Axisymmetric Drop Shape Shape Analysis with Anisotropic Stress Distribution In Quasi-Static Fluid/Fluid Interfaces: a Metric for Nanomembrane Mechanics

Fluid-fluid interfaces offer a unique opportunity for engineering self-assembled nanostructured membranes because of the access afforded by the adjoining bulk phase.  Although an increasing number of investigations describe new routes to produce these types of surface materials, detailed studies of mechanical and the constitutive parameters that describe them are relatively scarce.  This is because quantitative experimental techniques are limited due to the length scales involved. 

Recently, we introduced a new experimental technique to quantify mechanical behavior of soft nanomembranes using a pendant drop.  In short, a molecular template is adsorbed from solution onto the surface of a pendant drop.  The subphase of the drop is then cycled alternatively with other surface active species which self-assemble or react to form an ultrathin nanocomposite at the drop surface. 

To characterize the mechanical properties of the nanocomposite, the pendant drop is hydrostatically inflated, and the deformed shape is observed. Unless the inflation is purely spherical, anisotropic surface stresses develop in the two principle directions of the surface.  With the framework of linear elasticity, the surface stress is related to the deformation via the membrane’s elastic properties, the elastic modulus and Poisson ratio (E_s , ν). 

The equations of equilibrium for the nanomembrane relate the divergence of the surface stresses at any point in the nanomembrane to the jump in pressure across the membrane.  Coupled equations are then obtained which relate the undeformed and deformed shapes of the membrane to the constitutive parameters.  By comparing the experimentally measured deformed membrane profiles to theory and minimizing the error between theory and experiment, the parameters describing the mechanical behavior of the membrane are determined.  Solutions of the equations of equilibrium as a function of constitutive parameters are presented.  These form the basis for an inverse method for the measure of elastic constants of a variety of nanomembrane systems.  Comparison of theory and experiment for nanomembranes based on different chemistries are discussed.