Session X07: Rheology of Gels

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The interplay between pressure-driven flow and attractive interactions in colloidal gels results in complex particle trajectories and velocity profiles that are not evident from bulk rheological measurements. We use a colloidal gel system of nanoemulsion droplets of poly(dimethylsiloxane) suspended in a continuous phase, comprised of a liquid precursor that contains poly(ethylene glycol diacrylate). The nanoemulsions undergo self-assembly at elevated temperatures to form gel networks with different length scales. We use high-speed confocal microscopy to investigate its spatiotemporal evolution as it flows through a cylindrical channel at various temperatures and shear rates. The trajectories of fluorescent tracer beads in the oil-rich domains are tracked using 2D image processing. Comparison of the bead velocity profiles to those obtained from a Herschel-Bulkley fit to bulk rheometry data shows agreement at low temperature but not above the gel point. These data suggest that time-dependent variations in cluster properties are responsible for statistically significant deviations from theoretical predictions, especially when attractive interactions are strongest at elevated temperatures.   

Live

Aqueous suspensions of colloidal boehmite particles are used for the production of catalyst supports. The synthesis process involves an acidification step, turning the suspension into a colloidal gel due to the emergence of attractive forces between the particles. The suspension processability requires to maintain the sample’s viscosity within a specific range, which is achieved by applying a mechanical shear.
To understand the mechanisms by which the shear modifies the gel's structure after flow cessation, we study the rheological properties of a boehmite gel depending on the value of the preshear rate. We have identified a critical shear rate that separates two distinct behaviors. Soft solids obtained following a low shear intensity show a large elastic modulus with a glass-like viscoelastic spectrum and a low yield strain. On the contrary, a high pre-shear intensity leads to the formation of soft gels characterized by a three times lower elastic modulus and a higher yield strain. Such striking differences in the same sample's rheological properties indicate that two different microstructures are selected during the pre-shear step.
Complementary experiments coupling rheology to ultrasonic imaging allow us to associate each regime with distinctive flow behaviors during pre-shear.   

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Micron-sized nanosheets such as graphene, graphene oxide or clay platelets can be used to make conducting inks or as fillers in composites to enhance their mechanical properties. At high concentrations beyond rigidity percolation, nanosheet suspensions become yield stress fluids with a finite storage modulus. In this regime the elastic response of nano-sheet suspensions appears to be universal. The storage modulus plateau of few-layer graphene in NMP solvent, aqueous graphene oxide gels and clays exhibit a power law exponent close to 3 as a function of relative volume fraction.
We present a new analytical model that explains this behaviour and connects the bulk response to the elastic properties of single nanosheets and their size. This allows is to infer the magnitude of the bending stiffness of single nano-sheets from our rheological data.
This model opens up the possibility to infer elastic properties of different nanosheets from rheological data of the suspension rather than performing AFM experiments on single nano-sheets. Furthermore, this model may explain the mechanical enhancement of nanosheet composites where a similar exponent can be observed.   

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We study the phase behavior and mechanics of a colloid-polymer model system with bridging attractions, in which the strength of the polymer adsorption can be tuned through the pH of the system. We induced bridging interactions between trifluoromethyl methacrylate-co-tert-butyl methacrylate (TtMA) particles by adding poly(acrylic acid) (PAA). A bridging attraction at low pH is likely driven by hydrogen bonding between PAA and the stabilizers on the surface of the particles; these bonds weaken as the pH is increased. We find that at both low (φ = 0.15) and high (φ = 0.40) particle volume fractions, suspensions of TtMA particles and PAA polymers undergo a transition from fluid to gel as pH is decreased or polymer concentration is increased, and show preliminary data on suspension structure, dynamics, and mechanics. We expect that this model system may be useful for investigating mechanisms of gelation that are not driven by frustrated phase separation, and for understanding flocculation processes in practical settings such as wastewater treatment.   

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Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.   

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Carbopols are polyacrylic acid microgels used for controlled drug release applications due to their ability to tune the rheological properties by varying pH. Poor photooxidative stability and limited incorporation of drugs in these gels is overcome by additive incorporation. Understanding the interaction of these additives with the microgel and their effect on gel mechanical properties is of vital importance. Here, we investigate the pH-dependent interactions of microgels with carboxylated nanodiamonds (NDs), a relatively novel carbonaceous material, using rheology. At a lower pH 4.1, increasing the ND concentration significantly increases the yield stress and modulus of the gel network by up to two orders of magnitude compared to the base system. However, addition of NDs at pH 5.5 exhibits minor change in rheological characteristics. These results are interpretated in terms of the underlying colloidal interactions. We hypothesize that in the partially ionized state (pH 4.1), the carboxylic groups on the ND surface and those of the Carbopol interact via hydrogen bonding leading to the formation of a gel-like network whereas in the fully ionized state (pH 5.5) interplay between swelling, electrostatic repulsion and hydrogen bonding result in diminished effect of NDs.   

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The rheology and microstructure of colloidal dispersions of anisotropic particles is of significant interest to the field of science and technology. However, the effect of aspect ratio and interactions on the microstructure and viscoelastic behavior of anisotropic particles is still in its infancy. To quantify these effects, we study the temperature-induced state change of a colloidal anisotropic model system of octadecyl-coated silica rods with dimensions 30 – 300 nm, also termed as adhesive hard rods (AHR). On suspending AHR in tetradecane, it exhibits thermoreversible transition from a fluid-like state to gel state upon cooling from 40 to 15°C. While this temperature-driven change visually appears like a liquid - soft solid transition, we investigate the precise microstructure responsible for the soft solid state. The gelation behavior is studied at different aspect ratio and attraction strength of the AHR. We also study the flow behavior of AHR gels under deformation and correlate it with the local microstructural changes. The flow behavior of AHR system can guide in understanding the response of complex anisotropic biological systems.   

Live

Yielding in disordered materials is often characterized by a characteristic yield stress that marks the transition between solid-like and liquid-like responses. Despite the importance of yielding to the behavior of many soft materials, identifying the yield stress often requires arbitrary definitions of non-linear behavior, resulting in orders of magnitude differences between measurement techniques. These differences are further exaggerated for thixotropic fluids whose shear history affects their behavior. Here we propose a rheological strategy to quantify the yield stress in thixotropic materials. We measure the compliance of gels comprised of TEMPO-oxidized cellulose nanofibrils (CNFs) and identify a stress-controlled bifurcation in the yielding response as the gels age. For low stresses, the time to yield diverges with increasing sample age while at high stresses, it plateaus at a finite value. A critical stress bifurcates this response and leads to a power-law evolution of the yield time with sample age, similar to the Winter-Chambon criterion characterizing the gel transition. Separating the elastic solid-like and viscous liquid-like responses of the gel, this critical stress serves as an unambiguous measurement of the yield stress for thixotropic fluids.   

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Colloidal gels exhibit a variety of mechanical responses under different conditions. The consistent formation/rupture of interparticle bonds under flowing conditions determines the rheology of attractive colloidal system. Here, we study the origins of such mechanical and rheological features in short-range attractive colloids with respect to different characteristics of the particulate network. We decouple the role of different forces on particles, and also interrogate the evolution of the colloidal structure. Our results indicate that by increasing the Mason number (Mn), the micromechanics of interparticle interactions changes from attractive to hydrodyanmic dominated, with an intermediate transition regime where the competition between the two results in dynamical heterogeneities. By continuously tracking bonds, we present an analysis of their life and death mechanism. We show that at low Mn the old bonds are dominantly responsible for the mechanics of the gel, while at large Mn it is the young ones that determine the rheological response of the fluid. Finally, we present visual mapping of particle bond numbers, their lifetimes and the stress response under different conditions.   

Live

We present a detailed numerical study of composite colloidal gels obtained by arrested phase separation. Under deformation, we show that increasing the complexity in our gels, by adding multiple same gel components that are repulsive with each other, leads to softer solids that can accommodate progressively larger strains before yielding compared to mono-gels. The simulations highlight how this is the direct consequence of the steric repulsion between different components, that prevents compactification of the network and allows multi-gels to exhibit collective reorganization to resist deformations. Our work suggests new strategies of tuning the mechanics of soft composite materials by controlling the inter-gel interactions and may open the road to the design of new materials of great use in soft robotics, batteries and stretchable electronics.   

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We investigate the connection between the load-bearing network structure in soft particulate gels and their linear viscoelastic spectrum in a 3-D microscopic numerical model, using large scale simulations with Optimally Windowed Chirp (OWCh) signals. In the model, particles spontaneously self-assemble into disordered, stable porous networks (even at low volume fractions) that feature broad relaxation spectra, microscopic dynamics, and mechanics consistent with several observations in colloidal and protein gels. The main ingredients of the model are short-range attractive interactions and bending stiffness for the inter-particle bonds. Using the OWCh protocol we analyze the shape of the frequency-dependent dynamic modulus G*(ω) and its dependence on the gel connectivity and on the preparation protocol. We show that, over a wide range of network connectivities, the viscoelastic response of different gels can be captured in a unique master curve compactly described in terms of a fractional constitutive model. The master curve provides new insight into how fractal remnants of the gelation process at the onset of rigidity can determine the linear viscoelastic behavior of soft particulate gels.   

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The microstructure-rheology relationship for a model, thermoreversible nanoparticle gel is investigated using a new technique of time-resolved neutron scattering under steady and time-resolved large amplitude oscillatory shear (LAOS) flows. A 21 vol% gel is tested with varying strength of interparticle attraction. Shear-induced structural anisotropy is observed as butterfly scattering patterns and quantified through an alignment factor. The microstructure-rheology relationship is analyzed through a new type of structure-Lissajous plot that shows how the anisotropic microstructure is responsible for the observed LAOS response, which is beyond a response expected for a purely viscous gel with constant structure. The LAOS shear viscosities are observed to follow the “Delaware-Rutgers” rule. Rheological and microstructural data are successfully compared across a broad range of conditions by scaling the shear rate by the strength of attraction, providing a method to compare behavior between steady shear and LAOS experiments.   

Live

Gels due to their heterogeneous nature show a complex, yet characteristic delayed yielding behavior under the application of sub-critical stress^[1][2]. This makes us interested in understanding what are the signs or precursors existing within the material before the final catastrophic failure. Scattering studies hint toward microscopic changes well before failure^[3]. What we are interested in is the direct real-space observation of the gel microstructure under shear. For this, we have designed our own setup which is based on the principle of measuring the deflection of a cantilever. This setup is integrated into a confocal microscope to have simultaneous shear experiments and 3D image acquisition. Presently, the setup has a precision of 0.1mPa (on a 1cm²). area) which is at least two orders of magnitude higher than a conventional rheometer and one order higher than the best shear cell^[4]. Using image correlation, we are able to find the precursors and analyze their statistics.

[1] M. Leocmach, et al Phys.Rev. Lett., 2014, 113, 038303.
[2] S. Aime, et al, PNAS, 2018, 115, 3587–3592.
[3] L. Cipelletti et al, arXiv:1909.11961[cond-mat.soft].
[4] Lin, N. Y. C., et al, Rev. Sci. Instrum. 85.3 (2014), p. 033905.