Shape parameter of Weibull size statistics is a potential indicator of filler geometry in SiO2 reinforced polymer composites

Abstract

In a previous study [Physica A, 625 (2023), 129026], a relationship between the filler size distribution and the filler geometry of SiO2 particle reinforced polymer composites has been reported. It has been experimentally demonstrated that the size of hollow and solid SiO2 particles disperse in polymer matrix follows Weibull statistics with shape parameter at 2 and 3, respectively. This mechanism has not yet been verified in the one-dimensional (1D) case. In this paper, we study the length distribution of glass fibers in polymer composites. Our results show that the previous theory still holds for the 1D case. Thus, shape parameter of Weibull size statistics could be a potential indicator of filler geometry in SiO2 reinforced polymer composites. This interesting mechanism can be explained by the scaling nature behind the Weibull statistics. Our study has thus shed new light on the evolution of filler geometry during the fabrication process of polymer composites, and should be useful for the related fields.