Measuring surface topography with scanning electron microscopy. I. EZEImage: a program to obtain 3D surface data.

Scanning electron microscopy (SEM) is widely used in the science of materials and different parameters were developed to characterize the surface roughness. In a previous work, we studied the surface topography with fractal dimension at low scale and two parameters at high scale by using the variogram, that is, variance vs. step log-log graph, of a SEM image. Those studies were carried out with the FERImage program, previously developed by us. To verify the previously accepted hypothesis by working with only an image, it is indispensable to have reliable three-dimensional (3D) surface data. In this work, a new program (EZEImage) to characterize 3D surface topography in SEM has been developed. It uses fast cross correlation and dynamic programming to obtain reliable dense height maps in a few seconds which can be displayed as an image where each gray level represents a height value. This image can be used for the FERImage program or any other software to obtain surface topography characteristics. EZEImage also generates anaglyph images as well as characterizes 3D surface topography by means of a parameter set to describe amplitude properties and three functional indices for characterizing bearing and fluid properties.     

Collisions of ideal gas molecules with a rough/fractal surface. A computational study

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).     

Surface analysis of cryofixation-vacuum-freeze-dried polyaluminum chloride-humic acid (PACl-HA) flocs

The powder of polyaluminum chloride-humic acid (PACl-HA) flocs was prepared by cryofixation-vacuum-freeze-drying method. The FTIR spectra show that some characteristic functional groups in polyaluminum chloride (PACl), humic acid (HA), and kaolin still existed in the dried flocs. X-ray diffractometry (XRD) patterns indicate that these flocs are amorphous. Nitrogen adsorption-desorption isotherms were obtained for different samples of the dried PACl-HA flocs. The BET specific surface area, BJH cumulative absorbed volume and BJH desorption average pore diameter of them were determined. The peak values of 8.4-11.2 nm (pore diameter) for pore size distribution (PSD) curves indicate that the pores of the dried flocs are mostly mesopores. The surface fractal dimensions D(s) and the corresponding fractal scales determined from both SEM images and nitrogen adsorption-desorption data sets reveal the multi-scale surface fractal properties of the dried PACl-HA flocs, which exhibited two distinct fractal regimes: a regime of low fractal dimensions (2.07-2.26) at higher scales (23-387 nm), mainly belonging to exterior surface scales, and a higher fractal dimensions (2.24-2.37) at lower scales (0.80-7.81 nm), falling in pore surface scales. Both HA addition and kaolin reduction in dried floc can decrease the irregularity and roughness of external surface. However, for the irregularity and roughness of pore surface, the addition of HA or kaolin in dried floc can increase them. Furthermore, some difference was found between the pore surface fractal dimensions D(s) calculated from nitrogen adsorption and desorption data. The pore surface D(s) values calculated through thermodynamic model were much greater than three.     

固体催化剂活性表面的化学不均匀性

固体催化剂活性表面的化学不均匀性朱建军林西平＊（江苏石油化工学院化学工程系常州２１３０１６）关键词固体催化剂，活性表面，分形维，化学不均匀性１９９６－１０－２８收稿，１９９７－０３－１０修回中国石化总公司和回国留学服务中心资助项目本院九五届毕业生于晓...     

Studies of physico-chemical properties and fractal dimensions of MgB2 superconductor surface

The porous structure of MgB₂ has been investigated using atomic force microscopy (AFM) and sorption techniques. The fractal dimension and surface roughness parameters were evaluated from (AFM) and nitrogen adsorption?Cdesorption isotherms measured at ?196?°C for MgB₂ sample. Adsorption capacity, specific surface area, and fractal dimensions were determined from adsorption?Cdesorption isotherms. The sorption isotherms of MgB₂ samples were S-shaped and belong to type II according to the IUPAC classification. The results of fractal dimensions of MgB₂ surface determined on the basis sorptometry and AFM data are compared.     

Evaluation of surface roughness of hydrogels by fractal texture analysis during swelling

The surface of a biomaterial reacts in contact with biological fluids. Hydrogels are used to prepare biomaterials. The surface roughness of materials can be explored by several techniques. However, when considering hydrogels, the surface examined in the dry state does not reflect the final conformation. How the surface roughness is affected by swelling has been little explored by quantitative methods. We have evaluated the surface roughness of poly(2-hydroxyethyl methacrylate) (i.e., pHEMA) by image analysis. Images of disks, prepared from linear pHEMA, were obtained on a light microscope after various incubation times in saline. Fractal texture analysis was done on images to determine the fractal dimension D. In this study, D exhibited a significant decrease during swelling and was highly correlated with the swelling ratio (r2 = 0.994, p < 0.00001). Water uptake by the surface of the polymer affected the surface roughness. Image analysis using fractal algorithms appears to be the most interesting technique for the quantitative exploration of surfaces of hydrated materials that cannot be measured by conventional methods.     

A fractal analysis of analyte-estrogen receptor binding and dissociation kinetics using biosensors: environmental effects

A fractal analysis is used to model the binding and dissociation kinetics between analytes in solution and estrogen receptors (ER) immobilized on a sensor chip of a surface plasmon resonance (SPR) biosensor. Both cases are analyzed: unliganded as well as liganded. The influence of different ligands is also analyzed. A better understanding of the kinetics provides physical insights into the interactions and suggests means by which appropriate interactions (to promote correct signaling) and inappropriate interactions such as with xenoestrogens (to minimize inappropriate signaling and signaling deleterious to health) may be better controlled. The fractal approach is applied to analyte-ER interaction data available in the literature. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor chip surface. In general, the binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity on the surface. For example, the binding rate coefficient, k, exhibits a 4.60 order of dependence on the fractal dimension, D(f), for the binding of unliganded and liganded VDR mixed with GST-RXR in solution to Spp-1 VDRE (1,25-dihydroxyvitamin D(3) receptor element) DNA immobilized on a sensor chip surface (Cheskis and Freedman, Biochemistry 35 (1996) 3300-3318). A single-fractal analysis is adequate in some cases. In others (that exhibit complexities in the binding or the dissociation curves) a dual-fractal analysis is required to obtain a better fit. A predictive relationship is also presented for the ratio K(A)(=k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). This has biomedical and environmental implications in that the dissociation and binding rate coefficients may be used to alleviate deleterious effects or enhance beneficial effects by selective modulation of the surface. The K(A) exhibits a 112-order dependence on the ratio of the fractal dimensions for the ligand effects on VDR-RXR interaction with specific DNA.     

Multifractal analysis of drop‐casted copper (II) tetrasulfophthalocyanine film surfaces on the indium tin oxide substrates

This paper applies multifractal spectrum theory to characterize the structural complexity of 3D surface roughness of copper (II) tetrasulfophthalocyanine (CuTsPc) films on the indium tin oxide (ITO) substrate, obtained with atomic force microscopy (AFM) analysis. CuTsPc films were prepared by drop cast method on ITO substrate. CuTsPc films surface roughness was studied by AFM in tapping‐mode?, in air, on square areas of 2500 µm². A novel approach, on the basis of computational algorithms for analysis of 3D roughness surface applied for AFM data, was presented. Results revealed that the 3D surface roughness of CuTsPc films prepared by drop cast method on ITO substrate can be described using the multifractal geometry. The generalized dimensions D_q and the multifractal spectrum f(α) provided quantitative values that characterize the local scale properties of CuTsPc films surface geometry at nanometer scale. Data provide valuable information to describe the spatial arrangement of 3D surface roughness of CuTsPc films on ITO substrate, which was not taken into account by classical surface statistical parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

Pore surface fractal analysis of palladium-alumina ceramic membrane using Frenkel-Halsey-Hill (FHH) model

The alumina ceramic membrane has been modified by the addition of palladium in order to improve the H(2) permeability and selectivity. Palladium-alumina ceramic membrane was prepared via a sol-gel method and subjected to thermal treatment in the temperature range 500-1100 degrees C. Fractal analysis from nitrogen adsorption isotherm is used to study the pore surface roughness of palladium-alumina ceramic membrane with different chemical composition (nitric acid, PVA and palladium) and calcinations process in terms of surface fractal dimension, D. Frenkel-Halsey-Hill (FHH) model was used to determine the D value of palladium-alumina membrane. Following FHH model, the D value of palladium-alumina membrane increased as the calcinations temperature increased from 500 to 700 degrees C but decreased after calcined at 900 and 1100 degrees C. With increasing palladium concentration from 0.5 g Pd/100 ml H(2)O to 2 g Pd/100 ml H(2)O, D value of membrane decreased, indicating to the smoother surface. Addition of higher amount of PVA and palladium reduced the surface fractal of the membrane due to the heterogeneous distribution of pores. However, the D value increased when nitric acid concentration was increased from 1 to 15 M. The effect of calcinations temperature, PVA ratio, palladium and acid concentration on membrane surface area, pore size and pore distribution also studied.     

Fractal analysis of hydroxyapatite from nitrogen isotherms

Samples of calcium hydroxyapatite, CaHap, were prepared via a wet method and subjected to thermal treatment in air in the temperature range 100-900 degrees C. Nitrogen adsorption-desorption isotherms were obtained on different samples, and their data points were used to analyze the fractal properties of the obtained solids. Both FHH and Neimark's equations were used for such purpose, and the agreement or disagreements between obtained results on using both equations are discussed. Considering the appropriate values of the obtained surface fractal dimensions D, it was concluded that an appreciable defractalization of the prepared hydroxyapatite is only noted upon calcinations at 900 degrees C. Below this temperature the loss in surface area and pore volume result from simultaneous bulk and surface mass transport, which conserve the initial surface roughness and average pore radius. Calcination at 900 degrees C caused sintering to proceed via bulk mass transport, with a consequent pore widening and a decrease in surface roughness.     

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.     

煤焦外表面分形维数在燃烧过程中的变化

煤燃烧的化学反应及其物质输运过程均具有非线性动力特征，燃烧过程是孔洞分形体的变化过程，其外表面结构的变化部分的反映出颗粒内部孔结构的变化过程，本文利用分形理论及其相关的图像处理方法对不同煤种，不同燃烧阶段煤焦外表面结构的SEM图像进行研究，研究结果表明，XIE法较适合计算煤焦表面分形维数，在燃烧过程中煤焦的外表面分形数呈现两种变化趋势，通过最小二乘法多项式拟合确定煤焦外表面分形维数与燃尽率之间的关系式，并得到不同煤种的方程参数。     

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.     

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.     

The surface properties of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane after partial solution in nitro esters

The thermophysical properties and surface structure of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (TNCO) particles before and after their contact with liquid nitro esters were studied by differential scanning calorimetry and small-angle X-ray scattering. The thermophysical properties of TNCO changed after contact with nitro esters, and the temperature range of the transition from the β to δ polymorph broadened. This peculiarity was explained in terms of the fracton theory by changes in the heat capacity of particles related to the formation of nanoscale roughness with a fractal (scale-invariant) organization as a result of surface etching by solvents such as nitro esters, which are thermodynamically “bad” with respect to TNCO. The volume properties of particles did not change. The possibility of determining the fractal dimension of the surface of TNCO particles by differential scanning calorimetry was demonstrated. The rate of heating was then used as a “scale ruler” (“yardstick”), and the temperature range of the transition from the β to δ polymorph, as a measured parameter. The dimension of the surface fractal was also determined by an independent method (small-angle X-ray scattering). The results obtained by the two methods were closely similar.     

TiO2纳米膜表面结构形态特征

采用反胶束法制备TiO2纳米溶胶,用浸渍提拉法在不同的条件下制备了三种TiO2多孔纳米薄膜,并利用AFM、SEM、XRD等方法对膜表面结构物理化学特性进行表征.结果表明三种膜基本上由粒径约为59 nm的纳米粒子以不同的方式堆积而成,溶胶刚生成时浸提一次,干燥、焙烧得到膜上纳米粒子分布均匀,所生成的二次粒子粒径最小,二次粒子形成的二次表面粗糙度最小,浸提10次得到膜上纳米粒子间存在较丰富缝隙结构,二次粒子粒径及其形成的表面粗糙度较大,而溶胶制备好陈化6 h后浸提得到的膜上二次粒子粒径最大,表面粗糙度最高.由分形理论估算得到三种膜的分形维数分别是2.22、2.20和2.27. XRD测试表明,膜上TiO2为锐钛矿晶相.这些结果表明,采用不同制备步骤得到的膜,其表面结构形态存在较大的差异.     

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.     

Thermo-mechanical method for the determination of the fractal dimension of fat crystal networks

The physical properties of a fat are determined by its thermal history, processing conditions, chemical composition, polymorphism and spatial distribution of mass. The mass fractal dimension of a fat crystal network can be determined from the slope of the log–log plot of the storage modulus (G′) versus the solid fat content (SFC). Different SFCs were obtained by melting the fat, diluting it to different extents in liquid oil, and crystallizing the blends under specific conditions. One of the major drawbacks of this method is the inability of characterizing the native structure of an already crystallized fat. In the thermo-mechanical method developed in this study, SFC is changed via temperature variations instead. At each temperature, the G′ and SFC were measured and the fractal dimension calculated as described above. The thermomechanical method proved to be a simpler and more reliable estimator of the fractal dimension of a fat crystal network than the dilution method.