A FRACTAL MODEL FOR SUPERIONIC AEROGELS

Ion conducting aerogels are a new class of superionic conductors expec ted to have interesting properties. Aerogels are extremely porous and have very high surface area. Such porous materials often exhibit self- similarity in structure within certain length scales, so they can be m odelled as fractals. This is confirmed by small angle neutron and x-ra y scattering experiments. In the present paper we suggest a simple fra ctal model which is consistent with the different data available on ty pical aerogels. We construct a basic fractal unit which is repeated in a periodic array to form the gel. We assume a surface conductivity si gma(s) different from the bulk conductivity sigma(b). As porosity incr eases the proportion of the bulk material decreases but surface area i ncreases. We have studied the effective conductivity of the aerogel re sulting from the competing effects for different sigma(s)/sigma(b) rat ios. We expect such studies to be helpful in tailoring new superionic materials for specific use.