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.

PEG-in-PDMS drops stabilised by soft silicone skins as a model system for elastocapillary emulsions with explicit morphology control.

HYPOTHESIS: The morphology of ordinary macro-emulsions is controlled by their high interfacial energies, i.e., by capillarity, leading to well-known structural features which can be tuned only over a narrow range. We claim here that a more explicit control over a much wider range of morphologies can be obtained by producing "elastocapillary emulsions" in which interfacial elasticity acts simultaneously with interfacial tension. EXPERIMENTS: We develop a model-system composed of PEG-in-PDMS emulsions, in which a catalyst diffuses from the PEG drops into the silicone matrix containing two reactive silicone polymers, which are cross-linked in a non-reactive silicone matrix to form a silicone gel of controlled thickness and mechanical properties on the drop surface. We characterise the cross-linking process of the gel in bulk and at the interface, and we analyse the skin growth kinetics. We then use the obtained understanding to produce emulsions with controlled elastocapillary interfaces using in-flow-chemistry in a purpose-designed millifluidic circuit. FINDINGS: We show that this approach allows to create interfaces over the full range of elastocapillary properties, and that very different emulsion morphologies can be generated depending on whether capillarity or elasticity dominates. These findings advance our fundamental understanding of the morphology of emulsions with complex interfaces, and they are of importance for the design of polymerised High Internal Phase Emulsions (polyHIPEs) with original structure/property relations. They will also be useful for the design of silicone capsules with fine-tuned mechanical properties.

Perturbing the catenoid: Stability and mechanical properties of nonaxisymmetric minimal surfaces.

Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability, and mechanical stresses of minimal surfaces spanning specific geometric boundaries. The "catenoid" is the best-known example where an analytical solution is known which describes the form and stability of a minimal surface held between two parallel, concentric circular frames. Here we extend this problem to nonaxisymmetric, parallel frame shapes of different orientations by developing a perturbation approach around the known catenoid solution. We show that the predictions of the perturbation theory are in good agreement with experiments on soap films and finite element simulations (Surface Evolver). Combining theory, experiment, and simulation, we analyze in depth how the shapes, stability, and mechanical properties of the minimal surfaces depend on the type and orientation of elliptic and three-leaf clover shaped frames. In the limit of perfectly aligned nonaxisymmetric frames, our predictions show excellent agreement with a recent theory established by Alimov et al. [Phys. Fluids 33, 052104 (2021)1070-663110.1063/5.0047461]. Moreover, we put in evidence the intriguing capacity of minimal surfaces between nonaxisymmetric frames to transmit a mechanical torque despite being completely liquid. These forces could be interesting to exploit for mechanical self-assembly of soft matter systems or as highly sensitive force captors.

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.

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.

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.

Less is more: Unstable foams clean better than stable foams.

HYPOTHESIS: Foamed surfactant solutions can clean surfaces! We hypothesise that the cleaning efficiency depends on the liquid fraction and on the stability of the foam. We also hypothesise that the cleaning efficiency is the better the smaller the average bubble size is. EXPERIMENTS: The double syringe technique was used to generate foams with varying liquid fractions but the same, very small bubble sizes with and without perfluorohexane in the gas phase. We performed cleaning tests in which the foams were applied to glass substrates contaminated with a fluorescent oil. FINDINGS: We found that unstable foams clean better than stable foams. Three cleaning mechanisms were identified: (1) imbibition at low liquid fractions, (2) wiping, i.e., shifting of the contact line between oil, foam and glass, at all liquid fractions, and (3) drainage at high liquid fractions. The change of the liquid fraction and of the foam stability lead to different combinations of these mechanisms and thus to different cleaning results.

Tailoring and visualising pore openings in gelatin-based hydrogel foams.

HYPOTHESIS: While tailoring the pore diameters in hydrogel foams has been demonstrated in numerous studies, fine control over the diameters of the pore openings is still a challenge. We hypothesise that this can be achieved by controlling the size of the thin films which separate the bubbles in the liquid foam template. If this is the case, systematic changes of the template's gas fraction ϕ (the higher ϕ, the larger are the thin films) will lead to corresponding changes of the pore opening diameter. EXPERIMENTS: Since the size of the thin films depends on both bubble size 〈Db〉 and gas fraction ϕ, we need to decouple both parameters to control the film size. Thus, we generated foams with constant bubble sizes via microfluidics and adjusted the gas fractions via two different techniques. The foams were solidified using UV light. Subsequently, they were analysed with confocal fluorescence microscopy. FINDINGS: We were able to change the pore opening diameter 〈dp〉 at a constant pore diameter 〈Dp〉 by adjusting the gas fraction of the foam template. The obtained 〈dp〉/〈Dp〉 ratios are between those obtained theoretically for disordered foams and FCC ordered foams, respectively.

Microfluidic thin film pressure balance for the study of complex thin films.

Investigations of free-standing liquid films enjoy an increasing popularity due to their relevance for many fundamental and applied scientific problems. They constitute soap bubbles and foams, serve as membranes for gas transport or as model membranes in biophysics. More generally, they provide a convenient tool for the investigation of numerous fundamental questions related to interface- and confinement-driven effects in soft matter science. Several approaches and devices have been developed in the past to characterise reliably the thinning and stability of such films, which were commonly created from low-viscosity, aqueous solutions/dispersions. With an increasing interest in the investigation of films made from strongly viscoelastic and complex fluids that may also solidify, the development of a new generation of devices is required to manage reliably the constraints imposed by these formulations. We therefore propose here a microfluidic chip design which allows for the reliable creation, control and characterisation of free-standing films of complex fluids. We provide all technical details and we demonstrate the device functioning for a larger range of systems via a selection of illustrative examples, including films of polymer melts and gelling hydrogels.

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.

Corrigendum: A simple collision model for small bubbles (2017 J. Phys.: Condens. Matter 29 124005).

The original manuscript contains scribal errors in the main equation. This corrigendum contains the correct equations. Results and conclusions in the original manuscript are not affected.

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.

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.

Liquid foam templating - A route to tailor-made polymer foams.

Solid foams with pore sizes between a few micrometres and a few millimetres are heavily exploited in a wide range of established and emerging applications. While the optimisation of foam applications requires a fine control over their structural properties (pore size distribution, pore opening, foam density, …), the great complexity of most foaming processes still defies a sound scientific understanding and therefore explicit control and prediction of these parameters. We therefore need to improve our understanding of existing processes and also develop new fabrication routes which we understand and which we can exploit to tailor-make new porous materials. One of these new routes is liquid templating in general and liquid foam templating in particular, to which this review article is dedicated. While all solid foams are generated from an initially liquid(-like) state, the particular notion of liquid foam templating implies the specific condition that the liquid foam has time to find its "equilibrium structure" before it is solidified. In other words, the characteristic time scales of the liquid foam's stability and its solidification are well separated, allowing to build on the vast know-how on liquid foams established over the last 20 years. The dispersed phase of the liquid foam determines the final pore size and pore size distribution, while the continuous phase contains the precursors of the desired porous scaffold. We review here the three key challenges which need to be addressed by this approach: (1) the control of the structure of the liquid template, (2) the matching of the time scales between the stability of the liquid template and solidification, and (3) the preservation of the structure of the template throughout the process. Focusing on the field of polymer foams, this review gives an overview of recent research on the properties of liquid foam templates and summarises a key set of studies in the emerging field of liquid foam templating. It finishes with an outlook on future developments. Occasional references to non-polymeric foams are given if the analogy provides specific insight into a physical phenomenon.

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.

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.

Interfacial tension of reactive, liquid interfaces and its consequences.

Dispersions of immiscible liquids, such as emulsions and polymer blends, are at the core of many industrial applications which makes the understanding of their properties (morphology, stability, etc.) of great interest. A wide range of these properties depend on interfacial phenomena, whose understanding is therefore of particular importance. The behaviour of interfacial tension in emulsions and polymer blends is well-understood - both theoretically and experimentally - in the case of non-reactive stabilization processes using pre-made surfactants. However, this description of the interfacial tension behaviour in reactive systems, where the stabilizing agents are created in-situ (and which is more efficient as a stabilization route for many systems), does not yet find a consensus among the community. In this review, we compare the different theories which have been developed for non-reactive and for reactive systems, and we discuss their ability to capture the behaviour found experimentally. Finally, we address the consequences of the reactive stabilization process both on the global emulsions or polymer blend morphologies and at the interfacial scale.

A simple collision model for small bubbles.

In this work, a model for the interaction force between a small bubble and a wall or another bubble is presented. The formulation is especially designed for Lagrangian calculations of bubble or soft sphere trajectories, with or without resolution of the continuous fluid. The force only relies on position and velocity of the bubble. The model does not include any empirical parameter that would have to be calibrated. Therefore, this force model is easy to implement. The formulation of the force is explicit, which means low computational effort. The collision of a small bubble with an inclined top wall is investigated numerically and experimentally. The computational results achieved with the new collision model show good agreement with the experiment.

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.