J. Phys. France
Volume 51, Numéro 24, décembre 1990
Page(s) 2843 - 2853
J. Phys. France 51, 2843-2853 (1990)
DOI: 10.1051/jphys:0199000510240284300

Dynamics of dilute solutions of randomly branched polymers

M. Daoud

Laboratoire Léon Brillouin , C.E.N. Saclay, 91191 Gif sur Yvette Cedex, France

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.

6125H - Macromolecular and polymer solutions; polymer melts; swelling.

Key words
percolation -- polymer solutions