Gravitational compression of colloidal gels

Patchy colloidal gels under the influence of gravity

In this contribution, gravitational effects in gel-forming patchy colloidal systems are studied. We focus on how the gel structure is modified by gravity. Through Monte Carlo computer simulations of gel-like states recently identified by the rigidity percolation criterion [J. A. S. Gallegos et al., Phys. Rev. E 104, 064606 (2021)], the influence of the gravitational field, characterized by the gravitational Péclet number, Pe, on patchy colloids is studied in terms of the patchy coverage, χ. Our findings point out that there exists a threshold Péclet number, Pe_g, that depends on χ above which the gravitational field enhances the particle bonding and, in consequence, promotes the aggregation or clustering of particles; the smaller the χ value, the higher the Pe_g. Interestingly, when χ ∼ 1 (near the isotropic limit), our results are consistent with an experimentally determined threshold Pe value where gravity affects the gel formation in short-range attractive colloids. In addition, our results show that the cluster size distribution and the density profile undergo variations that lead to changes in the percolating cluster, i.e., gravity is able to modify the structure of the gel-like states. These changes have an important impact on the structural rigidity of the patchy colloidal dispersion; the percolating cluster goes from a uniform spatially network to a heterogeneous percolated structure, where an interesting structural scenario emerges, namely, depending on the Pe value, the new heterogeneous gel-like states can coexist with both diluted and dense phases or they simply reach a crystalline-like state. In the isotropic case, the increase in the Pe number can shift the critical temperature to higher temperatures; however, when Pe > 0.01, the binodal disappears and the particles fully sediment at the bottom of the sample cell. Furthermore, gravity moves the rigidity percolation threshold to lower densities. Finally, we also note that within the values of the Péclet number here explored, the cluster morphology is barely altered.

Phase mechanics of colloidal gels: osmotic pressure drives non-equilibrium phase separation

Although dense colloidal gels with interparticle bonds of order several kT are typically described as resulting from an arrest of phase separation, they continue to coarsen with age, owing to the dynamics of their temporary bonds. Here, k is Boltzmann's constant and T is the absolute temperature. Computational studies of gel aging reveal particle-scale dynamics reminiscent of condensation that suggests very slow but ongoing phase separation. Subsequent studies of delayed yield reveal structural changes consistent with re-initiation of phase separation. In the present study we interrogate the idea that mechanical yield is connected to a release from phase arrest. We study aging and yield of moderately concentrated to dense reversible colloidal gels and focus on two macroscopic hallmarks of phase separation: increases in surface-area to volume ratio that accompanies condensation, and minimization of free energy. The interplay between externally imposed fields, Brownian motion, and interparticle forces during aging or yield, changes the distribution of bond lengths throughout the gel, altering macroscopic potential energy. The gradient of the microscopic potential (the interparticle force) gives a natural connection of potential energy to stress. We find that the free energy decreases with age, but this slows down as bonds get held stretched by glassy frustration. External perturbations break just enough bonds to liberate negative osmotic pressure, which we show drives a cascade of bond relaxation and rapid reduction of the potential energy, consistent with renewed phase separation. Overall, we show that mechanical yield of reversible colloidal gels releases kinetic arrest and can be viewed as non-equilibrium phase separation.

Consolidation of strong colloidal gels under arbitrary compressive loadings

Although highly successful, classical constitutive theories for the consolidation of strong colloidal gels are limited to one-dimensional (1D) uniaxial consolidation. Many consolidation applications are inherently multidimensional and there currently exists little understanding and no constitutive theory for how strong colloidal gels consolidate under arbitrary compressive loadings. In this study, we address this shortcoming by considering the consolidation mechanics of strong colloidal gels under arbitrary compressive loadings via 2D DEM biaxial simulations of assemblies of cohesive frictional particles. We show that although particle-scale consolidation differs significantly between uniaxial and isotropic consolidation, the maximum normal stress during consolidation is a unique function of the volumetric strain and hence the concentration of the solids phase. We use these insights to develop a generalised constitutive model for the macroscopic compressive rheology under arbitrary compressive loadings that is consistent with the classical constitutive model for uniaxial consolidation. Surprisingly, we find that this generalized constitutive model can predict multidimensional consolidation under arbitrary compressive loadings without need for further characterisation beyond uniaxial consolidation. These results provide significant insights into the consolidation of strong colloidal gels and facilitate prediction of multi-dimensional consolidation over a wide range of applications, and so represents an initial foray toward the development of a tensorial rheology of strong colloidal gels.

Dynamic behaviors of sedimenting colloidal gel materials: hydrodynamic interactions

It is a highly nonlinear poromechanics phenomenon that colloidal gel materials that are exposed to a gravitational stress greater than their yield stress undergo elastic compression.

Understanding the multiscale self-assembly of metal-organic polyhedra towards functionally graded porous gels

Spatial heterogeneity and gradients within porous materials are key for controlling their mechanical properties and mass/energy transport, both in biological and synthetic materials. However, it is still challenging to induce such complexity in well-defined microporous materials such as crystalline metal-organic frameworks (MOFs). Here we show a method to generate a continuous gradient of porosity over multiple length scales by taking advantage of the amorphous nature of supramolecular polymers based on metal-organic polyhedra (MOPs). First, we use time-resolved dynamic light scattering (TRDLS) to elucidate the mechanism of hierarchical self-assembly of MOPs into colloidal gels and to understand the relationship between the MOP concentrations and the architecture of the resulting colloidal networks. These features directly impact the viscoelastic response of the gels and their mechanical strength. We then show that gradients of stiffness and porosity can be created within the gel by applying centrifugal force at the point of colloidal aggregation. These results with the creation of asymmetric and graded pore configuration in soft materials could lead to the emergence of advanced properties that are coupled to asymmetric molecule/ion transport as seen in biological systems.

Gravitational collapse of colloidal gels: non-equilibrium phase separation driven by osmotic pressure

Delayed gravitational collapse of colloidal gels is characterized by initially slow compaction that gives way to rapid bulk collapse, posing interesting questions about the underlying mechanistic origins. Here we study gel collapse utilizing large-scale dynamic simulation of a freely draining gel of physically bonded particles subjected to gravitational forcing. The hallmark regimes of collapse are recovered: slow compaction, transition to rapid collapse, and long-time densification. Microstructural changes are monitored by tracking particle positions, coordination number, and bond dynamics, along with volume fraction, osmotic pressure, and potential energy. Together these reveal the surprising result that collapse can occur with a fully intact network, where the tipping point arises when particle migration dissolves strands in a capillary-type instability. While it is possible for collapse to rupture a gel network into clusters that then sediment, and hydrodynamic interactions can make interesting contributions, neither is necessary. Rather, we find that the "delay" arises from gravity-enhanced coarsening, which triggers the re-emergence of phase separation. The mechanism of this transition is a leap toward lower potential energy of the gel, driven by bulk negative osmotic pressure that condenses the particle phase: the gel collapses in on itself under negative osmotic pressure allowing the gel, to tunnel through the equilibrium phase diagram to a higher volume fraction "state". Remarkably, collapse stops when condensation stops, when gravitational advection produces a positive osmotic pressure, re-arresting the gel.

Reversible Size Modulation of Aqueous Microgels via Orthogonal or Combined Application of Thermo- and Phototriggers

Aqueous microgels that respond orthogonally to external temperature and light stimuli and to a combination of both stimuli were developed. N-Vinylcaprolactam (VCL) was copolymerized with small feed amounts (<5 mol %) of 4-[(4-methacryloyloxy)phenylazo] benzenesulfonic acid (ABSA) and cross-linked with N,N'-methylenebis(acrylamide) (BIS) to synthesize monodisperse and colloidally stable P(VCL-BIS-ABSA) microgels. The volume phase transition information on the microgels under both orthogonal and combined application of temperature and light stimuli was investigated in situ by dynamic light scattering (DLS) instrument. Modeling of this information by the Flory-Rehner theory describes and aids the preliminary understanding of the main features in the volume phase transition of these photoresponsive microgels. Interestingly, the microgels rapidly deswell upon UV irradiation (λ = 365 nm), even as the trans-ABSA pendant groups are converted to the more polar cis state. The variation in the content of the pendant azobenzene groups in the microgels allows for reversible modulation of the phototriggered volume change. We propose that the approach of the sulfonic acid groups of cis-ABSA toward the polymer backbone causes the disruption of hydrogen bonding interactions between water molecules and the carbonyl groups of VCL.

Highly nonlinear dynamics in a slowly sedimenting colloidal gel

We use a combination of original light scattering techniques and particles with unique optical properties to investigate the behavior of suspensions of attractive colloids under gravitational stress, following over time the concentration profile, the velocity profile, and the microscopic dynamics. During the compression regime, the sedimentation velocity grows nearly linearly with height, implying that the gel settling may be fully described by a (time-dependent) strain rate. We find that the microscopic dynamics exhibit remarkable scaling properties when time is normalized by the strain rate, showing that the gel microscopic restructuring is dominated by its macroscopic deformation.

Centrifugal compression of soft particle packings: theory and experiment

An exact method is developed for computing the height of an elastic medium subjected to centrifugal compression, for arbitrary constitutive relation between stress and strain. Example solutions are obtained for power-law media and for cases where the stress diverges at a critical strain--for example as required by packings composed of deformable but incompressible particles. Experimental data are presented for the centrifugal compression of thermo-responsive N-isopropylacrylamide (NIPA) microgel beads in water. For small radial acceleration, the results are consistent with Hertzian elasticity, and are analyzed in terms of the Young elastic modulus of the bead material. For large radial acceleration, the sample compression asymptotes to a value corresponding to a space-filling particle volume fraction of unity. Therefore we conclude that the gel beads are incompressible, and deform without deswelling. In addition, we find that the Young elastic modulus of the particulate gel material scales with cross-link density raised to the power 3.3±0.8, somewhat larger than the Flory expectation.

The role of polymer polydispersity in phase separation and gelation in colloid-polymer mixtures

Mixtures of nonadsorbing polymer and colloidal particles exhibit a range of different morphologies depending on the particle and polymer concentrations and their relative size ratios. These can be very important for technological applications, where gelation can produce a weak solidlike structure that can help reduce phase separation, extending product shelf life. However, industrial products are typically formulated with polydisperse polymers, and the consequences of this on the phase behavior of the mixture are not known. We investigate the role of polymer polydispersity and show that a small amount of larger polymer in a distribution of nominally much smaller polymer can drastically modify the behavior. It can induce formation of a solidlike gel structure, abetted by the small polymer, but still allow further evolution of the phase separation process, as is seen with a monodisperse distribution of larger polymer. This coarsening ultimately leads to gravitational collapse. We describe the full phase behavior for polydisperse polymer mixtures and account for the origin of the behavior through measurements of the structure and dynamics and by comparing to the behavior with monodisperse polymers.