Single-particle brownian dynamics for characterizing the rheology of fluid langmuir monolayers

The Brownian movement of a submicron diameter sphere has been used to study the rheology of Langmuir monolayers of short-chain surfactants in the low-density limit (liquidexpanded phase). We show how the shear viscosity can be derived from previously measured diffusion coefficients (Sickert M. and Rondelez F., Phys. Rev. Lett. 90 (2003) 126104) by using recent theoretical models for a sphere of size much larger than the monolayer thickness. We report the surface viscosity as a function of the occupied surface fraction, which we believe are the first such estimates based on physically consistent experiments and theory. The two models yield values of the surface viscosity 1-5×10^-10 Ns/m and 2-8×10^-10 Ns/m over the entire range of surface densities of the liquid-expanded phase.