Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram.

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle-particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system's variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network's resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid-liquid phase boundary using a single volume fraction of particles well beyond this phase boundary.

Elastohydrodynamic friction of robotic and human fingers on soft micropatterned substrates.

Frictional sliding between patterned surfaces is of fundamental and practical importance in the haptic engineering of soft materials. In emerging applications such as remote surgery and soft robotics, thin fluid films between solid surfaces lead to a multiphysics coupling between solid deformation and fluid dissipation. Here, we report a scaling law that governs the peak friction values of elastohydrodynamic lubrication on patterned surfaces. These peaks, absent in smooth tribopairs, arise due to a separation of length scales in the lubricant flow. The framework is generated by varying the geometry, elasticity and fluid properties of soft tribopairs and measuring the lubricated friction with a triborheometer. The model correctly predicts the elastohydrodynamic lubrication friction of a bioinspired robotic fingertip and human fingers. Its broad applicability can inform the future design of robotic hands or grippers in realistic conditions, and open up new ways of encoding friction into haptic signals.

Counterpropagating Gradients of Antibacterial and Antifouling Polymer Brushes.

We report on the formation of counterpropagating density gradients in poly([2-dimethylaminoethyl] methacrylate) (PDMAEMA) brushes featuring spatially varying quaternized and betainized units. Starting with PDMAEMA brushes with constant grafting density and degree of polymerization, we first generate a density gradient of quaternized units by directional vapor reaction involving methyl iodide. The unreacted DMAEMA units are then betainized through gaseous-phase betainization with 1,3-propanesultone. The gas reaction of PDMAEMA with 1,3-propanesultone eliminates the formation of byproducts present during the liquid-phase modification. We use the counterpropagating density gradients of quaternized and betainized PDMAEMA brushes in antibacterial and antifouling studies. Completely quaternized and betainized brushes exhibit antibacterial and antifouling behaviors. Samples containing 12% of quaternized and 85% of betainized units act simultaneously as antibacterial and antifouling surfaces.

Jamming Distance Dictates Colloidal Shear Thickening.

We report experimental and computational observations of dynamic contact networks for colloidal suspensions undergoing shear thickening. The dense suspensions are comprised of sterically stabilized poly(methyl methacrylate) colloids that are spherically symmetric and have varied surface roughness. Confocal rheometry and dissipative particle dynamics simulations show that the shear thickening strength ß scales exponentially with the scaled deficit contact number and the scaled jamming distance. Rough colloids, which experience additional rotational constraints, require an average of 1.5-2 fewer particle contacts as compared to smooth colloids, in order to generate the same ß. This is because the surface roughness enhances geometric friction in such a way that the rough colloids do not experience a large change in the free volume near the jamming point. The available free volume for colloids of different roughness is related to the deficiency from the maximum number of nearest neighbors at jamming under shear. Our results further suggest that the force per contact is different for particles with different morphologies.

Migration and Morphology of Colloidal Gel Clusters in Cylindrical Channel Flow.

We report the cluster-level structural parameters of colloidal thermogelling nanoemulsions in channel flow as a function of attractive interactions and local shear stress. The spatiotemporal evolution of the gel microstructure is obtained by directly visualizing the dispersed phase near the edge of a cylindrical channel. We observe the flow of the nanoemulsion gels in a range of radial positions (r) and shear stresses between 70 and 220 Pa, finding that the r-dependent cluster sizes are due to a balance between shear forces that yield bonds and attractive interactions that rebuild the inter-colloid bonds. In addition, the largest clusters appear to be affected by confinement and accumulate toward the central axis of the channel, resulting in a volume fraction gradient. Cluster size and volume fraction variabilities are most prominent when the attractive interactions are the strongest. Specifically, a distinct transition from sparse, fluidized clusters near the walls to concentrated, large clusters toward the center is observed. These two structural states coincide with a velocity-based transition from higher shear rates near the walls to lower shear rates toward the center of the channel. We find a compounding effect where larger gel clusters, formed under strong attractions and low shear stresses, are susceptible to shear-induced migration that intensifies r-dependent heterogeneity and deviations in the flow behavior from predictive models.

Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity.

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant. We resolve this apparent contradiction by conducting a normal-mode analysis of experimentally measured bond networks of gels of colloidal particles with short-ranged attraction. We find that structural heterogeneity of the gels, which leads to floppy modes and a nonaffine-affine crossover as frequency increases, evolves as a function of the volume fraction and is key to understanding the frequency-dependent elasticity. Without any free parameters, we achieve good qualitative agreement with the measured mechanical response. Furthermore, we achieve universal collapse of the shear moduli through a phenomenological spring-dashpot model that accounts for the interplay between fluid viscosity, particle dissipation, and contributions from the affine and non-affine network deformation.

Contact criterion for suspensions of smooth and rough colloids.

We report a procedure to obtain the search distance used to determine particle contact in dense suspensions of smooth and rough colloids. This method works by summing physically relevant length scales in an uncertainty analysis and does not require detailed quantification of the surface roughness. We suspend sterically stabilized, fluorescent poly(methyl methacrylate) colloids in a refractive index-matched solvent, squalene, in order to ensure hard sphere-like behavior. High speed centrifugation is used to pack smooth and rough colloids to their respective jamming points, φJ. The jammed suspensions are subsequently diluted with known volumes of solvent to φ < φJ. Structural parameters obtained from confocal laser scanning micrographs of the diluted colloidal suspensions are extrapolated to φJ to determine the mean contact number at jamming, 〈z〉J. Contact below jamming refers to nearest neighbors at a length scale below which the effects of hydrodynamic or geometric friction come into play. Sensitivity analyses show that a deviation of the search distance by 1% of the particle diameter results in 〈z〉 changing by up to 10%, with the error in contact number distribution being magnified in dense suspensions (φ > 0.50) due to an increased number of nearest neighbors in the first coordination shell.

Interfacial Rheology of Gallium-Based Liquid Metals.

Gallium and its alloys react with oxygen to form a native oxide that encapsulates the liquid metal with a solid "skin". The viscoelasticity of this skin is leveraged in applications such as soft electronics, 3D printing, and components for microfluidic devices. In these applications, rheological characterization of the oxide skin is paramount for understanding and controlling liquid metals. Here, we provide a direct comparison of the viscoelastic properties for gallium-based liquid metals and illustrate the effect of different subphases and addition of a dopant on the elastic nature of the oxide skin. The du Noüy ring method is used to investigate the interfacial rheology of oxide skins formed by gallium-based liquid metal alloys. The results show that the oxide layer on gallium, eutectic gallium-indium, and Galinstan are viscoelastic with a yield stress. Furthermore, the storage modulus of the oxide layer is affected by exposure to water or when small amounts of aluminum dopant are added to the liquid metals. The former scenario decreases the interfacial storage modulus of the gallium by 35-85% while the latter increases the interfacial storage modulus by 25-45%. The presence of water also changes the chemical composition of the oxide skin. Scanning electron microscopy, energy-dispersive X-ray spectroscopy (EDS), and X-ray photoelectron spectroscopy suggest that a microstructural evolution of the interface occurs when aluminum preferentially migrates from the bulk to the surface. These studies provide guidance on selecting liquid metals as well as simple methods to optimize their rheological behavior for future applications.

Rheological State Diagrams for Rough Colloids in Shear Flow.

To assess the role of particle roughness in the rheological phenomena of concentrated colloidal suspensions, we develop model colloids with varying surface roughness length scales up to 10% of the particle radius. Increasing surface roughness shifts the onset of both shear thickening and dilatancy towards lower volume fractions and critical stresses. Experimental data are supported by computer simulations of spherical colloids with adjustable friction coefficients, demonstrating that a reduction in the onset stress of thickening and a sign change in the first normal stresses occur when friction competes with lubrication. In the quasi-Newtonian flow regime, roughness increases the effective packing fraction of colloids. As the shear stress increases and suspensions of rough colloids approach jamming, the first normal stresses switch signs and the critical force required to generate contacts is drastically reduced. This is likely a signature of the lubrication films giving way to roughness-induced tangential interactions that bring about load-bearing contacts in the compression axis of flow.

Multiple particle tracking study of thermally-gelling nanoemulsions.

We perform multiple particle tracking (MPT) on a thermally-gelling oil-in-water nanoemulsion system. Carboxylated and plain polystyrene probes are used to investigate the role of colloidal probe size and surface chemistry on MPT in the nanoemulsion system. As temperature increases, hydrophobic groups of PEG-based gelators (PEGDA) partition into the oil/water interface and bridge droplets. This intercolloidal attraction generates a wide variety of microstructures consisting of droplet-rich and droplet-poor phases. By tailoring the MPT colloidal probe surface chemistry, we can control the residence of probes in each domain, thus allowing us to independently probe each phase. Our results show stark differences in probe dynamics in each domain. For certain conditions, the mean squared displacement (MSD) can differ by over four orders of magnitude for the same probe size but different surface chemistry. Carboxylated probe surface chemistries result in "slippery" probes while plain polystyrene probes appear to tether to the nanoemulsion gel network. We also observe probe hopping between pores in the gel for carboxylated probes. Our approach demonstrates that probes with different surface chemistries are useful in probing the local regions of a colloidal gel and allows the measurement of local properties within structurally heterogeneous hydrogels.

Translational and rotational dynamics in dense suspensions of smooth and rough colloids.

We demonstrate that colloidal particles with surface roughness exhibit hindered rotational diffusion in quiescent dense suspensions. This is accomplished by the use of confocal microscopy and particle tracking to follow the translational and rotational dynamics of smooth and rough colloids suspended in a refractive index and density matched organic solvent. Measurement of the three-dimensional rotational diffusion is enabled by the addition of inert Janus tracers made of native colloids coated with a thin layer of aluminum. These experiments show that the mean square displacement (MSD) is unaffected by particle roughness, while the mean square angular displacement (MSAD) decreases for rough colloids at high volume fractions. Our results quantify the slowdown in the rotational dynamics of rough colloids, which is evidently due to steric frustration caused by the surface topography of the particles.

3D printing of self-assembling thermoresponsive nanoemulsions into hierarchical mesostructured hydrogels.

Spinodal decomposition and phase transitions have emerged as viable methods to generate a variety of bicontinuous materials. Here, we show that when arrested phase separation is coupled to the time scales involved in three-dimensional (3D) printing processes, hydrogels with multiple length scales spanning nanometers to millimeters can be printed with high fidelity. We use an oil-in-water nanoemulsion-based ink with rheological and photoreactive properties that satisfy the requirements of stereolithographic 3D printing. This ink is thermoresponsive and consists of poly(dimethyl siloxane) droplets suspended in an aqueous phase containing the surfactant sodium dodecyl sulfate and the cross-linker poly(ethylene glycol) dimethacrylate. Control of the hydrogel microstructure can be achieved in the printing process due to the rapid structural recovery of the nanoemulsions after large strain-rate yielding, as well as the shear thinning behavior that allows the ink to conform to the build platform of the printer. Wiper operations are used to ensure even spreading of the yield stress ink on the optical window between successive print steps. Post-processing of the printed samples is used to generate mesoporous hydrogels that serve as size-selective membranes. Our work demonstrates that nanoemulsions, which belong to a class of solution-based materials with flexible functionalities, can be printed into prototypes with complex shapes using a commercially available 3D printer with a few modifications.

Celebrating Soft Matter's 10th Anniversary: Sequential phase transitions in thermoresponsive nanoemulsions.

We report the coexistence of stress-bearing percolation with arrested phase separation in a colloidal system of thermoresponsive nanoemulsions spanning a broad range of volume fractions (0.10 ≤ ϕ ≤ 0.33) and temperatures (22 °C ≤ T ≤ 65 °C). Here, gelation is driven by short-range interdroplet polymer bridging at elevated temperatures. Direct visualization of the gel microstructure shows that nanoemulsions undergo a homogenous percolation transition prior to phase separation. Rheological characterization shows that both the percolated and the phase separated structures are capable of supporting a significant amount of elastic stress. As the system is heated, the sequential onset of these phase transitions is responsible for the unusual two-step increase in the linear viscoelasticity of the gels. In addition, we find that slowing the heating rate significantly reduces the elasticity of the gels at high temperatures. Our results suggest that the formation of metastable gelled states not only depends on the attraction strength and volume fraction of the system, but is also sensitive to the rate at which the attraction strength is increased.

Role of isostaticity and load-bearing microstructure in the elasticity of yielded colloidal gels.

We report a simple correlation between microstructure and strain-dependent elasticity in colloidal gels by visualizing the evolution of cluster structure in high strain-rate flows. We control the initial gel microstructure by inducing different levels of isotropic depletion attraction between particles suspended in refractive index matched solvents. Contrary to previous ideas from mode coupling and micromechanical treatments, our studies show that bond breakage occurs mainly due to the erosion of rigid clusters that persist far beyond the yield strain. This rigidity contributes to gel elasticity even when the sample is fully fluidized; the origin of the elasticity is the slow Brownian relaxation of rigid, hydrodynamically interacting clusters. We find a power-law scaling of the elastic modulus with the stress-bearing volume fraction that is valid over a range of volume fractions and gelation conditions. These results provide a conceptual framework to quantitatively connect the flow-induced microstructure of soft materials to their nonlinear rheology.

Role of shear-induced dynamical heterogeneity in the nonlinear rheology of colloidal gels.

We report the effect of flow-induced dynamical heterogeneity on the nonlinear elastic modulus of weakly aggregated colloidal gels that have undergone yielding by an imposed step strain deformation. The gels are comprised of sterically stabilized poly(methyl methacrylate) colloids interacting through short-ranged depletion attractions. When a step strain of magnitude varying from γ = 0.1 to 80.0 is applied to the quiescent gels, we observe the development of a bimodal distribution in the single-particle van Hove self-correlation function. This distribution is consistent with the existence of a fast and slow subpopulation of colloids within sheared gels. We evaluate the effect of incorporating the properties of the slow, rigid subpopulation of the colloids into a recent mode coupling theory for the nonlinear elasticity of colloidal gels.

Interacting collagen and tannic acid Particles: Uncovering pH-dependent rheological and thermodynamic behaviors.

HYPOTHESIS: Biomaterials such as collagen and tannic acid (TA) particles are of interest in the development of advanced hybrid biobased systems due to their beneficial therapeutic functionalities and distinctive structural properties. The presence of numerous functional groups makes both TA and collagen pH responsive, enabling them to interact via non-covalent interactions and offer tunable macroscopic properties. EXPERIMENT: The effect of pH on the interactions between collagen and TA particles is explored by adding TA particles at physiological pH to collagen at both acidic and neutral pH. Rheology, isothermal titration calorimetry (ITC), turbidimetric analysis and quartz crystal microbalance with dissipation monitoring (QCM-D) are used to study the effects. FINDINGS: Rheology results show significant increase in elastic modulus with an increase in collagen concentration. However, TA particles at physiological pH provide stronger mechanical reinforcement to collagen at pH 4 than collagen at pH 7 due to the formation of a higher extent of electrostatic interaction and hydrogen bonding. ITC results confirm this hypothesis, with larger changes in enthalpy, |ΔH|, observed when collagen is at acidic pH and |ΔH| > |TΔS| indicating enthalpy-driven collagen-TA interactions. Turbidimetric analysis and QCM-D help to identify structural differences of the collagen-TA complexes and their formation at both pH conditions.

What makes epoxy-phenolic coatings on metals ubiquitous: Surface energetics and molecular adhesion characteristics.

HYPOTHESIS: Wetting characteristics of epoxy and phenolic resins on metals depend on the molecular interactions between resins' functional groups and metal surface. Those interactions affect the practical adhesion strength of epoxy-phenolic coatings on metals. Estimation of the theoretical adhesion energies can reveal this system's microscopic adhesion mechanisms. EXPERIMENTS: Adhesion is estimated theoretically based on resins' wettability on metals, and experimentally through pull-off adhesion testing of cured coatings. The effect of various functional groups on adhesion is decoupled using epoxy and phenolic resins with different functionalities. To assess the impact of the metal passivation on adhesion, tinplated and tin-free steel substrates are used. Differences in their surface chemical composition and polarity are investigated using XPS. FINDINGS: Theoretical adhesion results reveal a superior adhesion of epoxy compared to phenolic resins. Moreover, epoxy resins having a higher content of epoxide-to-hydroxyl groups show improved theoretical and practical adhesion. The importance of epoxides in driving resins' initial adhesion on metals is attributed to the formation of direct chemical bonds with active hydrogen on metal surfaces. The adhesion of coatings on tin-free steel is found to be higher than on tinplated steel. This is associated to the increased hydroxyl fraction on tin-free steel surface leading to more hydrogen bonds formation.

Interfacial Contributions in Nanodiamond-Reinforced Polymeric Fibers.

We study the interfacial energy parameters that explain the reinforcement of polymers with nanodiamond (ND) and the development of mechanical strength of electrospun ND-reinforced composites. Thermodynamic parameters such as the wettability ratio, work of spreading and dispersion/aggregation transition are used to derive a criterion to predict the dispersibility of carboxylated ND (cND) in polymeric matrices. Such a criterion for dispersion (Dc) is applied to electrospun cND-containing poly(vinyl alcohol) (PVA), polyacrylonitrile (PAN), and polystyrene (PS) fiber composites. The shifts in glass transition temperature (ΔTg), used as a measure of polymer/cND interfacial interactions and hence the reinforcement capability of cNDs, reveal a direct correlation with the thermodynamic parameter Dc in the order of PAN < PS < PVA. Contrary to expectation, however, the tensile strength of the electrospun fibers correlates with the Dc and ΔTg only for semicrystalline polymers (PAN < PVA) while the amorphous PS displays a maximum reinforcement with cND. Such conflicting results reveal a synergy that is not captured by thermodynamic considerations alone but also factor in the contributions of polymer/cND interface stress transfer efficiency. Our findings open the possibility for tailoring the interfacial interactions in polymer-ND fiber composites to achieve maximum mechanical reinforcement.

Printable homocomposite hydrogels with synergistically reinforced molecular-colloidal networks.

The design of hydrogels where multiple interpenetrating networks enable enhanced mechanical properties can broaden their field of application in biomedical materials, 3D printing, and soft robotics. We report a class of self-reinforced homocomposite hydrogels (HHGs) comprised of interpenetrating networks of multiscale hierarchy. A molecular alginate gel is reinforced by a colloidal network of hierarchically branched alginate soft dendritic colloids (SDCs). The reinforcement of the molecular gel with the nanofibrillar SDC network of the same biopolymer results in a remarkable increase of the HHG's mechanical properties. The viscoelastic HHGs show >3× larger storage modulus and >4× larger Young's modulus than either constitutive network at the same concentration. Such synergistically enforced colloidal-molecular HHGs open up numerous opportunities for formulation of biocompatible gels with robust structure-property relationships. Balance of the ratio of their precursors facilitates precise control of the yield stress and rate of self-reinforcement, enabling efficient extrusion 3D printing of HHGs.

Colloidal gel elasticity arises from the packing of locally glassy clusters.

Colloidal gels formed by arrested phase separation are found widely in agriculture, biotechnology, and advanced manufacturing; yet, the emergence of elasticity and the nature of the arrested state in these abundant materials remains unresolved. Here, the quantitative agreement between integrated experimental, computational, and graph theoretic approaches are used to understand the arrested state and the origins of the gel elastic response. The micro-structural source of elasticity is identified by the l-balanced graph partition of the gels into minimally interconnected clusters that act as rigid, load bearing units. The number density of cluster-cluster connections grows with increasing attraction, and explains the emergence of elasticity in the network through the classic Cauchy-Born theory. Clusters are amorphous and iso-static. The internal cluster concentration maps onto the known attractive glass line of sticky colloids at low attraction strengths and extends it to higher strengths and lower particle volume fractions.