Xianan Qin (1) (2), Huan Jin (1), Xiaomin Liao (1), Shunli Xiao (3), Wangyang Lu (1) (2)
Physica A: Statistical Mechanics and its applications. (July 8 2023). DOI: https://doi.org/10.1016/j.physa.2023.129026

Keywords

Particle size distribution, weibull statistics, laplacian statistics, shape parameter, polymer composite, maximal entropy principle

Abstract

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.

How Our Software Was Used

Dragonfly was used to analyze particle size.

Author Affiliation

(1) School of Material Science and Engineering and National Engineering Lab of Textile Fiber Materials and Processing Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China
(2) Zhejiang Provincial Innovation Center of Advanced Textile Technology, Shaoxing 312000, China
(3) Tongkun Incorporated Co. Ltd., Tongxiang 314500, China