Dynamics of drying colloidal suspensions, measured by optical coherence tomography.

Colloidal suspensions are the basis of a wide variety of coatings, prepared as liquids and then dried into solid films. The processes at play during film formation, however, are difficult to observe directly. Here, we demonstrate that optical coherence tomography (OCT) can provide fast, non-contact, precise profiling of the dynamics within a drying suspension. Using a scanning Michelson interferometer with a broadband laser source, OCT creates cross-sectional images of the optical stratigraphy of a sample. With this method, we observed the drying of colloidal silica in Hele-Shaw cells with 10 µm transverse and 1.8 µm depth resolution, over a 1 cm scan line and a 15 s sampling period. The resulting images were calibrated to show how the concentration of colloidal particles varied with position and drying time. This gives access to important transport properties, for example, of how collective diffusion depends on particle concentration. Looking at early-time behaviours, we also show how a drying front initially develops, and how the induction time before the appearance of a solid film depends on the balance of diffusion and evaporation-driven motion. Pairing these results with optical microscopy and particle tracking techniques, we find that film formation can be significantly delayed by any density-driven circulation occurring near the drying front.

Active Spaghetti: Collective Organization in Cyanobacteria.

Filamentous cyanobacteria can show fascinating examples of nonequilibrium self-organization, which, however, are not well understood from a physical perspective. We investigate the motility and collective organization of colonies of these simple multicellular lifeforms. As their area density increases, linear chains of cells gliding on a substrate show a transition from an isotropic distribution to bundles of filaments arranged in a reticulate pattern. Based on our experimental observations of individual behavior and pairwise interactions, we introduce a nonreciprocal model accounting for the filaments' large aspect ratio, fluctuations in curvature, motility, and nematic interactions. This minimal model of active filaments recapitulates the observations, and rationalizes the appearance of a characteristic length scale in the system, based on the Péclet number of the cyanobacteria filaments.

Measuring and upscaling micromechanical interactions in a cohesive granular material.

The mechanical properties of a disordered heterogeneous medium depend, in general, on a complex interplay between multiple length scales. Connecting local interactions to macroscopic observables, such as stiffness or fracture, is thus challenging in this type of material. Here, we study the properties of a cohesive granular material composed of glass beads held together by soft polymer bridges. We characterise the mechanical response of single bridges under traction and shear, using a setup based on the deflection of flexible micropipettes. These measurements, along with information from X-ray microtomograms of the granular packings, then inform large-scale discrete element model (DEM) simulations. Although simple, these simulations are constrained in every way by empirical measurement and accurately predict mechanical responses of the aggregates, including details on their compressive failure, and how the material's stiffness depends on the stiffness and geometry of its parts. By demonstrating how to accurately relate microscopic information to macroscopic properties, these results provide new perspectives for predicting the behaviour of complex disordered materials, such as porous rock, snow, or foam.

Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters.

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, c_{s}, and volume fractions, ϕ. Upon increasing ϕ, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high ϕ and c_{s} is explained by the interaction (charge) polydispersity and vibrational entropy.

Controlling the drying-induced peeling of colloidal films.

In this work, we investigated the effect of the suspension properties on the drying dynamics and the resulting film peeling instability. To do so, a comprehensive series of experiments were conducted using drops of aqueous mixtures of colloidal silica dispersions and polyethylene oxide (PEO) additives. Time-lapse digital microscope images of the evaporating droplets show that film peeling can be discouraged and eventually eliminated with an increase in PEO concentration and molecular weight. This is due to the additives modifying the suspension properties which in turn modify the drying front length across the evaporating surface. Our result extends the understanding of the physics of film failure which is relevant information for various industrial processes such as in inkjet printing and coating applications.

Drying colloidal systems: Laboratory models for a wide range of applications.

The drying of complex fluids provides a powerful insight into phenomena that take place on time and length scales not normally accessible. An important feature of complex fluids, colloidal dispersions and polymer solutions is their high sensitivity to weak external actions. Thus, the drying of complex fluids involves a large number of physical and chemical processes. The scope of this review is the capacity to tune such systems to reproduce and explore specific properties in a physics laboratory. A wide variety of systems are presented, ranging from functional coatings, food science, cosmetology, medical diagnostics and forensics to geophysics and art.

Mapping heterogeneities through avalanche statistics.

Avalanche statistics of various threshold-activated dynamical systems are known to depend on the magnitude of the drive, or stress, on the system. Such dependences exist for earthquake size distributions, in sheared granular avalanches, laboratory-scale fracture and also in the outage statistics of power grids. In this work, we model threshold-activated avalanche dynamics and investigate the time required to detect local variations in the ability of model elements to bear stress. We show that the detection time follows a scaling law where the scaling exponents depend on whether the feature that is sought is either weaker, or stronger, than its surroundings. We then look at earthquake data from Sumatra and California, demonstrate the trade-off between the spatial resolution of a map of earthquake exponents (i.e. the b-values of the Gutenberg-Richter Law) and the accuracy of those exponents, and suggest a means to maximize both.This article is part of the theme issue 'Statistical physics of fracture and earthquakes'.

Statistical physics of fracture and earthquakes.

Manifestations of emergent properties in stressed disordered materials are often the result of an interplay between strong perturbations in the stress field around defects. The collective response of a long-ranged correlated multi-component system is an ideal playing field for statistical physics. Hence, many aspects of such collective responses in widely spread length and energy scales can be addressed by the tools of statistical physics. In this theme issue, some of these aspects are treated from various angles of experiments, simulations and analytical methods, and connected together by their common base of complex-system dynamics.This article is part of the theme issue 'Statistical physics of fracture and earthquakes' .

Fracture of a model cohesive granular material.

We study experimentally the fracture mechanisms of a model cohesive granular medium consisting of glass beads held together by solidified polymer bridges. The elastic response of this material can be controlled by changing the cross-linking of the polymer phase, for example. Here we show that its fracture toughness can be tuned over an order of magnitude by adjusting the stiffness and size of the polymer bridges. We extract a well-defined fracture energy from fracture testing under a range of material preparations. This energy is found to scale linearly with the cross-sectional area of the bridges. Finally, X-ray microcomputed tomography shows that crack propagation is driven by adhesive failure of about one polymer bridge per bead located at the interface, along with microcracks in the vicinity of the failure plane. Our findings provide insight into the fracture mechanisms of this model material, and the mechanical properties of disordered cohesive granular media in general.

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations.

We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB_{2}, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and it suggests routes for designing self-assembling colloidal crystals from the bottom up.

How do polydisperse repulsive colloids crystallize?

A modified version of the Gibbs-ensemble Monte-Carlo method reveals how polydisperse charged colloidal particles can build complex colloidal crystals. It provides general rules that are applicable to this fractionated crystallization that stems from size segregation. It explains the spontaneous formation of complex crystals with very large unit-cells in suspensions of nanoparticles with a broad size distribution.

Crack patterns over uneven substrates.

Cracks in thin layers are influenced by what lies beneath them. From buried craters to crocodile skin, crack patterns are found over an enormous range of length scales. Regardless of absolute size, their substrates can dramatically influence how cracks form, guiding them in some cases, or shielding regions from them in others. Here we investigate how a substrate's shape affects the appearance of cracks above it, by preparing mud cracks over sinusoidally varying surfaces. We find that as the thickness of the cracking layer increases, the observed crack patterns change from wavy to ladder-like to isotropic. Two order parameters are introduced to measure the relative alignment of these crack networks, and, along with Fourier methods, are used to characterise the transitions between crack pattern types. Finally, we explain these results with a model, based on the Griffith criteria of fracture, that identifies the conditions for which straight or wavy cracks will be seen, and predicts how well-ordered the cracks will be. Our metrics and results can be applied to any situation where connected networks of cracks are expected, or found.

Formation of Shear Bands in Drying Colloidal Dispersions.

In directionally dried colloidal dispersions regular bands can appear behind the drying front, inclined at ±45° to the drying line. Although these features have been noted to share visual similarities with shear bands in metal, no physical mechanism for their formation has ever been suggested, until very recently. Here, through microscopy of silica and polystyrene dispersions, dried in Hele-Shaw cells, we demonstrate that the bands are indeed associated with local shear strains. We further show how the bands form, that they scale with the thickness of the drying layer, and that they are eliminated by the addition of salt to the drying dispersions. Finally, we reveal the origins of these bands in the compressive forces associated with drying, and show how they affect the optical properties (birefringence) of colloidal films and coatings.

Interfacial mechanisms in active emulsions.

Active emulsions, i.e., emulsions whose droplets perform self-propelled motion, are of tremendous interest for mimicking collective phenomena in biological populations such as phytoplankton and bacterial colonies, but also for experimentally studying rheology, pattern formation, and phase transitions in systems far from thermal equilibrium. For fuelling such systems, molecular processes involving the surfactants which stabilize the emulsions are a straightforward concept. We outline and compare two different types of reactions, one which chemically modifies the surfactant molecules, the other which transfers them into a different colloidal state. While in the first case symmetry breaking follows a standard linear instability, the second case turns out to be more complex. Depending on the dissolution pathway, there is either an intrinsically nonlinear instability, or no symmetry breaking at all (and hence no locomotion).

Plasticity and fracture in drying colloidal films.

Cracks in drying colloidal dispersions are typically modeled by elastic fracture mechanics, which assumes that all strains are linear, elastic, and reversible. We tested this assumption in films of a hard latex, by intermittently blocking evaporation over a drying film, thereby relieving the film stress. Here we show that although the deformation around a crack tip has some features of brittle fracture, only 20%-30% of the crack opening is relieved when it is unloaded. Atomic force micrographs of crack tips also show evidence of plastic deformation, such as microcracks and particle rearrangement. Finally, we present a simple scaling argument showing that the yield stress of a drying colloidal film is generally comparable to its maximum capillary pressure, and thus that the plastic strain around a crack will normally be significant. This also suggests that a film's fracture toughness may be increased by decreasing the interparticle adhesion.

A structural systems biology approach for quantifying the systemic consequences of missense mutations in proteins.

Gauging the systemic effects of non-synonymous single nucleotide polymorphisms (nsSNPs) is an important topic in the pursuit of personalized medicine. However, it is a non-trivial task to understand how a change at the protein structure level eventually affects a cell's behavior. This is because complex information at both the protein and pathway level has to be integrated. Given that the idea of integrating both protein and pathway dynamics to estimate the systemic impact of missense mutations in proteins remains predominantly unexplored, we investigate the practicality of such an approach by formulating mathematical models and comparing them with experimental data to study missense mutations. We present two case studies: (1) interpreting systemic perturbation for mutations within the cell cycle control mechanisms (G2 to mitosis transition) for yeast; (2) phenotypic classification of neuron-related human diseases associated with mutations within the mitogen-activated protein kinase (MAPK) pathway. We show that the application of simplified mathematical models is feasible for understanding the effects of small sequence changes on cellular behavior. Furthermore, we show that the systemic impact of missense mutations can be effectively quantified as a combination of protein stability change and pathway perturbation.

Drying dip-coated colloidal films.

We present the results from a small-angle X-ray scattering (SAXS) study of lateral drying in thin films. The films, initially 10 µm thick, are cast by dip-coating a mica sheet in an aqueous silica dispersion (particle radius 8 nm, volume fraction ϕ(s) = 0.14). During evaporation, a drying front sweeps across the film. An X-ray beam is focused on a selected spot of the film, and SAXS patterns are recorded at regular time intervals. As the film evaporates, SAXS spectra measure the ordering of particles, their volume fraction, the film thickness, and the water content, and a video camera images the solid regions of the film, recognized through their scattering of light. We find that the colloidal dispersion is first concentrated to ϕ(s) = 0.3, where the silica particles begin to jam under the effect of their repulsive interactions. Then the particles aggregate until they form a cohesive wet solid at ϕ(s) = 0.68 ± 0.02. Further evaporation from the wet solid leads to evacuation of water from pores of the film but leaves a residual water fraction ϕ(w) = 0.16. The whole drying process is completed within 3 min. An important finding is that, in any spot (away from boundaries), the number of particles is conserved throughout this drying process, leading to the formation of a homogeneous deposit. This implies that no flow of particles occurs in our films during drying, a behavior distinct to that encountered in the iconic coffee-stain drying. It is argued that this type of evolution is associated with the formation of a transition region that propagates ahead of the drying front. In this region the gradient of osmotic pressure balances the drag force exerted on the particles by capillary flow toward the liquid-solid front.

Nonequilibrium scale selection mechanism for columnar jointing.

Crack patterns in laboratory experiments on thick samples of drying cornstarch are geometrically similar to columnar joints in cooling lava found at geological sites such as the Giant's Causeway. We present measurements of the crack spacing from both laboratory and geological investigations of columnar jointing, and show how these data can be collapsed onto a single master scaling curve. This is due to the underlying mathematical similarity between theories for the cracking of solids induced by differential drying or by cooling. We use this theory to give a simple quantitative explanation of how these geometrically similar crack patterns arise from a single dynamical law rooted in the nonequilibrium nature of the phenomena. We also give scaling relations for the characteristic crack spacing in other limits consistent with our experiments and observations, and discuss the implications of our results for the control of crack patterns in thin and thick solid films.

Structural mechanics of filamentous cyanobacteria.

Filamentous cyanobacteria, forming long strands of connected cells, are one of the earliest and most successful forms of life on Earth. They exhibit self-organized behaviour, forming large-scale patterns in structures like biomats and stromatolites. The mechanical properties of these rigid structures have contributed to their biological success and are important to applications like algae-based biofuel production. For active polymers like these cyanobacteria, one of the most important mechanical properties is the bending modulus, or flexural rigidity. Here, we quantify the bending stiffness of three species of filamentous cyanobacteria, of order Oscillatoriales, using a microfluidic flow device where single filaments are deflected by fluid flow. This is complemented by measurements of Young's modulus of the cell wall, via nanoindentation, and the cell wall thickness. We find that the stiffness of the cyanobacteria is well-captured by a simple model of a flexible rod, with most stress carried by a rigid outer wall. Finally, we connect these results to the curved shapes that these cyanobacteria naturally take while gliding, and quantify the forces generated internally to maintain this shape. The measurements can be used to model interactions between cyanobacteria, or with their environment, and how their collective behaviour emerges from such interactions.

Dispersive transport dynamics in porous media emerge from local correlations.

Understanding and controlling transport through complex media is central for a plethora of processes ranging from technical to biological applications. Yet, the effect of micro-scale manipulations on macroscopic transport dynamics still poses conceptual conundrums. Here, we demonstrate the predictive power of a conceptual shift in describing complex media by local micro-scale correlations instead of an assembly of uncorrelated minimal units. Specifically, we show that the non-linear dependency between microscopic morphological properties and macroscopic transport characteristics in porous media is captured by transport statistics on the level of pore junctions instead of single pores. Probing experimentally and numerically transport through two-dimensional porous media while gradually increasing flow heterogeneity, we find a non-monotonic change in transport efficiency. Using analytic arguments, we built physical intuition on how this non-monotonic dependency emerges from junction statistics. The shift in paradigm presented here broadly affects our understanding of transport within the diversity of complex media.