Fractals in Solid-State Processes

Abstract

Heterogeneous condensed-state processes take place at interfaces of different phases. In general, the surfaces are not perfectly flat and their properties are not homogeneous: they are mostly rough with many irregularities and inhomogeneities. Surface geometric inhomogeneity is reflected in its chemical inhomogeneity. For the description of the structure of physical objects with inhomogeneous properties (roughness, mass density, heat density, etc.), the methods of fractal geometry can be applied (Šesták J, Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, Amsterdam, 2005). The word “fractal” originates from the Latin word “fractus,” meaning broken. It is indicated that fractals are widespread and that the fractal geometry is the geometry of Nature (Barnsley MF, Fractals everywhere. Academic, New York, 1993). Classical geometry provides a first approximation to the structure of physical objects; it is the language that we use to communicate the designs of technological products and, very approximately, the forms of natural creations. Fractal geometry is an extension of classical geometry. It can be used to make precise models of physical structures of rough surfaces, disordered layers on surfaces and porous objects (such as heterogeneous catalysts). Furthermore, gels, soot, and smoke, and most macromolecules, are also fractals (Sadana A, Engineering biosensors: kinetics and design applications. Academic, New York, 2002).