Effects of droplet fluctuations on the scattering of neutrons and light by microemulsions

Beginning from the first neutron spin-echo study of the shape fluctuations of microemulsion droplets [J.S. Huang, S.T. Milner, B. Farago, and D. Richter, Phys. Rev. Lett. 59, 2600 (1987)] these experiments are incorrectly interpreted in the literature. This is due to an inappropriate account for the fluctuations and the erroneous application of the original theory to the experiments (see [V. Lisy and B. Brutovsky, Czech. J. Phys. 50, 239 (2000)]). In the presented work both these shortcomings are corrected. We develop the theory of static and dynamic light and neutron scattering from droplet microemulsions. The fluids inside and out of the droplets are separated by a surfactant layer of arbitrary thickness. The scattering functions consistently take into account thermal fluctuations of the shapes of such double-layered spheres to the second order in the changes of their radius. The relaxation times and correlation functions of the fluctuations are found within the Helfrich's theory of interfacial elasticity. The theory is applied to the quantitative description of small-angle neutron scattering, neutron spin-echo spectroscopy and dynamic light scattering experiments. Basic characteristics of the microemulsions, extracted from the fits to the experimental data, significantly differ from those determined in the original works. We include into the consideration the viscosity of the surface layer and give its estimation for the octane-C10E5- water microemulsion.