Geometric fluctuations of a micellar particle

Abstract

When organic molecules containing hydrophobic and hydrophilic parts are dispersed in aqueous solutions micellar structures (micelles) are formed. These are spherical particles with hydrophilic “heads” at the surface and hydrophobic “tails” on the inside. They range from 20 to 1000 A in size. To within a certain approximation the micelle is a liquid drop with surface tension whose magnitude is determined by the interaction between the molecules forming the micelle. This holds true as long as the variation of the external influences with time remains sufficiently slow. In the presence of high-frequency external forces the micelle may be regarded as a solid spherical particle with a certain thickness and elasticity containing liquid on the inside. In this article a rigorous theoretical description of the fluctuations of the shape of the micellar particle is given over a broad interval of particle sizes and it is shown that the abovementioned models of a micellar particle are equally possible, since the corresponding vibration spectra are similar in form. The decisive influence of viscosity and surface tension relaxation processes on the vibration spectra of small micelles is also demonstrated.