Bonded straight and helical flagellar filaments form ultra-low-density glasses.

We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semidilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are microns-long helical or straight filaments assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape-diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics. Consequently, the shape-diblock filaments become permanently jammed at exceedingly low densities. We also measure the rheological properties of semidilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semidilute fibrous suspensions.

Correction: Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation.

Correction for 'Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation' by Noémie Dagès et al., Soft Matter, 2022, 18, 6645-6659, https://doi.org/10.1039/D2SM00481J.

Interpenetration of fractal clusters drives elasticity in colloidal gels formed upon flow cessation.

Colloidal gels are out-of-equilibrium soft solids composed of attractive Brownian particles that form a space-spanning network at low volume fractions. The elastic properties of these systems result from the network microstructure, which is very sensitive to shear history. Here, we take advantage of such sensitivity to tune the viscoelastic properties of a colloidal gel made of carbon black nanoparticles. Starting from a fluidized state at an applied shear rate 0, we use an abrupt flow cessation to trigger a liquid-to-solid transition. We observe that the resulting gel is all the more elastic when the shear rate 0 is low and that the viscoelastic spectra can be mapped on a master curve. Moreover, coupling rheometry to small angle X-ray scattering allows us to show that the gel microstructure is different from gels solely formed by thermal agitation where only two length scales are observed: the dimension of the colloidal and the dimension of the fractal aggregates. Competition between shear and thermal energy leads to gels with three characteristic length scales. Such gels structure in a percolated network of fractal clusters that interpenetrate each other. Experiments on gels prepared with various shear histories reveal that cluster interpenetration increases with decreasing values of the shear rate 0 applied before flow cessation. These observations strongly suggest that cluster interpenetration drives the gel elasticity, which we confirm using a structural model. Our results, which are in stark contrast to previous literature, where gel elasticity was either linked to cluster connectivity or to bending modes, highlight a novel local parameter controlling the macroscopic viscoelastic properties of colloidal gels.

Force-Induced Formation of Twisted Chiral Ribbons.

We demonstrate that an achiral stretching force transforms disk-shaped colloidal membranes composed of chiral rods into twisted ribbons with handedness opposite the preferred twist of the rods. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and the ribbon shape. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve and the force-induced twisted shape.

Colloidal transport in bacteria suspensions: from bacteria collision to anomalous and enhanced diffusion.

Swimming microorganisms interact and alter the dynamics of Brownian particles and tend to modify their transport properties. In particular, dilute colloids coupled to a bath of swimming cells generically display enhanced diffusion on long time scales. This transport dynamics stems from a subtle interplay between the active and passive particles that still resists our understanding despite decades of intense research. Here, we tackle the root of the problem by providing a quantitative characterisation of the single scattering events between a colloid and a bacterium, a smooth running E. coli. Based on our experiments, we build a minimal model that quantitatively predicts the geometry of the scattering trajectories, and enhanced colloidal diffusion at long times. This quantitative confrontation between theory and experiments elucidates the microscopic origin of enhanced transport. Collisions are solely ruled by stochastic contact interactions and the ratio of the drag coefficients of the colloid and the bacteria. Such description accounts both for genuine anomalous diffusion at short times and enhanced diffusion at long times with no ballistic regime at any scale.

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes.

In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length-thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

Equation of state of colloidal membranes.

In the presence of a non-adsorbing polymer, monodisperse rod-like colloids assemble into one-rod-length thick liquid-like monolayers, called colloidal membranes. The density of the rods within a colloidal membrane is determined by a balance between the osmotic pressure exerted by the enveloping polymer suspension and the repulsion between the colloidal rods. We developed a microfluidic device for continuously observing an isolated membrane while dynamically controlling the osmotic pressure of the polymer suspension. Using this technology we measured the membrane rod density over a range of osmotic pressures than is wider that what is accessible in equilibrium samples. With increasing density we observed a first-order phase transition, in which the in-plane membrane order transforms from a 2D fluid into a 2D solid. In the limit of low osmotic pressures, we measured the rate at which individual rods evaporate from the membrane. The developed microfluidic technique could have wide applicability for in situ investigation of various soft materials and how their properties depend on the solvent composition.

Redox-Induced Molecular Metamorphism Promoting a Sol/Gel Phase Transition in a Viologen-Based Coordination Polymer.

We have developed a strategy enabling control over the organization of ditopic molecular tectons within a palladium-based self-assembled system. The key electron-responsive sub-unit is a viologen-based mechanical hinge that can toggle under electric stimulation between a folded and a stretched position, the driving force of the folding motion being the π-dimerisation of the electrogenerated viologen cation radicals. The title ditopic tecton features two planar, N2-type, triazole/pyridine-based bidentate binding units, providing the tecton with the ability to chelate two palladium ions both in its folded and in its elongated conformations. Association of this ditopic redox-responsive tecton with palladium to form 1D self-assembled architectures undergoing large scale reorganizations in solution under electric stimulation, has been established on the ground of spectroscopic, electrochemical, spectro-electrochemical and rheological data. Our result reveal that addition of metal leads to a significant stabilization of the π-dimer species in solution and that the redox-triggered reorganisation of the tectons comes along in suitable conditions with a macroscopic sol/gel-type phase transition.

Reconfigurable self-assembly through chiral control of interfacial tension.

From determining the optical properties of simple molecular crystals to establishing the preferred handedness in highly complex vertebrates, molecular chirality profoundly influences the structural, mechanical and optical properties of both synthetic and biological matter on macroscopic length scales. In soft materials such as amphiphilic lipids and liquid crystals, the competition between local chiral interactions and global constraints imposed by the geometry of the self-assembled structures leads to frustration and the assembly of unique materials. An example of particular interest is smectic liquid crystals, where the two-dimensional layered geometry cannot support twist and chirality is consequently expelled to the edges in a manner analogous to the expulsion of a magnetic field from superconductors. Here we demonstrate a consequence of this geometric frustration that leads to a new design principle for the assembly of chiral molecules. Using a model system of colloidal membranes, we show that molecular chirality can control the interfacial tension, an important property of multi-component mixtures. This suggests an analogy between chiral twist, which is expelled to the edges of two-dimensional membranes, and amphiphilic surfactants, which are expelled to oil-water interfaces. As with surfactants, chiral control of interfacial tension drives the formation of many polymorphic assemblages such as twisted ribbons with linear and circular topologies, starfish membranes, and double and triple helices. Tuning molecular chirality in situ allows dynamical control of line tension, which powers polymorphic transitions between various chiral structures. These findings outline a general strategy for the assembly of reconfigurable chiral materials that can easily be moved, stretched, attached to one another and transformed between multiple conformational states, thus allowing precise assembly and nanosculpting of highly dynamical and designable materials with complex topologies.

Predicting and assessing rupture in protein gels under oscillatory shear.

Soft materials may break irreversibly upon applying sufficiently large shear oscillations, a process whose physical mechanism remains largely elusive. In this work, the rupture of protein gels made of sodium caseinate under an oscillatory stress is shown to occur in an abrupt, brittle-like manner. Upon increasing the stress amplitude, the build-up of harmonic modes in the strain response can be rescaled for all gel concentrations. This rescaling yields an empirical criterion to predict the rupture point way before the samples are significantly damaged. "Fatigue" experiments under stress oscillations of constant amplitude can be mapped onto the former results, which indicates that rupture is independent of the temporal pathway in which strain and damage accumulate. Finally, using ultrasonic imaging, we measure the local mechanical properties of the gels before, during and after breakdown, showing that the strain field remains perfectly homogeneous up to rupture but suddenly gives way to a solid-fluid phase separation upon breakdown.

Entropic forces stabilize diverse emergent structures in colloidal membranes.

The depletion interaction mediated by non-adsorbing polymers promotes condensation and assembly of repulsive colloidal particles into diverse higher-order structures and materials. One example, with particularly rich emergent behaviors, is the formation of two-dimensional colloidal membranes from a suspension of filamentous fd viruses, which act as rods with effective repulsive interactions, and dextran, which acts as a condensing, depletion-inducing agent. Colloidal membranes exhibit chiral twist even when the constituent virus mixture lacks macroscopic chirality, change from a circular shape to a striking starfish shape upon changing the chirality of constituent rods, and partially coalesce via domain walls through which the viruses twist by 180°. We formulate an entropically-motivated theory that can quantitatively explain these experimental structures and measurements, both previously published and newly performed, over a wide range of experimental conditions. Our results elucidate how entropy alone, manifested through the viruses as Frank elastic energy and through the depletants as an effective surface tension, drives the formation and behavior of these diverse structures. Our generalizable principles propose the existence of analogous effects in molecular membranes and can be exploited in the design of reconfigurable colloidal structures.

Multiple yielding processes in a colloidal gel under large amplitude oscillatory stress.

Fatigue refers to the changes in material properties caused by repeatedly applied loads. It has been widely studied for, e.g., construction materials, but much less has been done on soft materials. Here, we characterize the fatigue dynamics of a colloidal gel. Fatigue is induced by large amplitude oscillatory stress (LAOStress), and the local displacements of the gel are measured through high-frequency ultrasonic imaging. We show that fatigue eventually leads to rupture and fluidization. We evidence four successive steps associated with these dynamics: (i) the gel first remains solid, (ii) it then slides against the walls, (iii) the bulk of the sample becomes heterogeneous and displays solid-fluid coexistence, and (iv) it is finally fully fluidized. It is possible to homogeneously scale the duration of each step with respect to the stress oscillation amplitude σ0. The data are compatible with both exponential and power-law scalings with σ0, which hints at two possible interpretations of delayed yielding in terms of activated processes or of the Basquin law. Surprisingly, we find that the model parameters behave nonmonotonically as we change the oscillation frequency and/or the gel concentration.

Orthotropic organization of a cellulose nanocrystal suspension realized via the combined action of frontal ultrafiltration and ultrasound as revealed by in situ SAXS.

HYPOTHESIS: Rodlike cellulose nanocrystals (CNCs) exhibit significant potential as building blocks for creating uniform, sustainable materials. However, a critical hurdle lies in the need to enhance existing or devise novel processing that provides improved control over the alignment and arrangement of CNCs across a wide spatial range. Specifically, the challenge is to achieve orthotropic organization in a single-step processing, which entails creating non-uniform CNC orientations to generate spatial variations in anisotropy. EXPERIMENTS: A novel processing method combining frontal ultrafiltration (FU) and ultrasound (US) has been developed. A dedicated channel-cell was designed to simultaneously generate (1) a vertical acoustic force thanks to a vibrating blade at the top and (2) a transmembrane pressure force at the bottom. Time-resolved in situ small-angle X-ray scattering permitted to probe the dynamical structural organization/orientation of CNCs during the processing. FINDINGS: For the first time, a typical three-layer orthotropic structure that resembles the articular cartilage organization was achieved in one step during the FU/US process: a first layer composed of CNCs having their director aligned parallel to the horizontal membrane surface, a second intermediate isotropic layer, and a third layer of CNCs with their director vertically oriented along the direction of US wave propagation direction.

Unexpected decoupling of stretching and bending modes in protein gels.

We show that gels formed by arrested spinodal decomposition of protein solutions exhibit elastic properties in two distinct frequency domains, both elastic moduli exhibiting a remarkably strong dependence on volume fraction. Considering the large difference between the protein size and the characteristic length of the network we model the gels as porous media and show that the high and low frequency elastic moduli can be respectively attributed to stretching and bending modes. The unexpected decoupling of the two modes in the frequency domain is attributed to the length scale involved: while stretching mainly relates to the relative displacement of two particles, bending involves the deformation of a strand with a thickness of the order of a thousand particle diameters.

Light-Controlled Aggregation and Gelation of Viologen-Based Coordination Polymers.

Ditopic bis-(triazole/pyridine)viologens are bidentate ligands that self-assemble into coordination polymers. In such photo-responsive materials, light irradiation initiates photo-induced electron transfer to generate π-radicals that can self-associate to form π-dimers. This leads to a cascade of events: processes at the supramolecular scale associated with mechanical and structural transition at the macroscopic scale. By tuning the irradiation power and duration, we evidence the formation of aggregates and gels. Using microscopy, we show that the aggregates are dense, polydisperse, micron-sized, spindle-shaped particles which grow in time. Using microscopy and time-resolved micro-rheology, we follow the gelation kinetics which leads to a gel characterized by a correlation length of a few microns and a weak elastic modulus. The analysis of the aggregates and the gel states vouch for an arrested phase separation process, a new scenario to supramolecular systems.

Irreversible hardening of a colloidal gel under shear: The smart response of natural rubber latex gels.

Natural rubber is obtained by processing natural rubber latex, a liquid colloidal suspension that rapidly gels after exudation from the tree. We prepared such gels by acidification, in a large range of particle volume fractions, and investigated their rheological properties. We show that natural rubber latex gels exhibit a unique behavior of irreversible strain hardening: when subjected to a large enough strain, the elastic modulus increases irreversibly. Hardening proceeds over a large range of deformations in such a way that the material maintains an elastic modulus close to, or slightly higher than the imposed shear stress. Local displacements inside the gel are investigated by ultrasound imaging coupled to oscillatory rheometry, together with a Fourier decomposition of the oscillatory response of the material during hardening. Our observations suggest that hardening is associated with irreversible local rearrangements of the fractal structure, which occur homogeneously throughout the sample.

A simple patchy colloid model for the phase behavior of lysozyme dispersions.

We propose a minimal model for spherical proteins with aeolotopic pair interactions to describe the equilibrium phase behavior of lysozyme. The repulsive screened Coulomb interactions between the particles are taken into account assuming that the net charges are smeared out homogeneously over the spherical protein surfaces. We incorporate attractive surface patches, with the interactions between patches on different spheres modeled by an attractive Yukawa potential. The parameters entering the attractive Yukawa potential part are determined using information on the experimentally accessed gas-liquid-like critical point. The Helmholtz free energy of the fluid and solid phases is calculated using second-order thermodynamic perturbation theory. Our predictions for the solubility curve are in fair agreement with experimental data. In addition, we present new experimental data for the gas-liquid coexistence curves at various salt concentrations and compare these with our model calculations. In agreement with earlier findings, we observe that the strength and the range of the attractive potential part only weakly depend on the salt content.

Direct Liquid to Crystal Transition in a Quasi-Two-Dimensional Colloidal Membrane.

Using synchrotron-based small-angle X-ray scattering, we study rigid fd viruses assembled into isolated monolayers from mixtures with a nonabsorbing polymer, which acts as an osmotic agent. As the polymer concentration increases, we observe a direct liquid to crystal transition, without an intermediate hexatic phase, in contrast with many other similar systems, such as concentrated DNA phases or packings of surfactant micelles. We tentatively attribute this effect to the difference in stiffness. The liquid phase can be well described by a hard-disk fluid, while we model the crystalline one as a hexagonal harmonic lattice and we evaluate its elastic constants.

Filamentous phages as building blocks for reconfigurable and hierarchical self-assembly.

Filamentous bacteriophages such as fd-like viruses are monodisperse rod-like colloids that have well defined properties of diameter, length, rigidity, charge and chirality. Engineering these viruses leads to a library of colloidal rods, which can be used as building blocks for reconfigurable and hierarchical self-assembly. Their condensation in an aqueous solution with additive polymers, which act as depletants to induce attraction between the rods, leads to a myriad of fluid-like micronic structures ranging from isotropic/nematic droplets, colloid membranes, achiral membrane seeds, twisted ribbons, π-wall, pores, colloidal skyrmions, Möbius anchors, scallop membranes to membrane rafts. These structures, and the way that they shape-shift, not only shed light on the role of entropy, chiral frustration and topology in soft matter, but also mimic many structures encountered in different fields of science. On the one hand, filamentous phages being an experimental realization of colloidal hard rods, their condensation mediated by depletion interactions constitutes a blueprint for the self-assembly of rod-like particles and provides a fundamental foundation for bio- or material-oriented applications. On the other hand, the chiral properties of the viruses restrict the generalities of some results but vastly broaden the self-assembly possibilities.

Hierarchical wrinkling in a confined permeable biogel.

Confined thin surfaces may wrinkle as a result of the growth of excess material. Elasticity or gravity usually sets the wavelength. We explore new selection mechanisms based on hydrodynamics. First, inspired by yoghurt-making processes, we use caseins (a family of milk proteins) as pH-responsive building blocks and the acidulent glucono-δ-lactone to design a porous biogel film immersed in a confined buoyancy-matched viscous medium. Under specific boundary conditions yet without any external stimulus, the biogel film spontaneously wrinkles in cascade. Second, using a combination of titration, rheology, light microscopy, and confocal microscopy, we demonstrate that, during continuous acidification, the gel first shrinks and then swells, inducing wrinkling. Third, taking into account both Darcy flow through the gel and Poiseuille flow in the surrounding solvent, we develop a model that correctly predicts the wrinkling wavelength. Our results should be universal for acid-induced protein gels because they are based on pH-induced charge stabilization/destabilization and therefore could set a benchmark to gain fundamental insights into wrinkled biological tissues, to texture food, or to design surfaces for optical purposes.