Modeling Synthesis of Aerogels: From Nucleation to Drying

Abstract

Aerogels are most well-known for their extraordinarily low thermal conductivity, sparking significant interest in their study and reverse engineering. To accelerate their development, a computational description of their gelation process and resultant material characteristics is desirable. Among the known methodologies to model the formation of inorganic aerogels like silica aerogel, the diffusion- or reaction-limited cluster-cluster aggregation (DLCA/RLCA) model has proven to be a prominent approach for simulating particle motion (via Brownian motion) and the structural development throughout aerogel formation. However, these models have traditionally been limited to simulating systems with uniform particle sizes and have not thoroughly investigated the growth mechanisms of the particles. In this study, we present a novel computational strategy to investigate the nucleation-driven growth and subsequent gelation observed in inorganic aerogels. Our approach begins with the use of Cayley trees to model the polycondensation reactions responsible for nucleation and the initial growth of primary particles. This modeling choice facilitates the depiction of polydispersity in the particle size distribution as they evolve, while accounting for the growth of particles starting with monomers. Additionally, the dynamics of particle formation and their interactions are regulated through rate equations, allowing for a comprehensive simulation of the network's growth and gelation processes. Moreover, we extend our methodology by incorporating finite element method (FEM) simulations to analyze the impact of stress concentrations introduced during the supercritical drying process on alcogel structures. This integrated modeling framework significantly enhances existing techniques by offering a detailed representation of both the gelation phase and the effects of drying on the microstructure, with a particular focus on pore shrinkage. By integrating simulation outcomes with experimental data, the research aims to validate the computational model and assess its ability to accurately reflect the real-world physical properties of inorganic aerogels.