Branched Crystalline Patterns Formed Around Poly(ethylene oxide) Dots in Humidity

Branched patterns reminiscent of diffusion‐limited aggregation form around poly(ethylene oxide) dots on Au surfaces in humidity by crystallization of polymer chains in water‐assisted diffusion, involving fractal‐like structure and dense branching‐like morphology (DBM). Higher humidity leads to a slower growth of crystal lamellae. Crystal growth promotes outward diffusion. Fractal‐like lamellae are viewed flat‐on. Due to the reduction of chain availability in the diffusion field, the fractal‐like structure turns into DBM.     

Fractal Characterization of Silica Sol Prepared by the Sol-Gel Method: From the Sol Formation to the Flocculation Process

The fractal characterization of silica particles prepared by the sol-gel method was obtained; from the beginning of the sol-gel synthesis to the aggregation process of these particles by adding metal ions in solution, the fractal dimension was determined. At the beginning of the sol-gel process, unstable structures were formed due, essentially, to the auto-catalytic nature of the sol-gel condensation reactions; these particles are fractal structures with a fractal exponent corresponding to a reaction limited aggregation regime. As the time proceeds, the reactants are consumed approaching the system to equilibrium, stabilizing the size of the silica particles. The silica sol can be flocculated by adding metal ions in solution. The fractal exponent for the aggregation process was determined, obtaining a value corresponding to a diffusion limited aggregation regime.     

Hierarchical assembly of diphenylalanine into dendritic nanoarchitectures

Highly ordered, multi-dimensional dendritic nanoarchitectures were created via self-assembly of diphenylalanine from an acidic buffer solution. The self-similarity of dendritic structures was characterized by examining their fractal dimensions with the box-counting method. The fractal dimension was determined to be 1.7, which demonstrates the fractal dimension of structures generated by diffusion limited aggregation on a two-dimensional substrate surface. By confining the dendritic assembly of diphenylalanine within PDMS microchannels, the self-similar dendritic growth could be hierarchically directed to create linearly assembled nanoarchitectures. Our approach offers a novel pathway for creating and directing hierarchical nanoarchitecture from biomolecular assembly.     

SYNTHESIS AND CHARACTERIZATION OF A NEW THREE-ARMS-NINE-CHAINS DISCOTIC LIQUID CRYSTAL

A new three-arms-nine-chains discotic molecule has been synthesized,and theaggregation structure of the compound was measured by x-ray diffraction,infraredspectra,polarizing microscope,etc.From these evidences,the new discotic liquid crystalis found to have the discotic lammelar phase.     

Formation process and fractal growth model of HCFC-141b refrigerant gas hydrate

The microscopic visualization experiment on the formation process of HCFC-141b refrigerant gas hydrate has been investigated, and the morphological photos of hydrate formation process have been obtained. The results show that gas hydrate originally nucleated on the interface of refrigerant HCFC-141b and water under the condition of supercooling, then the hydrate grows continually due to the inducement of formed nucleation and diffusion of refrigerant. The formation of gas hydrate presents an arboreous phenomenon. The fractal dimension of the hydrate formation morphology on different stages was calculated. The calculating results indicate that the initial stage of the hydrate formation belongs to fractal growth, and the dimension is about 1.52. Based on the fractal theory, an RIN-DLA (random inducement nucleation-diffusion limited aggregation) model for the HCFC-141b hydrate growth was developed. The hydrate growth process was simulated with the developed model, and the fractal dimension for the simulated     

Magnetomesogens: Bis(1,3-di(4'-decoxyphenyl)propane-1,3-dionato)oxovanadium (IV)

β-Diketonate complexes of oxovanadium (IV) have been synthesized and their mesomorphic behaviour investigated. The title complex exhibits a short range monotropic columnar discotic phase, identified by its optical texture and by miscibility studies. The optical texture of the phase is retained on cooling to the crystal. As a consequence of the unpaired electron on vanadium the complexes are paramagnetic.     

Multifractal Properties of Copper Sulfide Film Formed in Self-Organizing Chemical System

The growth of fractal films of copper sulfide formed during the oxidation of ascorbic acid by aerial oxygen in the presence of a copper coordination compound and sodium sulfide has been studied. The process of growth of the film can be divided into three parts: 1) generation of CuS centers of growth; 2) growth of CuS according to the diffusion limitation of aggregation mechanism; and 3) in the final stage the structure of the film does not change. A method is developed to obtain films with uniform fractal dimensions, but different values of fractal divergence.     

Studies of Lead Zirconate Titanate Sol Aging Part II: Particle Growth Mechanisms and Kinetics

The kinetics of particle growth in lead zirconate titanate sol gel precursor solutions has been investigated. It was found that chemical reaction limited aggregation was responsible for most of the sol aging, followed by diffusion limited aggregation in the later stage. At the beginning, particles grow by reaction between initial polymers and particles. As the particle number-density increases, a particle-particle aggregation characterised by an exponential growth law becomes the predominant mechanism. When particles grow larger, towards gel formation, the aggregation changes to diffusion limited. Mathematical models derived according to the above mechanisms agreed well with experimentally measured particle growth profiles.     

The cellular optical texture of the lyotropic nematic phase of the caesium pentadecafluoro-octanoate(CsPFO)/water system in cylindrical tubes

The nematic phase of the CsPFO/water system, when held in a cylindrical glass tube, spontaneously forms a detailed 'cellular' texture with an axial S = +1 disclination. This texture is the lyotropic discotic analogue of that previously found for a calamitic thermotropic system.     

Linking phase behavior and reversible colloidal aggregation at low concentrations: simulations and stochastic mean field theory

We have studied the link between the kinetics of clustering and the phase behavior of dilute colloids with short range attractions of moderate strength. This was done by means of computer simulations and a theoretical kinetic model originally developed to deal with reversible colloidal aggregation. Three different regions of the phase diagram were accessed. For weak attractions, a gas phase of small clusters in equilibrium forms in the system. For intermediate attractions, the system undergoes liquid-gas separation, which is signatured by the formation of a few large droplike aggregates, a gas phase of small clusters, and an overall kinetics where a few seeds succeed in explosively growing at long times, after a lag time. Finally, for very strong attractions, fractal unbreakable clusters form and grow following DLCA-like (diffusion limited cluster aggregation) kinetics; liquid-gas separation is prevented by the strength of the bonds, which do not allow restructuration. Good qualitative and quantitative agreement is found between the dynamic simulations and the kinetic model in all the three regions.     

C60 thin film growth on graphite: Coexistence of spherical and fractal-dendritic islands

The initial growth stage of C(60) thin film on graphite substrate has been investigated by scanning tunneling microscopy in ultrahigh vacuum at room temperature. The C(60) layer grows in a quasi-layer-by-layer mode and forms round, monolayer high islands on the graphite surface. The islands are confined by terraces on the graphite surface and the mobility of C(60) fullerenes across steps is low in all layers. The second and all subsequent layers adopt a fractal-dendritic shape, which was confirmed by calculating the fractal dimension (D=1.74 prior to island coalescence) and is in agreement with a diffusion limited aggregation. The profound differences between the growth of C(60) layers on graphite (first layer) and on C(60) surfaces (second and higher layers) are caused by the restriction of the C(60) mobility on the highly corrugated fullerene surfaces. The orientation of the fractal islands follows the hexagonal symmetry of the densely packed (111) surface of the fullerene lattice, which introduces a bias in the direction of molecule movement. The differences in surface topography on the nanoscale determine the mode of film growth in this van der Waals bonded system.     

Structures and their influence factors of three‐dimensional fractal cadmium layer formed by electrodeposition

Three‐dimensional fractal structure of the electrodeposited cadmium layer was investigated. The results suggested that the fractal growth begin with nanometer scale aggregate within which the atoms arrange in hexagonal close‐packed lattice (the normal cadmium lattice). The fractal structure is correlated to the current density. The higher the current density is, the larger the size of fractal growth will be. Fractal structures can emerge in both the complete diffusion‐limited process and the combination‐limited process of the electrochemical reaction and diffusion. The fractal structure obtained from the simple hydrated ion electrolyte is different from that obtained from the complex ion electrolyte, which indicates they grow in different modes. The fractal dimensionality of deposit from the simple hydrated ion electrolyte is 2.592, smaller than that (2.608) from the complex ion electrolyte.     

Phase-field modeling of two-dimensional solute precipitation∕dissolution: solid fingers and diffusion-limited precipitation

Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the chemical reaction at the solid-liquid interface has similarities with diffusion-limited aggregation (DLA). The diffusion-limited precipitation is attained by setting the chemical reaction rate much larger compared to the solute diffusion to eliminate the effect of the interface growth kinetics. The phase-field simulation results were in reasonable agreement with the analytical solutions. The fractal solid fingers can be formed in the diffusion-limited precipitation and have a fractal dimension measured d(f)=1.68, close to 1.64, the fractal dimensionality of large square lattice DLA clusters.     

Hierarchical organization in aggregates of protein molecules

The aggregation of proteins into small clusters is studied by atomic force and electron microscopy. Scaling laws and fractal behaviour in the growth of the aggregates and in the correlation between aggregates is seen. A phase diagram of the aggregation process where the protonic concentration of the solution and the density of protein are varied shows the existence of specific growth processes resulting in different branch-like structures. The resulting structures are strongly influenced by the shape of each protein molecule. Lysozyme and ribonuclease are found to form spherical structures with a narrow size distribution.     

Eutectic mixtures with plastic columnar discotics: molecular structure,phase morphology and kinetics of phase separation

We report the properties of eutectic mixtures of triphenylenes displaying a highly ordered columnar phase with a low molar mass non‐discotic compound. Such highly ordered triphenylenes display large charge carrier mobilities which are strongly controlled by the state of order in the discotic phase. The motivation was to establish how the state of order—molecular order, phase morphology, temperature ranges of phase stabilities and macroscopic orientational order—can be influenced by mixing. The studies reveal that the molecular order, in particular the mutual arrangement of the columns and the intracolumnar order, are unaffected by dilution of the discotic compound, whereas the phase morphology and the kinetics of phase separation change significantly with dilution. Rod‐shaped discotic domains with a hexagonal cross‐sectional area are formed via a nucleation process and the rods grow linearly as a function of time. Both the pure discotic phase as well as the discotic domains forming during phase separation can be macroscopically ordered by orientation layers.     

A fractal model for the molecular organization in the alkylbenzenesulphonate/electrolyte/water system

Under conditions where individual molecules are no longer soluble, the association of amphiphiles occurs as a sequence of growth and aggregation processes: the formation of dimers, bilayers and multilayer assemblies culminates with the production of myelin cylinders and chains or spherulitic arrays of focal-conic units. We have examined this process using the alkylbenzenesulphonate/electrolyte/water system as a model. The phase diagram was obtained using optical microscopy. The kinetics of the aggregation process were followed by lightscattering measurements and the structures of the one- and two-phase regions were examined by optical microscopy and freeze-fracture electron microscopy. The fractal nature of the aggregation process was investigated using an indirect Fourier transform study of the lightscattering data. The fractal character of the whole self-assembly process was confirmed and an experimental value of 2.17 was determined for the fractal dimension (in close agreement with the expected theoretical value of 2.16).     

A bidimensional simulation of particle-cluster aggregation with variable active sites particles

 In this work a simple program has been developed which simulates the process of particle– cluster aggregation limited by diffusion. All the simulation have been carried out using 2d square lattices with square “particles” having a variable number of active inter-action sites (from 3 to 8) for each particle in order to analyze the effect of such limitation on the fractal dimension of the aggregates. The fractal dimension of such aggregates was calculated by the so-called “box counting” method. It has been shown that there is no change in the value of the fractal dimension (1.70) as the active site number is increased. Instead it appears that there is an average number of active sites of about 2.3 for all the structures no matter how many active interaction sites the particles have. This appears as an interesting result in connection with the aggregation of particles such as renneted casein micelles, which could present differences in the surface density of active sites. Received: 11 February 1997 Accepted: 8 January 1998     

Alignment behaviour of the discotic nematic phase of 2,3,6,7,10,11-hexa(4-n-octyloxybenzoyloxy)triphenylene on polyimide and cetyltrimethylammonium bromide coated substrates

The orientational behaviour of the nematic discotic phase of 2,3,6,7,10,11-hexa(4-n-octyloxybenzoyloxy)triphenylene (C8OBT) on substrates coated with a polyimide or cetyltrimethylammonium bromide (CTAB) was investigated by polarizing optical microscopy. The averaged order parameters and directions of the triphenylene core and the carbonyl groups of C8OBT were evaluated by an infrared dichroic method. The discotic nematic (N_D) phase of C8OBT exhibits a homeotropic alignment on a polyimide film, a typical nematic schlieren texture on a glass substrate, and a tilted or planar homogeneous alignment on a CTAB-coated substrate. The order parameter of the triphenylene core is higher on a polyimide film (S = 0.6) than on a CTAB-coated substrate (S = 0.2), whereas that of the carbonyl groups remains roughly constant at 0.2 to 0.3 independent of the substrate for the N_D phase.     

NMR relaxation of rigid molecules in the nematic phase of a discotic liquid crystal

Frequency and temperature dependent NMR relaxation measurements were performed on deuteriated benzene, pyrene and triphenylene dissolved in the nematic phase of a discotic liquid crystal. The results show a strong frequency dependence of the spectral densities. Based on the symmetries of the system and the usual model for director fluctuations this frequency dependence should be equal for J₁ and J₂. From fitting the commonly used model of rotational diffusion and director fluctuations to the data we see that this is not the case for benzene and triphenylene, even though the fits themselves are satisfactory. Values for the elastic constants, effective viscosity and translational diffusion in similar discotic liquid crystals do not account quantitatively for the frequency dependence of benzene. For both pyrene and triphenylene quantitative comparison was impossible due to lack of translational diffusion data. We also find that the so-called cut-off wave-length is of the order of the dimensions of the liquid crystal molecules, just as in ordinary nematics.     

Light-induced formation of curved needle texture by circularly polarized light irradiation on a discotic liquid crystal containing a racemic chromium complex

We have found that the discotic nematic liquid crystal, hexakis(4-nonylphenylethynyl)benzene (HNEB), doped with the racemic chromium complex Cr(Ocacac)₃, shows a novel straight-needle texture with hexagonal columnar alignments, changing to a curved-needle texture under irradiation of circularly polarized light (CPL). This novel phenomenon is specific to the mixture of HNEB and Cr(Ocacac)₃. The formation of curved needles means that chiroselective photoinversion of racemic Cr(Ocacac)₃ by CPL irradiation induces a needle direction change in a discotic liquid crystal. The change in chirality of Cr(Ocacac)₃ in HNEB induced by CPL irradiation, and the resulting nano-segregation of its enantiomers during cooling from the isotropic to mesophase of HNEB, are considered to influence changes in the alignment of columns and/or small domains of column aggregates in the discotic liquid crystal.