Shear-driven memory effects in carbon black gels

We examine the microstructural and mechanical changes which occur during oscillatory shear flow and reformation after flow cessation of an intermediate volume fraction colloidal gel using rheometry and Brownian Dynamics (BD) simulations. A model depletion colloid-polymer mixture is used, comprising a hard sphere colloidal suspension with the addition of non-adsorbing linear polymer chains. The results reveal three distinct regimes depending on the strain amplitude of oscillatory shear. Large shear strain amplitudes fully break the structure which results in a more homogenous and stronger gel after flow cessation. Intermediate strain amplitudes densify the clusters and lead to highly heterogeneous and weak gels. Shearing the gel to even lower strain amplitudes creates a less heterogonous stronger solid. These three regimes of shearing are connected to the microscopic shear-induced structural heterogeneity. A comparison with steady shear flow reveals that the latter does not produce structural heterogeneities as large as oscillatory shear. Therefore oscillatory shear is a much more efficient way of tuning the mechanical properties of colloidal gels. Moreover, colloidal gels presheared at large strain amplitudes exhibit a distinct nonlinear response characterized largely by a single yielding process while in those presheared at lower rates a two-step yielding process is promoted due to the creation of highly heterogeneous structures.

Shear history plays an important role in determining the linear and nonlinear rheological response of colloidal gels and can be used for tuning their structure and flow properties. Increasing the colloidal particle aspect ratio lowers the critical volume fraction for gelation due to an increase in the particle excluded volume. Using a combination of rheology and confocal microscopy, we investigate the effect of steady and oscillatory preshear history on the structure and rheology of colloidal gels formed by silica spheres and rods of length L and diameter D (L/D = 10) dispersed in 11 M CsCl solution. We use a non-dimensional Mason number, Mn (=Fvisc./Fattr.), to compare the effect of steady and oscillatory preshear on gel viscoelasticity. We show that after preshearing at intermediate Mn, attractive sphere gel exhibits strengthening, whereas attractive rod gel exhibits weakening. Rheo-imaging of gels of attractive rods shows that at intermediate Mn, oscillatory preshear induces large compact rod clusters in the gel microstructure, compared to steady preshear. Our study highlights the impact of particle shape on gel structuring under flow and viscoelasticity after shear cessation.

A combination of experiments and Brownian Dynamics (BD) simulations is utilized to examine internal stresses in colloidal gels brought to rest from steady shear at different shear rates. A model colloidal gel with intermediate volume fraction is chosen where attractions between particles are introduced by adding non-adsorbing linear polymer chains. After flow cessation, the gel releases the stress in two distinct patterns: at high shear rates, where shear forces dominate over attractive forces, the shear-melted gel behaves as a liquid and releases stresses to zero after flow cessation. After low shear rates, though, stresses relax only partially, similar to the response of hard sphere glasses and jammed soft particles. The balance between shear and attractive forces which determines the intensity of structural distortion controls the amplitude of the residual stresses through a universal scaling. Stress decomposition to repulsive and attractive contributions in BD simulations reveals that internal stresses mainly originate from attractive forces. Moreover, analysis of particle dynamics indicates that internal stresses are associated with sub-diffusive particle displacements on average smaller than the attraction range as such short-range displacements are not sufficient to completely erase structural anisotropy caused during the course of shear.

Recent significant advances in theoretical liquid crystalline rheology are presented. Dynamic simulations are performed using a complete theory which include the three major effects of liquid crystalline materials: (1) short range order elasticity, (2) long range order elasticity, and (3) viscous flow effects. The results and discussions include rectilinear simple shear flow, complex non-linear phenomena such as defect texture generation and coarsening processes under quiescent and shear conditions, and pattern formation such as banded texture during and after cessation of flow. The complete theory predicts four in-plane (1-D orientation) flow modes and five out-of-plane (2-D orientation) flow modes in one-dimensional shear flow, depending on the magnitudes of R (ratio of short to long range order elasticity) and Er (Ericksen number: ratio of viscous to elastic force). The multistability of these flow modes is clearly explained in terms of degrees of freedoms in the nematic orientation. The number of degrees of freedom increases with increasing the spatial dimension of the system, and thus more complex orientation patterns arise in the higher dimension. Well-known defect structures arise and coarsen during simulations of the isotropic to nematic phase transition. The effect of shear flow on the defect generation process is to suppress the defect nucleation, and the simulations suggest a method of how to create defect-free nematic samples. The banded textures during and after cessation of flow are also captured by the complete theory.

Colloidal gels possess a memory of previous shear events, both steady and oscillatory. This memory, embedded in the microstructure, affects the mechanical response of the gel, and therefore enables precise tuning of the material properties under careful preparation. Here we demonstrate how the dynamics of a deformable inclusion, namely a bubble, can be used to locally tune the microstructure of a colloidal gel. We examine two different phenomena of bubble dynamics that apply a local strain to the surrounding material: dissolution due to gas diffusion, with a characteristic strain rate of ∼10−3 s−1; and volumetric oscillations driven by ultrasound, with a characteristic frequency of ∼104 s−1. We characterise experimentally the microstructure of a model colloidal gel around bubbles in a Hele-Shaw geometry using confocal microscopy and particle tracking. In bubble dissolution experiments, we observe the formation of a pocket of solvent next to the bubble surface, but marginal changes to the microstructure. In experiments with ultrasound-induced bubble oscillations, we observe a striking rearrangement of the gel particles into a microstructure with increased local ordering. High-speed bright-field microscopy reveals the occurrence of both high-frequency bubble oscillations and steady microstreaming flow; both are expected to contribute to the emergence of the local order in the microstructure. These observations open the way to local tuning of colloidal gels based on deformable inclusions controlled by external pressure fields.

Colloidal gelation, percolation and structural arrest

Semicrystalline polymers constitute well over half of all the polymers produced worldwide. Their material properties depend sensitively on the thermal and flow history experienced during processing which strongly influences the kinetics of phase change and the morphology of the final crystalline microstructure. Therefore, it is of considerable interest to understand the mechanisms of flow effects on the rate and geometry of nucleation and crystal growth. Microstructural development under the influence of flow is controlled by the interplay between melt relaxation processes and crystallization processes: the thermodynamic and kinetic aspects give rise to rich physics that are not well understood. This thesis elucidates key fundamentals of this process. We develop novel instrumentation that improves over prior approaches by examining the development of order at all the length scales of interest (in-situ rheo-optics, synchrotron small angle X-ray scattering (SAXS), and wide angle X-ray diffraction (WAXD), and ex-situ electron and optical microscopy); and by reducing the sample requirement by about three orders of magnitude, opening the way to study of model materials. We investigate a polydisperse, commercial Ziegler-Natta isotactic polypropylene (iPP) using the short term shearing protocol pioneered by the group of Janeschitz-Kriegl which imposes a well defined thermal and flow history on the polymer. Rheo-optical investigations reveal that imposition of brief intervals of shear (less than a thousandth of the quiescent crystallization time) reduces the crystallization time by two orders of magnitude at a crystallization temperature of 141°C. Above a critical value of the shear stress, there is a transition to highly oriented growth with increase in shearing duration. This transition is correlated with changes in the transient behavior during flow and the semicrystalline morphology observed exsitu. During flow, we observe the generation of long-lived, highly oriented structures (evident in the transient birefringence) under all conditions that induce subsequent growth of highly oriented crystallites. In turn, the development of oriented crystallites observed in-situ after cessation of flow correlates with development of a skin-core morphology observed ex-situ. The transient structures that develop during flow are identified as oriented [alpha]-phase crystals by WAXD, and show an unexpected temperature dependence for their time of formation: with increase in temperature, they occur at shorter times after startup of flow. This very unusual temperature dependence is strikingly similar to that for rheological processes, and is in contrast to the exponential increase expected for crystallization time-scales. Thus, the transition to anisotropic nucleation in polymers subjected to flow follows a non-classical kinetic pathway controlled by the formation of a transient, highly oriented metastable melt state. In-situ synchrotron SAXS and WAXD reveal that for shearing conditions that lead to anisotropic morphologies, crystals that are highly oriented in the flow direction develop during shear, templating the formation of crystallites after flow cessation. In the densely nucleated skin regions, ex-situ TEM shows lamellae growing radially from oriented central shish structures until they impinge to form the shish-kebab or row-nucleated structures. Under milder shear conditions, the rate of crystallization is gradual compared to strong shearing, and less oriented morphologies develop. Interestingly the ratio of parent to the crosshatched, epitaxial daughter lamellae for the oriented crystallites increases with increase in shearing time, imposed wall shear stress and temperature. Our data suggests a mechanistic model for shear-enhanced crystallization: the rheologically-controlled formation of a critical anisotropic distribution of chain segments in the melt upon imposition of flow nucleates oriented crystallites. For intense shearing conditions, these line-nuclei are long and dense. Row nucleated structures develop from these line nuclei as lamellae grow radially to form fully impinged structures. For milder shearing conditions, lower nucleation densities lead to the development of less oriented structures.

Colloidal gels exhibit rich rheological responses under flowing conditions. A clear understanding of the coupling between the kinetics of the formation/rupture of colloidal bonds and the rheological response of attractive gels is lacking. In particular, for gels under different flow regimes, the correlation between the complex rheological response, the bond kinetics, microscopic forces, and an overall micromechanistic view is missing in previous works. Here, we report the bond dynamics in short-range attractive particles, microscopically measured stresses on individual particles and the spatiotemporal evolution of the colloidal structures in different flow regimes. The interplay between interparticle attraction and hydrodynamic stresses is found to be the key to unraveling the physical underpinnings of colloidal gel rheology. Attractive stresses, mostly originating from older bonds dominate the response at low Mason number (the ratio of shearing to attractive forces) while hydrodynamic stresses tend to control the rheology at higher Mason numbers, mostly arising from short-lived bonds. Finally, we present visual mapping of particle bond numbers, their life times and their borne stresses under different flow regimes.

The spatial organization of particles in a colloidal gel controls the macroscopic properties, such as the rheological ones or the macroscopic gel stability. However, the suspension microstructure depends in a non-trivial manner on the colloidal interactions, the concentration and the flow history. Especially the effect of the latter is so far ill-understood and difficult to study in bulk suspensions. In the present work, well-characterized two dimensional suspensions are used to study the flow-induced structure in colloidal gels. Both a parallel band apparatus and a four roll mill are used to generate surface flows and the resulting steady state structures are analyzed using video microscopy. Because of the 2D nature of the suspensions, a high temporal and spatial resolution can be obtained, rendering the visualization for a wide range of surface coverages and flow rates possible. In this wide parameter space, two different regimes can be distinguished. At low surface coverages or high shear rates, only isolated flocs exist, whereas at high surface coverages or low shear rates, a transient network structure is encountered. In the two micro structural regimes the evolution of the characteristic length scales, the dominant orientation and anisotropy and the local aggregate or cluster densities is investigated. For individual aggregates, a simple analysis of hydrodynamic forces on the aggregates is used to evaluate the shear rate dependence of the aggregate size and aggregate density.

Cessation of flow in yield stress fluids results in a stress relaxation process that eventually leads to a finite residual stress. Both the rate of stress relaxation and the magnitude of the residual stresses systematically depend on the preceding flow conditions. To assess the microscopic origin of this memory effect, we combine experiments with large-scale computer simulations, exploring the behavior of jammed suspensions of soft repulsive particles. A spatiotemporal analysis of particle motion reveals that memory formation during flow is primarily governed by the emergence of domains of spatially correlated nonaffine displacements. These domains imprint the configuration of stress imbalances that drive dynamics upon flow cessation, as evidenced by a striking equivalence of the spatial correlation patterns in particle displacements observed during flow and upon flow cessation. Additional contributions to stress relaxation result from the particle packing that reorganizes to minimize the resistance to flow by decreasing the number of locally stiffer configurations. Regaining rigidity upon flow cessation drives further relaxation and effectively sets the magnitude of the residual stress. Our findings highlight that flow in yield stress fluids can be seen as a training process during which the material stores information of the flowing state through the development of domains of correlated particle displacements and the reorganization of particle packings optimized to sustain the flow. This encoded memory can then be retrieved in flow cessation experiments.

Glassy materials rapidly quenched from a liquid to a solid state upon flow cessation or cooling solidify in an out-of-equilibrium configuration, trapping residual stresses and retaining the memory of the processing conditions for very long times, which compromises their physical characterization and can adversely affect processing operations. Erasing the mechanical history encoded in disordered materials constitutes a great challenge. Here, we address this problem using experiments and particle dynamic simulations for the case of colloidal glasses made of soft particles densely packed at high volume fractions. We propose a conceptual framework that connects residual stresses, directional memory, and aging of colloidal glasses to the distribution of local shear stresses in the shearing plane. The mean value of the distribution corresponds to the macroscopic stress, the skewness carries information about directional memory, and the standard deviation is related to mechanical aging. Periodically training soft particle glasses near the yield point with a sequence of stress-controlled oscillations provides a fine-tuning of the particle stress distribution. Asymmetric shear stress distributions resulting from previous flow are transformed into symmetric distributions, thereby successfully erasing residual stresses and directional memory. The same methodology is successfully applied to colloidal and polymer gels with thixotropic properties, suggesting that it is general and may be extended to other classes of disordered materials. Published by the American Physical Society 2025

The rheological properties of a ceramic moulding compound, silicon powder with a polypropylene binder system, were studied using a Rheometrics mechanical spectrometer RMS-800 and an Instron capillary rheometer. The study included steady simple shear flow, transient start-up shear flow, stress relaxation upon cessation of steady shear flow, stress relaxation after a sudden shear displacement, and dynamic oscillatory shear flow. Yield behaviour was observed in both steady-shear and dynamic measurements. The empirical Cox-Merz rule which is usually applicable to polymer melts and solutions was found to be invalid for this material. The modified Cox-Merz rule, in which the apparent viscosity versus shear rate is equal to the complex viscosity versus the shear-rate amplitude in the highly nonlinear region, was found to be valid for this material system. A series of anomalous phenomena were also observed during the shear-flow experiments including work hardening in the very-low-shear-rate region, stress oscillation in the high-shear-rate region, and stress relaxation followed by substantial stress growth in the stress-relaxation measurements.

The effect of bulkiness of pendent side groups on the rheology of semiflexible main-chain thermotropic liquid-crystalline polymers (TLCPs) was investigated. The TLCPs investigated have aromatic triads with 10 methylene groups as flexible spacer and varying pendent side groups: ethoxy group, tert-butyl group, and phenylsulfonyl group. The TLCP having ethoxy pendent side groups (PEHQ10) undergoes smectic−nematic transition at 148 °C and nematic−isotropic (N−I) transition at 239 °C, the TLCP having tert-butyl pendent side groups (PTHQ10) undergoes only N−I transition at 193 °C, and the TLCP having phenylsulfonyl pendent side groups (PSHQ10) undergoes only N−I transition at 179 °C. Comparison of the rheological behavior of the three TLCPs was made at 40 °C below the N−I transition temperature (TNI) and at 15 °C above the TNI. The following observations were made. Upon startup of shear flow all three TLCPs exhibited a large overshoot in shear stress (σ) followed by monotonic decay and a very large overshoot in first normal stress difference (N1) followed by oscillatory decay. The peak values of overshoot in both σ and N1 increased with increasing bulkiness of pendent side groups, and only positive N1 was observed over the entire range of shear rates and temperatures investigated. Upon cessation of steady-state shear flow the relaxation rate of both σ and N1 decreased with increasing bulkiness of pendent side groups, and during rest after cessation of steady-state shear flow the rate of increase in reduced dynamic loss modulus was fastest in PTHQ10 and slowest in PSHQ10. In the nematic state the differences in bulkiness of pendent side groups played an important role, while in the isotropic state the differences in molecular weight played an important role in determining the viscosities of the TLCPs.

A capillary rheometer with quenching capability was used to study the formation of microstructure in mesophase pitch—a discotic nematic liquid crystal—under the flow conditions of fiber spinning. We report here some observations by reflected polarized‐light micrography on polished sections of specimens quenched during shear and elongational flow, or quenched during relaxation after cessation of flow. A prominent feature of mesophase flow in a capillary is the formation of ‘‘rippled’’ structures that appear to be due to the instability of shear flow in an anisotropic liquid. The ripples display a regular pattern of misorientation from the flow direction. The fully developed microstructures near the capillary exit consist of three microconstituents distributed in a concentric pattern: a fibrous core, surrounded by fine concentric bands with the mesophase layers in zig‐zag radial arrays, and a fine‐textured rim. Upon relaxation, the fine microstructures rapidly decay to disclination arrays, and coarsening continues by disclination‐annihilation reactions. The draw‐down cone, from which a filament is spun, showed no evidence of rippled structures, but instead a tendency to reorient mesophase layers to the axial direction. The rheological memory of mesophase pitch was observed in spinning experiments in which an orthogonal gridlike pattern is imposed by a screen placed above the spinneret. The ripples formed upon passage through the screen dissipate within seconds after flowing past the shear field. In contrast, the orthogonal pattern is much longer lived; its persistence upon reduction to extruded rod or drawn filament is dependent upon the viscosity determined by the spinning temperature.

The capability to describe time-dependent rheological material behavior is a necessary element of any new proposed viscoelastic equation. Recently, Leonov1,2 published a rheological equation, based upon irreversible thermodynamics, which describes the behavior of elastic polymeric fluids over a wide range of elastic strain. This model has subsequently been used for predicting flow orientation in injection molding3, where it was shown that the time-dependent rheological behavior is important for predicting frozen-in birefringence in molded parts. In the present paper, by using the Leonov equation together with numerical methods, the following two time-dependent problems are considered: (1) transient simple shear flow with impulsive change from zero shear rate to non-zero constant shear rate with subsequent relaxation following cessation of flow; (2) oscillatory shear flow in the linear and non-linear regimes.