Based on a formulation applied in the theory of stochastic processes, a master equation is introduced for the size distribution which describes a size reduction process. Using an absolute size constant and a scaling concept, we can get a generalized form of the Gaudin-Schuhmann equation and of the Rosin-Rammler equation for size-reduced products and show the intimate relationship between these two formulae.
F(a) functions (wherea is the rate of conversion), frequently referred to when considering non-isothermal heterogeneous processes, are reconsidered
from a fractal viewpoint. This is achieved on the basis of previous studies on the fundamental properties of powders, which
show that any powder obtained by mechanical size reduction yields a fractal particle-size distributionP(X,t), whereX is a scaled particle size, with a material-dependent powern asP(X,t)∝Xn, and that the obtained powder has a specific surface area,S, expressed with the fractal particle sizex asS∝xD-3 with the fractal dimensionD. This can be interpreted to show that a powder obtained by mechanical grinding has a uniqueD for a specified particle-size range, and, in fact, TA results dependent on thisD were obtained.
We also show that a mechanical size reduction process produces fractal surfaces. The phenomenologically known laws which relate
input energy and the powder product are theoretically derived by assuming that the energy is consumed in producing fractal
surfaces. The well-known reaction functions which relate the conversion rate with the physical and geometrical factors governing
a reaction process are reconsidered from a fractal viewpoint. The validity of conventionalF(a) expressions based on integer dimensions are questioned.
Authors:R. Ozao, H. Ogura, M. Ochiai, and S. Tsutsumi
A DSC method for evaluating the surface area of etched Al foils for use in high performance electrolytic capacitors is presented. A linear relationship between the etching degree (effective surface area) and the thermal resistance of the sample is obtained by means of DSC, based on the transient phenomenon. This method using the transient state in DSC measurement is not only novel, but also rapid and simple in evaluating the surface area of an etched aluminum foil. The method is effective even when the Al foil has a naturally oxidized surface.
Authors:R. Ozao, M. Ochiai, Y. Ichimura, H. Takahashi, and T. Takano
The previously described method involving the use of transient DSC was applied to pharmaceutical powder compacts and to ceramic
powder compacts. The samples were prepared by compressing powders of pentaerythritol tetraacetate and two kinds of alumina
powder (differing in particle size distribution) up to a pressure of 20 MPa by using a jig. For pentaerythritol tetraacetate,
a linear relationship was obtained between the parameter obtained by DSC and the compaction pressure.
Authors:R. Ozao, H. Yoshida, T. Inada, and M. Ochiai
Nanoporous alumina membrane prepared by anodic oxidation using sulfuric acid electrolyte was subjected to TG-DTA and X-ray
Photoelectron Spectroscopy (XPS or ESCA) to further study the distribution of sulfur. In XPS study, Ar+ ion bombardment was performed on the sample to etch the surface at a rate of 3 nm min-1. As a result, sulfur was found to be concentrated within a depth of 3nm from the surface. The S content of the surface was
found to be 2.70.5 wt%, and that at a depth of ca. 3 nm and ca. 10 nm was found to be as low as about 0.60.11 wt% (5.371.0
wt%→ 1.260.2wt% SO2). In TG-DTA, the mass loss of 7.3% was in fair agreement with that calculated on XPS results (7.11.2%).
Authors:R. Ozao, H. Yoshida, Y. Ichimura, T. Inada, and M. Ochiai
The thermal change of anodic alumina (AA), particularly the exothermic peak followed by the endothermic peak at ca 950C was
studied in detail by mainly using simultaneous TG-DTA/FTIR. The gradual loss of mass up to ca 910C is attributed to dehydration.
When heated at a constant rate by using TG-DTA, an exothermic peak with subsequent endothermic peak is observed at ca 950C,
but the exothermic peak becomes less distinct with decreasing heating rate. It has been found that gaseous SO2 accompanying a small amount of CO2 is mainly discharged at this stage. The reaction in this stage can be considered roughly in two schemes. The first scheme
can be said collectively as crystallization, in which the migration of S or C trapped inside the crystal lattice of the polycrystalline
phase (γ-, δ-, and θ-Al2O3, which presumably accompanies a large amount of amorphous or disordered phase) occurs. In the second scheme, the initial
polycrystalline (+amorphous) phase crystallizes into a quasi-crystallineγ-Al2O3-like metastable phase after amorphization. Conclusively,after the distinct exo- and endothermic reactions, the amorphous
phase crystallizes intoγ-Al2O3, presumably accompanying small amount of δ-Al2O3. It is also found that, when maintained isothermally, the metastable phases undergo transformation into the stable α-Al2O3 at 912C.
Authors:R. Ozao, M. Ochiai, H. Yoshida, Y. Ichimura, and T. Inada
Gamma-alumina membrane was prepared from anodic (amorphous) alumina (AA) obtained in a sulphuric acid electrolyte. The transformation
scheme, i.e., the crystallization to form metastable alumina polymorphs and the final transition to α-Al2O3 with heating was studied by TG-DTA and X-ray diffraction (XRD) using fixed time (FT) method. When heating at a constant rate,
the crystallization occurred at 900C or higher and the final formation of α-Al2O3 occurred at 1250C or higher, which temperatures were higher than the case of using anodic (amorphous) alumina prepared from
oxalic acid electrolyte. Relative content of S of the products was obtained by transmission electron microscope (TEM)-energy
dispersive spectroscopy (EDS). The proposed thermal change of anodic alumina membrane prepared from sulphuric acid is as follows:
1. At temperatures lower than ca 910C: Formation of a quasi-crystalline phase or a polycrystalline phase (γ-, δ- and θ-Al2O3);
2. 910–960C: Progressive crystallization by the migration of S toward the surface within the amorphous or the quasi-crystalline
phase, forming S-rich region near the surface;
3. 960C: Change of membrane morphology and the quasi-crystalline phase due to the rapid discharge of gaseous SO2;
4. 960–1240C: Crystallization of γ-Al2O3 accompanying δ-Al2O3; and
5. 1240C: Transition from γ-Al2O3 (+tr. δ-Al2O3) into the stable α-Al2O3.
The amorphization which occurs by the exothermic and the subsequent endothermic reaction suggests the incorporation of SO3 groups in the quasi-crystalline structure.