Design of schwarzite templates based on energy minimization of surfaces

Abstract

• Schwarzite structure, which is a crystalline carbon allotrope with negative curvatures, is designed based on energy minimization. • Carbon fullerene, carbon nanotube and catenoid are utilized as basis units, and applied mathematical techniques are employed to join these three nano-scaled structures to form a schwarzite network. • Surface area and volume of schwarzite are determined for the use in storage applications. Fullerene, nanotube and catenoid are utilized as basis units, and applied mathematical techniques are employed to join these three nano-scaled structures to form a schwarzite network. They are schwarzite networks consisting of 8 units where (a) is the joining between fullerene and catenoid, and (b) is the joining between fullerene, catenoid and nanotube. 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.