Interfacial rheology of linearly growing polyelectrolyte multilayers at the water-air interface: from liquid to solid viscoelasticity.

Despite the long history of investigations of polyelectrolyte multilayer formation on solid or liquid surfaces, important questions remain open concerning the construction of the first set of layers. These are generally deposited on a first anchoring layer of different chemistry, influencing their construction and properties. We propose here an in-depth investigation of the formation of NaPSS/PAH multilayers at the air/water interface in the absence of a chemically different anchoring layer, profiting from the surface activity of NaPSS. To analyse the mechanical properties of the different layers, we combine recently established analysis techniques of an inflating/deflating bubble exploiting simultaneous shape and pressure measurement: bubble shape elastometry, general stress decomposition and capillary meniscus dynanometry. We complement these measurements by interfacial shear rheology. The obtained results allow us to confirm, first of all, the strength of the aforementioned techniques to characterize complex interfaces with non-linear viscoelastic properties. Furthermore, their sensitivity allows us to show that the multilayer properties are highly sensitive to the temporal and mechanical conditions under which they are constructed and manipulated. We nevertheless identify a robust trend showing a clear transition from a liquid-like viscoelastic membrane to a solid-like viscoelastic membrane after the deposition of 5 layers. We interpret this as the number of layers required to create a fully connected multilayer, which is consistent with previous results obtained on solid or liquid interfaces.

Solidification of Polyurethane Model Foams via Catalyst Drainage from a Secondary Foam.

Due to their unique mechanical and thermal properties, polyurethane foams are widely used in multiple fields of applications, including cushioning, thermal insulation or biomedical engineering. However, the way polyurethane foams are usually manufactured - via chemical foaming - produces samples where blowing and gelling occurs at the same time, resulting in a morphology control achieved by trial and error processes. Here, we introduce a novel strategy to build model homogeneous polyurethane foams of controlled density with millimetric bubbles from liquid templates. We show that by producing a polyurethane foam via physical bubbling without a catalyst and gently depositing a secondary foam containing catalyst on the top of this first foam, we can take advantage of drainage mechanisms to trigger the solidification of the bottom foam. The characterisation of our samples performed by X-ray microtomography allows us to study quantitatively the structure of the final solid foam, at the global and at the local scale. Using the tomographic three-dimensional images of the foam architectures, we show that the superimposed foam technique introduced in this article is promising to produce foams with a good homogeneity along the vertical direction, with a density controlled by varying the concentration of catalyst in the secondary foam. This article is protected by copyright. All rights reserved.

Elastocapillary deformation of thin elastic ribbons in 2D foam columns.

The ability of liquid interfaces to shape slender elastic structures provides powerful strategies to control the architecture of mechanical self assemblies. However, elastocapillarity-driven intelligent design remains unexplored in more complex architected liquids - such as foams. Here we propose a model system which combines an assembly of bubbles and a slender elastic structure. Arrangements of soap bubbles in confined environments form well-defined periodic structures, dictated by Plateau's laws. We consider a 2D foam column formed in a container with square cross-section in which we introduce an elastomer ribbon, leading to architected structures whose geometry is guided by a competition between elasticity and capillarity. In this system, we quantify both experimentally and theoretically the equilibrium shapes, using X-ray micro-tomography and energy minimisation techniques. Beyond the understanding of the amplitude of the wavy elastic ribbon deformation, we provide a detailed analysis of the profile of the ribbon, and show that such a setup can be used to grant a shape to a UV-curable composite slender structure, as a foam-forming technique suitable to miniaturisation. In more general terms, this work provides a stepping stone towards an improved understanding of the interactions between liquid foams and slender structures.

Investigating Pore-Opening of Hydrogel Foams at the Scale of Freestanding Thin Films.

Controlling the pore connectivity of polymer foams is key for most of their applications, ranging from liquid uptake, mechanics, and acoustic/thermal insulation to tissue engineering. Despite their importance, the scientific phenomena governing the pore-opening processes remain poorly understood, requiring tedious trial-and-error procedures for property optimization. This lack of understanding is partly explained by the high complexity of the different interrelated, multiscale processes which take place as the foam transforms from an initially fluid foam into a solid foam. To progress in this field, this work takes inspiration from long-standing research on liquid foams and thin films to develop model experiments in a microfluidic "Thin Film Pressure Balance." These experiments allow the investigation of isolated thin films under well-controlled environmental conditions reproducing those arising within a foam undergoing cross-linking and drying. Using the example of alginate hydrogel films, the evolution of isolated thin films undergoing gelation and drying is correlated with the evolution of the rheological properties of the same alginate solution in bulk. The overall approach is introduced and a first set of results is presented to propose a starting point for the phenomenological description of the different types of pore-opening processes and the classification of the resulting pore-opening types.

Pressure-deformation relations of elasto-capillary drops (droploons) on capillaries.

An increasing number of multi-phase systems exploit complex interfaces in which capillary stresses are coupled with solid-like elastic stresses. Despite growing efforts, simple and reliable experimental characterisation of these interfaces remains a challenge, especially of their dilational properties. Pendant drop techniques are convenient, but suffer from complex shape changes and associated fitting procedures with multiple parameters. Here we show that simple analytical relationships can be derived to describe reliably the pressure-deformation relations of nearly spherical elasto-capillary droplets ("droploons") attached to a capillary. We consider a model interface in which stresses arising from a constant interfacial tension are superimposed with mechanical extra-stresses arising from the deformation of a solid-like, incompressible interfacial layer of finite thickness described by a neo-Hookean material law. We compare some standard models of liquid-like (Gibbs) and solid-like (Hookean and neo-Hookean elasticity) elastic interfaces which may be used to describe the pressure-deformation relations when the presence of the capillary can be considered negligible. Combining Surface Evolver simulations and direct numerical integration of the drop shape equations, we analyse in depth the influence of the anisotropic deformation imposed by the capillary on the pressure-deformation relation and show that in many experimentally relevant circumstances either the analytical relations of the perfect sphere may be used or a slightly modified relation which takes into account the geometrical change imposed by the capillary. Using the analogy with the stress concentration around a rigid inclusion in an elastic membrane, we provide simple non-dimensional criteria to predict under which conditions the simple analytical expressions can be used to fit pressure-deformation relations to analyse the elastic properties of the interfaces via "Capillary Pressure Elastometry". We show that these criteria depend essentially on the drop geometry and deformation, but not on the interfacial elasticity. Moreover, this benchmark case shows for the first time that Surface Evolver is a reliable tool for predictive simulations of elastocapillary interfaces. This opens doors to the treatment of more complex geometries/conditions, where theory is not available for comparison. Our Surface Evolver code is available for download in the ESI.

Impact of Fluorocarbon Gaseous Environments on the Permeability of Foam Films to Air.

A foam film, free to move and stabilized with tetradecyltrimethylammonium bromide or sodium dodecylsulfate surfactants, is deposited inside of a cylindrical tube. It separates the tube into two distinct gaseous compartments. The first compartment is filled with air, while the second one contains a mixture of air and perfluorohexane vapor (C6F14), which is a barely water-soluble fluorinated compound. This foam film thus acts as a liquid semipermeable membrane for gases equivalent to the solid semipermeable membranes conventionally used in fluid separation processes. To infer the rate of air transfer through the membrane, we measure the displacement of the mobile foam film. From this, we deduce the instantaneous permeability of the membrane. In contrast to the permeability of solid membranes, which inexorably decreases over time because they become clogged, an anticlogging effect is observed with a permeability that systematically increases over time. Because the thickness of the film is constant over time, we attribute this to the possibility of adsorbing or desorbing fluorinated gas molecules on the liquid membrane. Indeed, because the partial pressure of the fluorinated gas is high at the beginning of the experiment, the density of the adsorbed molecules is also high, which leads to a low permeability to air transfer. On the contrary, at the end of the experiment, the partial pressure in fluorinated gas and thus the density of the adsorbed molecules are low. This leads to a higher permeability and a less clogged membrane.

Validation of Milner's visco-elastic theory of sintering for the generation of porous polymers with finely tuned morphology.

Sacrificial sphere templating has become a method of choice to generate macro-porous materials with well-defined, interconnected pores. For this purpose, the interstices of a sphere packing are filled with a solidifying matrix, from which the spheres are subsequently removed to obtain interconnected voids. In order to control the size of the interconnections, viscous sintering of the initial sphere template has proven a reliable approach. To predict how the interconnections evolve with different sintering parameters, such as time or temperature, Frenkel's model has been used with reasonable success over the last 70 years. However, numerous investigations have shown that the often complex flow behaviour of the spheres needs to be taken into account. To this end, S. Milner [arXiv:1907.05862] developed recently a theoretical model which improves on some key assumptions made in Frenkel's model, leading to a slightly different scaling. He also extended this new model to take into account the visco-elastic response of the spheres. Using an in-depth investigation of templates of paraffin spheres, we provide here the first systematic comparison with Milner's theory. Firstly, we show that his new scaling describes the experimental data slightly better than Frenkel's scaling. We then show that the visco-elastic version of his model provides a significantly improved description of the data over a wide parameter range. We finally use the obtained sphere templates to produce macro-porous polyurethanes with finely controlled pore and interconnection sizes. The general applicability of Milner's theory makes it transferable to a wide range of formulations, provided the flow properties of the sphere material can be quantified. It therefore provides a powerful tool to guide the creation of sphere packings and porous materials with finely controlled morphologies.

Juggling bubbles in square capillaries: an experimental proof of non-pairwise bubble interactions.

The physical properties of an ensemble of tightly packed particles like bubbles, drops or solid grains are controlled by their interactions. For the case of bubbles and drops it has recently been shown theoretically and computationally that their interactions cannot generally be represented by pair-wise additive potentials, as is commonly done for simulations of soft grain packings. This has important consequences for the mechanical properties of foams and emulsions, especially for strongly deformed bubbles or droplets well above the jamming point. Here we provide the first experimental confirmation of this prediction by quantifying the interactions between bubbles in simple model foams consisting of trains of equal-volume bubbles confined in square capillaries. The obtained interaction laws agree quantitatively with Surface Evolver simulations and are well described by an analytically derived expression based on the recently developed non-pairwise interaction model of Höhler et al. [Soft Matter, 2017, 13(7), 1371], based on Morse-Witten theory. While all experiments are done at Bond numbers sufficiently low for the hydrostatic pressure variation across one bubble to be negligible, we provide the full analysis taking into account gravity in the appendix for the interested reader. Even though the article focuses on foams, all results directly apply to the case of emulsions.

Generation of Solid Foams with Controlled Polydispersity Using Microfluidics.

Many properties of solid foams depend on the distribution of the pore sizes and their organization in space. However, these two parameters are very difficult to control with most traditional foaming techniques. Here we show how microfluidics can be used to tune the polydispersity of the foams (mono- vs different polydispersities) and the spatial organization of the pores (ordered vs disordered). For this purpose, the microfluidic flow-focusing technique was modified such that the gas pressure oscillates periodically, which translates into periodically oscillating bubble sizes in the liquid foam template. The liquid foams were generated from chitosan solutions and then gelled via cross-linking with genipin before we freeze-dried them to obtain a solid foam with a specific structure. The study at hand fills two existing scientific gaps. On the one hand, we present a novel approach for the generation of foams with controlled polydispersity. On the other hand, we obtained a solid foam with a new structure for foam templating consisting of rhombic dodecahedra. The controlled variation of the foam's structure will allow studying systematically structure-property relations. Moreover, being fully biobased, this type of solid foam is a suitable candidate for applications in tissue engineering.

Skinny emulsions take on granular matter.

Our understanding of the structural features of foams and emulsions has advanced significantly over the last 20 years. However, with a search for "super-stable" liquid dispersions, foam and emulsion science employs increasingly complex formulations which create solid-like visco-elastic layers at the bubble/drop surfaces. These lead to elastic, adhesive and frictional forces between bubbles/drops, impacting strongly how they pack and deform against each other, asking for an adaptation of the currently available structural description. The possibility to modify systematically the interfacial properties makes these dispersions ideal systems for the exploration of soft granular materials with complex interactions. We present here a first systematic analysis of the structural features of such a system using a model silicone emulsion containing millimetre-sized polyethylene glycol drops (PEG). Solid-like drop surfaces are obtained by polymeric cross-linking reactions at the PEG-silicone interface. Using a novel droplet-micromanipulator, we highlight the presence of elastic, adhesive and frictional interactions between two drops. We then provide for the first time a full tomographic analysis of the structural features of these emulsions. An in-depth analysis of the angle of repose, local volume fraction distributions, pair correlation functions and the drop deformations for different skin formulations allow us to put in evidence the striking difference with "ordinary" emulsions having fluid-like drop surfaces. While strong analogies with frictional hard-sphere systems can be drawn, these systems display a set of unique features due to the high deformability of the drops which await systematic exploration.

Emulsion and Foam Templating-Promising Routes to Tailor-Made Porous Polymers.

Emulsions, foams, and foamed emulsions have been used successfully as templates for the synthesis of macroporous polymers. Based on this knowledge this Minireview presents strategies to use, optimise, and upscale these templating methods to synthesise tailor-made porous polymers. The uniqueness of such polymers lies in the ability to tailor their structures and, therefore, their properties. However, systematic studies on structure-property relations are lacking mainly because the templating scientific community is "split into two": the polydisperse and monodisperse camps. Thus, it is time to build a bridge between the camps, that is, to synthesise porous polymers with very different structures from the same precursors to determine the relationship between the structure and the properties.

Creating Honeycomb Structures in Porous Polymers by Osmotic Transport.

Understanding why honeycombs are shaped the way they are has moved biologists, physicists, chemists, and mathematicians alike. It was only recently that the honeycombs' shape "at birth" was included in the ongoing discussions: at birth, the cells are spherical but then transform into the well-known hexagons. It was proposed that a flow of wax-driven by surface tension effects-is the reason for this transformation. Our recent work on synthetic polymer foams with honeycomb-like structures points towards a very different mechanism. Just like in honeycomb cells, we observe that a spherical "initial state" transforms into a hexagon-shaped "final state" during polymerization. We have experimental evidence that a concentration gradient arises during polymerization, which transports monomers such that the spherical template becomes a honeycomb structure with walls of homogeneous thickness. The knowledge about this mechanism suggests promising strategies for the development of lightweight materials with optimized mechanical properties.

Coalescence In Draining Foams Made of Very Small Bubbles.

We studied the stability of foams containing small bubbles (radius ≲ 50 µm). The foams are made from aqueous surfactant solutions containing various amounts of glycerol. The foams start breaking at their top, when the liquid volume fraction has decreased sufficiently during liquid drainage. Unlike in foams with larger bubbles, the liquid fraction at which the foam destabilizes is surprisingly high. In order to interpret this observation we propose that film rupture occurs during reorganization events (T1) induced by bubble coarsening, which is particularly rapid in the case of small bubbles. New films are therefore formed rapidly and if their thickness is too small, they cannot be sufficiently covered by surfactant and they break. Using literature data for the duration of T1 events and the thickness of the new films, we show that this mechanism is consistent with the behavior of the foams studied.

Life and death of not so "bare" bubbles.

In this paper, we investigate how the drainage and rupture of surfactant-stabilised bubbles floating at the surface of a liquid pool depend on the concentration of surface-active molecules in water. Drainage measurements at the apex of bubbles indicate that the flow profile is increasingly plug-like as the surfactant concentration is decreased from several times the critical micellar concentration (cmc) to just below the cmc. High-speed observations of bubble bursting reveal that the position at which a hole nucleates in the bubble cap also depends on the surfactant concentration. On average, the rupture is initiated close to the bubble foot for low concentrations (

The surface tells it all: relationship between volume and surface fraction of liquid dispersions.

The properties of liquid dispersions, such as foams or emulsions, depend strongly on the volume fraction ϕ of the continuous phase. Concentrating on the example of foams, we show experimentally and theoretically that ϕ may be related to the fraction ϕs of the surface at a wall which is wetted by the continuous phase - given an expression for the interfacial energy or osmotic pressure of the bulk system. Since the surface fraction ϕs can be readily determined from optical measurement and since there are good general approximations available for interfacial energy and osmotic pressure we thus arrive at an advantageous method of estimating ϕ. The same relationship between ϕ and ϕs is also expected to provide a good approximation of the fraction of the bubble or drop surface which is wetted by the continuous phase. This is a parameter of great importance for the rheology and ageing of liquid dispersions.

Generation of Silicone Poly-HIPEs with Controlled Pore Sizes via Reactive Emulsion Stabilization.

Macrocellular silicone polymers are obtained after solidification of the continuous phase of a poly(dimethylsiloxane) emulsion, which contains poly(ethylene glycol) drops of sub-millimetric dimensions. Coalescence of the liquid template emulsion is prohibited by a reactive blending approach. The relationship is investigated in detail between the interfacial properties and the emulsion stability, and micro- and millifluidic techniques are used to generate macrocellular polymers with controlled structural properties over a wider range of cell sizes (0.2-2 mm) and volume fractions of the continuous phase (0.1%-40%). This approach could easily be transferred to a wide range of polymeric systems.

Foams stabilised by mixtures of nanoparticles and oppositely charged surfactants: relationship between bubble shrinkage and foam coarsening.

We have studied foams stabilised by surfactant-decorated nanoparticles adsorbed at the bubble surfaces. We show that the controlled compression of a single bubble allows one to understand the coarsening behavior of these foams. When bubbles are compressed, the particles become tightly packed in the surface layer. They lose their mobility, and the interface becomes solid-like when the jammed state is reached. Further compression leads to interfacial buckling characterised by crumpled surfaces. We find that the surface concentration of particles at which the jamming and the buckling transitions occur are independent of the surfactant concentration. This is a surprising feature. It suggests that the surfactants are mandatory to help the particles adsorb at the interface and that they change the equilibrium surface concentration of the decorated particles. But they do not affect the surface properties once the particles are adsorbed. We measured the compression elastic modulus of the surface in the jammed state and found it to be compatible with the Gibbs condition for which the spontaneous dissolution of bubbles is arrested. Due to this effect, the coarsening process of a foam composed of many close-packed bubbles occurs in two steps. In the first step, coarsening is slow and coalescence of the bigger bubbles is observed. In the second step, a number of very small bubbles remains, which exhibit crumpled surfaces and are stable over long times. This suggests that foam coarsening is arrested once the smallest bubbles become fully covered after the initial shrinking step.

Adsorption, organization, and rheology of catanionic layers at the air/water interface.

We have investigated the adsorption and organization at the air/water interface of catanionic molecules released from a dispersion of solid-like catanionic vesicles composed of myristic acid and cetyl trimethylammonium chloride at the 2:1 ratio. These vesicles were shown recently to be promising foam stabilizers. Using Brewster angle microscopy, we observed the formation of a catanionic monolayer at the air/water interface composed of liquid-condensed domains in a liquid-expanded matrix. Further adsorption of catanionic molecules forced them to pack, thereby forming a very dense monolayer that prevented further vesicle rupture by avoiding contact of the vesicles with air. Moreover, confocal fluorescence microscopy revealed the presence of layers of intact vesicles that were progressively creaming toward this catanionic monolayer; the surface tension of the vesicle dispersion remained constant upon creaming. The catanionic monolayer behaved as a soft glassy material, an amorphous solid with time- and temperature-dependent properties. Using interfacial oscillatory rheology, we found that the monolayer relaxed mechanical stresses in seconds and melted at a temperature very close to the melting transition temperature of the vesicle bilayers. These results have potential application in the design of smart foams that have temperature-tunable stability.

Acoustic characterisation of liquid foams with an impedance tube.

Acoustic measurements provide convenient non-invasive means for the characterisation of materials. We show here for the first time how a commercial impedance tube can be used to provide accurate measurements of the velocity and attenuation of acoustic waves in liquid foams, as well as their effective "acoustic" density, over the 0.5-6kHz frequency range. We demonstrate this using two types of liquid foams: a commercial shaving foam and "home-made" foams with well-controlled physico-chemical and structural properties. The sound velocity in the latter foams is found to be independent of the bubble size distribution and is very well described by Wood's law. This implies that the impedance technique may be a convenient way to measure in situ the density of liquid foams. Important questions remain concerning the acoustic attenuation, which is found to be influenced in a currently unpredictible manner by the physico-chemical composition and the bubble size distribution of the characterised foams. We confirm differences in sound velocities in the two types of foams (having the same structural properties) which suggests that the physico-chemical composition of liquid foams has a non-negligible effect on their acoustic properties.

On how surfactant depletion during foam generation influences foam properties.

Although it is known that foaming a surfactant solution results in a depletion of the surfactant in the bulk phase, this effect is often overlooked and has never been quantified. Therefore, the influence of surfactant depletion on foam properties using solutions of the two nonionic surfactants, n-dodecyl-ß-D-maltoside (ß-C(12)G(2)) and hexaethyleneglycol monododecyl ether (C(12)E(6)), were investigated. These investigations were conducted in two steps. First, different foam volumes were generated with the same surfactant solution at a concentration of c = 2 cmc. It was found that the higher the foam volume, the larger the surfactant depletion. Second, two different bulk concentrations (c = 2 and 1.33 cmc) were used for the generation of 50 and 110 mL of foam, respectively. For a foam volume of 50 mL, no differences were observed, whereas generating 110 mL led to different results. The surfactant loss in the bulk solution was measured via surface tension measurements and then compared to the results of purely geometric considerations that take into account the amount of interface created in the foam. Both results were in very good agreement, which means that surfactant depletion can be calculated in the way suggested here. Under conditions where depletion plays a role, our approach can also be used to estimate the bubble size of a foam of known volume by measuring the surfactant concentration in the bulk solution after foaming.