Modeling of gyroidal mesoporous CMK-8 and CMK-9 carbon nanostructures and their X-Ray diffraction patterns

Powder X-ray diffraction (XRD) patterns of ordered mesoporous CMK-8 and CMK-9 carbon materials are simulated by geometric modeling. The materials are amorphous at the atomic length scale but exhibit highly symmetric gyroidal structures at the nanometer scale, corresponding to regular, continuous nanopore systems with cubic symmetry. Their structures lead to characteristic low-angle XRD signatures. We introduce a model based on geometrical considerations to simulate CMK-8 and CMK-9 structures with variable volume fraction of carbon (vs. pore volume, i.e., variable 'pore wall thickness'). In addition, we also simulate carbon materials with variable amounts of guest species (e.g., sulfur) residing in their pores. The corresponding XRD patterns are calculated. The carbon volume fraction turns out to have a significant impact on the relative diffraction peak intensities, especially in case of CMK-9 carbon that features a bimodal porosity. Likewise, the presence of guest species in the pores may also strongly affect the relative peak intensities. Our study suggests that careful evaluation of experimental low-angle XRD patterns of (real) CMK-8 or CMK-9 materials offers an opportunity to obtain detailed information about the nanostructural properties in addition to the mere identification of the pore systems geometry.