EPJ

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EPJ E - Soft Matter and Biological Physics
Soft Matter and Biological Physics


Eur. Phys. J. E 6, 231-236 (2001)

Anomalous dynamical light scattering in soft glassy gels

J.-P. Bouchaud1 and E. Pitard2

1  Service de Physique de l'État Condensé, Centre d'études de Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
2  Laboratoire de Physique Mathématique et Théorique, Université Montpellier II, UMR 5825, France

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(Received 23 July 2001)

Abstract
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, S. Manley, R.C. Ball, D.A. Weitz, 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 $t_{\rm w}$, quasi-exponentially at first, and then as $t_{\rm w}^{4/5}$ with logarithmic corrections.

PACS
82.70.Gg - Gels and sols.
81.40.Cd - Solid solution hardening, precipitation hardening, and dispersion hardening; aging.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001

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