Two-dimensional shear modulus of a Langmuir foam

Abstract

We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 $\pm$ 0.4 pJ$\cdot$m$^{-1}$) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, $\mu= 38 \pm 3 \mathrm{nN}\cdot \mathrm{m}^{-1}$. The foam effective rigidity is predicted to be $ 35 \pm 3 \mathrm {nN}\cdot \mathrm {m}^{- 1}$, which agrees with the value $37.5 \pm 0.8 \mathrm {nN}\cdot \mathrm {m}^{-1}$ obtained in an independent mechanical measurement.