金属锌电沉积过程的分形研究

对金属锌电沉积过程中的二维枝晶生长进行了研究,分析了外加电压、电解质浓度以及温度等实验条件对电沉积产物形貌及其分形维数的影响.结果表明,随着外加电压的增大,沉积产物形貌的变化趋势为由开放的分枝结晶向较为致密的生长形貌转变;随着硫酸锌浓度的增大,沉积产物具有分叉结构的致密纤维状枝晶簇和较为粗壮的开放型规则的分叉状枝晶,分形维数发生相应的变化;随着温度的升高,沉积产物的枝晶呈均匀化、致密化,沉积产物分形维数呈明显增大的趋势.     

Fractal dimensions of silica gels generated using reactive molecular dynamics simulations

We have used molecular dynamics simulations based on a three-body potential with charge transfer to generate nanoporous silica aerogels. Care was taken to reproduce the sol-gel condensation reaction that forms the gel backbone as realistically as possible and to thereby produce credible gel structures. The self-similarity of aerogel structures was investigated by evaluating their fractal dimension from geometric correlations. For comparison, we have also generated porous silica glasses by rupturing dense silica and computed their fractal dimension. The fractal dimension of the porous silica structures was found to be process dependent. Finally, we have determined that the effect of supercritical drying on the fractal nature of condensed silica gels is not appreciable.     

Three-dimensional assembly of flower-like Au structures: the synergistic effect of macroporous structures and surface nanoarchitectures on electrocatalysis and electroanalysis

We present the fabrication of a three-dimensional (3D) assembly of flower-like Au structures via the combination of 3D macroporous Au-coated microspheres and surface nanoarchitectures using electrodeposition of nanoplate Au structures. The 3D flower-like Au structures exhibit synergistically enhanced electrocatalytic activities regarding glucose oxidation and oxygen reduction compared to those of the individual 3D macroporous and nanoplate Au structures. The 3D flower-like Au structures can also be utilized as electroanalytical platforms retaining the combined advantages of both of the 3D macroporous and nanoplate Au structures.     

高磺化度聚苯胺体系中的分形结构研究

通过透射电镜的观察研究发现磺化聚苯胺的胶体聚集体和胶粒内部结构都具有分形体的特征 ,从而将分形的概念及其数学模型引入共轭导电聚合物体系之中 .磺化聚苯胺胶体的聚集体为很不均匀的分支状开放结构 ,其形成过程可用扩散控制集团聚集模型 (DLCA)进行模拟 ,计算机模拟生成的图形及其分形维数都与实验观测结果相当吻合 .胶粒由于是在分散介质所形成的平均化场中生成 ,屏蔽效应减弱 ,是比由它组成的聚集体要致密的球形结构 ,该结构的生成可用随机雨点模型模拟且结果相近 .     

Fractal Dimension of Microbead Assemblies Used for Protein Detection

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest–Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70–1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles.     

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.     

Self‐assembled supramolecular microgels: Fractal structure and aggregation mechanism

Multifunctional molecules were designed to produce microgels with specific structures. Both static light scattering and dynamic light scattering were employed to determine the fractal dimension of the microgels. The protein, avidin, was strongly bound to four biotin moieties. Biotin was attached covalently to specifically engineered peptide nucleic acid (PNA) oligomers. Three designed DNA oligomers self‐assembled to produce a trifunctional three‐way junction (TWJ) with single‐stranded ends that were complementary to the PNA sequence. The sizes of the supramolecular aggregates were characterized by dynamic light scattering. The fractal dimension was obtained from the angular dependence of the scattered intensity when the microgels were large enough. When the microgels were formed via cooling from a temperature above the melting point of the PNA–DNA helices, reversible structures with a fractal dimension of approximately 1.86 were formed, which is consistent with a cluster–cluster aggregation mechanism. When the microgels were formed by the slow addition of biotinylated PNA bound to the TWJ to a solution of avidin at room temperature, the observed fractal dimension approached 2.6, which is consistent with a point–cluster aggregation mechanism. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3037–3046, 2003     

Fractal structure of asphaltene aggregates

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.     

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.     

Mobility and aggregation of free clusters soft landed on amorphous and crystalline carbon substrates

Neutral antimony clusters produced by a gas aggregation source have been deposited at room temperature on thin films of amorphous carbon and cleavage surfaces (0001) of graphite. Antimony islands generated from different mean size distributions of preformed clusters Sb_n(n = 4, 90, 150, 250, 600, 2000) have been investigated by transmission electron microscopy. Only compact islands have been observed on amorphous carbon, whereas an evolution from compact to dendritic shapes occurs on graphite substrate as the mean size of the deposited clusters increases. For clusters containing more than 150 atoms the dendritic islands exhibit a fractal character whose dimensional analysis yields a fractal dimension of 1.63 ± 0.07. The different models for island growth are discussed in the light of these results.     

Pd沉积在聚乙烯醇缩甲醛衬底上分形结构研究

用透射电子显微镜（ＴＥＭ）研究了衬底和沉积速率对气相沉积在聚乙烯醇缩甲醛衬底上的Ｐｄ膜显微结构的影响，当衬底温度由高到低改变时，Ｐｄ膜结构由紧密岛向分形渐变，在２３３－２５３Ｋ时Ｐｄ膜具有分形结构，用Ｓａｎｄｂｏｘ方法测量了其分维数，在相同温度的衬底上，沉积速率不同时，基分形的图样不同，研究表明，上述分形结构是稳定的，利用有边缘扩散的ＤＬＡ模型了这些实验结果。     

Bilayer Molecular Assembly at a Solid/Liquid Interface as Triggered by a Mild Electric Field

The construction of a spatially defined assembly of molecular building blocks, especially in the vertical direction, presents a great challenge for surface molecular engineering. Herein, we demonstrate that an electric field applied between an STM tip and a substrate triggered the formation of a bilayer structure at the solid–liquid interface. In contrast to the typical high electric‐field strength (10⁹ V m^?1) used to induce structural transitions in supramolecular assemblies, a mild electric field (10⁵ V m^?1) triggered the formation of a bilayer structure of a polar molecule on top of a nanoporous network of trimesic acid on graphite. The bilayer structure was transformed into a monolayer kagome structure by changing the polarity of the electric field. This tailored formation and large‐scale phase transformation of a molecular assembly in the perpendicular dimension by a mild electric field opens perspectives for the manipulation of surface molecular nanoarchitectures.     

The fractal nature of Escherichia coli biological flocs

The fractal structures of Escherichia coli biological flocs were characterised in terms of fractal dimension, which is a measurement of how the bacteria in the flocs occupy space. The dimensional analysis methods, based on power law correlations between floc perimeter, projected area and maximum length, were used to determine the one- and two-dimensional fractal dimensions (D(1) and D(2)) of E. coli flocs formed by flocculation in chitosan solution with a concentration of 10.0 mg chitosan per g dry cell weight (DCW), giving D(1)=1.07+/-0.06 and D(2)=1.70+/-0.08 (+/-S.D.). The three-dimensional fractal dimension (D(3)) of the E. coli flocs was determined by the two-slopes method, using cumulative size distributions of floc length and solid volume, to be 1.99+/-0.08 (+/-S.D.), which is close to the value of D(3)=2.14+/-0.04 (+/-S.D.) measured by the small angle light scattering method. The results demonstrate that E. coli flocs flocculated with chitosan have a fractal nature, as their fractal dimensions D(1), D(2) and D(3) differ from the values of 1, 2 and 3 expected for the spherical Euclidean object, respectively.     

Self-organization of gold-containing hydrogen-bonded rosette assemblies on graphite surface

The self-organization of supramolecular structures, in particular gold-containing hydrogen-bonded rosettes, on highly oriented pyrolytic graphite (HOPG) surfaces was investigated by tapping-mode atomic force microscopy (TM-AFM) and scanning tunneling microscopy (STM). TM-AFM and high-resolution STM results show that these hydrogen-bonded assemblies self-organize to form highly ordered domains on HOPG surfaces. We find that a subtle change in one of the building blocks induces two different orientations of the assembly with respect to the surface. These results provide information on the control over the construction of supramolecular nanoarchitectures in 2D with the potential for the manufacturing of functional materials based on structural manipulation of molecular components.     

Analysis of the structure of very large bacterial aggregates by small-angle multiple light scattering and confocal image analysis

This work aims at developing a more accurate measurement of the physical parameters of fractal dimension and the size distribution of large fractal aggregates by small-angle light scattering. The theory of multiple scattering has been of particular interest in the case of fractal aggregates for which Rayleigh theory is no longer valid. The introduction of multiple scattering theory into the interpretation of scattering by large bacterial aggregates has been used to calculate the fractal dimension and size distribution. The fractal dimension is calculated from the form factor F(q) at large scattering angles. At large angles the fractal dimension can also be computed by considering only the influence of the very local environment on the optical contrast around a subunit. The fractal dimensions of E. coli strains flocculated with two different cationic polymers have been computed by two techniques: static light scattering and confocal image analysis. The fractal dimensions calculated with both techniques at different flocculation times are very similar: between 1.90 and 2.19. The comparison between two completely independent techniques confirms the theoretical approach of multiple scattering of large flocs using the Mie theory. Size distributions have been calculated from light-scattering data taking into account the linear independence of the structure factor S(q) relative to each size class and using the fractal dimension measured from F(q) in the large-angle range or from confocal image analysis. The results are very different from calculations made using hard-sphere particle models. The size distribution is displaced toward the larger sizes when multiple scattering is considered. Using this new approach to the analysis of very large fractal aggregates by static light multiple scattering, the fractal dimension and size distribution can be calculated using two independent parts of the scattering curve.     

The structure of percolating lipid monolayers

The lattice structure and in plane molecular organization of Langmuir monolayer of amphiphilic material is usually determined from grazing incidence X-ray diffraction (GIXD) or neutron reflectivity. Here we present results of a different approach for determination of monolayer lattice structure based on application of fractal analysis and percolation theory in combination with Brewster angle microscopy. The considerations of compressibility modulus and fractal dimension dynamics provide information on percolation threshold and consequently by application of percolation theory on the lattice structure of a monolayer. We have applied this approach to determine the monolayer lattice structures of single chain and double chain lipids. The compressibility moduli were determined from measured π-A isotherms and fractal dimensions from corresponding BAM images. The monolayer lattice structures of stearic acid, 1-hexadecanol, DPPC and DPPA, obtained in this way conform to the corresponding lattice structures determined previously by other authors using GIXD.     

Environmentally Friendly γ‐MnO2 Hexagon‐Based Nanoarchitectures: Structural Understanding and Their Energy‐Saving Applications

Although about 200,000 metric tons of γ‐MnO₂ are used annually worldwide for industrial applications, the γ‐MnO₂ structure is still known to possess a highly ambiguous crystal lattice. To better understand the γ‐MnO₂ atomic structure, hexagon‐based nanoarchitectures were successfully synthesized and used to elucidate its internal structure for the present work. The structural analysis results, obtained from the hexagon‐based nanoarchitectures, clearly show the coexistence of akhtenskite (ε‐MnO₂), pyrolusite (β‐MnO₂), and ramsdellite in the so‐called γ‐MnO₂ phase and verified the heterogeneous phase assembly of the γ‐MnO₂ state, which violates the well‐known “De Wolff” model and derivative models, but partially accords with Heuer's results. Furthermore, heterogeneous γ‐MnO₂ assembly was found to be a metastable structure under hydrothermal conditions, and the individual components of the heterogeneous γ‐MnO₂ system have structural similarities and a high lattice matches with pyrolusite (β‐MnO₂). The as‐obtained γ‐MnO₂ nanoarchitectures are nontoxic and environmentally friendly, and the application of such nanoarchitectures as support matrices successfully mitigates the common problems for phase‐change materials of inorganic salts, such as phase separation and supercooling‐effects, thereby showing prospect in energy‐saving applications in future “smart‐house” systems.     

Application of Brewster angle microscopy and fractal analysis in investigations of compressibility of Langmuir monolayers

The aim of this study was to investigate the connection between the lipid/amphiphile monolayer structure at the interface and its macroscopic/rheological properties, in particular, to establish the link between the fractality of the monolayer structure and its compressibility modulus. To that purpose we have used fractal analysis of images obtained by Brewster angle microscopy to infer the fractal dimension of the monolayer structure and relate its change to the corresponding changes in compressibility derived from a simultaneously measured π-A isotherm. The results of the study confirmed the starting assumption based on theoretical considerations that the fractal dimension of an amphiphilic monolayer and its compressibility should be correlated. We have shown that there exists a strong correlation between the fractal dimension and the corresponding compressibility modulus of different amphiphilic materials. Thus, confirming the link between the short ordered structure on the molecular level and the macroscopic property-compressibility of the monolayer. The established correlation between the fractal dynamics and compressibility modulus of the monolayer enabled identification of onset of percolation-a second-order phase transition that is otherwise not easy and unambiguously detectable. We have found that the signature of percolation in a monolayer, regardless of its composition, is the occurrence of a sharp increase (a jump) of compressibility modulus (at macroscopic level) at the characteristic value of the corresponding fractal dimension D = 1.89. This is the result of the abrupt establishment of a connected structure on the molecular level, consequently involving a change in the elastic properties of the monolayer on a macroscopic scale. The results of this investigation provide means for unambiguous identification of the onset of percolation in the Langmuir layer and should facilitate a more efficient application of the percolation theory in further study of processes and structures at the interface during the monolayer compression.     

Self-assembled π-conjugated macromolecular architectures — A soft solution process based on Schiff base coupling

Two-dimensional supramolecular covalent macromolecular architectures were visualized directly by in-situ scanning tunneling microcopy and colorful π-conjugated nanofilms with unique mesostructures formed spontaneously on hydrophobic substrates from aqueous solutions in the presence of simple aromatic building block molecules under ambient conditions. We thus report the results of surface-mediated polycondensation and chemical liquid deposition. The Schiff base coupling reaction applied for this soft solution process is a dynamic reversible covalent coupling reaction that can be managed by careful changes in solution conditions based on ‘adsorption’ and ‘polymerization’ equilibria. This low-cost and eco-friendly ‘bottom-up’ method allows great diversity in terms of the design of primary polymeric chemical structures by the selection of building blocks without the need to consider the solubility of the polymer. This paves the way to a true ‘bottom-up’ assembly of a vast array of solid-supported, designer supramolecular nanoarchitectures with potential use as functional materials for next-generation organic electronics.     

Structural characteristics of silica sonogels prepared with additions of isopropyl alcohol

Wet silica gels with approximately 1.4 x 10(-3) mol SiO2/cm3 and approximately 92 vol % liquid phase were obtained from sonohydrolysis of tetraethoxysilane (TEOS) with different additions of isopropyl alcohol (IPA). The IPA/TEOS molar ratio R was changed from 0 to 4. Aerogels were obtained by supercritical CO2 extraction. The samples were analyzed by small-angle X-ray scattering (SAXS) and nitrogen adsorption. The wet gels exhibit mass fractal structure with fractal dimension increasing from D approximately 2.10 to D approximately 2.22, characteristic length xi decreasing from approximately 9.5 to approximately 6.9 nm, as R increases from 0 to 4, and an estimated characteristic length for the primary silica particles lower than approximately 0.3 nm. The supercritical process apparently eliminates a fraction of the porosity, increasing the mass fractal dimension and shortening the fractality domain in the mesopore region. The fundamental role of isopropyl alcohol on the structure of the resulting aerogels is to decrease the porosity and the pore mean size as R changes from pure TEOS to R = 4. A secondary structure appearing in the micropore region of the aerogels can be described as a mass/surface fractal structure, with correlated mass fractal dimension Dm approximately 2.7 and surface fractal dimension Ds approximately 2.3, as inferred from SAXS and nitrogen adsorption data.