In silico approaches for aerogel

Aerogels are fascinating and versatile materials, featuring a highly porous network with low density and very high surface area. They can possess very different chemical compositions, from inorganic oxides such as silica, to organic polymers such as cellulose or carbon-based materials just like carbonized resorcinol-formaldehyde, graphene, and carbon nanotubes, among others. Silica-based aerogels are the most prominent type of aerogels and have by now found widespread use in commercial thermal insulation materials, adsorbents for chemical pollutants and catalytic supports, to name a few. However, the formation of these materials by the sol-gel process entails a very complex array of chemical and physical phenomena spanning very disparate scales, from the initial precursors to the primary and secondary particles, and from these to the final aerogel network. The interplay of these processes, which directly impacts the structural, mechanical, thermal, and surface properties of the aerogel, is not fully understood. In this regard, molecular simulation methods have helped to uncover crucial mechanistic details at different scales which otherwise could not be easily obtained through experimental data alone. This chapter offers an overview of the relevant atomistic and continuum models and simulation techniques used to study aerogels, along with the insights they provided about the structure and properties of these materials. The focus will be on silica-based aerogels as they fill most of the available literature, although a few works regarding other types of aerogels will be discussed as well. A bottom-up multiscale framework will guide the text, from the atomic scale up to the macroscopic scale (continuum), not only discussing the different methods typical of each individual scale, but also highlighting how they can intersect, thus paving the way for an integrated approach. Firstly, the use of quantum mechanics calculations will be discussed as a key methodology to obtain the structure of primary particles and to predict the mechanism and energetics of the hydrolysis and condensation reactions of the early sol-gel stages. The choice of the solvent model will be assessed in detail as a crucial aspect for the accuracy of this type of calculations. Then, the generation of realistic models of the fractal structure of the aerogel network through techniques based on classical molecular dynamics (MD) simulations will be examined, along with the main underlying force fields described in the literature. From these models, the mechanical, thermal, structural, and surface properties of the aerogel can be estimated with relatively good accuracy, especially in the case of large simulation boxes containing millions of atoms. Within the context of classical MD simulations, reactive force fields will also be presented as an alternative approach for the investigation of condensation reactions at the nanoscale. The limits of silica-based aerogel atomistic models can be pushed into to the mesoscale using coarse graining models, allowing MD simulations of aerogels with lower densities, complete mesoporosity and for longer physical times, while also establishing a bridge to continuum models. Finally, numerical approaches based on the diffusion-limited cluster aggregation (DLCA) model and/or the finite element method will be explored, as alternative ways to represent the fractal structure of aerogels and reliably estimate their structural, thermal and mechanical properties, at a scale much closer to experiment.