Fractal Dimension of Platinum Particles Dispersed in Highly Porous Carbonized Polyacrylonitrile Microcellular Foam

1997 ◽  
Vol 144 (5) ◽  
pp. 1734-1738 ◽  
Author(s):  
Siyu Ye ◽  
Ashok K. Vijh ◽  
Le⁁ H. Dao
Author(s):  
Steven D. Toteda

Zirconia oxygen sensors, in such applications as power plants and automobiles, generally utilize platinum electrodes for the catalytic reaction of dissociating O2 at the surface. The microstructure of the platinum electrode defines the resulting electrical response. The electrode must be porous enough to allow the oxygen to reach the zirconia surface while still remaining electrically continuous. At low sintering temperatures, the platinum is highly porous and fine grained. The platinum particles sinter together as the firing temperatures are increased. As the sintering temperatures are raised even further, the surface of the platinum begins to facet with lower energy surfaces. These microstructural changes can be seen in Figures 1 and 2, but the goal of the work is to characterize the microstructure by its fractal dimension and then relate the fractal dimension to the electrical response. The sensors were fabricated from zirconia powder stabilized in the cubic phase with 8 mol% percent yttria. Each substrate was sintered for 14 hours at 1200°C. The resulting zirconia pellets, 13mm in diameter and 2mm in thickness, were roughly 97 to 98 percent of theoretical density. The Engelhard #6082 platinum paste was applied to the zirconia disks after they were mechanically polished ( diamond). The electrodes were then sintered at temperatures ranging from 600°C to 1000°C. Each sensor was tested to determine the impedance response from 1Hz to 5,000Hz. These frequencies correspond to the electrode at the test temperature of 600°C.


Nanomaterials ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 2266
Author(s):  
Vinzent Olszok ◽  
Malte Bierwirth ◽  
Alfred P. Weber

Nanoparticles produced in technical aerosol processes exhibit often dendritic structures, composed of primary particles. Surprisingly, a small but consistent discrepancy was observed between the results of common aggregation models and in situ measurements of structural parameters, such as fractal dimension or mass-mobility exponent. A phenomenon which has received little attention so far is the interaction of agglomerates with admixed gases, which might be responsible for this discrepancy. In this work, we present an analytical series, which underlines the agglomerate morphology depending on the reducing or oxidizing nature of a carrier gas for platinum particles. When hydrogen is added to openly structured particles, as investigated by tandem differential mobility analysis (DMA) and transmission electron microscopy (TEM) analysis, Pt particles compact already at room temperature, resulting in an increased fractal dimension. Aerosol Photoemission Spectroscopy (APES) was also able to demonstrate the interaction of a gas with a nanoscaled platinum surface, resulting in a changed sintering behavior for reducing and oxidizing atmospheres in comparison to nitrogen. The main message of this work is about the structural change of particles exposed to a new environment after complete particle formation. We suspect significant implications for the interpretation of agglomerate formation, as many aerosol processes involve reactive gases or slightly contaminated gases in terms of trace amounts of unintended species.


2002 ◽  
Vol 2 (5-6) ◽  
pp. 337-343 ◽  
Author(s):  
S.A. Lee ◽  
T.D. Waite ◽  
A.G. Fane ◽  
R. Amal

Treatment of waters and wastewaters by microfiltration (MF) requires the addition of chemical coagulants to enhance the removal of dissolved substances. Under these conditions the feed to the MF contains flocculated particulates which must be retained by the membrane. While an extensive knowledge base on the effect of dispersed particles on membrane cake formation and fouling exists, much less information is available on the impact of aggregates on cake characteristics. Results of impact of the size and structure (as characterized by the fractal dimension) of particulate aggregates on microfiltration membrane fouling are in qualitative agreement with a simple model based on the Carman-Kozeny equation. Larger flocs form a cake with large inter-floc porosity which results in a significantly higher permeate flux than achieved for smaller flocs. Concomitantly, looser flocs (of low fractal dimension) are likely to form a cake that has higher intra-floc voidage thus flux is higher than a cake made of compact flocs of similar size. Analysis of cake compression indicates that compressibility is strongly influenced by trans-membrane pressure (TMP). The placement of highly porous aggregates onto the membrane results in formation of a highly porous cake layer provided a low TMP is maintained. Rapid compression of the cake occurs at higher TMPs as shown by the significantly lower porosity of the cake. Under high TMP conditions, the cake porosity exhibits a strong size dependence with larger floc sizes yielding higher porosities. This result possibly indicates formation of relatively impermeable assemblages (as a result of significant compaction) with flux controlled by inter-aggregate flow, i.e. flow around compressed flocs. In comparison, the marked lack of size dependence of porosity at low TMP suggests that permeate flux is dominated by flow through (rather than around) the highly permeable flocs. These results suggest that it should be possible to control both operating conditions (such as TMP) and floc characteristics such that high permeate flux at a given TMP or low cake resistance at a fixed flux is achievable.


2020 ◽  
Vol 1 (104) ◽  
pp. 19-22
Author(s):  
Kh. Kamilov ◽  
A. Zaitov ◽  
A. Tulaganov ◽  
A. Tulaganov

Purpose: The article is devoted to the determination of the fractal dimension of cellular concrete, in particular foam concrete, and the further clarification of the relationship between fractal dimension and porosity and average density of cellular concrete. Design/methodology/approach: In the theoretical description of disordered systems, the fundamentals of fractal theory are actively used, which allow obtaining statistical indicators of chaotic natural and artificially disordered systems, which include cellular concrete. The parameters of the pore structure are difficult to quantify by conventional methods because of the complexity and irregularity of the pore structure due to their random distribution. Findings: Formulas for calculating the fractal dimension and average density of highly porous material are calculated and proposed. The formula for calculating the average density takes into account the density of the material between the pore walls. Research limitations/implications: The calculation of the fractal dimension is one of the main factors affecting the practical application of the theory of fractals, a natural problem arises on a theoretical basis to justify these calculations. Practical implications: The formulas proposed in this work for calculating the fractal dimension and density of a highly porous structure improve research on methods for producing substances with a controlled fractal structure, which will help create materials with unusual mechanical properties, density, and porosity. Originality/value: The formula for calculating the fractal dimension obtained in the work improves the well-known Hausdorff-Bezikovich formula. On the other hand, it makes it possible to obtain a highly porous structure with a given density of the material under study.


Author(s):  
Ian M. Anderson ◽  
Arnulf Muan ◽  
C. Barry Carter

Oxide mixtures which feature a coexistence of phases with the wüstite and spinel structures are considered model systems for the study of solid-state reaction kinetics, phase boundaries, and thin-film growth, and such systems are especially suited to TEM studies. (In this paper, the terms “wüstite” and “spinel” will refer to phases of those structure types.) The study of wüstite-spinel coexistence has been limited mostly to systems near their equilibrium condition, where the assumptions of local thermodynamic equilibrium are valid. The cation-excess spinels of the type Ni2(1+x)Ti1-xO4, which reportedly exist only above 1375°C4, provide an excellent system for the study of wüstite-spinel coexistence under highly nonequilibrium conditions. The nature of these compounds has been debated in the literature. X-ray and neutron powder diffraction patterns have been used to advocate the existence of a single-phase, non- stoichiometric spinel. TEM studies of the microstructure have been used to suggest equilibrium coexistence of a stoichiometric spinel, Ni2TiO4, and a wüstite phase; this latter study has shown a coexistence of wüstite and spinel phases in specimens thought to have been composed of a single, non- stoichiometric spinel phase. The microstructure and nature of this phase coexistence is the focus of this study. Specimens were prepared by ball-milling a mixture of NiO and TiO2 powders with 10 wt.% TiO2. The mixture was fired in air at 1483°C for 5 days, and then quenched to room temperature. The aggregate thus produced was highly porous, and needed to be infiltrated prior to TEM sample preparation, which was performed using the standard techniques of lapping, dimpling, and ion milling.


1990 ◽  
Vol 26 (9) ◽  
pp. 2243-2244 ◽  
Author(s):  
David G. Tarboton

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (= coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17 ± 0.05 (mean ± SD) for the left hemisphere and 1.15 ± 0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04 ± 0.03 than in healthy controls. Conclusion: Within the limits of spatial resolution of SPECT, the heterogeneity of brain blood flow is well characterized by a fractal dimension. Fractal analysis may help brain scientists to assess age-, sex- and laterality-related anatomic and physiological changes of brain blood flow and possibly to improve precision of diagnostic information available for patient care.


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