Application of fractal geometry for studies of heterogeneity properties of nanomaterials

Calculations based on the fractal geometry in the estimation of surface heterogeneity are superior compared with conventional calculation methods (e.g. from the data of gas adsorption or X-ray radiation scattering) as they can be applied without limitation as far as the range of surface sizes of the studied structures is concerned. This paper presents structural characteristics of carbon and carbon- free nanomaterials based on the determined surface and volumetric fractal coefficients. Fractal coefficients were determined from the data obtained by means of two independent methods: sorptometry and atomic force microscopy (AFM). Correlation between porosity parameters and fractal coefficients is presented.     

Studies of heterogeneity properties of selected high-temperature superconductor surfaces

Nitrogen adsorption measured at 77 K was used to characterize the surface heterogeneity of high-temperature superconductor surfaces. Properties relating to adsorption and porosity of the solids (adsorption capacity, specific surface area, radii and volume of the pores, pore-size distribution function) were determined from nitrogen adsorption–desorption isotherms and atomic force microscopy (AFM) for a series of oxide superconductors. It is shown that the adsorption isotherms of all samples are S-shaped and belong to type II according to the IUPAC classification. On the basis of the nitrogen adsorption isotherms and AFM data, fractal dimensions were determined and correlations found with adsorption and porosity parameters.     

Studies of physico-chemical properties and fractal dimensions of selected high-temperature superconductor surfaces

Properties relating to porosity of solids (fractal dimensions, surface roughness parameters) were evaluated from atomic force microscopy (AFM) and nitrogen adsorption-desorption isotherms measured at 77 K for selected high-temperature [(RE) Ba₂Cu₃O_7−x, RE=Y, Sm] superconductors. Adsorption capacity, specific surface area, fractal dimensions were determined from adsorption-desorption isotherms. The adsorption isotherms of all samples were S-shaped and belong to type II according to the IUPAC classification. A linear relationship was demonstrated between the fractal coefficients calculated by using the two methods and values of adsorption capacity of monolayer.     

Estimation of total heterogeneity properties of carbon nanotubes

Physico-chemical properties (adsorption capacity, desorption energy distribution and pore-size distribution functions) of nanomaterial surfaces from selected materials, based on sorptometric and liquid thermodesorption measurements under quasi-equilibrium conditions, are presented. The fractal dimensions of nanotubes using sorptometric and AFM data have been evaluated. Comparison of thermogravimetric and other data provide new information about the adsorption and pore structure of the studied materials. The fractal dimensions of nanomaterial surfaces using sorptometry are in good agreement with those from AFM.     

Fractal dimensions from Q-TG data for estimation of surface heterogeneity

Programmed thermodesorption of n-butanol from Na-, La-montmorillonite, natural and commercial zeolite samples in quasi-isothermal conditions made. The new method of fractal dimension calculations from thermogravimetry data has been presented. On the basis of nitrogen adsorption-desorption isotherms from sorptometry and mercury porosimetry data the fractal dimensions of montmorillonites were calculated. The results from above independent and separated techniques were compared and good correlation were obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Adsorption and porosity properties of carbon-covered alumina surfaces

Uniformly carbon-covered alumina (CCA) was prepared via the carbonisation of sucrose highly dispersed on the alumina surface. Using special thermogravimetry and sorptometry methods physicochemical properties of carbon-covered alumina surfaces were investigated. A numerical and analytical procedure for the evaluation of total heterogeneous properties (desorption energy distribution and pore-size distribution functions) on the basis of liquid thermodesorption from the sample surfaces under the quasi-equilibrium conditions are presented. The desorption energy distribution was derived from the mass loss Q-TG and the differential mass loss Q-DTG curves of thermodesorption of pre-adsorbed polar and apolar liquid films. For the first time, the evaluation of the fractal dimensions of carbon-covered alumina using the sorptometry, thermogravimetry and AFM data is presented.     

Analytical TEM investigations of high-temperature superconductors

Electron diffraction and energy dispersive X-ray spectroscopy as analytical transmission electron microscopic methods have been applied to Y-Ba-Cu-O superconductors. The evaluation of diffraction patterns by means of the MS-WINDOWS program ELDISCA is demonstrated. The course of X-ray linescan signals in the transition range between YBa₂Cu₃O_7– matrix and Y₂BaCuO₅ inclusions is explained by calculations based on a mathematical model which is described. Errors of quantiative X-ray spectroscopic results and their reasons are shown.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

Adsorption and porosity properties of pure and modified carbon nanotube surfaces

Modified carbon multiwall nanotubes were prepared via the oxidation process by means of 65% nitric acid or ferric nitrate dissolved with 65% nitric acid. Using special thermogravimetry and sorptometry methods physicochemical properties of pure and modified nanotube surfaces were investigated. A numerical and analytical procedure for the evaluation of total heterogeneous properties on the basis of liquid thermodesorption from the sample surfaces under the quasi-equilibrium conditions are presented. The calculations of the fractal dimensions of carbon nanotubes using the sorptometry and thermogravimetry data is presented.     

Synthesis and characterization of high temperature superconductors

The high temperature superconductors of the system Bi-Pb-Sr-Ca-Cu-O show promising properties and large scale applications can be considered. The (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊ (Bi,Pb(2223)) phase is attractive because of its high superconducting temperature (110 K) and high current transport capabilities.Simultaneous DTA/TG has proved an excellent tool for synthesizing, characterizing these high temperature superconductors, confirming phase diagrams and finding the optimal annealing temperature for Bi,Pb(2223)/Ag tapes in order to obtain high critical current densities around 30 kA cm^–2 at 77 K and 0T. The identification of the main DTA peaks of measurement of different phase mixtures made it possible to observe the formation of an intermediate phase Bi,Pb(2212) during the formation of Bi,Pb(2223).     

Surface properties of silica gel samples modified by selected proteins

The adsorption of a polar (water) and a non-polar (n-octane) liquid on silica gels, modified by adsorption of proteins, has been studied by thermal analysis. Silica gels with physically adsorbed BSA and ovalbumin layers were used. Thermodesorption energies were determined from Q-TG and Q-DTG curves recorded under quasi-equilibrium conditions. Significant differences in liquid desorption were observed from the surfaces due to heterogeneous changes (energetic and geometrical) as a result of modification. These results are compared with those obtained for the samples heated at 160°C for 1 h.     

Studies of surface properties of Na- and La-montmorillonites

This paper presents possible applications of thermal analysis, sorptometry and porosimetry to study physico-chemical properties of Na- and La-montmorillonite samples, especially for determination of total surface heterogeneity. The quasi-isothermal thermogravimetric (Q-TG) mass loss and its first derivative (Q-DTG) curves with respect to temperature and time obtained during programmed liquid thermodesorption under quasi-isothermal conditions have been used to study adsorbed layers and heterogeneous properties of the Na- and La-montmorillonites. Calculations of the desorption energy distribution functions by analytical procedure using mass loss Q-TG and differential mass loss Q-DTG curves of thermodesorption under quasi-isothermal conditions of polar and non-polar liquid vapours preadsorbed on a material surface are presented. Parameters relating to porosity of samples were determined by sorptometry, mercury porosimetry and atomic force microscopy (AFM). From nitrogen sorption isotherms from sorptometry and porosimetry methods, the fractal dimensions of montmorillonites have been calculated. Moreover, a new approach is proposed to calculate fractal dimensions of materials obtained from Q-TG curve; this is compared with values obtained by the above methods. The total heterogeneous properties (energy distribution function and pore-size distribution functions) of samples studied were estimated. The radius and pore volume of the tested samples calculated on the basis of thermogravimetry, sorptometry and porosimetry techniques were compared and good correlations obtained.     

Preparation and characterization of electrophoretically deposited high-temperature superconductor coatings

The high-temperature superconductor, YBa₂Cu₃O_7–x (x = 0.1–0.2) [YBCO], was prepared using an optimized calcination and sintering process. Thin layers of a few microns of this material were deposited on a silver substrate by applying a simplified electrophoretic deposition technique in a suspension of the fine, < 10 m, superconductor powder in a non-aqueous liquid. To get a uniform and strongly adherent coating, the deposition process is repeated several times, followed by an appropriate sintering procedure. The initially prepared YBCO powder and the coatings produced were characterized for their superconducting properties by X-ray diffraction analysis (XRD), magnetization measurements with a Superconducting Quantum Interference Device (SQUID) and electrical resistivity measurements. By scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) the grain size of the YBCO film, its thickness and impurity content, respectively, were estimated.     

Characterization of physico-chemical properties of the high-temperature superconductor and LaCoO3surfaces

This paper presents possible applications of thermal analysis and sorptomatic methods to study physico-chemical properties of the high-T _csuperconductor Y₁B_a2Cu₃O_7-x and perovskite LaCoO₃. It is shown that both Y₁Ba₂Cu₃O_7-x and perovskite phase are highly sensitive to water vapour. Mechanism of adsorption of water on LaCoO₃depends largely on time activation (t _act). When the time of water vapour saturation was 0<t _act<180 s, physisorption process was observed. In the case of longer times water vapour action, t _act>180 s, chemical decomposition was observed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nucleation,growth, and fractal dimensions of icosahedral and polyicosahedral clusters

In this paper, the concept offractal geometry was applied to the growth of icosahedral and polyicosahedral clusters. Fractal dimensions were calculated for high-frequency icosahedral casters, vertex-sharing polyicosahedral clusters, and linked polyicosahedral clusters. These cluster growth pathways were compared with the fractal growth mechanisms of colloidal particles. Close similarities were found despite the tremendous differences in particle sizes and the forces governing their nucleation and growth processes.Dedicated to Prof. Lawrence F. Dahl on his 65th birthday; based in part on a lecture presented by BKT at the Dahl symposium held at the University of Wisconsin, Madison, Wisconsin on September 17, 1994.     

Effect of fractal dimension of porous catalysts on the macrokinetics of CO oxidation

A study was carried out on the oxidation of CO on catalysts with different fractal dimension in kinetic and internal diffusion modes. A linear relationship was found between the fractal dimension of the catalyst DF and the γ coefficient in the reaction-diffusion equation. The fractal dimension of the catalyst could be calculated from the macrokinetic measurements. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 4, pp. 236–240, July–August, 2006.     

Numerical computations of molecular reactions in associated systems caused by the formation of fractal structures

The interaction between particles in a system containing fractal clusters has been computationally simulated. The fractal structure of the system has been demonstrated to determine the kinetic characteristics of particle interaction. If a system in an N-dimensional space (N = 2, 3, 4) contains fractal clusters with the fractal dimension D > N-1, the rate of interaction of a free particle with particles belonging to clusters depends on their concentration according to the power law. The exponent gamma of this power law formally corresponds to the kinetic order of the reaction with respect to the concentration of particles belonging to the clusters. Its value is determined by the free surface of the clusters and depends on its fractal dimension D. The results of simulation qualitatively agree with the data on high, non-integral orders of many liquid phase molecular reactions characterized by self-organization of the medium via weak intermolecular interactions, such as hydrogen bonds.     

煤焦分形维数及其对比热容的影响研究

比热容是煤炭热物理性质之一,在煤矿的矿井防火、防止煤与瓦斯突出、井下降温设计及煤炭加工利用(如煤炭的燃烧、气化、焦化、液化等)等方面是关键参数之一,对提高煤炭热能利用率、提高经济效益、减少环境污染等,具有非常重要的意义。比热容的影响因素很多,如煤化程度、水分质量分数、热解温度等,煤焦微观结构的影响也是其中很重要的一方面。分形几何由Mandelbrot 1982年创立,是定量描述自相似或自相关等不规则形体的工具。研究表明,煤焦微观结构具有分形特征。在煤焦分形的研究中,常用的实验技术方法为吸附法、小角度X射线散射法和孔度法,采用扫描电子显微镜和数字图象处理方法研究煤焦的分形结构,能更加深入地理解其分形维数与性能的关系。     

The effect of fractal dimension of porous catalysts on the activation energy of CO oxidation

An approach based on the interrelationship between the activation energy of the rate-limiting step of a heterogeneous catalytic reaction and the structure of the catalyst surface expressed in terms of fractal geometry is presented for the example of the oxidation of carbon monoxide. The activation energy of this reaction was shown to increase with increasing nonuniformity of the catalyst surface given by the fractal dimension D_F. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 1, pp. 43–46, January–February, 2007.