From relaxation to buckling: A continuum elastic framework connecting surface instabilities of highly compressed lipid thin films.

Self-assembled thin films respond to external loads via surface instabilities that are critical to their functionality in both biology and technology. Lipid monolayers at the air-liquid interface are one such system. 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 underlying mechanistic generality. Yet, how in-plane relaxation occurs and how it is distinguished from folding remains elusive. Here, we use continuum mechanics, finite element (FE) simulations, and Langmuir trough fluorescence microscopy (FM) data to elucidate the underlying mechanisms of these elastic instability modes. Uniaxial loading of the Langmuir trough is evaluated in FE simulations, where the lipid monolayer is modeled as a thin sheet with a hyperelastic energy function developed to exhibit a relaxation mechanism. Results show that this material relaxation mechanism triggers tunable in-plane shear localization (shear banding). Furthermore, the simulation results of a heterogeneous model, built from fluorescence micrographs of lipid domains distributed in a continuous matrix, are rigorously compared with experimental data by domain organizational analyses. These analyses suggest shear bands are sufficient in inducing domain symmetry breaking that is characteristic of in-plane relaxation and, without such shear bands, domain organization remains in powder structure, characteristic of folding lipid monolayers. Our findings develop a hyperelastic model validated against experimental FM images that can connect the observed lipid monolayer instabilities of folding and in-plane relaxation, establishing a generalized framework with the potential to unify all other monolayer instability modes and characterize other thin film systems.