Heitkam, S., Drenckhan, W., Weaire, D., & Froehlich, J. (2016). Beam model for the elastic properties of material with spherical voids. Archive Of Applied Mechanics, 86(12, Si), 165–176.
Abstract: The elastic properties of a material with spherical voids of equal volume are analysed using a new model, with particular attention paid to the hexagonal closepacked and the facecentred cubic arrangement of voids. Void fractions well above 74 % are considered, yielding overlapping voids as in an opencell foam and hence a connected pore structure. The material is represented by a network of beams. The elastic behaviour of each beam is derived analytically from the material structure. By computing the linear elastic properties of the beam network, the Young's moduli and Poisson ratios for different directions are evaluated. In the limit of rigidity loss, a power law is obtained, describing the relation between Young's modulus and void fraction with an exponent of 5/2 for bendingdominated and 3/2 for stretchingdominated directions. The corresponding Poisson ratios vary between 0 and 1. With decreasing void fraction, these exponents become 2.3 and 1.3, respectively. The data obtained analytically and from the new beam model are compared to finite element simulations carried out in a companion study, and good agreement is found. The hexagonal closepacked void arrangement features anisotropic behaviour, comparable to that of fibrereinforced materials. This may give rise to new applications of opencell materials.


Champougny, L., Roche, M., Drenckhan, W., & Rio, E. (2016). Life and death of not so “bare” bubbles. Soft Matter, 12(24), 5276–5284.
Abstract: In this paper, we investigate how the drainage and rupture of surfactantstabilised bubbles floating at the surface of a liquid pool depend on the concentration of surfaceactive molecules in water. Drainage measurements at the apex of bubbles indicate that the flow profile is increasingly pluglike as the surfactant concentration is decreased from several times the critical micellar concentration (cmc) to just below the cmc. Highspeed 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 (<cmc) while its locus moves towards the top of the bubble cap as the concentration increases above the cmc. In order to explain this transition, we propose that marginal regeneration may be responsible for bubble rupture at low concentrations but that bursting at the apex for higher concentrations is driven by gravitational drainage.


Forel, E., Rio, E., Schneider, M., Beguin, S., Weaire, D., Hutzler, S., et al. (2016). The surface tells it all: relationship between volume and surface fraction of liquid dispersions. Soft Matter, 12(38), 8025–8029.
Abstract: The properties of liquid dispersions, such as foams or emulsions, depend strongly on the volume fraction phi of the continuous phase. Concentrating on the example of foams, we show experimentally and theoretically that phi may be related to the fraction phi(s) 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 phi(s) 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 phi. The same relationship between phi and phi(s) 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.


BricenoAhumada, Z., Drenckhan, W., & Langevin, D. (2016). Coalescence In Draining Foams Made of Very Small Bubbles. Physical Review Letters, 116(12).
Abstract: We studied the stability of foams containing small bubbles (radius less than or similar to 50 mu m). 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.


Quell, A., de Bergolis, B., Drenckhan, W., & Stubenrauch, C. (2016). How the Locus of Initiation Influences the Morphology and the Pore Connectivity of a Monodisperse Polymer Foam. Macromolecules, 49(14), 5059–5067.
Abstract: The properties of polymer foams are tightly linked to the porous structure of the material: two of the most decisive parameters are the interconnectivity of the pores and the thickness of the pore walls. Despite the vital importance of these parameters, a deep understanding of the processes that control the wall thickness and the pore opening is still lacking. We tackle these questions by studying monodisperse, highly ordered polymer foams which are generated via emulsion templating using microfluidic labonachip techniques. We explore the influence of different processing parameters, and we show that the most crucial parameter is the locus where the polymerization is initiated. If initiation starts within the continuous monomer matrix, the morphology of the liquid template is “frozen in” with pore openings arising where neighboring drops are separated by thin films. However, if the locus of initiation is at the interface, not only do the pores remain closed, but we evidence a hitherto unexplained mechanism which leads to an osmotically driven redistribution of monomer in the walls during polymerization. This changes dramatically the pore morphology (polyhedral pores with thick walls) and therefore the final material properties opening the pathway to new applications of low weight or acoustic bandgap materials.


Heitkam, S., Drenckhan, W., Titscher, T., Weaire, D., Kreuter, D. C., Hajnal, D., et al. (2016). Elastic properties of solid material with various arrangements of spherical voids. European Journal Of Mechanics ASolids, 59, 252–264.
Abstract: In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The voids are arranged on crystalline lattices (SC, BCC, FCC and HCP structure) or randomly, and may overlap in order to produce connected voids. In that way, the entire range of void fraction between 0.00 and 0.95 is covered, including closedcell and opencell structures. For each arrangement of voids and for different void fractions the full stiffness tensor is computed. From this, the Young's modulus and Poisson ratios are derived for different orientations. Special care is taken of assessing and reducing the numerical uncertainty of the method. In that way, a reliable quantitative comparison of different void structures is carried out. Among other things, this work shows that the Young's modulus of FCC in the (1 1 1) plane differs from HCP in the (0 0 0 1) plane, even though these structures are very similar. For a given void fraction SC offers the highest and the lowest Young's modulus depending on the direction. For BCC at a critical void fraction a switch of the elastic behaviour is found, as regards the direction in which the Young's modulus is maximised. For certain crystalline void arrangements and certain directions Poisson ratios between 0 and 1 were found, including values that exceed the bounds for isotropic materials. For subsequent investigations the full stiffness tensor for a range of void arrangements and void fractions are provided in the supplemental material. (C) 2016 Elsevier Masson SAS. All rights reserved.


Giustiniani, A., Guegan, P., Marchand, M., Poulard, C., & Drenckhan, W. (2016). Generation of Silicone PolyHIPEs with Controlled Pore Sizes via Reactive Emulsion Stabilization. Macromolecular Rapid Communications, 37(18), 1527–1532.
Abstract: Macrocellular silicone polymers are obtained after solidification of the continuous phase of a poly(dimethylsiloxane) emulsion, which contains poly(ethylene glycol) drops of submillimetric 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 macro cellular polymers with controlled structural properties over a wider range of cell sizes (0.22 mm) and volume fractions of the continuous phase (0.1%40%). This approach could easily be transferred to a wide range of polymeric systems.


Salonen, A., Gay, C., Maestro, A., Drenckhan, W., & Rio, E. (2016). Arresting bubble coarsening: A twobubble experiment to investigate grain growth in the presence of surface elasticity. Epl, 116(4).
Abstract: Many twophase materials suffer from grain growth due to the energy cost which is associated with the interface that separates both phases. While our understanding of the driving forces and the dynamics of grain growth in different materials is well advanced by now, current research efforts address the question of how this process may be slowed down, or, ideally, arrested. We use a model system of two bubbles to explore how the presence of a finite surface elasticity may interfere with the coarsening process and the final grain size distribution. Combining experiments and modelling in the analysis of the evolution of two bubbles, we show that clear relationships can be predicted between the surface tension, the surface elasticity and the initial/final size ratio of the bubbles. We rationalise these relationships by the introduction of a modified Gibbs criterion. Besides their general interest, the present results have direct implications for our understanding of foam stability. Copyright (C) EPLA, 2016


Amalian, J.  A., Trinh, T. T., Lutz, J.  F., & Charles, L. (2016). MS/MS Digital Readout: Analysis of Binary Information Encoded in the Monomer Sequences of Poly(triazole amide)s. Analytical Chemistry, 88(7), 3715–3722.
Abstract: Tandem mass spectrometry was evaluated as a reliable sequencing methodology to read codes encrypted in monodisperse sequencecoded oligo(triazole amide)s. The studied oligomers were composed of monomers containing a triazole ring, a short ethylene oxide segment, and an amide group as well as a short alkyl chain (propyl or isobutyl) which defined the 0/1 molecular binary code. Using electrospray ionization, oligo(triazole amide)s were best ionized as protonated molecules and were observed to adopt a single charge state, suggesting that adducted protons were located on every other monomer unit. Upon collisional activation, cleavages of the amide bond and of one ether bond were observed to proceed in each monomer, yielding two sets of complementary product ions. Distribution of protons over the precursor structure was found to remain unchanged upon activation, allowing charge state to be anticipated for product ions in the four series and hence facilitating their assignment for a straightforward characterization of any encoded oligo(triazole amide)s.


Wolff, J., Komura, S., & Andelman, D. (2016). Budding transition of asymmetric twocomponent lipid domains. Phys. Rev. E, 94(3), 032406.

