Dynamics of dilute solutions of randomly branched polymers

Abstract
We consider the time dependent scattered intensity S(q, t ) by a dilute solution of randomly branched polymers. We assume a Zimm dynamics and take into account the very broad polydispersity that is characteristic of their percolation-like synthesis. For q → 0, we conjecture a stretched exponential behavior due to interpolymer interactions, S(q → 0, t ) ~ e - Ct3/2. For very small q, larger than the inverse average interpolymer distance, we find a diffusion law, S(q, t) ˜ e -Dzq2t, with Dz ˜ R-1z ˜ N-5/8 w. For larger values of q, still with qRz <<; 1 but with Dz q2 t >> 1, the exponential is corrected by a power law, S(q, t ) ˜ CN w(1/Dz q2 t) e- Dzq2t. For still larger q, qR z >> 1, internal modes are taken into account and lead to a stretched exponential behavior. We find, for qRz >> 1, S(q, t )˜ Cq-8/5 e-q2t2/3 for qt1/3 <<; 1 and The latter stretched exponentials are simply due to the internal mode contributions and are already present for linear chains. Thus except for the very low q's, we do not expect dramatic changes because of polydispersity. This is to be contrasted with the static scattering case where effective exponents appear.