Grazing-Incidence, Small-angle X-ray Scattering (GI-SAXS) is an excellent tool to characterize nanoscale morphologies, especially in thin-films. Recent reports in literature have applied scattering-intensity scaling laws like Porod's law or the Debye-Bueche law to yield quantitative information about length of inhomogeneity and surface-to-volume ratios in nanostructured systems. However, these laws were intended for isotropic, three-dimensional two-phase systems, and as such, their application to anisotropic, lower-dimensional nanostructured materials requires verification. In this work, we present a method to verify Porod's law in two and three dimensions for simulated morphologies of varying anisotropy, from the limiting case of lamella/slabs to uniformly isotropic, spinodal-like systems. The methods involve a �brute-force� ray casting method, in which random lines through simulated morphologies are analyzed of their average content of phase one or phase two, and the length of inhomogeneity compared to that calculated from the inverse-space scattering information. This method can also be applied to real-space data such as AFM or SEM images, which when used in conjunction with scattering data provides information about the ratio of the two phases. This methodology is applicable to any two-phase nanostructured system which is pseudo-isotropic or 2D due to ultra-thin film form factors, making it useful for characterizing block copolymers, nanostructured carbons or metals, and bulk heterojunction polymer/fullerene blends. 

Quantitative measurements of anisotropic nanostructured two-phase materials

248th National Meeting (2014)

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