Prediction of the thermo-physical properties of FGPM aerogels, regarding the development of the Sierpinski carpet model

Abstract

The Sierpinski carpet is mainly used to model the structure and properties of homogeneous media because of the unique characteristics of fractal materials (self-similarity) and the reduction of calculations complexity. Later, the unit cell of the Sierpinski carpet was modified once with a binomial distribution function to model the functionally gradient aerogels synthesized by the layering method. In this work, the structure and thermal properties of functionally gradient Novolac aerogels are introduced and synthesized by the thermal gradient device (a monolithic, continuous, and controllable method). The structural parameters of the proposed model are determined due to the changes in the sample concentration and gyration radius of colloid particles caused by the thermodiffusion effect. The appropriate range of structural parameters is 0.1 <C/L< 0.93, t = 0, and n = 1. The accuracy of the proposed model is reviewed by experimental samples, which showed suitable matches and reasonable agreement. The main challenge of this study is to involve the effect of the synthesis method (thermal gradient device) in modeling the structure and properties of the Sierpinski carpet in a functionally graded heterogeneous structure.