The application of percolation theory in powder technology

Abstract

It is about 10 years ago since the author of this invited paper started to apply percolation theory in the field of (pharmaceutical) powder technology. Thus the invited paper summarizes 10 years of experience in the application of percolation theory. The goal of the paper is to share this experience and to stimulate a broader use of percolation theory. The application of percolation theory is a fast growing field in very different areas of science and technology. However, percolation theory has not yet reached as broad an application in the field of powder technology as it should deserve. For this purpose, within this article a strong emphasis is put on a condensed but still rigorous introduction to the concepts of percolation theory to facilitate a broader application in powder technology. In this respect it is important to get a deeper knowledge and understanding of the basic power law of percolation theory to describe a desired property X = S* ( p - pc) q , where S* is the scaling factor, p is the (bond or site) occupation probability, pc is the percolation threshold and q is the critical exponent, close to the percolation threshold. A prerequisite is a geometrical or a physical phase transition at pc. An explicit statement about the nature of the percolation threshold phenomenon should be part of the system and model analyzed. The question of the universal character of a critical exponent q, which depends only on the dimensionality d of a system, plays an important role as well as the concept of percolation threshold pc, which reflects the microstructure of a system. Different examples illustrate the successful application of percolation theory in (pharmaceutical) powder technology, covering important unit operations such as the compression of powder and the dissolution of an active substance from a binary powder compact, etc. Percolation theory provides key tools for a more rational design of pharmaceutical dosage forms and for the development of robust formulations. Thus the development time can be speeded up and time to market can be reduced. The examples presented show the range of application and possible limitations of percolation theory. An outlook is given for a broader application as well as for a possible fruitful application of percolation theory in nanoscience and nanotechnology.