Dynamic scaling method and interface growth

The dynamic scaling approach is an important tool for describing the time evolution of rough interfaces. It computes dynamic scaling parameters alpha and beta, which characterize surface and time correlations. Applications of dynamic scaling to random deposition and ballistic deposition are discussed. A model of random adsorption on fractal substrates is presented. Then the influence of surface diffusion on adsorption is analyzed. The dependence of alpha and beta on the substrate fractal dimension, together with the dependence of the fractal dimension of the gas-solid interface on adsorption coverage are computed.     

Spontaneous formation of fractal structures on triglyceride surfaces with reference to their super water-repellent properties

Alkylketene dimer (AKD), a kind of wax, has been known to form fractal surfaces spontaneously and show super water-repellency. Such formation of water-repellent and fractal surfaces was also found in this work for triglycerides. Since the crystal phase transitions of these waxes were well studied, we studied the formation of their fractal surfaces through contact angle measurements, differential scanning calorimetry (DSC), and X-ray diffraction (XRD). From time-dependent contact angle measurements, it was found that the formation of super water-repellent surfaces with fractal structures occurred spontaneously also on the triglyceride surfaces at different temperatures. The freshly solidified triglyceride surfaces were almost transparent, and their initial contact angles of water were close to 110 degrees. The surfaces then became rough and clouded after being incubated for a certain time at a specified temperature. The super water-repellent surfaces were quite rough and showed fractal structures with the dimension of ca. 2.2 calculated from the scanning electron microscopic (SEM) images by the box-counting method. The phase transformation from a metastable state to a stable cystalline one after the solidification from the melt of triglycerides was clearly observed by DSC and XRD measurements. The fractal crystalline structures and the super water-repellency resulted from this phase transformation and the crystal growth. Ensuring the initial sample solidified into the metastable state and curing the surface at an appropriate temperature are key factors for the successful preparation of fractal triglyceride surfaces by the solidification method.     

二次电子衬度曲线法研究PVC/MBS共混物断面的分形特征

利用二次电子衬度曲线法测定了聚氯乙烯甲基丙烯酸甲酯丁二烯苯乙烯共聚物(PVCMBS)共混物冲击断面的形貌特征及对应的分形维数值.结果表明,材料的断口或微观结构并不是严格的分形结构,这种自相似性仅存在于一定尺码范围内,不同断面形貌特征所对应的分形维数测量值不同,随着MBS用量增加,PVCMBS共混物缺口冲击强度随满足自相似原理的形貌特征所对应的分形维数值增大而增大.本文从理论上讨论了材料断裂韧性与分形维数的关系.     

Surface structural analysis of fine silica powder modified with butyl alcohol

The surface structure of modified silica powder has been studied by various experiments and simulations. In addition, the effect of surface structure on wettability has also been investigated. Nonporous silica powder was modified with n-and t-butyl alcohol. Two series of the modified silica surfaces were characterized by fractal dimension analysis from isotherms with some kinds of adsorptives. The fractal dimensions of the two series of modified surfaces were different from each other with an increase in modified ratio. The fractal dimension of the surface modified with t-butyl alcohol (t-modified surface) increased monotonously with butoxy group density. It is thought that the structure of the t-butoxy group is rigid and that the t-butoxy group cannot change its conformation. On the other hand, the variation of the surface fractal dimension value for the surface modified with n-butyl alcohol (n-modified surface), whose structure is flexible, was unique compared with the t-modified surface. Such discrepancy was assumed to be caused by the difference in the structure of the modifier and the assembled state of modifiers between the t- and n-modified surfaces. In order to investigate the variation of surface structure of the surface modified by the butoxy group with an increase in modified ratio, molecular dynamics simulations were performed. By comparing the results of these simulations with experimental results, it has been clarified that the variation in the mobility of the methyl group in the n-butoxy groups was closely related to the change in the surface fractal dimension value for the n-modified surface. It was then elucidated that this mobility change was caused by steric hindrance among the groups. Furthermore, the variation of conformation in the n-butoxy groups, which was obtained from molecular dynamics simulations, was in good agreement with the change in the wettability of the n-modified surface. It is suggested that the surface density of the modifier, the covering structure and the bulkiness significantly influence the wettability of the modified surface. Received: 6 April 1999 /Accepted in revised form: 24 August 1999     

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.     

Boëder PDF Brownian simulations for macromolecular rod-like particles near uneven solid surfaces

A molecular dynamics simulation is presented to calculate the Probability Distribution Functions (PDF) for the spatial positions and angular orientations of macromolecular rod-like particles in dilute solutions, under hydrodynamic flow, in the vicinity of uneven solid boundaries. The Brownian and hydrodynamic restitution model for ideally flat surfaces is generalized to simulate the diffusive collisions between the macromolecular particles and an uneven solid surface. Two types of uneven surfaces are particularly considered: the periodic grating and the random rough, with characteristic profiles of heights and lateral variations. Different from ideally flat surfaces, the simulation results demonstrate that uneven surfaces have characteristic depletion layers, and characteristic and variable PDF. This is the case under varying conditions of hydrodynamic flow, Brownian movement and diffusive collisions. These characteristics uniquely identify Boeder PDF signatures for the uneven surface topography.     

An experimental study of gas adsorption on fractal surfaces

The validity of the fractal versions of the FHH and BET theories for describing the adsorption of butane and nitrogen on a variety of partially dehydroxylated silica surfaces has been tested. The fractal dimensions obtained from adsorption data have been compared with those obtained completely independently using SAXS. It was found that the fractal dimensions obtained from butane adsorption isotherms, using both the fractal FHH and fractal BET theories, agreed well with the corresponding values obtained from SAXS over overlapping length scales. However, in general, a systematic deviation between the fractal dimension obtained from nitrogen adsorption and that obtained from SAXS was observed. The fractal dimensions obtained from nitrogen adsorption were consistently larger than those obtained from SAXS, which is the opposite of what has often been found in the literature. It has been suggested that the differences in the suitability of the adsorption theories tested to describe butane and nitrogen adsorption is due to the significant difference between the interaction strengths of these two different molecules with silica surfaces. A modified theory that can account for the discrepancy between the fractal dimensions obtained from nitrogen adsorption and SAXS has been proposed. The implications of the new theory for the accuracy of nitrogen adsorption BET surface areas for silicas are discussed.     

An investigation of submicrostructural evolution of freshly precipitated ZrO2 in digestion for ultrafine sulfated ZrO2 catalysts by SAXS technique

Coupled with XRD, BET, and TEM, the small-angle X-ray scattering (SAXS) technique has been effectively used to probe and characterize the submicrostructure of freshly precipitated hydrous zirconia and its evolution during digestion. It has been found that fresh hydrous zirconia particles possess an average diameter of about 5 nm and rather rough surfaces describable in terms of fractal concepts. The digestion of zirconia precipitates at 100 degrees C with their mother liquors may remarkably smooth the particles' rough surface and provoke fractal aggregation of the particles but make little change in average particle dimensions. A local dissolution-reprecipitation mechanism is regarded as a basic process to accompany particle surface smoothing, particle aggregation, and coarsening at the neck areas between joint particles, which may greatly strengthen the particle networks and enhance their resistance to crumbling while calcinated at high temperatures. On the basis of the submicrostructural features unraveled by SAXS, a coherent and significant physical picture has been raised out to demonstrate and interpret the relationship underlying the submicrostructure, the surface area variation, and the heating behavior of hydrous zirconia precipitates.     

Rough silver films studied by surface enhanced raman spectroscopy and low temperature scanning tunnelling microscopy

The surface topography of Ag films and surface enhanced Raman scattering (SERS) from benzene on Ag films have been simultaneously recorded. The Ag films were formed by vacuum deposition at temperatures ranging from 100 K to 500 K. Analysis of scanning tunnelling microscopy (STM) images shows that films formed below 250 K are fractal structures with Hausdorff-Besicovitch dimension 2.55 < D < 2.72, while for those formed above 250 K, D≈2. The lower temperature, rough films exhibit strong surface enhanced Raman scattering but the higher temperature, smooth films do not. We consider the consequences of fractal character and the possible correlation between this and the SERS activity of these films.     

Fractal analysis of polyethylene catalysts surface morphologies based on wavelet transform modulus maxima method

Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies. Supported by the Chinese Petroleum & Chemical Corporation Development Department (Grant No. x504024)     

Measuring surface topography by scanning electron microscopy. II. Analysis of three estimators of surface roughness in second dimension and third dimension.

Scanning electron microscopy (SEM) is widely used in surface studies and continuous efforts are carried out in the search of estimators of different surface characteristics. By using the variogram, we developed two of these estimators that were used to characterize the surface roughness from the SEM image texture. One of the estimators is related to the crossover between fractal region at low scale and the periodic region at high scale, whereas the other estimator characterizes the periodic region. In this work, a full study of these estimators and the fractal dimension in two dimensions (2D) and three dimensions (3D) was carried out for emery papers. We show that the obtained fractal dimension with only one image is good enough to characterize the roughness surface because its behavior is similar to those obtained with 3D height data. We show also that the estimator that indicates the crossover is related to the minimum cell size in 2D and to the average particle size in 3D. The other estimator has different values for the three studied emery papers in 2D but it does not have a clear meaning, and these values are similar for those studied samples in 3D. Nevertheless, it indicates the formation tendency of compound cells. The fractal dimension values from the variogram and from an area versus step log-log graph were studied with 3D data. Both methods yield different values corresponding to different information from the samples.     

Structure and Adsorption Properties of Nanocrystalline Silicon

The structure of the particles of nanocrystalline silicon synthesized in argon plasma with added oxygen is studied. An amorphous shell composed of silicon oxide is formed on the surface of silicon nanoparticles. The particles form clusters with a fractal structure. The adsorption of nitrogen on a powder of nanocrystalline silicon at 77 K is studied, and adsorption isotherms obtained for nanocrystalline silicon and nonporous silica adsorbents with identical specific surface areas are compared. The values of surface fractal dimension of powdered nanocrystalline silicon are calculated using the Frenkel-Halsey-Hill equation for multilayer adsorption under the dominant contribution of van der Waals or capillary forces. It is shown that surface fractal dimension is a structure-sensitive parameter characterizing both the morphology of clusters and the structure (roughness) of the surface of particles and their aggregates.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 541–547.Original Russian Text Copyright © 2005 by Tutorskii, Belogorokhov, Ishchenko, Storozhenko.     

Electrochemical technique for the determination of fractal dimension of dental surfaces

Fractal dimension of a carious tooth surface was determined using an electrochemical method. The method was based on time-dependent diffusion towards electrode surfaces, which is one of the most useful and reliable methods for the determination of fractal dimension of electrode surfaces. For this purpose, the tooth was covered with a gold layer, which acted as an electrode in electrochemical experiments. It is suggested that the fractal dimension can be used as a quantitative measure of the state of dental surfaces. The method presented demonstrates the power of electrochemical techniques for the determination of fractal dimension of surface of non-conducting objects.     

Biomimetic creation of hierarchical surface structures by combining colloidal self-assembly and Au sputter deposition

Surfaces of hexagonally packed silica spheres have been functionalized with silanes containing different hydrocarbon or fluorocarbon chains. The resulting chemical and physical structures were studied to establish the effect of surface hydrophobicity on the measured contact angles on the rough surfaces. The results were used to assess the effects of surface modifications on the parameters in the Cassie equation. To achieve superhydrophobicity via a biomimetic approach, we created two-scale structures by first forming hexagonally packed SiO2 spheres, followed by Au deposition on the spheres and heat treatment to form Au nanoparticles on sphere surfaces. Contact angles over 160 degrees were achieved. This work provides improved understanding of the effect of the surface roughness and solid surface fraction on superhydrophobicity.     

An Evaluation of Cellular Analyte-Receptor Binding Kinetics Utilizing Biosensors: A Fractal Analysis

A fractal analysis is presented for cellular analyte-receptor binding kinetics utilizing biosensors. Data taken from the literature can be modeled by using (a) a single-fractal analysis and (b) a single- and a dual-fractal analysis. Case (b) represents a change in the binding mechanism as the reaction progresses on the biosensor surface. Relationships are presented for the binding rate coefficient(s) as a function of the fractal dimension for the single-fractal analysis examples. In general, the binding rate coefficient is rather sensitive to the degree of heterogeneity that exists on the biosensor surface. For example, for the binding of mutagenized and back-mutagenized forms of peptide E1037 in solution to salivary agglutinin immobilized on a sensor chip, the order of dependence of the binding rate coefficient, k, on the fractal dimension, D(f), is 13.2. It is of interest to note that examples are presented where the binding coefficient (k) exhibits an increase as the fractal dimension (D(f)) or the degree of heterogeneity increases on the surface. The predictive relationships presented provide further physical insights into the binding reactions occurring on the surface. These should assist us in understanding the cellular binding reaction occurring on surfaces, even though the analysis presented is for the cases where the cellular "receptor" is actually immobilized on a biosensor or other surface. The analysis suggests possible modulations of cell surfaces in desired directions to help manipulate the binding rate coefficients (or affinities). In general, the technique presented is applicable for the most part to other reactions occurring on different types of biosensors or other surfaces. Copyright 2000 Academic Press.     

Diblock copolymer lamellae on sinusoidal and fractal surfaces

A scaling analysis of equilibrium orientation of diblock copolymer molecules on fractal surfaces and a brief comparison with a particular experiment is presented in this paper. This work is motivated by a recent experimental finding that a diblock copolymer film of polystyrene-PMMA, when deposited on a rough substrate, can orient its lamellae from a parallel to a perpendicular configuration depending on the topographical characteristics of the substrate surface. It was found that the RMS height itself is not enough to effect the equilibrium configuration, but the fractal dimension of the surface is also important. In general, the orientation of lamellae is a function of the the power spectral density (PSD) curves of the underlying substrate surface. Assuming the diblock lamellae to behave like an Alexander-deGennes brush, we obtain the free energy expressions for this brush in both parallel and perpendicular orientations in various asymptotic regimes. Comparison of their free energy expressions predicts the equilibrium configuration. By examining the PSD curves and using our scaling results, we are able to qualitatively explain some aspects of the experimental observations regarding the equilibrium orientation of the diblock copolymer lamellae on rough surfaces.     

The effect of frequency on the plasma polymerization of ethane

The plasma polymerization of ethane has been studied in the frequency range of from 50 Hz to 13.56 MHz. The rate of polymer deposition is strongly dependent on frequency, with significantly higher rates being observed at frequencies below 6 MHz. The effects of frequency can be interpreted in terms of a mechanism that assumes that polymer is formed by the reaction of surface free radicals, created by the bombardment of the growing polymer by charged species, with gas phase free radicals, formed by collisions of energetic electrons with monomer molecules.     

DNA中编码序列的分形特征研究

随着基因组数据库的日益增大，如何从这庞大的数据库中提取有用的信息已成为全世界科学家迫在眉睫的难题。本文运用网格维数分别刻画了60个人类基因序列编码区的分形特征。研究结果表明：在同一个基因中，外显子的维数一般要大于整个蛋白质编码序列的维数，并通过对比随机序列的网格维数，证实了这一结论。结合分形理论及功率谱研究可以得出，具有较少外显子的基因，外显子中包含有较多的遗传信息，而对于较多外显子的基因则相反，遗传信息可能储存于内含子中。这些结论对内含子功能以及DNA序列的复杂性的研究具有一定的理论意义和实用价值。     

Menger sponge-like fractal body created by a novel template method

We have established experimental strategies on how to create a Menger sponge-like fractal body and how to control its fractal dimension. The essence was to utilize alkylketene dimer (AKD), which spontaneously forms super-water-repellent fractal surface. We prepared "fractal AKD particles" with fractal surface structure as templates of pores in fractal body. The fractal body was synthesized by filling the remained space between the packed template particles with a tetramethyl orthosilicate solution, solidifying it by the sol-gel process, and removing the template by calcinations. We have succeeded in systematically creating fractal bodies of silica with different cross-sectional fractal dimensions D(cs)=1.87, 1.84, and 1.80 using "fractal template particles" compressed under the ratio=1.0, 2.0, and 3.0, respectively. We also discussed the possibilities of their fractal geometries in comparison with mathematical models. We concluded that the created fractal bodies were close to a Menger sponge and its modified one. Our experimental strategy allows us to design fractality of porous materials.     

Kinetic adsorption energy distributions of rough surfaces: a computational study

The adsorption energy distribution usually refers to localized monolayers of adsorbate at thermodynamic equilibrium. Many papers have been published that analyze its influence on adsorption isotherms, heats of adsorption, and adsorption kinetics. However, the adsorption energy distribution, in its classical thermodynamic equilibrium sense, may be not as useful as expected. This is because many important processes involving adsorption have dynamic character and reactant particles have a finite time for penetration of the adsorbent. The above suggests that some adsorption centers located in less accessible fragments of the surface can be invisible in a dynamic process. However, under conditions allowing the thermodynamic equilibrium such adsorption centers could noticeably contribute to the adsorption energy distribution. The aim of this work is to measure the adsorption energy distributions of special rough surfaces using a dynamic method. This method is based on the molecular dynamics simulation of an ideal gas flowing over a sample surface. The ideal gas particles penetrate the surface, and at the moment of collision of a gas particle with the surface the Lennard-Jones potential energy is calculated. This energy can be identified with the adsorption energy at a given point on the surface. The surfaces used in the calculations have been created using two surface growth models (i.e., random deposition and ballistic deposition). The application of these highly disordered surfaces enables us to draw some general conclusions about the properties of real surfaces that are usually far from any deterministic geometry.