# Optimizing the Composition of Geopolymer Composites Incorporating Secondary Aluminium Industry By-Products Using Mathematical Modelling

## TL;DR

This paper presents a mathematical model to optimize the composition of geopolymer composites using secondary aluminum by-products, aiming to improve structural and environmental performance.

## Contribution

The novelty lies in the integrated use of Markov chains, criterion methods, and an orthogonal plan to optimize geopolymer composite composition.

## Key findings

- The optimal composition includes 1000 g metakaolin, 900 g activator, and 62.493 g secondary aluminum by-product.
- The model predicts improved mechanical, thermal, and environmental properties of the composites.
- Secondary aluminum by-products significantly influence the geopolymerization process and composite performance.

## Abstract

Geopolymer composite materials are a viable alternative to conventional construction materials. The research problem of geopolymer composites revolves around the imperative to comprehensively address their synthesis, structural performance, and environmental impact. The derived mathematical model facilitates precisely determining the optimal proportions of two crucial constituents in the geopolymer matrix: silica sand and secondary aluminum by-product. A mathematical model for optimizing the composition of geopolymer composites has been developed based on the integrated use of Markov chains, criterion methods, and an orthogonally compositional plan. The optimal composition of the geopolymer matrix is determined and predicted using a mathematical model. Specifically, the recommended content mixing ratio is as follows: metakaolin at 1000 g, activator at 900 g, silica fume at 1052.826 g, carbon fibre at 10 g, and secondary aluminum by-product at 62.493 g. This study analyzes the influence of different secondary aluminum industry by-products on the geopolymerization process and assesses the mechanical, thermal, and environmental properties of the resulting composites to establish a comprehensive understanding of their structural viability.