Visualizing shear-induced structures in carbon black gels by tomo-rheoscopy

Abstract

Suspensions of attractive particles form space-spanning networks that endow the suspension with solid-like behavior at rest. The microstructure of these colloidal gels depends sensitively on the shear history and on the path followed across the sol-gel transition, resulting in viscoelastic properties that can be tuned by shear. Here, we report in situ X-ray tomo-rheoscopy experiments on carbon black gels whose elastic properties exhibit a non-monotonic dependence on the shear intensity applied prior to flow cessation. By directly imaging the gel microstructure under a well-controlled rheological protocol, we reveal the emergence of pronounced structural heterogeneities extending from tens to hundreds of microns -- length scales far larger than those accessible by conventional scattering techniques such as Ultra-Small Angle X-ray Scattering. In particular, we show that only the low-shear reinforcement of elasticity correlates with a growing mesoscale correlation length, while high-shear strengthening occurs without detectable mesoscale reorganization. These observations demonstrate that flow memory in colloidal gels is not solely governed by local particle rearrangements, but is also encoded in a mesoscale structural organization extending up to 100 times the particle size. More broadly, this work highlights the power of X-ray tomo-rheoscopy to uncover large-scale structural signatures of flow history in soft materials, opening new perspectives to tailor their mechanical properties.

Figures (9)

• Figure 1: Representative Transmission Electron Microscopy (TEM) images of individual carbon black (Vulcan PF) particles. Scale bar is $100~\rm{nm}$. Samples were prepared by depositing a 5 µ L drop of a dilute ethanol dispersion of carbon black onto a carbon film (EMS CF300-Cu-UL Carbon Support Film), followed by drying in a dust-free environment.
• Figure 2: (a) Photo of the custom-made Couette cell geometry mounted on the dual motor rheometer. (b) Artificial rendering of the CAD design for the cup and bob, pictured separately. The scale is set by the outer cylinder inner diameter of $R_o=10~\rm mm$.
• Figure 3: Rheological properties of the $1.2~\%$ CB dispersion. (a) Steady-state shear stress $\sigma$ as a function of shear rate $\dot \gamma$. Colored symbols correspond to measurements performed during X-ray tomo-rheoscopy experiments using the $2~\rm mm$ gap 3D-printed geometry. The solid black line shows the flow curve measured by conventional rheometry at $T=25^\circ \rm C$ using a coaxial cylinder geometry in polycarbonate ($1~\rm mm$ gap and $40~\mathrm{mm}$ height). (b) Elastic modulus $G^{\prime}$ of the CB gels measured $300~\rm s$ after flow cessation as a function of the pre-shear rate $\dot \gamma_0$. Colored and black symbols correspond to X-ray tomo-rheoscopy and standard rheological measurements, respectively. Error bars indicate the standard deviation. The dotted black line indicates the lowest measurable modulus for the X-ray tomo-rheoscopy configuration, due to the low-torque limit of the rheometer.
• Figure 4: Structure of the $1.2~\%$ CB dispersion following a low pre-shear rate ($\dot{\gamma}_0 = 0.1~\mathrm{s}^{-1}$). (a) Horizontal slice taken in the middle of the coaxial cylinders geometry. (b) Orthogonal slice in the radial direction. Scale bar is $300~\mathrm{\mu m}$. For each image, the position in the gap is indicated by a red area in the associated scheme.
• Figure 5: (a) Schematic representation of the Couette gap divided into three regions used for image analysis: inner, middle, and outer sections. (b) Correlation length $\xi$ of the $1.2~\%$ CB structure as a function of the pre-shear rate $\dot \gamma_0$. Marker shapes indicate the gap region over which the autocorrelation function was computed: whole gap ($\bigcirc$), inner ($\nabla$), middle ($\square$), and outer ($\triangle$). The inset shows representative autocorrelation functions $\rho(r)$ as a function of radial distance $r$, together with their best exponential fits. (c) Representative reconstructed images of the gel microstructure in the $(r,v)$ plane for the three pre-shear rates. From top to bottom: $\dot{\gamma}_0 = 0.1$, $1$, and $100~\mathrm{s^{-1}}$.