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    Tracking microscopic inter-cycle irreversibility across the yielding transition through constant-amplitude oscillatory fatigue experiments in a colloidal fractal gel with Rheo-Echo-XPCS

    William Chèvremont1, Julien Bauland2, Emmeline Brassac2, Gonzalo Sanchez Vera3, Stefano Aime3, Frédéric Pignon4, and Thomas Gibaud2,5,*

    • *Contact author: thomas.gibaud@ens-lyon.fr

    Phys. Rev. Materials 10, 093606 – Published 22 September, 2026

    DOI: https://doi.org/10.1103/jb21-wwng

    Abstract

    Understanding how microscopic structural dynamics relate to macroscopic mechanical response during yielding remains a central challenge in soft-matter physics. Here, we introduce rheo-echo x-ray photon correlation spectroscopy (Rheo-Echo-XPCS) with nonlinear acquisition synchronized to oscillatory shear, enabling direct measurement of irreversible nanoscale dynamics under controlled strain amplitude. Applying this approach to a carbon black colloidal fractal gel, we resolve time-periodic echoes in the vorticity-direction intensity autocorrelation function, whose decay encodes cycle-to-cycle nonaffine structural rearrangements spanning the linear viscoelastic regime, nonlinear deformation, and the yielding regime beyond γy. We find: (i) ballisticlike decorrelation with τ∝q−1 at all strain amplitudes, where the decorrelation rate vτ=1/〈qτ〉 scales linearly with the loss tangent tanδ=G′′/G′, establishing tanδ as a macroscopic measure of the rate of irreversible structural decorrelation; (ii) a continuous evolution of the relaxation function from compressed exponential (α≃1.5) at low strain—consistent with three-dimensional dipolar strain fields in the intact network—to stretched exponential (α≃0.5) at high strain, interpreted as a dimensional reduction from df=3 to df=1 as stress transmission shifts from bulk to quasi-one-dimensional filamentary backbones during network fragmentation.

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