Structure and Thermal Conductivity of Silica Aerogels from Computer Simulations
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Structure and Thermal Conductivity of Silica Aerogels from Computer Simulations Brian S. Good NASA Glenn Research Center Cleveland, OH 44026, U.S.A. ABSTRACT 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 secondaryparticle 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.
INTRODUCTION Aerogels are low-density materials possessing properties that have maintained interest for a wide variety of applications [1-3]. In particular, the low thermal conductivities characteristic of such gels have led to the aerospace community’s interest in these materials as lightweight thermal insulation. Aerogels are also notoriously fragile, and to develop thermal insulation that is mechanically robust, researchers in our laboratory have developed a method for monomer-coating aerogels and cross-linking the coatings, so as to greatly improve the gels' strength while minimally impacting their insulating properties [4]. In order to provide a microscopic understanding of the thermal behavior of the gels, and to provide a predictive tool of use in their further development, we have constructed a model for solid thermal conduction in silica aerogels. The model is built on computer simulations using a modified diffusion-limited cluster aggregation (DLCA) scheme [5], with thermal
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conductivity calculated via methodology similar to the solution of the random resistor network problem [6].
STRUCTURAL MODEL Silica aerogels are known to exhibit
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