Morphological characterization of bicontinuous structures in polymer blends and microemulsions by the inverse-clipping method in the context of the clipped-random-wave model

A method is proposed to determine the spectral function of the clipped-random-wave (CRW) model directly from scattering data. The spectral function f(k) (k is a wave number) gives the distribution of the magnitude of wave vectors of the sinusoidal waves that describes the essential features of the two-phase morphology. The proposed method involves ''inverse clipping'' of a correlation function to obtain f(k) and does not require any a priori assumptions for f(k), A critical test of the applicability of the inverse-clipping method was carried out by using three-component bicontinuous microemulsions. The method was then used to determine f(k) of the bicontinuous structure of a phase-separating polymer blend. f(k) for the polymer blend turned out to be a multipeaked function, while f(k) for the microemulsions exhibits a single broad maximum representing periodicity of the morphology. These results indicate the presence of the long-range regularity in the morphology of the polymer blend. Three-dimensional (3D) morphology corresponding to the scattering data of the polymer blend was generated using the CRW model together with the multipeaked f(k). Interface curvatures of the 3D morphology calculated from SI (k) were measured and compared with those experimentally determined directly from the laser scanning confocal microscopy in the same blend.