Tracking microscopic inter-cycle irreversibility across the yielding transition through constant-amplitude oscillatory fatigue experiments in a colloidal fractal gel with Rheo-Echo-XPCS
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 . We find: (i) ballisticlike decorrelation with at all strain amplitudes, where the decorrelation rate scales linearly with the loss tangent , establishing as a macroscopic measure of the rate of irreversible structural decorrelation; (ii) a continuous evolution of the relaxation function from compressed exponential () at low strain—consistent with three-dimensional dipolar strain fields in the intact network—to stretched exponential () at high strain, interpreted as a dimensional reduction from to as stress transmission shifts from bulk to quasi-one-dimensional filamentary backbones during network fragmentation.