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.

submitted May 12, 2003 ; resubmitted Sept 9, 2003