Dense Branching Morphology Research Articles

Soluble VEGFR1 signaling guides vascular patterns into dense branching morphologies

Vascular patterning is a key process during development and disease. The diffusive decoy receptor sVEGFR1 (sFlt1) is a known regulator of endothelial cell behavior, yet the mechanism by which it controls vascular structure is little understood. We propose computational models to shed light on how vascular patterning is guided by self-organized gradients of the VEGF/sVEGFR1 factors. We demonstrate that a diffusive inhibitor can generate structures with a dense branching morphology in models where the activator elicits directed growth. Inadequate presence of the inhibitor leads to compact growth, while excessive production of the inhibitor blocks expansion and stabilizes existing structures. Model predictions were compared with time-resolved experimental data obtained from endothelial sprout kinetics in fibrin gels. In the presence of inhibitory antibodies against VEGFR1 vascular sprout density increases while the speed of sprout expansion remains unchanged. Thus, the rate of secretion and stability of extracellular sVEGFR1 can modulate vascular sprout density.

Pattern transition from dense branching morphology to fractal for copper and β′ brass electrodeposition in thin gap geometry

Copper and β′ brass are electrodeposited in thin gap geometry and a clear transition from dense branching to fractal like pattern is observed with the variation of electric potential and concentration. The transition electric potential is 6V – 5V for copper and 25V for β′ brass. The explanation of the pattern transition is done first using the Laplacian growth as in the Di-electric Breakdown Model (DBM) and then on the basis of ion dynamics in terms of viscosity, ionic mobility, drift and thermal velocity. The fractal growth is more likely at higher electric potential as the electric field dominates and more likely to be dense branched at lower electric field when thermal motion dominates. This work inspires for further studies on modification of our model for the two ions electrodeposition and their compositional variation with different deposition parameters.

In-Situ Microfluidic Study with Kinetic-Monte Carlo Simulations to Investigate Zn Electroplating Morphology at High Overpotentials

Despite the low cost and high energy density, use of Zinc anode in secondary batteries is limited due to the associated shape change of Zn during cycling. Vast literature on morphological studies of Zn in alkaline electrolyte indicates formation of varied structures ranging from mossy, to boulder-like and dendritic morphologies,1 primarily depending on the plating potential. Recently, Zinc plating at extremely high overpotentials 2 is shown to form a highly porous, conductive, ramified foam like morphology, called Hyper Dendritic Zinc (HD Zn). HD Zn has been demonstrated to act as an efficient secondary anode, with improved cycle life and kinetics 3. The fine (~60 nm) needle-like crystallite core microstructure that forms the dendrite makes this morphology unique. An important distinguishing feature from the previously known morphologies is that it grows in conformal layers, giving it an appearance of dense branching morphology, but instead of DLA like motifs it has Dendritic motifs. In this work, in-situ microfluidic studies coupled with Kinetic-Monte Carlo simulations are used to investigate plating and cycling behavior of HD Zn. While Monte Carlo simulations have been implemented in the past 4 to show growth of DLA like structures, we extend these to incorporate effect of crystal anisotropy in electrochemical systems. We hypothesize that growth at high overpotentials leads to the formation of a space charge region at the electrolyte/electrode interface due to high potential gradient. This space charge region is where migration becomes important. The migration length along with high concentration gradient built at the growth overpotentials gives rise to the HD Zn morphology.1. Naybour, R. D. et al. Electrochimica Acta 13.4 (1968): 763-769. 2. M. Chamoun et al., NPG Asia Materials, 7, e178 (2015). 3. T. Gupta et al., J. Power Sources, 305, 22–29 (2016). 4. Erlebacher, J. et al. Physical review letters 71.20 (1993): 3311.

Fabricating Superhydrophobic Surfaces via a Two-Step Electrodeposition Technique

This work presents a template-free electrochemical route to producing superhydrophobic copper coatings with the water contact angle of 160 ± 6° and contact angle hysteresis of 5 ± 2°. In this technique, copper deposit with multiscale surface features is formed through a two-step electrodeposition process in a concentrated copper sulfate bath. In the first step, applying a high overpotential results in the formation of structures with dense-branching morphology, which are loosely attached to the surface. In the second step, an additional thin layer of the deposit is formed by applying a low overpotential for a short time, which is used to reinforce the loosely attached branches on the surface. The work also presents a theoretical analysis of the effects of the fabrication parameters on the surface textures that cause the superhydrophobic characteristic of the deposit.

Self-similar evolution of a precipitate in inhomogeneous elastic media

In this paper, we present linear theory and nonlinear simulations to study the self-similar growth and shrinkage of a precipitate in a 2D elastic media. This work is motivated by a series of studies by Li et al., where the existence and morphological stability of self-similarly evolving crystals were demonstrated in a diffusional field. Here, we extend the theory and simulations to account for solid-state phase transformations where elasticity plays an important role in regularizing the evolution of the precipitate. For given applied strain or stress boundary conditions, we show that depending on the mass flux entering/exiting the system, there exist critical scalings of flux and elasticity at which compact self-similar growth/shrinkage occurs in the linear regime. We then develop a spectrally accurate boundary integral method combined with a rescaling scheme to investigate the effects of nonlinearity and the morphological stability of these linear self-similar precipitates. Our numerical results reveal that at long times there exists nonlinear stabilization that leads the precipitate to evolve to compact universal limiting shapes selected by the applied stress and mass diffusion flux. These theoretical and numerical results suggest that the classical Mullins–Sekerka instability, which drives precipitates to acquire dendritic or dense-branching morphologies, can be controlled. This could potentially provide a new route to controlling material microstructures.

In situ studies of different growth modes of silver crystals induced by the concentration field in an aqueous solution

An in situ observation of silver hierarchical crystal growth in a Zn/AgNO3 (aq.) replacement reaction system revealed that the morphological evolution of silver crystal strongly depended on the change of the silver ion concentrations. With the increasing concentration, the morphologies of the silver crystal transformed from loose fractal (LF) to dense branch morphology (DBM) and even to dendrite. The concentration field was in situ monitored using a Michelson interferometer during the reaction and the profile of the concentration field was studied based on experimental observation. The crystals morphology transform was induced by different growth modes. At low concentration, the growth mode was ion diffusion limited growth and at the high concentration the growth mode was protuberant growth which was decided by reaction limitation.

A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island

In this paper, we present a boundary integral method for computing the quasi-steady evolution of an epitaxial island. The problem consists of an adatom diffusion equation (with desorption) on terrace and a kinetic boundary condition at the step (island boundary). The normal velocity for step motion is determined by a two-sided flux. The integral formulation of the problem involves both double- and single-layer potentials due to the kinetic boundary condition. Numerical tests on a growing/shrinking circular or a slightly perturbed circular island are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient, and spectrally accurate in space. Nonlinear simulations for the growth of perturbed circular islands show that sharp tips and flat edges will form during growth instead of the usual dense branching morphology seen throughout physical and biological systems driven out of equilibrium. In particular, Bales–Zangwill instability is manifested in the form of wave-like fronts (meandering instability) around the tip regions. The numerical techniques presented here can be applied generally to a class of free/moving boundary problems in physical and biological science.

STUDIES ON CONFINED CRYSTALLIZATION BEHAVIOR OF POLYCAPROLACTONE THIN FILMS

The confined crystallization behavior of polycaprolactone(PCL) in thin and ultrathin films was studied by AFM(atomic force microscopy).It was found that the crystalline morphology of PCL depended on the film thickness.When the thickness d2R_g(radius of gyration),the polymer can crystallize into spherulites;when R_gd2R_g,the dense-branch morphology and dendrites could be found;when dR_g,the "islands" structure could be obtained.Moreover,the effects of the crystallization temperature,substrate and the molecular weight on the crystalline morphology were discussed.It was shown that the crystallization of PCL in thin film is a diffusion-controlled process,and it can be explained by diffusion-limited aggregation.

Diffusion-limited and advection-driven electrodeposition in a microfluidic channel

Self-terminating electrochemical fabrication was used within a microfluidic channel to create a junction between two Au electrodes separated by a gap of 75 microm . During the electrochemical process of etching from the anode to deposition at the cathode, flow could be applied in the anode-to-cathode direction. Without applied flow, dendritic growth and dense branching morphologies were typically observed at the cathode. The addition of applied flow resulted in a densely packed gold structure that filled the channel. A computer simulation was developed to explore regimes where the diffusion, flow, and electric field between the electrodes individually dominated growth. The model provided good qualitative agreement relating flow to the experimental results. The model was also used to contrast the effects of open and closed boundaries and electric field strength, as factors related to tapering.

Effects of photointensity gradient on directional crystal growth in blends of crystalline polymer and photoreactive monomer undergoing photopolymerization-induced phase transformation

Effects of light intensity gradient on development of intricate hierarchical morphology of semicrystalline polyethylene oxide (PEO) and photoreactive diacrylate (DA) blends undergoing photopolymerization-induced crystallization have been demonstrated experimentally and theoretically. The melting temperature of PEO was found to decline upon addition of DA monomer. A solid-liquid phase diagram has been established by self-consistently solving the combined phase field free energy of crystal solidification and Flory-Huggins (FH) free energy of liquid-liquid demixing. Dynamic calculations were performed using time-dependent Ginzburg-Landau (model C) equations by incorporating the combined phase field and FH free energy densities coupled with the photopolymerization kinetics. The spatiotemporal development of gradient morphology was computed under various intensity gradient profiles including linear, cylindrical, and Gaussian profiles. The observed seaweed or dense lamellar branching morphology of the PEO/DA blend is strikingly similar to the directionally grown interface structures observed in metals driven by external thermal gradients.

Morphological Evolution of Fractal Dendritic Silver Induced by Ions Walking within the Diffusion Layer

Fractal dendritic morphologies will be formed when metal materials are synthesized in nonequilibrium conditions. In the past, scientists mainly studied the effect of noise and anisotropy on morphology evolution. However, in this Article, fractal dendritic silver is synthesized through a simple wet-chemical method, spontaneous galvanic displacement between Ag ions and Zn plate, and through Monte Carlo simulation we found that walking of ions within the diffusion layer can affect the morphology of the whole shape, and anisotropy only affects the shape in local area. As the longitudinal velocity of silver ions walking within the diffusion layer increases, the ions are more easily distributed on the hollow part of fractal silver, and thus the fractal silver will transform from loose fractal (LF) to dense branch morphology (DBM), and shape densities and fractal dimensions of fractal morphologies also increase.

Pattern formation of nanoflowers during the vapor–liquid–solid growth of silicon nanowires

Pattern formation of nanoflowers during the vapor–liquid–solid growth of Si nanowires is reported. Using transmission electron microscopy, scanning electron microscopy, and energy dispersive spectrometer analysis, we show that the flower consists of an Au/SiO x core–shell structure. Moreover, the growth of flower starts at the interface between the gold catalyst and the silicon nanowire, presumably by enhanced oxidation at this interface. The pattern formation can be classified as dense branching morphology (DBM). It is the first observation of DBM in a spherical geometry and at the nanoscale. The analysis of the average branching distance of this pattern shows that the pattern is most likely formed during the growth process, not the cooling process, and that the curvature of the gold droplet plays a crucial role in the frequency of branching.

Alternating morphology transitions in crystallization ofNH4Clon agar plates

Two types of alternating morphology transitions have been observed in crystallization of NH4Cl on agar plates. One is the alternating morphology transitions between dense branching morphology and sparse branching morphology, and the other is the alternating morphology transitions between dense branching morphology and zigzag branching morphology. The appearance of them is found to depend on the mass proportion of agar to NH4Cl in the initial solution and the relative humidity. It is suggested that both the two alternating morphology transitions result from the oscillation of solute concentration in front of the growing interface caused by the competition of crystal growth and solute transfer at a moderate mass proportion. Which one of them occurs depends on the relative humidity, which controls the supersaturation.

Thin-layer electrodeposition of Zn in the agar gel medium

The preparation of Zn deposits has been performed by thin-layer electrodeposition in acidic zinc sulphate solution with and without agar, respectively. The morphological and structural characteristics of the deposits have been investigated by scanning electron microscopy (SEM) and X-ray diffraction (XRD). The study shows that the presence of agar has a significant influence on the morphology of the Zn deposits. Under the chosen conditions and without agar, the deposit shows a dendritic morphology, which is made of orderly arranged grains with a preferred orientation in [0001]. In the presence of agar, the deposit shows a dense branch morphology, which has a randomly oriented grain texture and diminished grain size in comparison with that of the dendritic morphology. This work contributes to understanding the influence of agar gel on the pattern formation in thin-layer electrodeposition.

Growth of Gold Fractal Nanostructures by Electrochemical Deposition in Organic Electrolytes: Morphologies and Their Transitions

We have studied the growth of gold fractal nanostructures by a novel electrochemical deposition (ECD) method. In our ECD process, instead of an aqueous solution of metallic salt, we use an organic solution (such as N,N-dimethylformamide (DMF) or acetonitrile) as the electrolyte and integrate the microscale ECD system into the SiO2/Si chip. Quasi-two-dimensional gold fractal nanostructures can be formed using the organic electrolyte. The morphology of the deposit strongly depends on the kind of organic electrolyte that has been used. A diffusion-limited aggregation (DLA) pattern can be formed in DMF. While in acetonitrile, aside from the DLA pattern, a variety of other typical morphologies can be identified, and they appear in consecutive patterns varying from a DLA fractal, to a dense branching morphology (DBM), to a ramified structure. In some cases the ramified structures can even evolve into nanoscale dendrites or nanowires. To the best of our knowledge, these phenomena have not been reported before. We propose a qualitative explanation for these phenomena based on the mass transfer equation and discuss possible applications of these nanostructures.

Studies on confined crystallization behavior of polycaprolactone thin films

The confined crystallization behavior of polycaprolactone (PCL) in thin and ultrathin films was studied by AFM (atomic force microscopy). It was found that the crystalline morphology of PCL depended on the film’s thickness. When the thickness is d > 2 Rg (radius of gyration), the polymer can crystallize into spherulites; when Rg < d < 2 Rg, a dense-branch morphology and dendrites could be found; when d < Rg, an “islands” structure could be obtained. Moreover, the effects of the crystallization temperature and the substrate and the molecular weight on the crystalline morphology were discussed. It was shown that the crystallization of PCL in thin films is a diffusion-controlled process, and it can be explained by diffusion-limited aggregation.

The Effect of rf-Irradiation on Electrochemical Deposition and Its Stabilization by Nanoparticle Doping

Qualitative observations of electrochemical deposition in thin circular cells have shown that radio-frequency (rf) irradiation of zinc sulfate solutions can dramatically affect the deposition patterns. For some growth parameters the rf-treatment can even induce morphology transitions between the dense branching morphology and dendritic growth. We found that the effects of rf-treatments can last for a long time (hours). In addition, detailed studies using electron microscopy observations reveal that the effects span on all scales, from the micrometer-scale organization to the self-organization of the macroscopic pattern. We propose that these changes of patterning on all scales resulted from singular effects of gas-filled submicrometer bubbles or nanobubbles, which are generated by the rf-irradiation. The idea is that hydration shells around the nanobubbles induce water ordering that acts as a new singular perturbation mechanism in the solution. The latter is in addition to the well studied microscale singular perturbation mechanisms in the deposit (surface tension and attachment kinetics). We also studied electrochemical deposition in zinc sulfate solutions prepared from water that is doped with nanoparticles under rf-irradiation, and found similar and even amplified effects. Moreover, the nanoparticle doping stabilizes the effects—they are retained months after the solutions were prepared.

Morphological Diagram of Bacterial Colony Pattern Simulated Using a Revised Mimura–Sakaguchi–Matsushita Model

In this Note we report the attempt of improving the Mimura–Sakaguchi–Matsushita (MSM) model of bacterial colony formation by revising the nonlinear diffusion term in the reaction diffusion equation. Using this revised MSM model, all five typical colony patterns are reproduced and the experimental morphological diagram of colony patterns are completely simulated. During the last few decades, much attention has been paid to self-assembly pattern formation in various fields. Among them, pattern formation in biological systems is the most sophisticated and interesting. Due to the complexity of biological systems, recoganizing the mechanism of pattern formation in biological systems is difficult. Therefore, investigation of simple biological objects, which is dominated by purely physical conditions, is a good choice. Here we focus on bacterial colony formation, which is one of the simplest biological objects. It is known that some kinds of bacteria such as Bacillus subtilis (B. subtilis) exhibit various colony patterns on an agar medium by changing the incubation conditions, i.e., the concentration of agar Ca and that of nutrient Cn in the medium. Cn determines the rate of division of active bacteria, and Ca controls the motivebility of bacteria. Ohgiwari et al. completed an experimental morphological diagram (see Fig. 1). It can be seen from region A (high Ca and low Cn) of Fig. 1 that the colony pattern exhibits tip-splitting growth with diffusion-limitted aggregation (DLA)-like ramified structures. Keeping a high Ca and increasing Cn (region B),the pattern becomes round with Eden-like rough interface. If Cn is high and Ca is low (region D), the pattern looks macroscopically disklike. The colony growth in region D is consistent with the solution of the two-dimentional Fisher equation. In region E, which is between regions A and D, the pattern shows highly branched structures similar to the dense-branching morphology (DBM). When Cn is high and Ca takes an appropriate intermediate value (region C), colony exhibits concentricring patterns which are produced alternately in the active state and inactive state of the bacteria. In order to explain these observations, various reaction diffusion models have been proposed. The MSM model is one of them, which is based on the assumption that there exist two types of bacteria; active ones that move, grow and divide, and inactive ones that do nothing at all. Using the MSM model with linear diffusion patterns A, C, D and E are reproduced. Using MSM model with nonlinear diffusion, pattern B is also generated. In the MSM model, the relation among the population density of active bacteria u, the density of the inactive bacteria w, and the nutrient concentration v is expressed by a set of equations as

Phase-field modeling on morphological landscape of isotactic polystyrene single crystals

Spatio-temporal growth of isotactic polystyrene single crystals during isothermal crystallization has been investigated theoretically based on the phase field model by solving temporal evolution of a nonconserved phase order parameter coupled with a heat conduction equation. In the description of the total free energy, an asymmetric double-well local free energy density has been adopted to represent the metastable melt and the stable solid crystal. Unlike the small molecule systems, polymer crystallization rarely reaches thermodynamic equilibrium; most polymer crystals are kinetically stabilized in some metastable states. To capture various metastable polymer crystals, the phase field crystal order parameter at the solidification potential has been treated to be supercooling dependent such that it can assume an intermediate value between zero (melt) and unity (perfect crystal), reflecting imperfect polycrystalline nature of polymer crystals. Two-dimensional simulations exhibit various single crystal morphologies of isotactic polystyrene crystals such as faceted hexagonal patterns transforming to nonfaceted snowflakes with increasing supercooling. Of particular interest is that heat liberation from the crystallizing front influences the curvature of the crystal-melt interface, leading to directional growth of lamellar tips and side branches. The landscape of these morphological textures has been established as a function of anisotropy of surface energy and supercooling. With increasing supercooling and decreasing anisotropy, the hexagonal single crystal transforms to the dense lamellar branching morphology in conformity with the experimental findings.

Double dendrite growth in solidification

We present experiments on the doublon growth morphology in directional solidification. Samples used are succinonitrile with small amounts of poly(ethylene oxide), acetone, or camphor as the solute. Doublons, or symmetry-broken dendrites, are generic diffusion-limited growth structures expected at large undercooling and low anisotropy. Low anisotropy growth is achieved by selecting a grain near the {111} plane leading to either seaweed (dense branching morphology) or doublon growth depending on experimental parameters. We find selection of doublons to be strongly dependent on solute concentration and sample orientation. Doublons are selected at low concentrations (low solutal undercooling) in contrast to the prediction of doublons at large thermal undercooling in pure materials. Doublons also exhibit preferred growth directions and changing the orientation of a specific doublonic grain changes the character and stability of the doublons. We observe transitions between seaweed and doublon growth with changes in concentration and sample orientation.