Understanding the relationship between the geometric characteristics and the Weibull size statistics of particles in SiO2/PET polymer composites

Weibull statistics has been found to characterize the size distribution of aggregates in many dispersing systems, including the filler size in polymer composites. However, the underlying physical meaning of this size distribution model remains elusive. In this paper, we present a theory for the Weibull statistics of the particle size in polymer composites which bridges the particle geometric characteristics and the shape parameter. The theory has been tested on SiO2/poly(ethylene terephthalate) (SiO2/PET) polymer composite whose filler structure is either hollow or solid. We show that Weibull statistics with shape parameter at 2 and 3 characterizes the size of hollow and solid fillers, respectively. The scaling law behind the Weibull statistics allows the size distribution of different structured particles to fall into a master distribution, i.e. the Laplacian distribution, which can be explained by maximizing the information entropy with constraint set on the mean scaled particle size.