Thermal shape fluctuations of spherical surfactant micelles

Abstract

In this paper we re-examine the issue of shape fluctuations of (closed) spherical surfactant micelles which we have considered previously assuming potential streaming. For this purpose a micelle is modelled as a viscous hydrocarbon liquid droplet immersed in a viscous water solution. To the surface of the droplet we attribute an interfacial tension caused by the unfavourable hydrocarbon/water contact and the electrostatic interactions at the charged micelle surface.

The method of analysis comprises a solution of the linearized Navier–Stokes equation using appropriate boundary conditions and application of the fluctuation-dissipation theorem. We find that the shape fluctuations take place on a broad time scale. For the important oblate-prolate ellipsoid shape fluctuations with l= 2 symmetry the time constant ω^–1₀ is 3.36 × 10 ^–10s. The spectral function is determined chiefly by the viscosities and is nearly constant for ω < ω₀ and tends to zero above ω₀.

The amplitudes of the shape fluctuations are determined solely by the value of the effective surface tension, γ. Careful considerations show that for spherical micelles, γ has a value not less than 25 mN m^–1. Furthermore, we argue that the shape fluctuations may take place essentially without affecting the overall conformational free energy of the hydrocarbon chains which constitute the micellar core. Typically, the standard deviation of the core radius R is ca. 0.1 R, in agreement with our previous calculations.