Abstract

A large part of the development of mathematics was driven by the desire to understand why objects in nature are found in a myriad of shapes and sizes and why certain forms are preferred over others. The area of mathematics called the calculus of variations has been utilized to handle the optimal forms in geometry and nature. It has been used to comprehend morphogenesis and the similarity, yet variety, of forms in the natural world. The mathematical underpinnings of natural form are beginning to influence the inorganic materials world, especially the unusual morphologies that arise in the field of self-assembly. These morphologies often exhibit curved shapes resembling those of minimal surfaces rather than familiar Platonic, polyhedral crystal habits. The curved shapes of mesostructured inorganic materials synthesized by supramolecular templating are striking examples of minimal surface area and energy principles at work in their growth and form.Key words: mesoporous materials, morphosynthesis, silica, supramolecular.

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