Visualization of 3D microstructure of bicontinuous microemulsions by combined SANS experiments and simulations

Abstract

SANS studies were made on a three-component microemulsion system, with equal volume fractions of water and oil, in the one-phase region near the three-phase body, at the hydrophile—lipophile balance temperature, as a function of surfactant volume fraction φs. A prominent peak was found in the scattering intensity distribution, the position of which (Qmax) scaled linearly with φs. This scaling relation can be derived from a model of bicontinuous microemulsions proposed by Teubner and Strey (J. Chem. Phys., 87 (1987) 3195). It can be shown that the generic microstructure of these microemulsions is bicontinuous, characterized by two length scales d and ξ, where d is the average inter-domain distance between two water or oil domains and d/ξ the disorder parameter measuring polydispersity of the domain sizes. Based on this idea, we propose a simulation scheme, which is an extension of an idea of Berk (Phys. Rev. Lett., 58 (1987) 2718-2721; Phys. Rev. A, 44 (1991) 5069-5079), which allows us to generate both the 3D microstructure and the associated Debye correlation function, which can be Fourier transformed to obtain the theoretical scattering intensity distribution function. The main input to this simulation is a spectral function which is an inverse of a sixth order polynomial, containing three length scales. 3D micro-structures are then generated which are fully consistent with the scattering data. Physical meaning of the three length scales so obtained is discussed and compared with the two length scales d and ξ obtained from fitting the Teubner—Strey model to the same data.