on the basis of a self-assembled localized microscopic electrochemical cell model. A process of diffusion-limited aggregation is suggested for the formation of the silver dendritic nanostructures. This nanostructured material is of great potential to be building blocks for assembling mini-functional devices of the next generation.

Formation and structure of stable aggregates in binary diffusion-limited cluster-cluster aggregation processes

Binary diffusion-limited cluster-cluster aggregation processes are studied as a function of the relative concentration of the two species. Both, short and long time behaviors are investigated by means of three-dimensional off-lattice Brownian Dynamics simulations. At short aggregation times, the validity of the Hogg-Healy-Fuerstenau approximation is shown. At long times, a single large cluster containing all initial particles is found to be formed when the relative concentration of the minority particles lies above a critical value. Below that value, stable aggregates remain in the system. These stable aggregates are composed by a few minority particles that are highly covered by majority ones. Our off-lattice simulations reveal a value of approximately 0.15 for the critical relative concentration. A qualitative explanation scheme for the formation and growth of the stable aggregates is developed. The simulations also explain the phenomenon of monomer discrimination that was observed recently in single cluster light scattering experiments.

Destabilization of polystyrene latex particles induced by adsorption of polyvinylamine: Mass, size and structure characteristics of the growing aggregates

The obviously visible aggregation of suspended colloidal particles resulting from the addition of polyvinylamine to the aqueous dispersion of polystyrene latex particles bearing surface sulfate groups set in with a delay of 24 h. The aggregation mechanisms and the fractal dimension of the aggregates were derived from the variations with time of the weight and number averaged masses of the aggregates as well as of the weight averaged harmonic mean diameter of the size distribution. Since the establishment of starved layers was determined to be relatively fast and to leave the liquid phase free of polymer, the delay for the obvious destabilization was attributed to the reconformation of adsorbed macromolecules that was expected to be extremely slow. This reconformation promoted the emergence of the diffusion-limited aggregation process that accompanies the permanent reaction-limited aggregation process. The fractal dimension of the latex particles/polyvinylamine aggregates was determined to be 2.12.

Self-assembled growth and enhanced blue emission of SiOxNy-capped silicon nanowire arrays

Unique structured SiOxNy-capped Si nanowire arrays were fabricated via electroless metal deposition on α-SiOxNy-covered Si wafer in ionic silver HF solution through selective chemical etching. A self-assembled localized microscopic electrochemical cell model and a diffusion-limited aggregation process are associated with the formation of the SiOxNy-capped Si nanowire arrays. An enhanced blue photoluminescence band has been recorded. Emission and excitation spectral analyses suggest that generation of photoexcited carriers takes place mainly in the quantum confined Si nanowires, whereas their radiative recombination occurs in the Si–N binding states of SiOxNy nanocaps.

Film formation of crystallizable polymers on microheterogeneous surfaces

Dewetting and crystallization of thin polyethyleneoxide (PEO) films obtained bydip-coating on microheterogeneous surfaces are investigated. Formation of thin polymerfilms and crystallization are characterized as sequential processes. Film topography andmorphology are influenced by surface pattern geometry and polymer solution properties.Under appropriate experimental conditions in which heterogeneous nucleation is avoided,ultrathin non-crystalline PEO films can be prepared which are stable with respect tocrystallization over a long time. The experimental procedure established generates films bydewetting on microheterogenous surfaces in which isolated amorphous micrometre-sizedareas surrounded from non-wetting barriers are formed. Within these amorphous PEOareas, crystallization can be initiated on request with respect to starting time and location.The crystallization in ultrathin PEO films results in highly branched lamellamorphology arising from a diffusion limited aggregation processes (DLA). Astime and location for onset of diffusion limited crystallization can be chosen, themorphological features characteristic for DLA growth processes such as correlationwidth and growth direction of branches can be tuned. In addition, influences oflimited material reservoirs in confined areas on film morphology are discussed.

Flocculation in mixtures of cationic polyelectrolytes and anionic surfactants

The phase behavior of mixtures of a cationic polyelectrolyte (‘Jaguar’) and an anionic surfactant (either sodium dodecyl sulfate or sodium lauryl ether sulfate) has been studied. For a given polyelectrolyte (and added NaCl) concentration, with increasing surfactant concentration, three phase regions were identified. The first region is a single homogeneous phase. Within this region, at some surfactant concentration, above the critical aggregation concentration, stable open-network ‘particles’ form, typically ∼100 nm in size, which are net positively charged. However, as the surfactant concentration is increased further, these particles aggregate and form a two-phase system, i.e. a separated gel phase, containing a high percentage of water, co-existing with an aqueous surfactant phase. At some higher surfactant concentration still, the particles become sufficiently negatively charged that they re-stabilize. Beyond this surfactant concentration, therefore, the system reverts to being a single, homogeneous phase. Within the two-phase (aggregated particle) region an iso-electric point for the particles has been observed at a certain surfactant concentration, by electrophoresis. Furthermore, in this aggregated, gel-phase region, there appear to be typically ∼2–4 surfactant molecules associated with each cationic site of the polymer chains. It is postulated that association of the anionic surfactant molecules occurs within the polyelectrolyte chains, binding them together, to form the particles referred to. These associated surfactant structures have been referred to here as ‘internal’ micelles. A crude estimate has been made, based on turbidity/time measurements, that there may be up to ∼1000 polymer chains in each primary particle, bound together by the internal surfactant micelles. Small-angle light scattering studies of the aggregating particles indicate a fractal dimension for the aggregates, which would correspond to a diffusion-limited aggregation process.

The Aggregation of Thermally Stable Particles in a Premixed Flat Flame Aerosol Reactor

Using a premixed flat flame, the aggregation process of thermally stable particles was studied. Based on the theoretical descriptions of the reaction limited aggregation process (RLAP) and the diffusion limited aggregation process (DLAP), the entire aggregation process was explained by a combination of the RLAP and the DLAP. Experiments were done to test the possibility of this explanation for the dynamic aggregation processes in terms of the parameters that are used in a normal chemical conversion process. By defining the primary particle as the basic unit of the aggregates, the aggregation process was divided into the early stage--when the primary particles are formed--and the stage of aggregation thereafter. Changing the combustion equivalence ratio of the premixed flat flame from 0.7 to 0.98 controlled the sizes of the primary particles. The deficiency of the oxygen in the combustion process controlled the final size of the primary particles in the aggregate. The morphological evolution of particles w...

Morphology and Organization of Phospholipid/Diacetylene Langmuir Films Studied by Brewster Angle Microscopy and Fluorescence Microscopy

The thermodynamic and morphological properties of binary films of phospholipids and diacetylene lipids deposited at the air−water interface have been studied. Brewster angle microscopy (BAM) and fluorescence microscopy have been applied to investigate the formation, organization, and structure of the film domains. BAM data acquired at different temperatures, film compositions, and surface pressures reveal the appearance of distinct patterns of the diacetylenic moieties. In particular, the exceptionally high-quality BAM images point to dendritic and fractal-like appearance of the diacetylene domains; these phenomena are discussed in a framework of diffusion-limited aggregation processes. The results of the microscopy analyses further indicate that the two molecular components already segregate at low compression pressures and that the combined effects of film composition and temperature influence the occurrence of transitions between different phases within the films. This study sheds light on the molecular and cooperative features of mixed lipid/diacetylene films and further helps to understand the unique biosensing properties of these assemblies.

Stereochemical effects in supramolecular self-assembly at surfaces: 1-D versus 2-D enantiomorphic ordering for PVBA and PEBA on Ag(111).

We present investigations on noncovalent bonding and supramolecular self-assembly of two related molecular building blocks at a noble metal surface: 4-[trans-2-(pyrid-4-yl-vinyl)]benzoic acid (PVBA) and 4-[(pyrid-4-yl-ethynyl)]benzoic acid (PEBA). These rigid, rodlike molecules comprising the same complementary moieties for hydrogen bond formation are comparable in shape and size. For PVBA, the ethenylene moiety accounts for two-dimensional (2-D) chirality upon confinement to a surface; PEBA is linear and thus 2-D achiral. Molecular films were deposited on a Ag(111) surface by organic molecular beam epitaxy and characterized by scanning tunneling microscopy. At low temperatures (around 150 K), both species form irregular networks of flat lying molecules linked via their endgroups in a diffusion-limited aggregation process. In the absence of kinetic limitations (adsorption or annealing at room temperature), hydrogen-bonded supramolecular assemblies form which are markedly different. With PVBA, enantiomorphic twin chains in two mirror-symmetric species running along a high-symmetry direction of the substrate lattice form by diastereoselective self-assembly of one enantiomer. The chirality signature is strictly correlated between neighboring twin chains. Enantiopure one-dimensional (1-D) supramolecular nanogratings with tunable periodicity evolve at intermediate coverages, reflecting chiral resolution in micrometer domains. In contrast, PEBA assembles in 2-D hydrogen-bonded islands, which are enantiomorphic because of the orientation of the supramolecular arrangements along low-symmetry directions of the substrate. Thus, for PVBA, chiral molecules form 1-D enantiomorphic supramolecular structures because of mesoscopic resolution of a 2-D chiral species, whereas with PEBA, the packing of an achiral species causes 2-D enantiomorphic arrangements. Model simulations of supramolecular ordering provide a deeper understanding of the stability of these systems.

Adsorption and aggregation of glycosylphosphatidyl inositol (GPI) anchored alkaline phosphatase on methylated glass surfaces studied by tapping mode atomic force microscopy

The adsorption of alkaline phosphatase (AP) from buffer solutions into hydrophilic and hydrophobic methylated glass was studied qualitatively by Tapping Mode Atomic Force Microscopy (TMAFM). Three protein samples were used: soluble AP lacking GPI-anchors (AP S); purified AP dimer with two GPI anchors (AP GPI); and the same purified protein treated with acetone in order to remove all residual lipids (AP GPI-AT). All the preparations have a better affinity for hydrophobic surfaces and only partially maintain their enzymatic activity. The adsorption is larger for AP GPI-AT. Adsorption and aggregation of GPI-anchored proteins on hydrophobic surfaces occurs in at least two different phases: large protein clusters adsorb rapidly on the surface (in approx. 5–10 min); and then they slowly rearrange in monolayers. The large cluster adsorption at short times suggests that the anchors favour protein aggregation in solution. AP S adsorb as individuals, which aggregate and form two-dimensional dendrites and branched structures after drying. Surfaces with GPI-anchored protein occasionally present dendrites after drying, but never surfaces imaged in solution. It indicates that these structures are formed during drying as a result of a diffusion-limited aggregation process.

Internal cohesion of agglomerates: I. An elementary approach for assemblies of weakly agglomerated 2d-clusters

The average internal cohesion function of two-dimensional (2d)-agglomerates formed by assemblage of fractal aggregates of masses i and j (the aggregates being previously obtained using the algorithms of the diffusion-limited aggregation processes) was determined on the basis of the frequency function P( v, i, j) of the number v of interaggregate connections forming the link. The agglomerate fragmentation threshold was set by choosing the number m of connections which may be broken. The amount of agglomerate sustaining break-up was found to be independent of the mass ( i+ j) of the final agglomerate and expressed by a Johnson–Mehl equation of the variable m. The porosity of platelets formed by the agglomeration of a great number of fractal aggregates was found to increase as a power law of the aggregate mass and this might explain the lower bending or flexural strength of platelets of large aggregates.

Heterogeneous growth of cordierite in low P/T Tsukuba metamorphic rocks from central Japan

AbstractThis paper examines the spatial statistics of matrix minerals and complex patterned cordierite porphyroblasts in the low‐pressure, high‐temperature (low P/T) Tsukuba metamorphic rocks from central Japan, using a density correlation function. The cordierite‐producing reaction is sillimanite + biotite + quartz = K‐feldspar + cordierite + water. The density correlation function shows that quartz is distributed randomly. However, the density correlation functions of biotite, plagioclase and K‐feldspar show that their spatial distributions are clearly affected by the formation of cordierite porphyroblasts. These observations suggest that cordierite growth occurred through a selective growth mechanism: quartz adjacent to cordierite has a tendency to prevent the growth of cordierite, whereas other matrix minerals adjacent to cordierite have a tendency to enhance the growth of cordierite. The density correlation functions of complex patterned cordierite porphyroblasts show power‐law behaviour. A selective growth mechanism alone cannot explain the origin of the power‐law behaviour. Comparison of the morphology and fractal dimension of cordierite with two‐dimensional sections from a three‐dimensional diffusion‐limited aggregation (DLA) suggests that the formation of cordierite porphyroblasts can be modelled as a DLA process. DLA is the simple statistical model for the universal fractal pattern developed in a macroscopic diffusion field. Diffusion‐controlled growth interacting with a random field is essential to the formation of a DLA‐like pattern. The selective growth mechanism will provide a random noise for the growth of cordierite due to random distribution of quartz. Therefore, a selective growth mechanism coupled with diffusion‐controlled growth is proposed to explain the power‐law behaviour of the density correlation function of complex patterned cordierite. The results in this paper suggest that not only the growth kinetics but also the spatial distribution of matrix minerals affect the progress of the metamorphic reaction and pattern formation of metamorphic rocks.

Fractal nucleation and growth model for the hydration of tricalcium silicate

The phase transformation kinetics of the tricalcium silicate reaction for the period of peak hydration rate can be described as a four-parameter exponential nucleation and growth model. The exponent in the model can take a noninteger value that may be an irrational number. Application of a fractal impingement model based on a mean field diffusion-limited aggregation (DLA) process results in a fractal nucleation and growth model. This indicates consistency between small-angle neutron scattering (microstructural) and quasi-elastic neutron scattering (kinetics) measurements. Also, the fractal basis of the exponent in the kinetics model precludes the interpretation of conventional grain growth processes. Concerning the analysis of kinetics data, the four-parameter form of the kinetics model means that the double logarithmic least squares fit to the kinetics data is not appropriate. Instead, a nonlinear curve fitting approach is necessary.