Space-resolved dynamic light scattering within a millimeter-sized drop: From Brownian diffusion to the swelling of hydrogel beads.

We present a dynamic light scattering setup to probe, with time and space resolution, the microscopic dynamics of soft matter systems confined within millimeter-sized spherical drops. By using an ad hoc optical layout, we tackle the challenges raised by refraction effects due to the unconventional shape of the samples. We first validate the setup by investigating the dynamics of a suspension of Brownian particles. The dynamics measured at different positions in the drop, and hence different scattering angles, are found to be in excellent agreement with those obtained for the same sample in a conventional light scattering setup. We then demonstrate the setup capabilities by investigating a bead made of a polymer hydrogel undergoing swelling. The gel microscopic dynamics exhibit a space dependence that strongly varies with time elapsed since the beginning of swelling. Initially, the dynamics in the periphery of the bead are much faster than in the core, indicative of nonuniform swelling. As the swelling proceeds, the dynamics slow down and become more spatially homogeneous. By comparing the experimental results to numerical and analytical calculations for the dynamics of a homogeneous, purely elastic sphere undergoing swelling, we establish that the mean square displacement of the gel strands deviates from the affine motion inferred from the macroscopic deformation, evolving from fast diffusivelike dynamics at the onset of swelling to slower, yet supradiffusive, rearrangements at later stages.

A double rigidity transition rules the fate of drying colloidal drops.

The evaporation of drops of colloidal suspensions plays an important role in numerous contexts, such as the production of powdered dairies, the synthesis of functional supraparticles, and virus and bacteria survival in aerosols or drops on surfaces. The presence of colloidal particles in the evaporating drop eventually leads to the formation of a dense shell that may undergo a shape instability. Previous works propose that, for drops evaporating very fast, the instability occurs when the particles form a rigid porous solid, constituted of permanently aggregated particles at random close packing. To date, however, no measurements could directly test this scenario and assess whether it also applies to drops drying at lower evaporation rates, severely limiting our understanding of this phenomenon and the possibility of harnessing it in applications. Here, we combine macroscopic imaging and space- and time-resolved measurements of the microscopic dynamics of colloidal nanoparticles in drying drops sitting on a hydrophobic surface, measuring the evolution of the thickness of the shell and the spatial distribution and mobility of the nanoparticles. We find that, above a threshold evaporation rate, the drop undergoes successively two distinct shape instabilities, invagination and cracking. While permanent aggregation of nanoparticles accompanies the second instability, as hypothesized in previous works on fast-evaporating drops, we show that the first one results from a reversible glass transition of the shell, unreported so far. We rationalize our findings and discuss their implications in the framework of a unified state diagram for the drying of colloidal drops sitting on a hydrophobic surface.

Spinning elastic beads: a route for simultaneous measurements of the shear modulus and the interfacial energy of soft materials.

Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a spinning drop tensiometer. We determine the equilibrium shapes of the beads from the competition between the centrifugal force and the restoring elastic and surface forces. Considering the beads as neo-Hookean up to large deformations, we show that their elastic modulus and interfacial energy constant can be simultaneously deduced from their equilibrium shape. Also, our results provide further support to the scenario in which interfacial energy and interfacial tension coincide for amorphous polymer gels.

The shape of hanging elastic cylinders.

Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: self-similar wrinkling hierarchies develop, and dimples appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.

Impact of Beads and Drops on a Repellent Solid Surface: A Unified Description.

We investigate freely expanding sheets formed by ultrasoft gel beads, and liquid and viscoelastic drops, produced by the impact of the bead or drop on a silicon wafer covered with a thin layer of liquid nitrogen that suppresses viscous dissipation thanks to an inverse Leidenfrost effect. Our experiments show a unified behavior for the impact dynamics that holds for solids, liquids, and viscoelastic fluids and that we rationalize by properly taking into account elastocapillary effects. In this framework, the classical impact dynamics of solids and liquids, as far as viscous dissipation is negligible, appears as the asymptotic limits of a universal theoretical description. A novel material-dependent characteristic velocity that includes both capillary and bulk elasticity emerges from this unified description of the physics of impact.

Gravity driven instability in elastic solid layers.

We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density ρ, shear modulus µ, put in a rigid cylindrical dish of depth h. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration g. It remains perfectly flat for ρgh/µ<α* with α*≃6, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.

Solid drops: large capillary deformations of immersed elastic rods.

Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends. These experimental results are compared to analysis and nonlinear simulations of neo-Hookean solids deformed by surface tension and are found to be in good agreement with each other.

Shape of an elastic loop strongly bent by surface tension: experiments and comparison with theory.

When a very flexible wire is dipped into a soapy solution, it collapses onto itself. We consider the regions of high curvature where the wire folds back onto itself, enclosing a capillary film. The shapes of these end loops are measured in experiments using soap films and compared to a known similarity solution. The sizes of these structures provide a simple and reliable way to measure surface tension.

Light and neutron scattering study of PEG-oleate and its use in emulsion polymerization.

Steric stabilization of colloids forms a robust mechanism to obtain colloids that are stable in a variety of environments, and that can be used to study the phase behavior of hard or soft spheres. We report the synthesis of sterically stabilized colloids in an aqueous environment using readily dissolvable surfactants, with an unsaturated hydrophobic tail. We synthesized a new surfactant by esterification of a poly(ethylene glycol) (PEG) chain of 4.1 kg/mol with oleic acid, called PEG4OA. The micellization of PEG4OA was characterized by light and neutron scattering, which yielded values for the aggregation number and the overall size that are in excellent agreement with a comparable surfactant with a saturated octadecane chain, Brij 700. We successfully used PEG4OA in the emulsion polymerization of polystyrene colloids. In comparison with the smaller surfactant Tween 80, PEG4OA yielded smaller colloids with radii around 50 nm, and the addition of 1-dodecanethiol reduced the formation of aggregates during the synthesis. A contrast variation study with small angle neutron scattering (SANS) showed that a dense PEG layer was grafted to the colloid surface.

Capillarity driven instability of a soft solid.

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.

Colloidal shape controlled by molecular adsorption at liquid crystal interfaces.

The ability to control finely the structure of materials remains a central issue in colloidal science. Due to their elastic properties, liquid crystals (LC) are increasingly used to organize matter at the micrometer scale in soft composites. Textures and shapes of LC droplets are currently controlled by the competition between elasticity and anchoring, hydrodynamic flows, or external fields. Molecules adsorbed specifically at LC interfaces are known to orient LC molecules (anchoring effect), but other induced effects have been poorly explored. Using specifically designed amphitropic surfactants, we demonstrate that large-shape transformations can be achieved in direct LC/water emulsions. In particular, we focus on unusual nematic filaments formed from spherical droplets. These results suggest new approaches to design new soft LC composite materials through the adsorption of molecules at liquid crystal interfaces.