SCALING PROPERTIES AND STRUCTURE OF AEROGELS

Young's modulus as well as solid thermal and electrical conductivity o f aerogels have been observed to scale with density. No quantitative e xplanations were available up to now for these experimental findings. To establish a quantitive relationship between morphological and topol ogical features of fractal gel networks, a simulation procedure is int roduced that allows to produce three-dimensional gel structures, from which two important parameters can be extracted: i) the fraction oc of interconnected mass of the gel network and ii) the ratio gamma of Pyt hagorean distance to minimum path length on the gel backbone. Surprisi ngly the product cry, which enters important macroscopic parameters su ch as elasticity or solid thermal (and electrical) conductivity, was f ound to scale with an exponent that is only a function of the mass fra ctal dimension D. Also, an analytical relation between modulus and con ductivity can be derived.