Growth of membranes formed by associating polymers at interfaces.

Polymer association at liquid-liquid interfaces is a promising way to spontaneously obtain soft self-healing membranes. In the case of reversible bonding between two polymers, the macromolecules are mobile everywhere within the membrane and they can be absorbed into it at both boundaries due to binding to macromolecules of the other type. In this work, we develop the theoretical model of membrane growth based on these assumptions. The asymptotic dependence of membrane thickness on time as h ∼ t1/2, as typically observed experimentally in a stationary regime, reveals an interdiffusion-controlled process, where the polymer fluxes sustain the polymer absorption. The membrane growth rate is mainly determined by the difference in equilibrium compositions at the boundaries, the association constant, the polymer lengths and mobilities. This model is further used to describe the growth of hydrogel membranes formed via H-bonding of polymers at the interface between a solution of poly(propylene oxide) (PPO) in isopropyl myristate and an aqueous solution of poly(methacrylic acid) (PMAA). The film thickness is measured by reflectometric methods. The growth rate slows down about 25 times for 500-nm-thick films at pH = 5.1 compared to the case of pH = 3. The ionization degree of PMAA solutions is studied by potentiometric methods. Even a small change in ionization is found to influence noticeably the growth rate of the film. In the diffusion-controlled regime, the slowdown can be explained by a drop in the composition gradient in the membrane, whereas the process becomes non-stationary if the absorption of PMAA is hindered by an interfacial electrostatic barrier.

Tuning the water intrinsic permeability of PEGDA hydrogel membranes by adding free PEG chains of varying molar masses.

We explore the effect of poly(ethylene glycol) (PEG) molar mass on the intrinsic permeability and structural characteristics of poly(ethylene glycol) diacrylate PEGDA/PEG composite hydrogel membranes. We observe that by varying the PEG content and molar mass, we can finely adjust the water intrinsic permeability by several orders of magnitude. Notably, we show the existence of maximum water intrinsic permeability, already identified in a previous study to be located at the critical overlap concentration C* of PEG chains, for the highest PEG molar mass studied. Furthermore, we note that the maximum intrinsic permeability follows a non-monotonic evolution with respect to the PEG molar mass and reaches its peak at 35 000 g mol-1. Besides, our results show that a significant fraction of PEG chains is irreversibly trapped within the PEGDA matrix even for the lowest molar masses down to 600 g mol-1. This observation suggests the possibility of covalent grafting of the PEG chains onto the PEGDA matrix. CryoSEM and AFM measurements demonstrate the presence of large micron-sized cavities separated by PEGDA-rich walls whose nanometric structures strongly depend on the PEG content. By combining our permeability and structural measurements, we suggest that the PEG chains trapped inside the PEGDA-rich walls induce nanoscale defects in the crosslinking density, resulting in increased permeability below C*. Conversely, above C*, we speculate that partially trapped PEG chains may form a brush-like arrangement on the surface of the PEGDA-rich walls, leading to a reduction in permeability. These two opposing effects are anticipated to exhibit molar-mass-dependent trends, contributing to the non-monotonic variation of the maximum intrinsic permeability at C*. Overall, our results demonstrate the potential to fine-tune the properties of hydrogel membranes, offering new opportunities for separation applications.

Coalescence of Elastic Blisters Filled with a Viscous Fluid.

Pockets of viscous fluid coalescing beneath an elastic sheet are encountered in a wide range of natural phenomena and engineering processes, spanning across scales. As the pockets merge, a bridge is formed with a height increasing as the sheet relaxes. We study the spatiotemporal dynamics of such an elastohydrodynamic coalescence process by combining experiments, lubrication theory, and numerical simulations. The bridge height exhibits an exponential growth with time, which corresponds to a self-similar solution of the bending-driven thin-film equation. We address this unique self-similarity and the self-similar shape of the bridge, both of which are corroborated in numerical simulations and experiments.

Lift at low Reynolds number.

Lift forces are widespread in hydrodynamics. These are typically observed for big and fast objects and are often associated with a combination of fluid inertia (i.e. large Reynolds numbers) and specific symmetry-breaking mechanisms. In contrast, the properties of viscosity-dominated (i.e. low Reynolds numbers) flows make it more difficult for such lift forces to emerge. However, the inclusion of boundary effects qualitatively changes this picture. Indeed, in the context of soft and biological matter, recent studies have revealed the emergence of novel lift forces generated by boundary softness, flow gradients and/or surface charges. The aim of the present review is to gather and analyse this corpus of literature, in order to identify and unify the questioning within the associated communities, and pave the way towards future research.

Sieving and Clogging in PEG-PEGDA Hydrogel Membranes.

Hydrogels are promising systems for separation applications due to their structural characteristics (i.e., hydrophilicity and porosity). In our study, we investigate the permeation of suspensions of rigid latex particles of different sizes through free-standing hydrogel membranes prepared by photopolymerization of a mixture of poly(ethylene glycol) diacrylate (PEGDA) and large poly(ethylene glycol) (PEG) chains of 300,000 g·mol-1 in the presence of a photoinitiator. Atomic force microscopy and cryoscanning electron microscopy (cryoSEM) were employed to characterize the structures of the hydrogel membranes. We find that the 20 nm particle permeation depends on both the PEGDA/PEG composition and the pressure applied during filtration. In contrast, we do not measure a significant permeation of the 100 nm and 1 µm particles, despite the presence of large cavities of 1 µm evidenced by the cryoSEM images. We suggest that the PEG chains induce local nanoscale defects in the cross-linking of PEGDA-rich walls separating the micrometer-sized cavities, which control the permeation of particles and water. Moreover, we discuss the decline of the permeation flux observed in the presence of latex particles compared to that of pure water. We suggest that a thin layer of particles forms on the surface of the hydrogels.

Surface and bulk relaxation of vapor-deposited polystyrene glasses.

We have studied the liquid-like response of the surface of vapor-deposited glassy films of polystyrene to the introduction of gold nanoparticles on the surface. The build-up of polymer material was measured as a function of time and temperature for both as-deposited films, as well as films that have been rejuvenated to become normal glasses cooled from the equilibrium liquid. The temporal evolution of the surface profile is well described by the characteristic power law of capillary-driven surface flows. In all cases, the surface evolution of the as-deposited films and the rejuvenated films is enhanced compared to bulk and is not easily distinguishable from each other. The temperature dependence of the measured relaxation times determined from the surface evolution is found to be quantitatively comparable to similar studies for high molecular weight spincast polystyrene. Comparisons to numerical solutions of the glassy thin film equation provide quantitative estimates of the surface mobility. For temperatures sufficiently close to the glass-transition temperature, particle embedding is also measured and used as a probe of bulk dynamics, and, in particular, bulk viscosity.

Numerical simulations of confined Brownian-yet-non-Gaussian motion.

Brownian motion is a central scientific paradigm. Recently, due to increasing efforts and interests towards miniaturization and small-scale physics or biology, the effects of confinement on such a motion have become a key topic of investigation. Essentially, when confined near a wall, a particle moves much slower than in the bulk due to friction at the boundaries. The mobility is therefore locally hindered and space-dependent, which in turn leads to the apparition of so-called multiplicative noises, and associated non-Gaussianities which remain difficult to resolve at all times. Here, we exploit simple, optimized and efficient numerical simulations to address Brownian motion in confinement in a broadrange and quantitative way. To do so, we integrate the overdamped Langevin equation governing the thermal dynamics of a negatively-buoyant single spherical colloid within a viscous fluid confined by two rigid walls, including surface charges. From the produced large set of long random trajectories, we perform a complete statistical analysis and extract all the key quantities, such as the probability distributions in displacements and their main moments. In particular, we propose a novel method to compute high-order cumulants by reducing convergence problems, and employ it to efficiently characterize the inherent non-Gaussianity of the confined process.

Non-Gaussian Diffusion Near Surfaces.

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

On the bridge hypothesis in the glass transition of freestanding polymer films.

Freestanding thin polymer films with high molecular weights exhibit an anomalous decrease in the glass-transition temperature with film thickness. Specifically, in such materials, the measured glass-transition temperature evolves in an affine way with the film thickness, with a slope that weakly depends on the molecular weight. De Gennes proposed a sliding mechanism as the hypothetical dominant relaxation process in these systems, where stress kinks could propagate in a reptation-like fashion through so-called bridges, i.e. from one free interface to the other along the backbones of polymer macromolecules. Here, by considering the exact statistics of finite-sized random walks within a confined box, we investigate in details the bridge hypothesis. We show that the sliding mechanism cannot reproduce the basic features appearing in the experiments, and we exhibit the fundamental reasons behind such a fact.

Nanoparticle Taylor Dispersion Near Charged Surfaces with an Open Boundary.

The dispersive spreading of microscopic particles in shear flows is influenced both by advection and thermal motion. At the nanoscale, interactions between such particles and their confining boundaries become unavoidable. We address the roles of electrostatic repulsion and absorption on the spatial distribution and dispersion of charged nanoparticles in near-surface shear flows, observed under evanescent illumination. The electrostatic repulsion between particles and the lower charged surface is tuned by varying electrolyte concentrations. Particles leaving the field of vision can be neglected from further analysis, such that the experimental ensemble is equivalent to that of Taylor dispersion with absorption. These two ingredients modify the particle distribution, deviating strongly from the Gibbs-Boltzmann form at the nanoscale studied here. The overall effect is to restrain the accessible space available to particles, which leads to a striking, tenfold reduction in the spreading dynamics as compared to the noninteracting case.

Near-critical spreading of droplets.

We study the spreading of droplets in a near-critical phase-separated liquid mixture, using a combination of experiments, lubrication theory and finite-element numerical simulations. The classical Tanner's law describing the spreading of viscous droplets is robustly verified when the critical temperature is neared. Furthermore, the microscopic cut-off length scale emerging in this law is obtained as a single free parameter for each given temperature. In total-wetting conditions, this length is interpreted as the thickness of the thin precursor film present ahead of the apparent contact line. The collapse of the different evolutions onto a single Tanner-like master curve demonstrates the universality of viscous spreading before entering in the fluctuation-dominated regime. Finally, our results reveal a counter-intuitive and sharp thinning of the precursor film when approaching the critical temperature, which is attributed to the vanishing spreading parameter at the critical point.

Nonlinear amplification of adhesion forces in interleaved books.

It is nearly impossible to separate two interleaved phonebooks by pulling their spines. The very slight force exerted by the outer sheets of the assembly is amplified as the exponential of the square of the number of sheets, meaning that even a small number of sheets can create a highly resistant system. We present a systematic and detailed study of the influences of the normal external force and the geometrical parameters of the booklets on the assembly strength. We conclude that the paper-paper adhesion force between the two outer sheets, on the order of a few [Formula: see text],  is the one amplified by the interleaved-book system. The two-phonebook experiment-which has attracted the attention of students and the non-scientific public all around the world as an outstanding demonstration of the strength of friction-appears to also be a spectacular macroscopic manifestation of the microscopic coupling of friction and adhesion.

Multifunctional Magnetic Nanocolloids for Hybrid Solar-Thermoelectric Energy Harvesting.

Present environmental issues force the research to explore radically new concepts in sustainable and renewable energy production. In the present work, a functional fluid consisting of a stable colloidal suspension of maghemite magnetic nanoparticles in water was characterized from the points of view of thermoelectrical and optical properties, to evaluate its potential for direct electricity generation from thermoelectric effect enabled by the absorption of sunlight. These nanoparticles were found to be an excellent solar radiation absorber and simultaneously a thermoelectric power-output enhancer with only a very small volume fraction when the fluid was heated from the top. These findings demonstrate the investigated nanofluid's high promise as a heat transfer fluid for co-generating heat and power in brand new hybrid flat-plate solar thermal collectors where top-heating geometry is imposed.

Growth Mechanism of Polymer Membranes Obtained by H-Bonding Across Immiscible Liquid Interfaces.

Complexation of polymers at liquid interfaces is an emerging technique to produce all-liquid printable and self-healing devices and membranes. It is crucial to control the assembly process, but the mechanisms at play remain unclear. Using two different reflectometric methods, we investigate the spontaneous growth of H-bonded PPO-PMAA (polypropylene oxide-polymetacrylic acid) membranes at a flat liquid-liquid interface. We find that the membrane thickness h grows with time t as h ∼ t1/2, which is reminiscent of a diffusion-limited process. However, counterintuitively, we observe that this process is faster as the PPO molar mass increases. We are able to rationalize these results with a model which considers the diffusion of the PPO chains within the growing membrane. The architecture of the latter is described as a gel-like porous network, with a pore size much smaller than the radius of the diffusing PPO chains, thus inducing entropic barriers that hinder the diffusion process. From the comparison between the experimental data and the result of the model, we extract some key piece of information about the microscopic structure of the membrane. This study opens the route toward the rational design of self-assembled membranes and capsules with optimal properties.

Mechanical properties of 2D aggregates of oil droplets as model mono-crystals.

We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.

Microscopic Picture of Erosion and Sedimentation Processes in Dense Granular Flows.

Gravity-driven flows of granular matter are involved in a wide variety of situations, ranging from industrial processes to geophysical phenomena, such as avalanches or landslides. These flows are characterized by the coexistence of solid and fluid phases, whose stability is directly related to the erosion and sedimentation occurring at the solid-fluid interface. To describe these mechanisms, we build a microscopic model involving friction, geometry, and a nonlocal cooperativity emerging from the propagation of collisions. This new picture enables us to obtain a detailed description of the exchanges between the fluid and solid phases. The model predicts a phase diagram including the limits of erosion and sedimentation, in quantitative agreement with experiments and discrete-element-method simulations.

Symmetrization of Thin Freestanding Liquid Films via a Capillary-Driven Flow.

We present experiments to study the relaxation of a nanoscale cylindrical perturbation at one of the two interfaces of a thin viscous freestanding polymeric film. Driven by capillarity, the film flows and evolves toward equilibrium by first symmetrizing the perturbation between the two interfaces and eventually broadening the perturbation. A full-Stokes hydrodynamic model is presented, which accounts for both the vertical and lateral flows and which highlights the symmetry in the system. The symmetrization time is found to depend on the membrane thickness, surface tension, and viscosity.

Rotation of a submerged finite cylinder moving down a soft incline.

A submerged finite cylinder moving under its own weight along a soft incline lifts off and slides at a steady velocity while also spinning. Here, we experimentally quantify the steady spinning of the cylinder and show theoretically that it is due to a combination of an elastohydrodynamic torque generated by flow in the variable gap, and the viscous friction on the edges of the finite-length cylinder. The relative influence of the latter depends on the aspect ratio of the cylinder, the angle of the incline, and the deformability of the substrate, which we express in terms of a single scaled compliance parameter. By independently varying these quantities, we show that our experimental results are consistent with a transition from an edge-effect dominated regime for short cylinders to a gap-dominated elastohydrodynamic regime when the cylinder is very long.

Cooperative strings and glassy dynamics in various confined geometries.

Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, by canceling and restarting any cooperative-chain realization reaching the boundary with a smaller number of steps than the bulk cooperativity, we account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale.

We present the first direct measurement of the elastohydrodynamic lift force acting on a sphere moving within a viscous liquid, near and along a soft substrate under nanometric confinement. Using atomic force microscopy, the lift force is probed as a function of the gap size, for various driving velocities, viscosities, and stiffnesses. The force increases as the gap is reduced and shows a saturation at small gap. The results are in excellent agreement with scaling arguments and a quantitative model developed from the soft lubrication theory, in linear elasticity, and for small compliances. For larger compliances, or equivalently for smaller confinement length scales, an empirical scaling law for the observed saturation of the lift force is given and discussed.