Nonlinear dielectric susceptibilities in supercooled liquids: A toy model

F. Ladieu 1, * C. Brun 1 D. l'Hôte 1
* Corresponding author
1 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
Abstract : We study a very simple model for the dielectric response of supercooled liquids is phenomenologically modeled by a set of Asymme-tric Double Wells (ADW), where each ADW contains a dynamical heterogeneity of Ncorr molecules. We find that the linear macroscopic susceptibility χ1 does not depend on Ncorr contrary to all higher order susceptibilities χ 2k+1. We show that χ 2k+1 is proportional to the k th moment of Ncorr, which could pave the way for new experiments on glass transition. In particular, as predicted by Bouchaud and Biroli on general grounds [Phys. Rev. B, 72, 064204 (2005)], we find that χ3 is proportional to the average value of Ncorr. We fully calculate χ3 and, with plausible values of few parameters our model accounts for the salient features of the experimental behavior of χ3 of supercooled glycerol.
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F. Ladieu, C. Brun, D. l'Hôte. Nonlinear dielectric susceptibilities in supercooled liquids: A toy model. Physical Review B : Condensed matter and materials physics, American Physical Society, 2012, 85, pp.184207. ⟨10.1103/PhysRevB.85.184207⟩. ⟨cea-01394728⟩

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