Dense Branching Morphology Research Articles

Crystalline morphology evolution in PCL thin films

AbstractThe transition of crystalline morphology is revealed in poly(ϵ‐caprolactone) (PCL) thin films as the polymer film thickness changes from hundreds of nanometers to several nanometers. The PCL can crystallize into spherulites, dense‐branching morphology (DBM), or dendrites, depending on the polymer film thickness. It was found that when the polymer film thickness approaches 2Rg (radius of gyration of polymer), there is a remarkable change in crystalline morphology. Under this condition, the polymer crystallization is a diffusion‐controlled process. When the value of polymer film thickness closes to Rg, PCL cannot crystallize, and a dewetting phenomenon will take place. Moreover, polymer morphology can be controlled by varying supercooling. The effect of molecular weight on polymer morphology has been investigated. The main factors that affected pattern formation in nonequilibrium crystallization are also discussed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1303–1309, 2005

The effect of cyanide and lead ions on the cementation rate, stoichiometry and morphology of silver in cementation from cyanide solutions with zinc powder

The cementation of silver on zinc powder from solutions with a wide concentration range of cyanide has been investigated in the absence and presence of lead ions through stirred reactor batch tests and scanning electron microscopy studies on the cementation product. The concentration of cyanide ions affected the morphology of the product, the nature of cementation reaction and the cementation kinetics. Three cyanide-dependent concentration regimes have been identified: a low cyanide concentration regime in which silver cementation followed an ion-exchange type reaction taking place at the zinc/aqueous solution interface, and the silver deposited around the zinc particle in a uniform growth; a high cyanide concentration regime, as in plant practices, in which the cementation of silver followed an overall chemical reaction involving the evolution of hydrogen and a one-to-one molar silver-to-zinc stoichiometry (In this regime, both the anodic oxidation and the cathodic reduction reactions occurred at distinct interfaces and the silver deposited in a dense-branching morphology.), and an intermediate cyanide concentration regime which is a transition between the two previous regimes. In the low and intermediate regimes, lead and cyanide ions did not affect the morphology of the cemented silver, but increased the silver cementation kinetics owing to Zn(OH) 2 instability. Within the high cyanide concentration regime, lead ions did not appreciably change the cementation kinetics. They modified the pattern of the silver deposit from a dense-branching to a dendritic morphology.

Colony formation in bacteria: experiments and modeling

We present experimental results of colony formation in bacteria as an example of pattern formation resulting from reproduction and movement in biological populations. The bacterium Bacillus subtilis is known to exhibit at least five distinct types of colony pattern, depending on the substrate softness and nutrient concentration: diffusion-limited aggregation (DLA), compact Eden-like, dense branching morphology (DBM), concentric ring-like, and disk. We established a morphological diagram of the colony patterns, and then examined and characterized both macroscopically and microscopically how the the colonies grow. There seem to be two kinds of bacterial cells – active and inactive – and the active form drives the colony interfaces outwards. The active cells may be clearly distinguished from the inactive ones as they form the characteristic fingernail-like structure at the tips of growing branches of the DBM colony. The concentric ring-like colony is formed as a consequence of repeated alternate migration and resting of the growing interface, the cycle time for which seems to be independent of the substrate softness and nutrient concentration. So far there have been several phenomenological models proposed to qualitatively explain or reproduce the patterns observed in bacterial colonies. A few of them are reviewed here, systematically and critically, in light of our experimental results.

Transition of Crystal Growth as a Result of Changing Polymer States in Ultrathin Poly(ethylene oxide)/Poly(methyl methacrylate) Blend Films with Thickness of <3 nm

The transition of crystal growth is revealed in ultrathin poly(ethylene oxide)/poly(methyl methacrylate) (PEO/PMMA) blend films (film thickness D < 3 nm) as the crystallization condition changes from vacuum to humidity. The PEO crystallizes into a fractal-like branched structure in a vacuum from a state mixed with PMMA, but in humidity into one reminiscent of dense branching morphology (DBM). The crystal lamellae in both conditions orient flat-on, but the DBM-like structure is much thicker and wider, indicating a crystallization more close to equilibrium. Results show that as a PEO/PMMA blend film is exposed to humidity, PEO chains demix with PMMA and segregate on a PMMA layer before or during crystallization. The crystal growth transition is attributed to the change in the factors that dominate the crystal growth at crystal growth fronts, that is, the kinetic and surface tension effects, as a result of changing the polymer states in the blend films. The crystal growth of the demixed PEO on the PMMA layer is dominated by a strong surface tension effect, while crystal growth of PEO in a blend/mixed state is dominated by either a kinetic effect or a weak surface tension effect depending on the film composition. The compositional dependence of the crystal growth in humidity is also elucidated on the basis of the changing of polymer states in the films.

Morphology Transition in Diffusion Field

In the previous paper [J. Crys. Growth237, 159 (2002)]1 we considered a two-dimensional coupled map lattice model for melt growth including the Gibbs-Thomson condition. In this paper we introduce a parameter, which represents the strength of surface tension anisotropy. Changing the parameter, we have found that the DBM (Dense-Branching morphology) and the doublon in an intermediate region where growth direction changes from &lt;11&gt; to &lt;10&gt;.

Modelling and Numerical Analysis of the Colony Formation of Bacteria

In this Note we report the attempt of generalization of Mimura et al. (MSM) model for colony formation of bacteria. We also show the numerical results, which are then compared with experiments. Bacterial species Bacillus subtilis exhibits various colony patterns in response to two environmental parameters, i.e., concentrations of nutrient Cn and agar Ca in a thin agar plate as incubation medium. They are observed in the regions of morphological diagram labeled as A–E in Fig. 1. If Cn is low and Ca is high (region A), colony patterns exhibit tipsplitting growth with diffusion-limitted aggregation (DLA)like ramified structures. In fact colony growth in this region can be explained by the DLA model. Increasing Cn with Ca fixed high (region B), they exhibit round shape with Edenlike rough interface. If Cn is high and Ca is low (region D), they look macroscopically disk-like. The colony growth in this region was found to be consistent with the solution of two-dimentional Fisher’s equation. Decreasing Cn with Ca fixed in-between (region E), they show highly branched structures reminiscent of dense-branching morphology (DBM). Finally, in the region C, colonies exhibit concentric-ring patterns which are produced through alternate migration and consolidation by bacterial cells. In order to explain these observations various reaction– diffusion models have already been proposed. They are, however, not very successful in that they can reproduce only some of the observed patterns such as DLA-like and DBMlike. MSM tried to make a unified model to reproduce all of the observed patterns. They assumed that bacterial cells consist of two types, active and inactive cells, based on experimental observations of colony growth. They proposed the following MSM model:

Dynamics of low anisotropy morphologies in directional solidification.

We report experimental results on quasi-two-dimensional diffusion limited growth in directionally solidified succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as a solute. Seaweed growth, or dense branching morphology, is selected by growing grains close to the [111] plane, where the in-plane surface tension is nearly isotropic. The observed growth morphologies are very sensitive to small anisotropies in surface tension caused by misorientations from the [111] plane. Different seaweed morphologies are found, including the degenerate, the stabilized, and the strongly tilted seaweeds. The degenerate seaweeds show a limited fractal scaling range and, with increased undercooling, suggests a transition from "fractal" to "compact" seaweed. Strongly tilted seaweeds demonstrate a significant twofold anisotropy. In addition, seaweed-dendrite transitions are observed in low anisotropy growth.

Abnormal morphology of amorphous germanium films in contact with palladium

The fractal and dense branching morphologies of amorphous germanium films in contact with palladium have been investigated by TEM. The experimental results suggest that the production of fractal morphology in Pd/a-Ge bilayer films was easier than that in a-Ge/Pd bilayer films. An island-like fractal morphology can be formed at the step and crevice hole areas annealed at higher temperatures. It is difficult for co-evaporated Pd–Ge films to realize fractal morphology. The formation of fractal morphology can be explained by a RSN model. The SAED patterns suggest that the dense branching morphology cannot be completely demonstrated by the Pd, Ge, Pa 2Ge, PdGe and Pd 25Ge 9, maybe it is a new phase.

CRYSTAL GROWTH OF ISOTACTIC POLYSTYRENE IN ULTRATHIN FILMS: FILM THICKNESS DEPENDENCE

The film thickness dependence of crystal growth is investigated for isotactic polystyrene (it-PS) in thin films for thicknesses from 20 down to 4 nm. The single crystals of it-PS grown at 180°C in the ultrathin films show a morphology typical of diffusion-controlled growth: dense branching morphology and fractal seaweed. The characteristic length of the morphology, i.e., the width of the branch, increases with decreasing film thickness. The thickness dependence of the crystal growth rate shows a crossover around the lamellar thickness of 8 nm. The thickness dependences of the growth rate and morphology are discussed in terms of the diffusion of chain molecules in thin films.

Dendrite and fractal patternsformed on the surface of bismuth-ion-implanted LiNbO3

The formation of dendrite and fractal patterns on the surface of350 keV bismuth-ion-implanted LiNbO3 samples is presented. Thedimensions of the dendrite and fractal patterns are 1.86±0.04 and1.84±0.02, respectively. For two different growth forms in oursystem we give some interesting experimental data. According totheir morphologies, the two kinds of structure are considered to bediffusion-limit-aggregation-like patterns and dense branchingmorphologies, respectively. A possible origin of the dendrite andfractal patterns is also presented in a preliminary manner.

Formation of Arrays of Straight Copper Wires on Solid Substrate by Electrodeposition

Straight copper wire arrays are electrochemically deposited on a silicon substrate without utilizing additives or templates. To suppress the influence of the factors which arouse the ramification of the copper electrodeposit, an ultrathin electrochemical deposition system and an initially homogeneous electric field are used. The width of the copper wires may vary from about 200 nm to about 1.5 µm depending on the control parameters. The microstructure of the copper wires and their electric resistance after vacuum-annealing at 200°C are studied. We suggest that this self-organized copper electrodeposition is helpful in gaining an understanding of the formation of dense-branching morphology. It also implies the potential application in microelectronics.

Pattern selection induced by electroconvection in the electrodeposition of iron

The morphology of iron electrodeposit is shown to relate closely to the pH of the electrolyte solution. Macroscopically, depending on the strength of the interbranch convection, which is associated with the concentration of H3O+ in the electrolyte, the deposit morphology varies from treelike pattern to meshlike pattern and dense-branching morphology. Microscopically the deposit is ramified and dense-branching at lower concentration of H3O+, while it becomes relatively smooth and stringy at higher H3O+ concentration. The symmetry of the convective vortices on the two sides of the growing tip is observed to decide the growth behavior of the tip. We suggest that H3O+ influences the pattern formation and pattern selection in the electrodeposition of iron from FeSO4 solution by either initiating interbranch convection or changing the effective interfacial energy of the deposit and the electrolyte.

Dense branching morphology in electrodeposition experiments: characterization and mean-field modeling

Dense branching morphologies (DBM) obtained in thin gap electrodeposition cells are characterized by a dense array of branches behind a flat advancing envelope. In this Letter, we show the existence in DBM of a new (porous) phase, qualitatively different from a (compact) metal deposit. The local porosity inside the branches is found to be much more robust than geometric characteristics such as the width or the distance between branches. This fact seems to be unreported in previous modeling of DBM. A mean-field model is proposed that displays overall features observed in the experiments, such as concentration profiles, front velocity, and branched internal structure.

Modeling Complex Patterns in Bacterial Colonies.

Colonies of bacteria grown on agar plates can display morphological patterns of surprising varieties depending on culture conditions. For instance, B. subtilis shows a dense-branching morphology on a nutrient-poor semi-solid agar medium, while some chemotactic strains of E. coli form a spot pattern on a pseudo-hexagonal lattice. Based on such experimental data, diffusion-reaction models that incorporate cell movements and interactions between bacterial cells and chemical substances have been constructed, and used to explain how the observed patterns are generated.

Formation of colony patterns by a bacterial cell population

Bacterial species Bacillus subtilis is known to exhibit various colony patterns, such as diffusion-limited aggregation (DLA)-like, compact Eden-like, dense branching morphology (DBM)-like, concentric ring-like and disk-like, depending on the substrate softness and nutrient concentration. We have established the morphological diagram of colony patterns, and examined and characterized both macroscopically and microscopically how they grow. For instance, we have found that there seem to be two kinds of bacterial cells; active and inactive cells, the former of which drive colony interfaces outward. The active cells are particularly distinguished from the inactive ones at the tips of growing branches of a DBM-like colony as the characteristic fingernail structure. We have also found that the concentric ring-like colony is formed as a consequence of alternate repetition of advancing and resting of the growing interface which consists of active cells. Based on our observations, we have constructed a phenomenological but unified model which produces characteristic colony patterns. It is a reaction–diffusion type model for the population density of bacterial cells and the concentration of nutrient. The essential assumption is that there exist two types of bacterial cells; active cells that move actively, grow and perform cell division, and inactive ones that do nothing at all. Our model is found to be able to reproduce globally all the colony patterns seen in the experimentally obtained morphological diagram, and is phenomenologically quite satisfactory.

Eden growth model for aggregation of charged particles

The stochastic Eden model of charged particles aggregation in two-dimensional systems is presented. This model is governed by two parameters: screening length of electrostatic interaction, $\lambda $, and short range attraction energy, $E$. Different patterns of finite and infinite aggregates are observed. They are of following types of morphologies: linear or linear with bending, warm-like, DBM (dense-branching morphology), DBM with nucleus, and compact Eden-like. The transition between the different modes of growth is studied and phase diagram of the growth structures is obtained in $\lambda, E $ co-ordinates. The detailed aggregate structure analysis, including analysis of their fractal properties, is presented. The scheme of the internal inhomogeneous structure of aggregates is proposed.

Experimental Investigation on the Formation of Dense-Branching-Morphology-Like Colonies in Bacteria

We have investigated experimentally the pattern formation of bacterial colonies. We have especially examined DBM (dense-branching-morphology)-like colonies of bacterial species Bacillus subtilis . It was found from microscopic observations that many active bacterial cells collect and make a group on the tip of each growing branch. Branches repel each other and split sometimes as they grow outward. It was confirmed macroscopically that both averaged branch width and averaged branch gap decrease systematically when increasing the nutrient concentration C n , while their ratio remains unchanged with the approximate value of one. It was also found that the distribution of branch lengths is very close to exponential, suggesting that the tip-splitting of branches takes place at random.

About Computations of Hele-Shaw Flow of Non-Newtonian Fluids

AbstractThe flow of a fluid confined between two solid plates (Hele-Shaw cell) is of considerable interest in a variety of applications. Further interest in two phase flow in this geometry stems from the close analogy between the dynamics of fluid-fluid interface and the propagation of the solidification front. While the flow of Newtonian fluids is rather well understood, it is much more complicated to compute flows of non-Newtonian fluids. We find that the dense-branching morphology of Newtonian liquids may be replaced by dendritic fingers with stable tips and sidebranches, and discuss resulting length scales.

Modeling Spatio-Temporal Patterns Generated byBacillus subtilis

Colonies of bacteria,Bacillus subtilis, that grow on the surface of thin agar plates show various morphological patterns in response to environmental conditions, such as the nutrient concentration, the solidity of an agar medium and temperature. For instance, the colony pattern shows a dense-branching morphology with a smooth circular envelope (DBM-like) in a nutrient-poor semi-solid agar medium, and it turns to a simple disk-like colony as both the nutrient concentration and the agar's softness increase. These patterns have been shown to involve cell movement inside colonies. In a DBM-like colony, individual cells actively move, particularly in the expanding periphery of the colony, while they become immotile at the inner region of the colony where nutrient is very low. In a disk-like colony, cells are highly active in the whole region of the colony. Based on such experimental observations, we develop a diffusion-reaction model, in which density dependent cell movements are incorporated by the level of nutrient concentration available for the cell. Numerical simulations of the model under different environmental conditions closely reproduce various colony patterns ranging from DBM-like pattern to the homogeneous disk-like one in a unifying manner. The analysis also predicts the growth velocity of a colony as a function of the nutrient concentration.

Nonequilibrium Domain Growth in Fatty Acid Ethyl Ester Monolayers

A variety of nonequilibrium growth structures is observed in fatty acid ethyl ester monolayers. In these monolayers, two different condensed phases exist: one with tilted chains and the other with erected chains. The formation of the domains ofthese phases from the fluid phase gives rise to completely different shapes under non-equilibrium. In the phase with tilted chains, a dendritic growth regime exists in ethyl stearate monolayers for intermediate compression rates. The arms of the dendrite have a tip-oscillating morphology. At extremely high compression rates the tips are no longer stable and the growth does not follow crystallographic directions. For the shorter chain (ethyl palmitate the dendritic growth regime is not observed in the phase with tilted chains at low temperatures. Here the domain wall only becomes unstable at extremely high compression rates and the morphology is then fractal-like. However, at temperatures T > 20 °C a dendritic growth regime occurs. The nonequilibrium structures in both ethyl stearate and ethyl palmitate monolayers are transformed into a circular equilibrium shape for the condensed phase with tilted chains during a few minutes. In ethyl palmitate monolayers, a phase with erected chains forms during the first-order phase transition at temperatures T > 26 °C. In this phase the nonequilibrium structures are quite stable and transform very slowly into a compact shape. Even at extremely low compression rates branchcd structures occur. An increase of the compression rate causes a continuous change from a more dendritic shape to one which is quite similar to the dense-branching morphology.