A Continuum Elastic Framework Connecting Surface Instabilities of Highly Compressed Lipid Thin Films

Self-assembled thin films, such as lipid monolayers at the air-liquid interface, respond to loads via surface instabilities that are critical to their functionality. Tunability between out-of-plane buckling (e.g., folding) and in-plane relaxation (e.g., reorganization of lipid domains) in highly compressed lipid monolayers suggests generality, yet the mechanism behind this remains elusive. Here, we use continuum mechanics, finite element (FE) simulations, and Langmuir trough fluorescence microscopy (FM) data to probe the mechanisms governing these elastic instability modes. Loading of the Langmuir trough is evaluated in FE simulations, where the lipid monolayer is modeled as a hyperelastic thin sheet developed to exhibit a relaxation that triggers tunable in-plane shear localization (shear banding). Simulation results of a heterogeneous model, built from FM images of condensed domain morphology, are rigorously compared to experimental domain organization. These analyses suggest shear bands are sufficient in inducing domain symmetry breaking that is characteristic of in-plane relaxation and, without shear bands, domain organization remains in powder structure, characteristic of folding. Our findings develop a hyperelastic model validated against experimental data that can connect lipid monolayer instabilities of folding and in-plane relaxation, establishing a generalized framework with the potential to unify monolayer instabilities and characterize other thin film systems.