We provide a C/C++ software for the shape analysis of deflated elastic capsules in a pendant capsule geometry, which is based on an elastic description of the capsule material as a quasi two-dimensional elastic membrane using shell theory. Pendant capsule elastometry provides a new in situ and non-contact method for interfacial rheology of elastic capsules that goes beyond determination of the Gibbs- or dilational modulus from area-dependent measurements of the surface tension using pendant drop tensiometry, which can only give a rough estimate of the elastic capsule properties as they are based on a purely liquid interface model. Given an elastic model of the capsule membrane, pendant capsule elastometry determines optimal elastic moduli by fitting numerically generated axisymmetric shapes optimally to an experimental image. For each digitized image of a deflated capsule elastic moduli can be determined, if another image of its undeformed reference shape is provided. Within this paper, we focus on nonlinear Hookean elasticity because of its low computational cost and its wide applicability, but also discuss and implement alternative constitutive laws. For Hookean elasticity, Young's surface modulus (or, alternatively, area compression modulus) and Poisson's ratio are determined; for Mooney-Rivlin elasticity, the Rivlin modulus and a dimensionless shape parameter are determined; for neo-Hookean elasticity, only the Rivlin modulus is determined, using a fixed dimensionless shape parameter. Comparing results for different models we find that nonlinear Hookean elasticity is adequate for most capsules. If series of images are available, these moduli can be evaluated as a function of the capsule volume to analyze hysteresis or aging effects depending on the deformation history or to detect viscoelastic effects for different volume change rates. An additional wrinkling wavelength measurement allows the user to determine the bending modulus, from which the layer thickness can be derived. We verify the method by analyzing several materials, compare the results to available rheological measurements, and review several applications. We make the software available under the GPL license at github.com/jhegemann/opencapsule.
This publication is focused on the structural origin of viscoelasticity in Langmuir monolayers. To improve the understanding of the structural origin of viscoelasticity of surfactant films, we systematically studied interfacial films of different sorbitan esters with saturated (Span 60 and 65) and unsaturated (Span 80 and 85) paraffin chains by means of surface rheology, Langmuir isotherms, X‐ray reflectometry (XRR), and Brewster angle microscopy (BAM). The results of two‐dimensional shear rheological measurements revealed the existence of temporarily cross‐linked networks. In dynamic BAM experiments, we observed a swinging motion of the monolayers as a result of a sudden externally initiated mechanical perturbation. The viscoelastic film response, which relaxed with time as the external force vanished, could be traced back to the presence of foam‐like supramolecular structures that interlinked solid‐condensed domains. The temperature dependence of the elastic response implied that the solid domains decomposed at temperatures close to the bulk melting point of Span 60 and Span 65. We concluded that insoluble surfactants formed solid domains at the interface, which were linked with each other by nonsolid areas, giving viscoelastic films. These newly discovered insights into coherent film formations could provide new opportunities for designing mechanically stable surfactant interfaces.
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