Design of schwarzite templates based on energy minimization of surfaces

Porous carbon network forming inside zeolite, referred as schwarzite, receives much attention in chemical industry for the storage application. To our knowledge, there is no study has mentioned a precise form of zeolite template which can be used to synthesize schwarzite. In this article, we employ Willmore energy function to model schwarzite network. The problem is considered as the joining between nanostructures to design a pattern of schwarzite and to calculate the surface area and the free volume inside and outside of the network. Catenoid which is a surface obtained by minimizing the Willmore energy is assumed to join between the nanostructures. Since the structure is symmetric, we investigate only the first quadrant in two-dimensional plane, which represents a quarter of unit for the three-dimensional network. Furthermore, we may increase the space between each unit by adding cylindrical nanotubes. This approach may be used to design the network of schwarzite, and to create a new pattern of other nano-scaled networks for a storage application.