Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

Percolation of nonequilibrium assemblies of colloidal particles in active chiral liquids

The growing interest in the non-equilibrium assembly of colloidal particles in active liquids is driven by the motivation to create novel structures endowed with tunable properties unattainable within the confines of equilibrium systems. Here, we present an experimental investigation of the structural features of colloidal assemblies in active liquids of chiral E. coli. The colloidal particles form dynamic clusters due to the effective interaction mediated by active media. The activity and chirality of the swimmers strongly influence the dynamics and local ordering of colloidal particles, resulting in clusters with persistent rotation, whose structure differs significantly from those in equilibrium systems with attractive interactions, such as colloid-polymer mixtures. Our colloid-bacteria mixture displays several hallmark features of a percolation transition at a critical density, where the clusters span the system size. A closer examination of the critical exponents associated with cluster size distribution, the average cluster size, and the correlation length in the vicinity of the critical density shows deviations from the prediction of the standard continuum percolation model. Therefore, our experiments reveal a richer phase behavior of colloidal assemblies in active liquids.

Refractive-index and density-matched emulsions with programmable DNA interactions

Emulsion droplets on the colloidal length scale are a model system of frictionless compliant spheres. Direct imaging studies of the microscopic structure and dynamics of emulsions offer valuable insights into fundamental processes, such as gelation, jamming, and self-assembly. A microscope, however, can only resolve the individual droplets in a densely packed emulsion if the droplets are closely index-matched to their fluid medium. Mitigating perturbations due to gravity additionally requires the droplets to be density-matched to the medium. Creating droplets that are simultaneously index-matched and density-matched has been a long-standing challenge for the soft-matter community. The present study introduces a method for synthesizing monodisperse micrometer-sized siloxane droplets whose density and refractive index can be precisely and independently tuned by adjusting the volume fraction of three silane precursors. A systematic optimization protocol yields fluorescently labeled ternary droplets whose densities and refractive indexes match, to the fourth decimal place, those of aqueous solutions of glycerol or dimethylsiloxane. Because all of the materials in this system are biocompatible, we functionalize the droplets with DNA strands to endow them with programmed inter-droplet interactions. Confocal microscopy then reveals both the three-dimensional structure and the network of droplet-droplet contacts in a class of self-assembled droplet gels, free from gravitational effects. This experimental toolbox creates opportunities for studying the microscopic mechanisms that govern viscoelastic properties and self-assembly in soft materials.

Mechanistic understanding of nanoparticle interactions to achieve highly-ordered arrays through self-assembly for sensitive surface-enhanced Raman scattering detection of trace thiram

Over the last few decades, there is increasing worldwide concern over human health risks associated with extensive use of pesticides in agriculture. Developing excellent SERS substrate materials to achieve highly sensitive detection of pesticide residues in the food is very necessary owing to their serious threat to human health through food chains. Self-assembled metallic nanoparticles have been demonstrated to be excellent SERS substrate materials. Hence, alkanethiols-protected gold nanoparticles have been successfully prepared for forming larger-scale two-dimensional monolayer films. These films can be disassembled into a fluid state and re-assembled back to crystallized structure by controlling surface pressure. Further investigations reveal that their self-assembled structures are mainly dependent on the diameter of gold nanoparticles and ligand length. These results suggest that the size ratio of nanoparticle diameter/ligand length within the range of 4.45-2.35 facilitates the formation of highly ordered 2D arrays. Furthermore, these arrays present excellent Surface-Enhanced Raman Scattering performances in the detection of trace thiram, which can cause environmental toxicity to the soil, water, animals and result in severe damage to human health. Therefore, the current study provides an effective way for preparing monodispersed hydrophobic gold nanoparticles and forming highly ordered 2D close-packed SERS substrate materials via self-assembly to detect pesticide residues in food. We believe that, our research provides not only advanced SERS substrate materials for excellent detection performance of thiram in food, but also novel fundamental understandings of self-assembly, manipulation of nanoparticle interactions, and controllable synthesis.

In situ aggregation and early states of gelation of gold nanoparticle dispersions

The aggregation and onset of gelation of PEGylated gold nanoparticles dispersed in a glycerol-water mixture is studied by small-angle X-ray scattering and X-ray photon correlation spectroscopy. Tracking structural dynamics with sub-ms time resolution over a total experimental time of 8 hours corresponding to a time windows larger than 108 Brownian times and varying the temperature between 298 K and 266 K we can identify three regimes. First, while cooling to 275 K the particles show Brownian motion that slows down due to the increasing viscosity. Second, upon further cooling the static structure changes significantly, indicated by a broad structure factor peak. We attribute this to the formation of aggregates while the dynamics are still dominated by single-particle diffusion. Finally, the relaxation functions become more and more stretched accompanied by an increased slow down of the dynamics. At the same time the structure changes continuously indicating the onset of gelation. Our observations further suggest that the colloidal aggregation and gelation is characterized first by structural changes with a subsequent slowing down of the systems dynamics. The analysis also reveals that the details of the gelation process and the gel structure strongly depend on the thickness of the PEG-coating of the gold nanoparticles.

Dilute gel networks vs. clumpy gels in colloidal systems with a competition between repulsive and attractive interactions

Using Brownian dynamics simulations we study gel-forming colloidal systems. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We apply reduction algorithms and observe that dilute networks and dense gels differ in the way structural properties like the thickness of strands emerge. We also analyze the percolation behavior and find that two different regimes of percolation exist which might be responsible for structural differences. In dilute networks we confirm that solidity is mainly a consequence of pentagonal bipyramids forming in the network. In dense gels, tetrahedral structures also influence solidity.

Direct observation of phase transitions in truncated tetrahedral microparticles under quasi-2D confinement

Colloidal crystals are used to understand fundamentals of atomic rearrangements in condensed matter and build complex metamaterials with unique functionalities. Simulations predict a multitude of self-assembled crystal structures from anisotropic colloids, but these shapes have been challenging to fabricate. Here, we use two-photon lithography to fabricate Archimedean truncated tetrahedrons and self-assemble them under quasi-2D confinement. These particles self-assemble into a hexagonal phase under an in-plane gravitational potential. Under additional gravitational potential, the hexagonal phase transitions into a quasi-diamond two-unit basis. In-situ imaging reveal this phase transition is initiated by an out-of-plane rotation of a particle at a crystalline defect and causes a chain reaction of neighboring particle rotations. Our results provide a framework of studying different structures from hard-particle self-assembly and demonstrates the ability to use confinement to induce unusual phases.

Variance and higher moments in the sigmoidal self-assembly of branched fibrils

Self-assembly of functional branched filaments, such as actin filaments and microtubules, or dysfunctional ones, such as amyloid fibrils, plays important roles in many biological processes. Here, based on the master equation approach, we study the kinetics of the formation of the branched fibrils. In our model, a branched fibril has one mother branch and several daughter branches. A daughter branch grows from the side of a pre-existing mother branch or daughter branch. In our model, we consider five basic processes for the self-assembly of the branched filaments, namely, the nucleation, the dissociation of the primary nucleus of fibrils, the elongation, the fragmentation, and the branching. The elongation of a mother branch from two ends and the elongation of a daughter branch from two ends can, in principle, occur with four different rate constants associated with the corresponding tips. This leads to a pronounced impact of the directionality of growth on the kinetics of the self-assembly. Here, we have unified and generalized our four previously presented models of branched fibrillogenesis in a single model. We have obtained a system of non-linear ordinary differential equations that give the time evolution of the polymer numbers and the mass concentrations along with the higher moments as observable quantities.

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.

Critical-Like Gelation Dynamics in Cellulose Nanocrystal Suspensions

We use time-resolved mechanical spectroscopy to offer a detailed picture of the gelation dynamics of cellulose nanocrystal (CNC) suspensions following shear cessation in the presence of salt. CNCs are charged, rodlike colloids that self-assemble into various phases, including physical gels serving as soft precursors for biosourced composites. Here, a series of linear viscoelastic spectra acquired across the sol-gel transition of CNC suspensions are rescaled onto two master curves that correspond to a viscoelastic liquid state prior to gelation and to a soft solid state after gelation. These two states are separated by a critical gel point, where all rescaling parameters diverge in an asymmetric fashion yet with exponents that obey hyperscaling relations consistent with previous works on isotropic colloids and polymer gels. Upon varying the salt content, we further show that these critical-like dynamics result in both time-connectivity and time-concentration superposition principles.

Structural Color from Cellulose Nanocrystals or Chitin Nanocrystals: Self-Assembly, Optics, and Applications

Widespread concerns over the impact of human activity on the environment have resulted in a desire to replace artificial functional materials with naturally derived alternatives. As such, polysaccharides are drawing increasing attention due to offering a renewable, biodegradable, and biocompatible feedstock for functional nanomaterials. In particular, nanocrystals of cellulose and chitin have emerged as versatile and sustainable building blocks for diverse applications, ranging from mechanical reinforcement to structural coloration. Much of this interest arises from the tendency of these colloidally stable nanoparticles to self-organize in water into a lyotropic cholesteric liquid crystal, which can be readily manipulated in terms of its periodicity, structure, and geometry. Importantly, this helicoidal ordering can be retained into the solid-state, offering an accessible route to complex nanostructured films, coatings, and particles. In this review, the process of forming iridescent, structurally colored films from suspensions of cellulose nanocrystals (CNCs) is summarized and the mechanisms underlying the chemical and physical phenomena at each stage in the process explored. Analogy is then drawn with chitin nanocrystals (ChNCs), allowing for key differences to be critically assessed and strategies toward structural coloration to be presented. Importantly, the progress toward translating this technology from academia to industry is summarized, with unresolved scientific and technical questions put forward as challenges to the community.

Compound effect and mechanism of oxidative damage induced by nanoplastics and benzo [a] pyrene

Nanoplastics and polycyclic aromatic hydrocarbons (PAHs) are ubiquitous in soil environments. In order to objectively evaluate the toxic interaction between polystyrene nanoplastics (PS NPs) and benzo [a] pyrene (BaP), oxidative damage at the level of earthworm cells and biomacromolecules was investigated by experiments combined with molecular dynamics simulation. Studies on cells reveal that PS NPs and BaP had synergistic toxicity when it came to causing oxidative stress. Cellular reactive oxygen species (ROS) levels under combined pollutant exposure were 24% and 19% higher, respectively than when PS NPs and BaP were exposed alone (compared to the blank group). In addition, BaP and PS NPs inhibited the ability of CAT to decompose H2O2 by affecting the structure of the proximal amino acid Tyr 357 in the active center of CAT, which exacerbated oxidative stress to a certain extent. Therefore, the synergistic toxic effect of BaP and PS NPs is due to the mutual complement of the two to the induction of protein structural looseness, and the strengthening of the stability of the conjugate (CAT-BaP-PS) under the weak interaction. This work provides a new perspective and approach on how to talk about the toxicity of combined pollutants.

Molecular-Level Relation between the Intraparticle Glass Transition Temperature and the Stability of Colloidal Suspensions

In many colloidal suspensions, the dispersed colloidal particles are amorphous solids, resulting from vitrification. A crucial open problem is understanding how colloidal stability is affected by the intraparticle glass transition. By dealing with the latter process from a solid-state perspective, we estabilish a proportionality relation between the intraparticle glass transition temperature, Tg, and the Hamaker constant, AH, of a generic suspension of nanoparticles. It follows that Tg can be used as a convenient parameter (alternative to AH) for controlling the stability of colloidal systems. Within the Derjaguin-Landau-Verwey-Overbeek theory, we show that the novel relationship, connecting Tg to AH, implies the critical coagulation ionic strength to be a monotonically decreasing function of Tg. We connect our predictions to recent experimental findings.

General theory of the viscosity of liquids and solids from nonaffine particle motions

A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.

Evidences of Conformal Invariance in 2D Rigidity Percolation

The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid connected component, or cluster. As a second-order phase transition it exhibits a scale invariant critical point, at which the rigid clusters are random fractals. We show, using numerical analysis, that these clusters are also conformally invariant, and we use conformal field theory to predict the form of universal finite-size effects. Furthermore, although connectivity and rigidity percolation are usually thought to be of fundamentally different natures, we provide evidence of unexpected similarities between the statistical properties of their random clusters at criticality. Our work opens a new research avenue through the application of the powerful 2D conformal field theory tools to understand the critical behavior of a wide range of physical and biological materials exhibiting such a mechanical transition.

Colloidal gelation with non-sticky particles

Colloidal gels are widely applied in industry due to their rheological character-no flow takes place below the yield stress. Such property enables gels to maintain uniform distribution in practical formulations; otherwise, solid components may quickly sediment without the support of gel matrix. Compared with pure gels of sticky colloids, therefore, the composites of gel and non-sticky inclusions are more commonly encountered in reality. Through numerical simulations, we investigate the gelation process in such binary composites. We find that the non-sticky particles not only confine gelation in the form of an effective volume fraction, but also introduce another lengthscale that competes with the size of growing clusters in gel. The ratio of two key lengthscales in general controls the two effects. Using different gel models, we verify such a scenario within a wide range of parameter space, suggesting a potential universality in all classes of colloidal composites.

Comparative study of the dynamics of colloidal glass and gel

We investigate and compare the difference in the dynamics of two arrested states: colloidal glass and colloidal gel. Real-space experiments reveal two distinct nonergodicity origins for their slow dynamics, namely, cage effects for the glass and attractive bondings for the gel. Such distinct origins lead to a faster decay of the correlation function and a smaller nonergodicity parameter of the glass than those of the gel. We also find that the gel exhibits stronger dynamical heterogeneity compared with the glass due to the greater correlated motions in the gel. Moreover, a logarithmic decay in the correlation function is observed as the two nonergodicity origins merge, consistent with the mode coupling theory.

Percolation transitions of confinement-induced layering and intralayer structural orders in three-dimensional Yukawa liquids

The disorder-order transitions of layering and intralayer structural orders of three-dimensional Yukawa liquids, under the enhanced confinement effect with decreasing normal distance z to the confinement boundary, is investigated numerically. The liquid between the two flat boundaries is segmented into many slabs parallel to the boundary, with the same slab width as the layer width. In each slab, particle sites are binarized into sites with layering order (LOSs)/ layering disorder (LDSs) and with intralayer structural order (SOSs)/disorder (SDSs). It is found that with decreasing z, a small fraction of LOSs starts to heterogeneously emerge in the form of small clusters in the slab, followed by the emergence of the large percolating LOS clusters spanning over the system. The smooth rapid rise of the fraction of LOSs from small values followed by their gradual saturations, and the scaling behavior of multiscale LOS clustering, are similar to those of the nonequilibrium systems governed by the percolation theory. The disorder-order transition of intraslab structural ordering also exhibits a similar generic behavior as that of layering with the same transition slab number. The spatial fluctuations of local layering order and local intralayer structural order are uncorrelated in the bulk liquid and the outmost layer next to the boundary. Approaching the percolating transition slab, their correlation gradually increases to the maximum.

Memory in aging colloidal gels with time-varying attraction

We report a combined rheology, x-ray photon correlation spectroscopy, and modeling study of gel formation and aging in suspensions of nanocolloidal spheres with volume fractions of 0.20 and 0.43 and with a short-range attraction whose strength is tuned by changing temperature. Following a quench from high temperature, where the colloids are essentially hard spheres, to a temperature below the gel point, the suspensions form gels that undergo aging characterized by a steadily increasing elastic shear modulus and slowing, increasingly constrained microscopic dynamics. The aging proceeds at a faster rate for stronger attraction strength. When the attraction strength is suddenly lowered during aging, the gel properties evolve non-monotonically in a manner resembling the Kovacs effect in glasses, in which the modulus decreases and the microscopic dynamics become less constrained for a period before more conventional aging resumes. Eventually, the properties of the gel following the decrease in attraction strength converge to those of a gel that has undergone aging at the lower attraction strength throughout. The time scale of this convergence increases as a power law with the age at which the attraction strength is decreased and decreases exponentially with the magnitude of the change in attraction. A model for gel aging in which particles attach and detach from the gel at rates that depend on their contact number reproduces these trends and reveals that the non-monotonic behavior results from the dispersion in the rates that the populations of particles with different contact number adjust to the new attraction strength.

Controlling Kinetic Pathways in Demixing Microgel-Micelle Mixtures

We investigate the temperature-dependent phase behavior of mixtures of poly(N-isopropylacrylamide) (pNIPAM) microgel colloids and a triblock copolymer (PEO-PPO-PEO) surfactant. Usually, gelation in these systems results from an increase in temperature. Here we investigate the role of the heating rate, and surprisingly, we find that this causes the mechanism of aggregation to change from one which is driven by depletion of the microgels by the micelles at low temperatures to the association of the two species at high temperatures. We thus reveal two competing mechanisms for attractions between the microgel particles which can be controlled by changing the heating rate. We use this heating-rate-dependent response of the system to access multiple structures for the same system composition. Samples were found to demix into phases rich and poor in microgel particles at temperatures below 33 °C, under conditions where the microgels particles are partially swollen. Under rapid heating full demixing is bypassed, and gel networks are formed instead. The temperature history of the sample, therefore, allows for kinetic selection between different final structures, which may be metastable.

Hub-collision avoidance and leaf-node options algorithm for fractal dimension and renormalization of complex networks

The box-covering method plays a fundamental role in the fractal property recognition and renormalization analysis of complex networks. This study proposes the hub-collision avoidance and leaf-node options (HALO) algorithm. In the box sampling process, a forward sampling rule (for avoiding hub collisions) and a reverse sampling rule (for preferentially selecting leaf nodes) are determined for bidirectional network traversal to reduce the randomness of sampling. In the box selection process, the larger necessary boxes are preferentially selected to join the solution by continuously removing small boxes. The compact-box-burning (CBB) algorithm, the maximum-excluded-mass-burning (MEMB) algorithm, the overlapping-box-covering (OBCA) algorithm, and the algorithm for combining small-box-removal strategy and maximum box sampling with a sampling density of 30 (SM30) are compared with HALO in experiments. Results on nine real networks show that HALO achieves the highest performance score and obtains 11.40%, 7.67%, 2.18%, and 8.19% fewer boxes than the compared algorithms, respectively. The algorithm determinism is significantly improved. The fractal dimensions estimated by covering four standard networks are more accurate. Moreover, different from MEMB or OBCA, HALO is not affected by the tightness of the hubs and exhibits a stable performance in different networks. Finally, the time complexities of HALO and the compared algorithms are all O(N²), which is reasonable and acceptable.

Experimental characterization of colloidal silica gel for water conformance control in oil reservoirs

High water production in oil fields is an area of concern due to economic issues and borehole/wellhead damages. Colloidal gels can be a good alternative to polymers to address this as they can tolerate harsh oil reservoir conditions. A series of bottle tests with different silica and NaCl concentrations were first conducted. The gelation time, cation valence, rheology, and viscosity were investigated to characterize the gels. The applicability of solid gels in porous media was finally inspected in a dual-patterned glass micromodel. Bottle test results showed that increasing NaCl concentration at a constant silica concentration can convert solid gels into two-phase gels and then viscous suspensions. Na⁺ replacement with Mg²⁺ resulted a distinctive behaviour probably due to higher coagulating ability of Mg²⁺. Rheology and viscosity results agreed with gelation times: gel with shortest gelation time had the highest viscosity and storage/loss modulus but was not the most elastic one. Water injection into glass micromodel half-saturated with crude oil and solid gel proved that the gel is strong against pressure gradients applied by injected phase which is promising for water conformance controls. The diverted injected phase recorded an oil recovery of 53% which was not feasible without blocking the water zone.

Alginate-Based Hydrogels and Tubes, as Biological Macromolecule-Based Platforms for Peripheral Nerve Tissue Engineering: A Review

Unlike the central nervous system, the peripheral nervous system (PNS) has an inherent capacity to regenerate following injury. However, in the case of large nerve defects where end-to-end cooptation of two nerve stumps is not tension-free, autologous nerve grafting is often utilized to bridge the nerve gaps. To address the challenges associated with autologous nerve grafting, neural guidance channels (NGCs) have been successfully translated into clinic. Furthermore, hydrogel-based drug delivery systems have been extensively studied for the repair of PNS injuries. There are numerous biomaterial options for the production of NGCs and hydrogels. Among different candidates, alginate has shown promising results in PNS tissue engineering. Alginate is a naturally occurring polysaccharide which is biocompatible, non-toxic, non-immunogenic, and possesses modifiable properties. In the current review, applications, challenges, and future perspectives of alginate-based NGCs and hydrogels in the repair of PNS injuries will be discussed.

On the dynamically arrested states of equilibrium and non-equilibrium gels: a comprehensive Brownian dynamics study

In this work a systematic study over a wide number of final thermodynamic states for two gel-forming liquids was performed. Such two kind of gel formers are distinguished by their specific interparticle interaction potential. We explored several thermodynamic states determining the thermodynamic, structural and dynamic properties of both liquids after a sudden temperature change. The thermodynamic analysis allows to identify that the liquid with short range attraction and long range repulsion lacks of a stable gas-liquid phase separation liquid, in contrast with the liquid with short range attractions. Thus, although for some thermodynamic states the structural behavior, measured by the static structure factor, is similar to and characteristic of the gel phase, for the short range attractive fluid the gel phase is a consequence of a spinodal decomposition process. In contrast, gelation in the short range attraction and long range repulsion liquid is not due to a phase separation. We also analyze the similarities and differences of the dynamic behavior of both systems through the analysis of the mean square displacement, the self part of the intermediate scattering function, the diffusion coefficient and theαrelaxation time. Finally, using one of the main results of the non-equilibrium self-consistent generalized Langevin equation theory (NE-SCGLE), we determine the dynamic arrest phase diagram in the volume fraction and temperature (φvsT) plane.

Tuning local microstructure of colloidal gels by ultrasound-activated deformable inclusions

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.

Microscopic structural origin behind slowing down of colloidal phase separation approaching gelation

The gelation of colloidal particles interacting through a short-range attraction is widely recognized as a consequence of the dynamic arrest of phase separation into colloid-rich and solvent-rich phases. However, the microscopic origin behind the slowing down and dynamic arrest of phase separation remains elusive. In order to access microscopic structural changes through the entire process of gelation in a continuous fashion, we used core–shell fluorescent colloidal particles, laser scanning confocal microscopy, and a unique experimental protocol that allows us to initiate phase separation instantaneously and gently. Combining these enables us to track the trajectories of individual particles seamlessly during the whole phase-separation process from the early stage to the late arresting stage. We reveal that the enhancement of local packing and the resulting formation of locally stable rigid structures slow down the phase-separation process and arrest it to form a gel with an average coordination number of z = 6–7. This result supports a mechanical perspective on the dynamic arrest of sticky-sphere systems based on the microstructure, replacing conventional explanations based on the macroscopic vitrification of the colloid-rich phase. Our findings illuminate the microscopic mechanisms behind the dynamic arrest of colloidal phase separation, the emergence of mechanical rigidity, and the stability of colloidal gels.

Polyurea Aerogels: Synthesis, Material Properties, and Applications

Polyurea is an isocyanate derivative, and comprises the basis for a well-established class of polymeric aerogels. Polyurea aerogels are prepared either via reaction of multifunctional isocyanates with multifunctional amines, via reaction of multifunctional isocyanates and water, or via reaction of multifunctional isocyanates and mineral acids. The first method is the established one for the synthesis of polyurea, the third is a relatively new method that yields polyurea doped with metal oxides in one step, while the reaction of isocyanates with water has become the most popular route to polyurea aerogels. The intense interest in polyurea aerogels can be attributed in part to the low cost of the starting materials-especially via the water method-in part to the extremely broad array of nanostructural morphologies that allow study of the nanostructure of gels as a function of synthetic conditions, and in part to the broad array of functional properties that can be achieved even within a single chemical composition by simply adjusting the synthetic parameters. In addition, polyurea aerogels based on aromatic isocyanates are typically carbonizable materials, making them highly competitive alternatives to phenolic aerogels as precursors of carbon aerogels. Several types of polyurea aerogels are already at different stages of commercialization. This article is a comprehensive review of all polyurea-based aerogels, including polyurea-crosslinked oxide and biopolymer aerogels, from a fundamental nanostructure-material properties perspective, as well as from an application perspective in thermal and acoustic insulation, oil adsorption, ballistic protection, and environmental cleanup.

Protein microparticles visualize the contact network and rigidity onset in the gelation of model proteins

Protein aggregation into gel networks is of immense importance in diverse areas from food science to medical research; however, it remains a grand challenge as the underlying molecular interactions are complex, difficult to access experimentally, and to model computationally. Early stages of gelation often involve protein aggregation into protein clusters that later on aggregate into a gel network. Recently synthesized protein microparticles allow direct control of these early stages of aggregation, decoupling them from the subsequent gelation stages. Here, by following the gelation of protein microparticles directly at the particle scale, we elucidate in detail the emergence of a percolating structure and the onset of rigidity as measured by microrheology. We find that the largest particle cluster, correlation length, and degree of polymerization all diverge with power laws, while the particles bind irreversibly indicating a nonequilibrium percolation process, in agreement with recent results on weakly attractive colloids. Concomitantly, the elastic modulus increases in a power-law fashion as determined by microrheology. These results give a consistent microscopic picture of the emergence of rigidity in a nonequilibrium percolation process that likely underlies the gelation in many more systems such as proteins, and other strongly interacting structures originating from (bio)molecules.

The Use of the ATD Technique to Measure the Gelation Time of Epoxy Resins

In this paper, we investigated the thermodynamics of the resin curing process, when it was a part of composition with graphite powder and cut carbon fibers, to precisely determine the time and temperature of gelation. The material for the research is a set of commercial epoxy resins with a gelation time not exceeding 100 min. The curing process was characterized for the neat resins and for resins with 10% by weight of flake graphite and cut carbon fibers. The results recorded in the analysis of temperature derivative (ATD) method unequivocally showed that the largest first derivative registered during the test is the gel point of the resin. The innovative approach to measuring the gelation time of resins facilitates the measurements while ensuring the stability of the curing process compared to the normative tests that introduce mechanical interaction. In addition, it was found during the research that the introduction of 10% by weight of carbon particles in the form of graphite and cut carbon fibers rather shortens the gelation time and lowers the temperature peak due to the effective absorption and storage of heat from the cross-linking system. The inhibiting (or accelerating) action of fillers is probably dependent on chemical activity of the cross-linking system.

Revealing viscoelastic bending relaxation dynamics of isolated semiflexible colloidal polymers

The viscoelastic properties of filaments and biopolymers play a crucial role in soft and biological materials from biopolymer networks to novel synthetic metamaterials. Colloidal particles with specific valency allow mimicking polymers and more complex molecular structures at the colloidal scale, offering direct observation of their internal degrees of freedom. Here, we elucidate the time-dependent viscoelastic response in the bending of isolated semi-flexible colloidal polymers, assembled from dipatch colloidal particles by reversible critical Casimir forces. By tuning the patch-patch interaction strength, we adjust the polymers' viscoelastic properties, and follow spontaneous bending modes and their relaxation directly on the particle level. We find that the elastic response is well described by that of a semiflexible rod with persistence length of order 1000 μm, tunable by the critical Casimir interaction strength. We identify the viscous relaxation on longer timescales to be due to internal friction, leading to a wavelength-independent relaxation time similar to single biopolymers, but in the colloidal case arising from the contact mechanics of the bonded patches. These tunable mechanical properties of assembled colloidal filaments open the door to "colloidal architectures", rationally designed (network) structures with desired topology and mechanical properties.

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.

Real space analysis of colloidal gels: triumphs, challenges and future directions

Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.

Life and death of colloidal bonds control the rate-dependent rheology of gels

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.

Structural and dynamical properties of dilute gel networks in colloid-polymer mixtures

The competition of short-ranged depletion attraction and long-ranged repulsion between colloidal particles in colloid-polymer mixtures leads to the formation of heterogeneous gel-like structures. Our special focus will be on the states where the colloids arrange in thin strands that span the whole system and that we will refer to as dilute gel networks. These states occur at low packing fractions for attractions that are stronger than those at both the binodal line of the equilibrium gas-liquid phase separation and the directed percolation transition line. By using Brownian dynamics simulations, we explore the formation, structure, and aging dynamics of dilute gel networks. The essential connections in a dilute gel network are determined by constructing reduced networks. We compare the observed properties to those of clumpy gels or cluster fluids. Our results demonstrate that both the structure and the (often slow) dynamics of the stable or meta-stable heterogeneous states in colloid-polymer mixtures possess distinct features on various length and time scales and thus are richly diverse.

Time-connectivity superposition and the gel/glass duality of weak colloidal gels

Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time-connectivity superposition principle a series of rapidly acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times it appears glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time-connectivity superposition principle for this class of soft glassy materials and provide a compact description for the dichotomous viscoelastic nature of weak colloidal gels.

An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation

Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density n c = 3.67 × 10-3 Å-2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density n g = 8.40 × 10-3 Å-2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension d F < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < n c, subdiffusive for n c ≤ n < n g, and blocked for n ≥ n g. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.

Directionality of growth and kinetics of branched fibril formation

The self-assembly of fibrils is a subject of intense interest, primarily due to its relevance to the formation of pathological structures. Some fibrils develop branches via the so-called secondary nucleation. In this paper, we use the master equation approach to model the kinetics of formation of branched fibrils. In our model, a branched fibril consists of one mother branch and several daughter branches. We consider five basic processes of fibril formation, namely, nucleation, elongation, branching, fragmentation, and dissociation of the primary nucleus of fibrils into free monomers. Our main focus is on the effect of the directionality of growth on the kinetics of fibril formation. We consider several cases. At first, the mother branch may elongate from one or from both ends, while the daughter branch elongates only from one end. We also study the case of branched fibrils with bidirectionally growing daughter branches, tangentially to the main stem, which resembles the intertwining process. We derive a set of ordinary differential equations for the moments of the number concentration of fibrils, which can be solved numerically. Assuming that the primary nucleus of fibrils dissociates with the fragmentation rate, in the limit of the zero branching rate, our model reproduces the results of a previous model that considers only the three basic processes of nucleation, elongation, and fragmentation. We also use the experimental parameters for the fibril formation of Huntingtin fragments to investigate the effect of unidirectional vs bidirectional elongation of the filaments on the kinetics of fibrillogenesis.

Nonequilibrium master kinetic equation modeling of colloidal gelation

We present a detailed study of the kinetic cluster growth process during gelation of weakly attractive colloidal particles by means of experiments on critical Casimir attractive colloidal systems, simulations, and analytical theory. In the experiments and simulations, we follow the mean coordination number of the particles during the growth of clusters to identify an attractive-strength independent cluster evolution as a function of mean coordination number. We relate this cluster evolution to the kinetic attachment and detachment rates of particles and particle clusters. We find that single-particle detachment dominates in the relevant weak attractive-strength regime, while association rates are almost independent of the cluster size. Using the limit of single-particle dissociation and size-independent association rates, we solve the master kinetic equation of cluster growth analytically to predict power-law cluster mass distributions with exponents -3/2 and -5/2 before and after gelation, respectively, which are consistent with the experimental and simulation data. These results suggest that the observed critical Casimir-induced gelation is a second-order nonequilibrium phase transition (with broken detailed balance). Consistent with this scenario, the size of the largest cluster is observed to diverge with power-law exponent according to three-dimensional percolation on approaching the critical mean coordination number.