Multiscale geometry and mechanics of lipid monolayer collapse

Langmuir monolayers at gas/liquid interfaces provide a rich framework to investigate the interplay between multi-scale geometry and mechanics. Monolayer collapse is investigated at a topological and geometric level by building a scale space M from experimental imaging data. We present a general lipid monolayer collapse phase diagram, which shows that wrinkling, folding, crumpling, shear banding, and vesiculation are a continuous set of mechanical states that can be approached by either tuning monolayer composition or temperature. The origin of the different mechanical states can be understood by investigating the monolayer geometry at two scales: fluorescent versus atomic force microscopy imaging. We show that an interesting switch in continuity occurs in passing between the two scales, C_AFM ∈M_AFM ≠C_FM ∈M. Studying the difference between monolayers that fold versus shear band, we show that shear banding is correlated to the persistence of a multilength scale microstructure within the monolayer at all surface pressures. A detailed analytical geometric formalism to describe this microstructure is developed using the theory of structured deformations. Lastly, we provide the first finite element simulations of lipid monolayer collapse utilizing a direct mapping from the experimental image space M into a simulation domain P. We show that elastic dissipation in the form of bielasticity is a necessary and sufficient condition to capture loss of in-plane stability and shear banding.