Simulation of bicontinuous microemulsions: comparison of simulated real-space microstructures with scattering experiments

The ubiquitous scattering peak found in all disordered bicontinuous microemulsions, when scattering measurements are made with an oil-water contrast, is attributed to the existence of two length scales in the system. The two lengths, d and ξ, appear explicitly in the Debye correlation function for the microemulsion in a phenomenological model proposed by Teubner & Strey [J. Chem. Phys. (1987), 87, 3195–3200] (T–S model). The precise physical meaning of these two lengths, however, was not clear in the original paper. Cahn's scheme for simulating the morphology of the late-stage spinodal decomposition of a phase-separating two-component alloy is extended to the case of bicontinuous microemulsions with an equal volume fraction of oil and water. In the simulation, a length scale =2π/, representing the average interdomain distance (proportional to the average domain size), and another parameter z, relating to the dispersion of the domain size by Δk/ = (z + 1)^−1/2, are imposed. It is shown that the ratio ξ/d in the T–S model is a unique function of the parameter 1/z. The extended Cahn model gives both the real-space structure of a disordered bicontinuous microemulsion and the exact Debye correlation function for the calculation of the corresponding scattering intensity. A criterion is given for the realisation of the disordered bicontinuous structure in terms of a universal range for the dispersion (i.e. ξ/d). The existence of the two lengths, having a universal ratio, also implies that the scattering function I(Q) satisfies a certain scaling relation. Our SANS data are used to support the validity of such a scaling relation.