Incoherent scattering near a sol gel transition

Abstract

We consider the self correlation function for one monomer in a gelating system near the sol gel transition. Our analysis is based on the Stauffer distribution function for cluster sizes, plus a scaling ansatz for the viscosity at different spatial scales. 1) In the sol phase, the intermediate scattering function Ik(t) (for wavevector k) is predicted to decrease like t-β/( ν+s) where β, v, and s are critical exponents for the gel fraction, the correlation length, and the macroscopic viscosity (t being the time). 2) In the gel phase, Ik (t → ∞) is finite and defines a Debye Waller factor. Near k = 0, this is equal to the gel fraction. These properties might be checked by photon beat methods, using a dilute set of labelled monomers