A method to calculate the location of all Bragg diffraction peaks from nanostructured thin films for arbitrary angles of incidence from just above the critical angle to transmission perpendicular to the film is reported. At grazing angles, the positions are calculated using the distorted wave Born approximation (DWBA), whereas for larger angles where the diffracted beams are transmitted though the substrate, the Born approximation (BA) is used. This method has been incorporated into simulation code (called NANOCELL) and may be used to overlay simulated spot patterns directly onto two-dimensional (2D) grazing angle of incidence small-angle X-ray scattering (GISAXS) patterns and 2D SAXS patterns. The GISAXS simulations are limited to the case where the angle of incidence is greater than the critical angle (alpha(i) > alpha(c)) and the diffraction occurs above the critical angle (alpha(f) > alpha(c)). For cases of surfactant self-assembled films, the limitations are not restrictive because, typically, the critical angle is around 0.2 degrees but the largest d spacings occur around 0.8 degrees 2theta. For these materials, one finds that the DWBA predicts that the spot positions from the transmitted main beam deviate only slightly from the BA and only for diffraction peaks close the critical angle. Additional diffraction peaks from the reflected main beam are observed in GISAXS geometry but are much less intense. Using these simulations, 2D spot patterns may be used to identify space group, identify the orientation, and quantitatively fit the lattice constants for SAXS data from any angle of incidence. Characteristic patterns for 2D GISAXS and 2D low-angle transmission SAXS patterns are generated for the most common thin film structures, and as a result, GISAXS and SAXS patterns that were previously difficult to interpret are now relatively straightforward. The simulation code (NANOCELL) is written in Mathematica and is available from the author upon request.

Nanoporous silica films with the double-gyroid structure offer tremendous technological potential for sensors and separations because of their high surface area and potentially facile transport properties. Further, metals and semiconductors with similar structure open up new opportunities for high-surfacearea electrodes, photoelectrochemical devices, photovoltaics, and thermoelectrics. Here, we report a new robust synthesis of highly ordered nanoporous silica films with the double-gyroid structure by evaporationinduced self-assembly (EISA) at room temperature and laboratory humidity using a commercially available EO 17 -PO 12 -C 14 surfactant. The continuous nanoporous films are synthesized on conducting electrodes. Electrochemical impedance spectroscopy is then used to quantitatively measure the accessible surface area of the underlying electrode via transport through the pore system. It is found that the double-gyroidstructure silica films expose a much higher fraction of the electrode than other commonly synthesized nanostructures such as 2D centered rectangular or 3D rhombohedral nanostructures. The double-gyroid nanoporous-film-coated electrodes are then used to fabricate inverse double-gyroid platinum nanostructures by electrodeposition, followed by etching to remove the silica. The structure of both the nanoporous silica films and the nanoporous platinum films (after etching) have been elucidated using high-resolution field-emission scanning electron microscopy (FESEM), comparing measured and simulated 2D grazing angle-of-incidence small-angle X-ray scattering (GISAXS) patterns, and comparing observed and simulated transmission electron microscopy (TEM) images. Both films are highly (211) oriented and described by a cubic Ia3 hd space group that has undergone uniaxial contraction perpendicular to the substrate. Upon this contraction, Ia3 hd symmetry is broken, but the films retain the double-gyroid topology. The nanoporous silica and the platinum nanowires have a characteristic wall or wire thicknesses of approximately 3 nm. This nanofabrication process opens up a facile general route for fabrication of ordered structures on the sub-5 nm length scale.

Ordered nanoporous silica films have attracted great interest for their potential use to template nanowires for photovoltaics and thermoelectrics. However, it is crucial to develop films such that an electrode under the nanoporous film is accessible to solution species via facile mass transport through well-defined pores. Here, we quantitatively measure the electrode accessibility and the effective species diffusivity for nearly all the known nanoporous silica film structures formed by evaporation-induced self-assembly upon dip-coating or spin-coating. Grazing-angle of incidence small-angle X-ray scattering was used to verify the nanoscale structure of the films and to ensure that all films were highly ordered and oriented. Electrochemical impedance spectroscopy (EIS) was then used to assess the transport properties. A model has been developed that separates the electrode/film kinetics and the film transport properties from the film/solution interface and bulk solution effects. Accounting for this, the accessible area of the nanoporous film coated FTO electrode (1-theta) is obtained from the high-frequency data, while the effective diffusivity of the ferrocene dimethanol (D(FDM)) redox couple is obtained from intermediate frequencies. It was found that the degree of order and orientation in the film, in addition to the symmetry/topology, is a dominant factor that determines these two key parameters. The EIS data show that the (211) oriented double gyroid, (110) oriented distorted body center cubic, and (211) distorted primitive cubic silica films have significant accessibility (larger than 26% of geometric area). However, the double-gyroid films showed the highest diffusivity by over an order of magnitude. Both the (10) oriented 2D hexagonal and (111) oriented rhombohedral films were found to be highly blocking with only small accessibility due to microporosity. The impedance data were also collected to study the stability of the nanoporous silica films in aqueous solutions as a function of pH. The distorted primitive silica film showed much faster degradation in pH 7 solution when compared to a blocking film such as the 2D hexagonal. However, silica films maintained their structure at pH 2 for at least 12 h.

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