Aerogels are of current interest in the aerospace community due to their light weight and low thermal conductivity, making them suitable for a variety of applications, notably cryotank insulation.
These gels typically exhibit a complex structure; the smallest feature is a “primary” particle of amorphous silica, typically 2-5nm in diameter. The primary particles aggregate to form “secondary” particles, typically an order of magnitude larger, and these, in turn, form pearl-necklace structures whose details depend on the density. The gels appear to exhibit fractal dimensionality, at least over a small range of length scales.
In this work, we investigate the relationship between the structure of the gels, their dimensionality and density, and their thermal conductivity. We model the secondary-particle aggregate structure using a modified Diffusion Limited Cluster Aggregation (DLCA) model. The model produces qualitatively different structures at low and high densities that are consistent with experimental observation. At lower densities, we find evidence for a transition from fractal behavior at small length scales to approximately compact behavior at larger lengths.
We model the thermal conductivity using a variant of the random resistor network approach that has been used to describe, e.g. hopping electrical conduction in doped semiconductors. In our model, each secondary particle is assigned an effective thermal conductance that depends on the particle's size, and on the details of its contacts with neighboring particles; the conductivity of the gel network is obtained using standard numerical techniques. The scaling of the thermal conductivity with density and fractal dimension is discussed.