Experimental investigation of the structure of nonionic microemulsions and their relation to the bending elasticity of the amphiphilic film

Oil-in-water microemulsions of nonionic surfactants of type ${\mathrm{C}}_n{E}_j$ with various hydrocarbons have been characterized by means of small-angle-neutron-scattering (SANS) (carried out at the Laboratoire Leon Brillouin, CEA-CNRS, Saclay, France) and interfacial tension measurements. The obtained structural parameters (radius $R$ and polydispersity index $p$) of this droplet system and the interfacial tension $\gamma$ were related to the bending elasticity of the amphiphilic film that can be described by the spontaneous curvature and two elastic constants, bending modulus $\kappa$ and saddle-splay modulus $\overline{\kappa }$. The validity of our method to extract $p$ from the shape analysis of the scattering curves has been confirmed by an independent contrast variation experiment. Both $p$ and $\gamma$ lead independently for all systems to very similar values for the elastic moduli. Their sum $2\kappa +\overline{\kappa }$ is proportional to the chain length of the surfactant but independent of our employed hydrocarbons (hexane→decane). Finally, we also performed SANS experiments for a dilution series, where from the concentration dependence of $R$ and $p$ we are able to deduce independently this sum of the elastic constants that agrees well with the values obtained before. The elastic theory of the amphiphilic film allows for a self-consistent interpretation of structural and interfacial tension data and also to reliably predict one of these quantities from the knowledge of the other ones.