MESOSCOPIC PICTURES OF THE SOL-GEL TRANSITION - LADDER MODELS AND FRACTAL NETWORKS

In this work we introduce mechanical networks which highlight the relation between viscoelastic and structural properties of chemical systems at the sol-gel transition. Cross-linking polymers at the gel point show in general a power law behavior of the complex modulus, i.e., G*(omega) proportional to (i omega)(alpha) (0 < alpha < 1), which is related to the (constitutive) gel equation. We present a mechanical ladder model whose stress-strain relation obeys the gel equation with alpha = 1/2 and which consists of an infinite number of springs and dashpots. Furthermore, we investigate terminated ladder arrangements which mimic pre- and postgel behavior. To elucidate the complex dependence of alpha on structural properties which one observes for systems near to the gel point, we analyze mechanical fractal networks.