Thermal analysis and self-similarity law in particle size distribution of powder samples. Part 1

Abstract

Based on the self-similarity law (or fractal nature) in particle size distribution introduced recently by Ochiai et al. (Proc. Inst. Stat. Math., 38 (1990) 257) the DTA and TG curves for the decomposition reaction of dolomite are interpreted. The phenomenologically well-known Rosin-Rammler and Gaudin-Schuhmann functions are derived by a statistical approach, and the functions thus re-written (with a particle size scaled with the absolute size constant) obey a power law. The particles of a powder obtained by a mechanical size reduction can be seen therefore to be distributed in a self-similar manner. This also states that the majority of powders obtained by comminution have a distribution of a fractal nature. Dolomite samples composed of particles whose size distributions obey the self-similarity law all undergo a similar decomposition reaction as observed in the TG-DTA curves. That is, they all appear to react smoothly and swiftly. Those having narrow particle size distibution, and to which the self-similar particle size distribution does not apply, appear to undergo a much delayed reaction; they yield irregular DTA peaks accompanied by small additional peaks or shoulders. This indicates that powder samples of dolomite having a fractal particle size distribution undergo an apparently regular and favorable reaction, and that the TG-DTA curves, though not strictly qualitative, provide speedy and useful information on the powder characteristics.