Ordered Bicontinuous Films of Amphiphiles and Biological Membranes

Films of amphiphilic molecules form layers, with complex as well as simple topologies. Well-defined examples of surfaces in chemical systems with the topologies of the subtly related P, D and G triply periodic minimal surfaces (TPMS) are examined. The analysis is extended to the biological structures of etioplasts found in green plants which are more complex. The analysis shows how local order constrains global order. Local order may indicate a metric only achievable in a higher dimensional space and the requirements of our actual space lead to ingenious compromises.