Anomalous dynamical light scattering in soft glassy gels

Abstract:

We compute the dynamical structure factor S(q,τ) 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 θ. In an early time regime, the logarithm of the structure factor behaves as (qτ)^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 (qτ)^5/4 behaviour. Finally, the asymptotic long-time regime is found to behave as q ^3/2τ. 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.