On the origin of power-scaling exponents in silica aerogels

The macroscopic properties of open-porous cellular materials hinge upon the microscopic skeletal architecture and features of the material. Typically, bulk material properties, viz. the elastic modulus, strength of the material, thermal conductivity, and acoustic velocity, of such porous materials are expressed in terms of power-scaling laws against their density. In particular, the relation between the elastic modulus and the density has been intensively investigated. While the Gibson and Ashby model predicts an exponent of 2 for ideally connected foam-like open-cellular solids, the exponent is found to lie between 3 and 4 for silica aerogels. In this paper, we investigate the origins of this scaling exponent. Particularly, the effect of the pearl-necklace-like skeletal features of the pore walls and that of the random spatial arrangement is extensively computationally studied. It is shown that the latter is the driving factor in dictating the scaling exponent and the rest of the features play a negligible or no role in quantifying the scaling exponent.