Anomalous dynamical light scattering in soft glassy gels.
We compute the dynamical structure factor S( q,tau) of an elastic medium where force dipoles appear at random in space and in time, due to "micro-collapses" of the structure. Various regimes are found, depending on the wave vector q and the collapse time theta. In an early time regime, the logarithm of the structure factor behaves as (q tau)(3/2), as predicted in (L. Cipelletti et al., Phys. Rev Lett. 84, 2275 (2000)) using heuristic arguments. However, in an intermediate-time regime we rather obtain a (q tau)(5/4) behaviour. Finally, the asymptotic long-time regime is found to behave as q(3/2)tau. We also give a plausible scenario for aging, in terms of a strain-dependent energy barrier for micro-collapses. The relaxation time is found to grow with the age t(w), quasi-exponentially at first, and then as t(w)(4/5) with logarithmic corrections.
Bouchaud
J-P
JP
Service de Physique de l'Etat Condensé, Centre d'études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France. bouchau@spec.saclay.cea.fr
Pitard
E
E