Topological Data Analysis for Particulate Gels.

Soft gels, formed via the self-assembly of particulate materials, exhibit intricate multiscale structures that provide them with flexibility and resilience when subjected to external stresses. This work combines particle simulations and topological data analysis (TDA) to characterize the complex multiscale structure of soft gels. Our TDA analysis focuses on the use of the Euler characteristic, which is an interpretable and computationally scalable topological descriptor that is combined with filtration operations to obtain information on the geometric (local) and topological (global) structure of soft gels. We reduce the topological information obtained with TDA using principal component analysis (PCA) and show that this provides an informative low-dimensional representation of the gel structure. We use the proposed computational framework to investigate the influence of gel preparation (e.g., quench rate, volume fraction) on soft gel structure and to explore dynamic deformations that emerge under oscillatory shear in various response regimes (linear, nonlinear, and flow). Our analysis provides evidence of the existence of hierarchical structures in soft gels, which are not easily identifiable otherwise. Moreover, our analysis reveals direct correlations between topological changes of the gel structure under deformation and mechanical phenomena distinctive of gel materials, such as stiffening and yielding. In summary, we show that TDA facilitates the mathematical representation, quantification, and analysis of soft gel structures, extending traditional network analysis methods to capture both local and global organization.

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.

Soft matter physics of the ground beneath our feet.

The soft part of the Earth's surface - the ground beneath our feet - constitutes the basis for life and natural resources, yet a general physical understanding of the ground is still lacking. In this critical time of climate change, cross-pollination of scientific approaches is urgently needed to better understand the behavior of our planet's surface. The major topics in current research in this area cross different disciplines, spanning geosciences, and various aspects of engineering, material sciences, physics, chemistry, and biology. Among these, soft matter physics has emerged as a fundamental nexus connecting and underpinning many research questions. This perspective article is a multi-voice effort to bring together different views and approaches, questions and insights, from researchers that work in this emerging area, the soft matter physics of the ground beneath our feet. In particular, we identify four major challenges concerned with the dynamics in and of the ground: (I) modeling from the grain scale, (II) near-criticality, (III) bridging scales, and (IV) life. For each challenge, we present a selection of topics by individual authors, providing specific context, recent advances, and open questions. Through this, we seek to provide an overview of the opportunities for the broad Soft Matter community to contribute to the fundamental understanding of the physics of the ground, strive towards a common language, and encourage new collaborations across the broad spectrum of scientists interested in the matter of the Earth's surface.

Local Mechanism Governs Global Reinforcement of Nanofiller-Hydrogel Composites.

We reveal the mechanism for the strong reinforcement of attractive nanofiller-hydrogel composites. Measuring the linear viscoelastic properties of hydrogels containing filler nanoparticles, we show that a significant increase of the modulus can be achieved at unexpectedly low volume fractions of nanofillers when the filler-hydrogel interactions are attractive. Using three-dimensional numerical simulations, we identify a general microscopic mechanism for the reinforcement, common to hydrogel matrices of different compositions and concentrations and containing nanofillers of varying sizes. The attractive interactions induce a local increase in the gel density around the nanofillers. The effective fillers, composed of the nanofillers and the densified regions around them, assemble into a percolated network, which constrains the gel displacement and enhances the stress coupling throughout the system. A global reinforcement of the composite is induced as the stresses become strongly coupled. This physical mechanism of reinforcement, which relies only on attractive filler-matrix interactions, provides design strategies for versatile composites that combine low nanofiller fractions with an enhanced mechanical strength.

Stress-stress correlations reveal force chains in gels.

We investigate the spatial correlations of microscopic stresses in soft particulate gels using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space. This leads to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis of the model particulate gels at low particle volume fractions demonstrates that stress-stress correlations in these soft materials have characteristics very similar to those in granular solids and can be used to identify force chains. We show that the stress-stress correlations can distinguish floppy from rigid gel networks and that the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification.

Microscopic dynamics underlying the stress relaxation of arrested soft materials.

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Ion Specificity of Confined Ion-Water Structuring and Nanoscale Surface Forces in Clays.

Ion specificity and related Hofmeister effects, which are ubiquitous in aqueous systems, can have spectacular consequences in hydrated clays, where ion-specific nanoscale surface forces can determine large-scale cohesive swelling and shrinkage behaviors of soil and sediments. We have used a semiatomistic computational approach and examined sodium, calcium, and aluminum counterions confined with water between charged surfaces representative of clay materials to show that ion-water structuring in nanoscale confinement is at the origin of surface forces between clay particles which are intrinsically ion-specific. When charged surfaces strongly confine ions and water, the amplitude and oscillations of the net pressure naturally emerge from the interplay of electrostatics and steric effects, which cannot be captured by existing theories. Increasing confinement and surface charge densities promote ion-water structures that increasingly deviate from the ions' bulk hydration shells, being strongly anisotropic, persistent, and self-organizing into optimized, nearly solid-like assemblies where hardly any free water is left. Under these conditions, strongly attractive interactions can prevail between charged surfaces because of the dramatically reduced dielectric screening of water and the highly organized water-ion structures. By unravelling the ion-specific nature of these nanoscale interactions, we provide evidence that ion-specific solvation structures determined by confinement are at the origin of ion specificity in clays and potentially a broader range of confined aqueous systems.

Like-Charge Attraction at the Nanoscale: Ground-State Correlations and Water Destructuring.

Like-charge attraction, driven by ionic correlations, challenges our understanding of electrostatics both in soft and hard matter. For two charged planar surfaces confining counterions and water, we prove that, even at relatively low correlation strength, the relevant physics is the ground-state one, oblivious of fluctuations. Based on this, we derive a simple and accurate interaction pressure that fulfills known exact requirements and can be used as an effective potential. We test this equation against implicit-solvent Monte Carlo simulations and against explicit-solvent simulations of cement and several types of clays. We argue that water destructuring under nanometric confinement drastically reduces dielectric screening, enhancing ionic correlations. Our equation of state at reduced permittivity therefore explains the exotic attractive regime reported for these materials, even in the absence of multivalent counterions.

The physics of cement cohesion.

Cement is the most produced material in the world. A major player in greenhouse gas emissions, it is the main binding agent in concrete, providing a cohesive strength that rapidly increases during setting. Understanding how such cohesion emerges is a major obstacle to advances in cement science and technology. Here, we combine computational statistical mechanics and theory to demonstrate how cement cohesion arises from the organization of interlocked ions and water, progressively confined in nanoslits between charged surfaces of calcium-silicate-hydrates. Because of the water/ions interlocking, dielectric screening is drastically reduced and ionic correlations are proven notably stronger than previously thought, dictating the evolution of nanoscale interactions during cement hydration. By developing a quantitative analytical prediction of cement cohesion based on Coulombic forces, we reconcile a fundamental understanding of cement hydration with the fully atomistic description of the solid cement paste and open new paths for scientific design of construction materials.

Microscopic interactions and emerging elasticity in model soft particulate gels.

We discuss a class of models for particulate gels in which the particle contacts are described by an effective interaction combining a two-body attraction and a three-body angular repulsion. Using molecular dynamics, we show how varying the model parameters allows us to sample, for a given gelation protocol, a variety of gel morphologies. For a specific set of the model parameters, we identify the local elastic structures that get interlocked in the gel network. Using the analytical expression of their elastic energy from the microscopic interactions, we can estimate their contribution to the emergent elasticity of the gel and gain new insight into its origin.

Competitive Supramolecular Associations Mediate the Viscoelasticity of Binary Hydrogels.

Supramolecular polymers are known to form strong and resilient hydrogels which can take up large amounts of water while exhibiting ease of processing and self-healing. They also possess similarities with networks of biological macromolecules. The combination of these features makes supramolecular polymers ideal candidates for studying mechanisms and consequences of self-assembly, which are relevant to biological materials. At the same time, this renders investigations of mixed hydrogels based on different supramolecular compounds necessary, since this substantially widens their applicability. Here, we address unusual viscoelastic properties of a class of binary hydrogels made by mixing fibrillar supramolecular polymers that are formed from two compounds: 1,3,5-benzene-tricarboxamide decorated with aliphatic chains terminated by tetra(ethylene glycol) (BTA) and a 20 kg/mol telechelic poly(ethylene glycol) decorated with the same hydrogen bonding BTA motif on both ends (BTA-PEG-BTA). Using a suite of experimental and simulation techniques, we find that the respective single-compound-based supramolecular systems form very different networks which exhibit drastically different rheology. More strikingly, mixing the compounds results in a non-monotonic dependence of modulus and viscosity on composition, suggesting a competition between interactions of the two compounds, which can then be used to fine-tune the mechanical properties. Simulations offer insight into the nature of this competition and their remarkable qualitative agreement with the experimental results is promising for the design of mixed hydrogels with desired and tunable properties. Their combination with a sensitive dynamic probe (here rheology) offer a powerful toolbox to explore the unique properties of binary hydrogel mixtures.

Emergence and persistence of flow inhomogeneities in the yielding and fluidization of dense soft solids.

In three-dimensional computer simulations of model non-Brownian jammed suspensions, we compute the time required to reach homogeneous flow upon yielding, by analyzing stresses and particle packing at different shear rates, with and without confinement. We show that the stress overshoot and persistent shear banding preceding the complete fluidization are controlled by the presence of overconstrained microscopic domains in the initial solids. Such domains, identifiable with icosahedrally packed regions in the model used, allow for stress accumulation during the shear startup. Their structural reorganization under deformation controls the emergence and the persistence of the shear banding.

Computational study of transient shear banding in soft jammed solids.

We have designed three-dimensional numerical simulations of a soft spheres model, with size polidispersity and in athermal conditions, to study the transient shear banding that occurs during yielding of jammed soft solids. We analyze the effects of different types of drag coefficients used in the simulations and compare the results obtained using Lees-Edwards periodic boundary conditions with the case in which the same model solid is confined between two walls. The specific damping mechanism and the different boundary conditions indeed modify the load curves and the velocity profiles in the transient regime. Nevertheless, we find that the presence of a stress overshoot and of a related transient banding phenomenon, for large enough samples, is a robust feature for overdamped systems, where their presence do not depend on the specific drag used and on the different boundary conditions.

Multi-component colloidal gels: interplay between structure and mechanical properties.

We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of components leads to softer solids that can accommodate progressively larger strains before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work provides new insight into mechanisms at play for controlling the material properties and opens a road to new design principles for soft composite solids.

Correlated Rigidity Percolation and Colloidal Gels.

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence, the emergence of rigidity at colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

Revealing the principal attributes of protein adsorption on block copolymer surfaces with direct experimental evidence at the single protein level.

Understanding protein adsorption onto polymer surfaces is of great importance in designing biomaterials, improving bioanalytical devices, and controlling biofouling, to name a few examples. Although steady research efforts have been advancing this field, our knowledge of this ubiquitous and complex phenomenon is still limited. In this study, we elucidate competitive protein adsorption behaviors sequentially occurring onto nanoscale block copolymer (BCP) surfaces via combined experimental and computer simulation approaches. The model systems chosen for our investigation are immunoglobulin G and fibrinogen introduced in different orders into the self-assembled nanodomains of poly(styrene)-block-poly(methylmethacrylate). We unambiguously reveal the adsorption, desorption, and replacement events of the same protein molecules via single protein tracking with atomic force microscopy. We then ascertain adsorption-related behaviors such as lateral mobility and self-association of proteins. We provide the much-needed, direct experimental proof of sequential adsorption events at the biomolecular level, which was virtually nonexistent before. We determine key protein adsorption pathways and dominant tendencies of sequential protein adsorption. We also reveal preadsorbed surface-associated behaviors in sequential adsorption, distinct from situations involving initially empty surfaces. We perform Monte-Carlo simulations to further substantiate our experimental outcomes. Our endeavors in this study may facilitate a well-guided mechanistic understanding of protein-polymer interactions by providing definite experimental evidence of competitive, sequential adsorption at the nanoscale. Increasingly, biomaterial and biomedical applications rely on systems of multicomponent proteins and chemically intricate, nanoscale polymer surfaces. Hence, our findings can also be beneficial for the development of next-generation nanobiomaterials and nanobiosensors exploiting self-assembled BCP nanodomain surfaces.

Disease-causing mutation in α-actinin-4 promotes podocyte detachment through maladaptation to periodic stretch.

α-Actinin-4 (ACTN4) bundles and cross-links actin filaments to confer mechanical resilience to the reconstituted actin network. How this resilience is built and dynamically regulated in the podocyte, and the cause of its failure in ACTN4 mutation-associated focal segmental glomerulosclerosis (FSGS), remains poorly defined. Using primary podocytes isolated from wild-type (WT) and FSGS-causing point mutant Actn4 knockin mice, we report responses to periodic stretch. While WT cells largely maintained their F-actin cytoskeleton and contraction, mutant cells developed extensive and irrecoverable reductions in these same properties. This difference was attributable to both actin material changes and a more spatially correlated intracellular stress in mutant cells. When stretched cells were further challenged using a cell adhesion assay, mutant cells were more likely to detach. Together, these data suggest a mechanism for mutant podocyte dysfunction and loss in FSGS-it is a direct consequence of mechanical responses of a cytoskeleton that is brittle.

Rate Dependence of Elementary Rearrangements and Spatiotemporal Correlations in the 3D Flow of Soft Solids.

We use a combination of confocal microscopy, rheology, and molecular dynamics simulations to investigate jammed emulsions under shear, by analyzing the 3D droplets rearrangements in the shear frame. Our quantitative analysis of local dynamics reveals elementary nonaffine rearrangements that underlie the onset of the flow at small strains. We find that the mechanism of unjamming and the upturn in the material flow curve are associated to a qualitative change in spatiotemporal correlations of such rearrangements with the applied shear rate. At high shear rates, droplet clusters follow coordinated, stringlike motion. Conversely, at low shear rates, the elementary nonaffine rearrangements exhibit longer-ranged correlations, with complex spatiotemporal patterns. The 3D microscopic details provide novel insights into the specific features of the material flow curve, common to a large class of technologically relevant soft disordered solids and new fundamental ingredients for constitutive models.