Evaporation-Induced Polyelectrolyte Complexation: The Role of Base Volatility and Cosolvents.

Film formation is a vital step for coating applications where a homogeneous, defect-free solid phase should be obtained, starting from a liquid casting formulation. Recently, an alternative waterborne-coating approach was proposed, based on the formation of a polyelectrolyte complex film. In this approach, an evaporating base induces a pH change during drying that initiates the complexation of oppositely charged polyelectrolytes, followed by further densification. In previous studies, ammonia was used as the evaporative base, leading to relatively fast evaporation and resulting in films showing significant brittleness, which tended to crack at low relative humidity or larger thicknesses. We hypothesize that slower complexation and/or evaporation can reduce the problematic stress build-up in the prepared polyelectrolyte complex coatings. For this reason, we studied the changes in the film formation process when there are different bases and cosolvents. We found that reducing the evaporation rate by changing ammonia to the slower evaporating dimethylamine or by adding DMSO as a cosolvent, led to less internal stress build-up during film formation, which could be beneficial for film application. Indeed, films prepared with ammonia showed cracking after 1 h, while films prepared with dimethylamine only showed cracking after one month. The fast evaporation of ammonia was also found to cause a temporary turbid phase, indicating phase separation, while for the slower evaporating bases, this did not occur. All prepared films remained sensitive to humidity, which poses the next challenge for these promising coatings.

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions.

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

Cross-linker Mobility Governs Fracture Behavior of Catch-Bonded Networks.

While most chemical bonds weaken under the action of mechanical force (called slip bond behavior), nature has developed bonds that do the opposite: their lifetime increases as force is applied. While such catch bonds have been studied quite extensively at the single molecule level and in adhesive contacts, recent work has shown that they are also abundantly present as crosslinkers in the actin cytoskeleton. However, their role and the mechanism by which they operate in these networks have remained unclear. Here, we present computer simulations that show how polymer networks crosslinked with either slip or catch bonds respond to mechanical stress. Our results reveal that catch bonding may be required to protect dynamic networks against fracture, in particular for mobile linkers that can diffuse freely after unbinding. While mobile slip bonds lead to networks that are very weak at high stresses, mobile catch bonds accumulate in high stress regions and thereby stabilize cracks, leading to a more ductile fracture behavior. This allows cells to combine structural adaptivity at low stresses with mechanical stability at high stresses.

Quantitative imaging methods for heterogeneous multi-component films.

The drying of multi-component dispersions is a common phenomenon in a variety of everyday applications, including coatings, inks, processed foods, and cosmetics. As the solvent evaporates, the different components may spontaneously segregate laterally and/or in depth, which can significantly impact the macroscopic properties of the dried film. To obtain a quantitative understanding of these processes, high-resolution analysis of segregation patterns is crucial. Yet, current state-of-the-art methods are limited to transparent, non-deformable labeled colloids, limiting their applicability. In this study, we employ three techniques that do not require customized samples, as their imaging contrast relies on intrinsic variations in the chemical nature of the constituent species: confocal Raman microscopy, cross-sectional Raman microscopy, and a combination of scanning electron microscopy and energy dispersive X-ray analysis (SEM-EDX). For broad accessibility, we offer a thorough guide to our experimental steps and data analysis methods. We benchmark the capabilities on a film that dries homogeneously at room temperature but exhibits distinct segregation features at elevated temperature, notably self-stratification, i.e., autonomous layer formation, due to a colloidal size mismatch. Confocal Raman microscopy offers a direct means to visualize structures in three dimensions without pre-treatment, its accuracy diminishes deeper within the film, making cross-sectional Raman imaging and SEM-EDX better options. The latter is the most elaborate method, yet we show that it can reveal the most subtle and small-scale microseparation of the two components in the lateral direction. This comparative study assists researchers in choosing and applying the most suitable technique to quantify structure formation in dried multi-component films.

Spatially heterogenous dynamics in colloidal gels during syneresis.

Syneresis, the compaction of a material accompanied by fluid expulsion, is a typical mechanical instability which exists among colloidal gel based materials and that negatively affects the quality of relevant applications. We shed light onto the internal dynamics of model colloidal gels undergoing syneresis using Laser Speckle Imaging (LSI). The resulting dynamical maps capture the distinct differences in spatial and temporal relaxation patterns between colloidal gels comprising solid and liquid particles. This indicates different mechanisms of syneresis between the two systems and highlights the importance of the constituent particles and their mobile or restrictive interfaces in the mechanical relaxation of the colloidal gels during syneresis.

Connectivity and plasticity determine collagen network fracture.

Collagen forms the structural scaffold of connective tissues in all mammals. Tissues are remarkably resistant against mechanical deformations because collagen molecules hierarchically self-assemble in fibrous networks that stiffen with increasing strain. Nevertheless, collagen networks do fracture when tissues are overloaded or subject to pathological conditions such as aneurysms. Prior studies of the role of collagen in tissue fracture have mainly focused on tendons, which contain highly aligned bundles of collagen. By contrast, little is known about fracture of the orientationally more disordered collagen networks present in many other tissues such as skin and cartilage. Here, we combine shear rheology of reconstituted collagen networks with computer simulations to investigate the primary determinants of fracture in disordered collagen networks. We show that the fracture strain is controlled by the coordination number of the network junctions, with less connected networks fracturing at larger strains. The hierarchical structure of collagen fine-tunes the fracture strain by providing structural plasticity at the network and fiber level. Our findings imply that low connectivity and plasticity provide protective mechanisms against network fracture that can optimize the strength of biological tissues.

Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations.

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. In addition, in colloidal gels, an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.

Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness.

By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point and when the rupture thresholds are small. However, irrespective of network and spring properties, a more brittle fracture is observed upon increasing system size. Differently from most of the fracture descriptors, the maximum stress drop, a proxy for brittleness, displays a universal nonmonotonic dependence on system size. Based on this uncommon trend it is possible to identify the characteristic system size L^{*} at which brittleness kicks in. The more the disorder in network connectivity or in spring thresholds, the larger L^{*}. Finally, we speculate how this size-induced brittleness is influenced by thermal fluctuations.

The role of temperature in the rigidity-controlled fracture of elastic networks.

We study the influence of thermal fluctuations on the fracture of elastic networks, via simulations of the uniaxial extension of central-force spring networks with varying rigidity. Studying their failure response, both at the macroscopic and microscopic level, we find that an increase in temperature corresponds to a more homogeneous stress (re)distribution and induces thermally activated failure of springs. As a consequence, the material strength decreases upon increasing temperature, the microscopic damage spreads over a larger area and a more ductile fracture process is observed. These effects are modulated by network rigidity and can therefore be tuned via the network connectivity and the rupture threshold of the springs. Knowledge of the interplay between temperature and rigidity improves our understanding of the fracture of elastic network materials, such as (biological) polymer networks, and can help to refine design principles for tough soft materials.

Plasticity in colloidal gel strands.

Colloidal gels are space-spanning networks of aggregated particles. The mechanical response of colloidal gels is governed, to a large extent, by the properties of the individual gel strands. To study how colloidal gels respond to repeated deformations, we perform Brownian dynamics simulations on single strands of aggregated colloidal particles. While current models assume that gel failure is due to the brittle rupture of gel strands, our simulations show that gel strands undergo large plastic deformations prior to breaking. Rearrangement of particles within the strands leads to plastic lengthening and softening of the strands, which may ultimately lead to strand necking and ductile failure. This failure mechanism occurs irrespective of the thickness and length of the strands and the range and strength of the interaction potential. Rupture of gel strands is more likely for long and thin strands and for a long-ranged interaction potential.

Gravity-driven syneresis in model low-fat mayonnaise.

Low-fat food products often contain natural, edible polymers to retain the desired mouth feel and elasticity of their full-fat counterparts. This type of product, however, can suffer from syneresis: densification due to the expulsion of fluid. Gaining insight into the physical principles governing syneresis in such soft hybrid dispersions remains a challenge from a theoretical perspective, as experimental data are needed to establish a basis. We record non-accelerated syneresis in a model system for low-fat mayonnaise: a colloid polymer mixture, consisting of oil in water emulsion with starch in the aqueous phase. We find the flow rate of expelled fluid to be proportional to the difference in hydrostatic pressure over the system. The osmotic pressure of the added starch, while being higher than the hydrostatic pressure, does not prevent syneresis because the soluble starch is lost to the expelled fluid. From these findings, we conclude that forced syneresis in these systems can be described as a gravity-driven porous flow through the densely packed emulsion, explainable with a model based on Darcy's law.

Tuning the Interactions in Multiresponsive Complex Coacervate-Based Underwater Adhesives.

In this work, we report the systematic investigation of a multiresponsive complex coacervate-based underwater adhesive, obtained by combining polyelectrolyte domains and thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) units. This material exhibits a transition from liquid to solid but, differently from most reactive glues, is completely held together by non-covalent interactions, i.e., electrostatic and hydrophobic. Because the solidification results in a kinetically trapped morphology, the final mechanical properties strongly depend on the preparation conditions and on the surrounding environment. A systematic study is performed to assess the effect of ionic strength and of PNIPAM content on the thermal, rheological and adhesive properties. This study enables the optimization of polymer composition and environmental conditions for this underwater adhesive system. The best performance with a work of adhesion of 6.5 J/m2 was found for the complex coacervates prepared at high ionic strength (0.75 M NaCl) and at an optimal PNIPAM content around 30% mol/mol. The high ionic strength enables injectability, while the hydrated PNIPAM domains provide additional dissipation, without softening the material so much that it becomes too weak to resist detaching stress.

Strand Plasticity Governs Fatigue in Colloidal Gels.

The repeated loading of a solid leads to microstructural damage that ultimately results in catastrophic material failure. While posing a major threat to the stability of virtually all materials, the microscopic origins of fatigue, especially for soft solids, remain elusive. Here we explore fatigue in colloidal gels as prototypical inhomogeneous soft solids by combining experiments and computer simulations. Our results reveal how mechanical loading leads to irreversible strand stretching, which builds slack into the network that softens the solid at small strains and causes strain hardening at larger deformations. We thus find that microscopic plasticity governs fatigue at much larger scales. This gives rise to a new picture of fatigue in soft thermal solids and calls for new theoretical descriptions of soft gel mechanics in which local plasticity is taken into account.

Linking slow dynamics and microscopic connectivity in dense suspensions of charged colloids.

The quest to unravel the nature of the glass transition, where the viscosity of a liquid increases by many orders of magnitude, while its static structure remains largely unaffected, remains unresolved. While various structural and dynamical precursors to vitrification have been identified, a predictive and quantitative description of how subtle changes at the microscopic scale give rise to the steep growth in macroscopic viscosity is missing. It was recently proposed that the presence of long-lived bonded structures within the liquid may provide the long-sought connection between local structure and global dynamics. Here we directly observe and quantify the connectivity dynamics in liquids of charged colloids en route to vitrification using three-dimensional confocal microscopy. We determine the dynamic structure from the real-space van Hove correlation function and from the particle trajectories, providing upper and lower bounds on connectivity dynamics. Based on these data, we extend Dyre's model for the glass transition to account for particle-level structural dynamics; this results in a microscopic expression for the slowing down of relaxations in the liquid that is in quantitative agreement with our experiments. These results indicate how vitrification may be understood as a dynamical connectivity transition with features that are strongly reminiscent of rigidity percolation scenarios.

Highly cooperative stress relaxation in two-dimensional soft colloidal crystals.

Stress relaxation in crystalline solids is mediated by the formation and diffusion of defects. Although it is well established how externally generated stresses relax, through the proliferation and motion of dislocations in the lattice, it remains relatively unknown how crystals cope with internal stresses. We investigate, both experimentally and in simulations, how highly localized stresses relax in 2D soft colloidal crystals. When a single particle is actively excited, by means of optical tweezing, a rich variety of highly collective stress relaxation mechanisms results. These relaxation processes manifest in the form of open strings of cooperatively moving particles through the motion of dissociated vacancy-interstitial pairs, and closed loops of mobile particles, which either result from cooperative rotations in transiently generated circular grain boundaries or through the closure of an open string by annihilation of a vacancy-interstitial pair. Surprisingly, we find that the same collective events occur in crystals that are excited by thermal fluctuations alone; a large thermal agitation inside the crystal lattice can trigger the irreversible displacements of hundreds of particles. Our results illustrate how local stresses can induce large-scale cooperative dynamics in 2D soft colloidal crystals and shed light on the stabilization mechanisms in ultrasoft crystals.

Enhanced stiffness of silk-like fibers by loop formation in the corona leads to stronger gels.

We study the self-assembly of protein polymers consisting of a silk-like block flanked by two hydrophilic blocks, with a cysteine residue attached to the C-terminal end. The silk blocks self-assemble to form fibers while the hydrophilic blocks form a stabilizing corona. Entanglement of the fibers leads to the formation of hydrogels. Under oxidizing conditions the cysteine residues form disulfide bridges, effectively connecting two corona chains at their ends to form a loop. We find that this leads to a significant increase in the elastic modulus of the gels. Using atomic force microscopy, we show that this stiffening is due to an increase of the persistence length of the fibers. Self-consistent-field calculations indicate a slight decrease of the lateral pressure in the corona upon loop formation. We argue that this small decrease in the repulsive interactions affects the stacking of the silk-like blocks in the core, resulting in a more rigid fiber.

Multi-step control over self-assembled hydrogels of peptide-derived building blocks and a polymeric cross-linker.

We present a detailed study of self-assembled hydrogels of bundled and cross-linked networks consisting of positively charged amyloid-like nanofibers and a triblock copolymer with negatively charged end blocks as a cross-linker. In a first step small oligopeptides self-assemble into macrocycles which are held together by reversible disulfide bonds. Interactions between the peptides cause the macrocycles to assemble into nanofibers, which form a reversible hydrogel. The physical properties of the hydrogel are tuned using various methods such as control over the fibre length, addition of a cross-linking copolymer, and addition of salt. We establish a relationship between the bulk mechanical properties, the properties of the individual fibers and the hydrogel morphology using characterization techniques operating at different length scales such as rheology, atomic force microscopy (AFM) and cryo transmission electron microscopy (Cryo-TEM). This allows for a precise control of the elastic behaviour of these networks.

Reversible polypeptide hydrogels from asymmetric telechelics with temperature-dependent and Ni(2+)-dependent connectors.

An asymmetric ('hybrid') triblock polypeptide TR4H with two different, orthogonally self-assembling end blocks has been constructed by conjugating a long (37 kDa) random coil block (R4) with a triple helix former T = (Pro-Gly-Pro)9 at the N terminus, and a histidine hexamer ('Histag', H) at the C terminus. This molecule can form trimers at room temperature by assembly of the T blocks, which can in turn assemble upon addition of Ni(2+), by association of Ni complexes involving the H block. This results in reversible hydrogels with dual responsiveness. We have studied mechanical properties of these gels, and compared them to gels formed by the symmetric triblock TR8T which is equivalent to a dimer of TR4H, but can only form triple helix-based networks. We find that there is an optimum mole ratio for Ni(2+) with respect to the polypeptide of about 1; gels are weaker at both lower and higher Ni(2+) dose. At the optimum dose, the high-frequency storage modulus is in between the value expected for nickel-induced dimerization and trimerization of the H blocks. We also find that the gels relax on time scales of about 50 s, which is two orders of magnitude faster than for TR8T gels, implying that relaxation is dominated by the dynamics of the Ni(2+) complex.

Capillarity-induced ordering of spherical colloids on an interface with anisotropic curvature.

Objects floating at a liquid interface, such as breakfast cereals floating in a bowl of milk or bubbles at the surface of a soft drink, clump together as a result of capillary attraction. This attraction arises from deformation of the liquid interface due to gravitational forces; these deformations cause excess surface area that can be reduced if the particles move closer together. For micrometer-sized colloids, however, the gravitational force is too small to produce significant interfacial deformations, so capillary forces between spherical colloids at a flat interface are negligible. Here, we show that this is different when the confining liquid interface has a finite curvature that is also anisotropic. In that case, the condition of constant contact angle along the three-phase contact line can only be satisfied when the interface is deformed. We present experiments and numerical calculations that demonstrate how this leads to quadrupolar capillary interactions between the particles, giving rise to organization into regular square lattices. We demonstrate that the strength of the governing anisotropic interactions can be rescaled with the deviatoric curvature alone, irrespective of the exact shape of the liquid interface. Our results suggest that anisotropic interactions can easily be induced between isotropic colloids through tailoring of the interfacial curvature.

Caterpillar-Inspired Design and Fabrication of A Self-Walking Actuator with Anisotropy, Gradient, and Instant Response.

A caterpillar-mimetic bilayer actuator is reported, based on a wrinkled polydimethylsiloxane elastomer decorated with a hydroresponsive polyelectrolyte brush. The actuator can fold ultrafast into complex three-dimensional structures upon a change in relative humidity of the surrounding air. The folding direction is determined by the geometry of the actuator, the orientation of the wrinkles, and the gradient in polymer height on the surface. And some unique structures such as helicoid and gradient can be obtained that are seldom reported in the case of bilayered devices. The adaptive bending movement is very fast, anisotropic, highly efficient, and reversible. When the environmental humidity is repeatedly cycled up and down, the small device walks on a surface with a roughness gradient, which is reminiscent of the muscle-like movements.