Measurement of the bending elasticity of a monolayer: ellipsometry and reflectivity

Abstract

The bending elasticity of a monolayer at a liquid interface can be deduced from the analysis of the optical properties of the interface which are sensitive to interfacial thermal fluctuations of short wavelengths. There are two techniques; the first is ellipsometry which is very sensitive to short wavelengths and therefore is an accurate method to measure the bending elasticity but needs large thermal fluctuations. It is limited to liquid interfaces of low surface tension (γ ∼ 10⁻² mN/m) and low bending elasticity (K ∼ κ _B T) and our analysis takes into account the coupling between thermal modes through a renormalization of the surface tension and the bending elasticity with the scale. The second method consists of the measurement of x-ray reflectivity which is sensitive to the whole spectrum of the thermal fluctuations and, consequently, is less accurate than ellipsometry; however, it allows study of monolayers of large surface tension at the free surface of a liquid. It has recently given interesting information about the jumps of the bending elasticity of a monolayer at some phase transitions.