Micelles and Foams: 2-D Manifolds Arising from Local Interactions

Abstract

Surfaces as 2-D manifolds play an important role in the description of structures, from inorganic materials to biological systems. These surfaces which can be planar, spherical or hyperbolic (saddle-shaped), arise as a consequence of interatomic forces. We are concerned with the generation and application of 2-D manifolds, in particular, periodic minimal surfaces. We show that surfaces can be decorated with atoms to obtain structures with different curvatures, related to the mean coordination number CN. When CN = 6 a planar surface or a cylinder can be obtained, if CN < 6 we get a closed spherical surface as in Buckminsterfullerenes, and if CN > 6, an infinite structure, periodic or otherwise, can be generated. Regarding the case CN > 6, we have found that the existence of ordered graphite foams with topologies similar to periodic minimal surfaces is quite possible, various transformations of surfaces, such as the Bonnet transformation, the Goursat transformation and a new combination of both, are analysed, since they might be useful in the description of physical and biological processes.KeywordsMinimal SurfaceGaussian CurvaturePrincipal CurvaturePeriodic SurfaceNegative Gaussian CurvatureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.