Hydrophobically-driven self-assembly: A geometric packing analysis

We present a new approach to the problem of finding the minimum-energy structures resulting from the self-assembly of amphiphile nanoparticles possessing a hydrophobic "tail" and a hydrophilic "head". When the repulsive interactions between the "heads" are of hard-sphere type, the approach is rigorous and is reduced to a simple geometric problem of finding the highest density structure allowed by the nanoparticle shape. Our results show that spherical micelles always have higher fractional density for cone or truncated cone nanoparticles. This does not always agree with previous, widely used, approximate methods which have served as guides in designing new nanoscale-structured materials.