Abstract
Emergent nanoscale order in materials such as self-assembled lipid phases, colloidal materials and metal-organic frameworks is often characterized by small-angle X-ray scattering (SAXS). Frequently, residual disorder in these materials prevents high-resolution 3D structural characterization. Here we demonstrate that angular intensity variations in SAXS patterns can provide previously inaccessible information about local 3D structure via a rich, real-space distribution of three- and four-body statistics. We present the many-body characterisation of a monoolein-based hexagonal phase doped with a phospholipid, revealing non-uniform curvature in the lipid channels, likely due to phase separation of the lipids in the membrane. Our many-body technique has general applicability to nanomaterials with order in the range 10 nm−1 μm currently targeted by synchrotron SAXS and has the potential to impact diverse research areas within chemistry, biology and materials science.
Highlights
Emergent nanoscale order in materials such as self-assembled lipid phases, colloidal materials and metal-organic frameworks is often characterized by small-angle X-ray scattering (SAXS)
We have proposed that the intensity correlation data can be converted into a three- and four-body real space distribution[16] that we call the pair-angle distribution function (PADF)
The relationship we have found between the PADF and the fluctuation diffraction data requires that the local structures or crystal domains have no preferred orientation with respect to the beam axis, which is further discussed in Supplementary Methods S1
Summary
Emergent nanoscale order in materials such as self-assembled lipid phases, colloidal materials and metal-organic frameworks is often characterized by small-angle X-ray scattering (SAXS). The angular intensity variations contain 3D structural information that is targeted by emerging X-ray fluctuation diffraction techniques such as X-ray cross-correlation analysis[7,8,9], largely inspired by the pioneering work of Kam in the 1970s on the fluctuations of small-angle protein scattering[10] These methods study intensity correlations of pairs of pixels on the detector as a function of scattering vector magnitude and angular separation averaged over a large number of independent measurements. The X-ray scattering of structural models must be forward simulated to compare to q-space intensity calculations and it is not always obvious how to improve models to rectify discrepancies between simulation and experiment To address this limitation, we have proposed that the intensity correlation data can be converted into a three- and four-body real space distribution[16] that we call the pair-angle distribution function (PADF) (see Fig. 1c). The PADF analysis accounts for Ewald sphere curvature and the PADF symmetry persists even at high scattering angles where diffraction centrosymmetry is broken by Ewald sphere curvature
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