Scaling properties and structure of aerogels

Young’s modulus as well as solid thermal and electrical conductivity of aerogels have been observed to scale with density. No quantitative explanations were available up to now for these experimental findings. To establish a quantitive relationship between morphological and topological features of fractal gel networks, a simulation procedure is introduced that allows to produce three-dimensional gel structures, from which two important parameters can be extracted: i) the fraction α of interconnected mass of the gel network and ii) the ratio γ of Pythagorean distance to minimum path length on the gel backbone. Surprisingly the product αγ, which enters important macroscopic parameters such as elasticity or solid thermal (and electrical) conductivity, was found to scale with an exponent that is only a function of the mass fractal dimensionD. Also, an analytical relation between modulus and conductivity can be derived.