Fractal nature and thermal analysis of powders

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)∝X _n , and that the obtained powder has a specific surface area,S, expressed with the fractal particle sizex asS∝x ^D-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.