Towards predicting shear-banding instabilities in lipid monolayers.

Langmuir monolayers are advantageous systems used to investigate how lipid membranes get involved in the physiology of many living structures, such as collapse phenomena in alveolar structures. Much work focuses on characterizing the pressure-bearing capacity of Langmuir films, expressed in the form of isotherm curves. These show that monolayers experience different phases during compression with an according evolution of their mechanical response, incurring into instability events when a critical stress threshold is overcome. Although well-known state equations, which establish an inverse relationship between surface pressure and area change, are able to properly describe monolayer behaviour during liquid expanded phase, the modelling of their nonlinear behaviour in the subsequent condensed region is still an open issue. In this regard, most efforts are addressed to explain out-of-plane collapse by modelling buckling and wrinkling mainly resorting to linearly elastic plate theory. However, some experiments on Langmuir monolayers also show in-plane instability phenomena leading to the formation of the so-called shear bands and, to date, no theoretical description of the onset of shear banding bifurcation in monolayers has been yet provided. For this reason, by adopting a macroscopic description, we here study material stability of the lipid monolayers and exploit an incremental approach to find the conditions that kindle shear bands. In particular, by starting from the widely assumed hypothesis that monolayers behave elastically in the solid-like region, in this work a hyperfoam hyperelastic potential is introduced as a new constitutive strategy to trace back the nonlinear response of monolayer response during densification. In this way, the obtained mechanical properties together with the adopted strain energy are successfully employed to reproduce the onset of shear banding exhibited by some lipid systems under different chemical and thermal conditions.

Interfacial rheology of coexisting solid and fluid monolayers.

Biologically relevant monolayer and bilayer films often consist of micron-scale high viscosity domains in a continuous low viscosity matrix. Here we show that this morphology can cause the overall monolayer fluidity to vary by orders of magnitude over a limited range of monolayer compositions. Modeling the system as a two-dimensional suspension in analogy with classic three-dimensional suspensions of hard spheres in a liquid solvent explains the rheological data with no adjustable parameters. In monolayers with ordered, highly viscous domains dispersed in a continuous low viscosity matrix, the surface viscosity increases as a power law with the area fraction of viscous domains. Changing the phase of the continuous matrix from a disordered fluid phase to a more ordered, condensed phase dramatically changes the overall monolayer viscosity. Small changes in the domain density and/or continuous matrix composition can alter the monolayer viscosity by orders of magnitude.

Wilhelmy plate artifacts in elastic monolayers.

A recent article [L. Pocivavsek et al., Soft Matter4, 2019 (2008)] by some of us pointed out difficulties in interpreting Wilhelmy plate measurements on elastic Langmuir monolayers that support anisotropic stress. Using a simplified geometry it showed conditions in which the Wilhelmy plate measures significantly different stress from the ambient stress. We correct a serious error in this analysis and strengthen its conclusion, showing that the Wilhelmy stress and the ambient stress can have opposite signs.

Microscopic folds and macroscopic jerks in compressed lipid monolayers.

We report hitherto unrecognized cooperative behavior in the stochastic collapse of certain compressed lipid monolayers implicated in pulmonary function. The cooperativity emerges from a statistical analysis of the collapse events captured using fluorescence microscopy and digital image analysis. The collapse events involve folding of the monolayer on a micron scale, yet each event produces a macroscopic jerk of the layer. The cooperative collapse is striking for its temporal sharpness and large spatial extent.

Surface charge relaxation and the pearling instability of charged surfactant tubes.

The pearling instability of bilayer surfactant tubes was recently observed during the collapse of fluid monolayers of binary mixtures of Dimyristoylphosphocholine (DMPC): Palmitoyloleoylphosphoglycerol (POPG) and Dipalmitoylphosphocholine (DPPC):POPG surfactants. It can be explained by a Rayleigh-like instability under the action of the bilayer surface tension. The magnitude of surface tension is dictated by the electrostatic interaction between charged surfactants. Relaxation of charged molecules is proposed here as an additional mechanism driving the instability. We find the functional dependence of the electrostatic surface tension and relaxation energies on the screening length kappa(-1) explicitly. Relaxation lowers the cost of bending a tube into pearls making the cylindrical tube even more unstable. It is known that for the weak screening case in which the tube radius is smaller than the screening length of the solution, this effect is important. However, for the case of strong screening it is negligible. For the experiments mentioned, the situation is marginal. In this case, we show that the effect of relaxation remains small. It contributes about 20% to the total electrostatic energy.