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.

We present theoretical studies of peptide amphiphile nanostructures created by Stupp and co-workers [Hartgerink, J. D.; Stupp, S. I. Science 2001, 294, 1684 and show that these amphiphiles exhibit attractiVe electrostatic interactions between their hydrophilic headgroups. These interactions prevail in their competition with the hydrophobic attraction between the amphiphile "tails" for the shape of the self-assembly, leading to cylindrical micelles of nanoscale dimension. The theory is supported by Monte Carlo simulations which show that in the absence of the directional electrostatic interactions between the headgroups the amphiphiles self-assemble into spherical micelles, in accord with our recent formal calculations [Tsonchev,

The Lattice Field Theory approach to the statistical mechanics of a classical Coulomb gas [R.D. Coalson and A. Duncan, J. Chem. Phys. 97, 5653 (1992)

We construct a phase diagram for self-assembling biologically active peptide amphiphiles. The structure and stability of the assemblies are studied as a function of pH and salinity of the solution. The general features of the phase diagram are predicted based on theoretical modeling of the self-assembly process, as well as experimental data, and further experiments are performed to verify and ascertain the boundary locations of the diagram. Depending on solution conditions, the amphiphiles can form cylindrical or spherical micelles, intermediate structures between these, or may not assemble at all. We also demonstrate that changing conditions may result in phase transitions among these structures. This type of phase diagram could be useful in the design of certain supramolecular nanostructures by providing information on the necessary conditions to form them.

The structures of self-assembled peptide amphiphiles are studied using empirical force fields and atomistic molecular dynamics calculations. The hydrophilic headgroups of these amphiphiles possess a lower, rigid part and an upper, flexible part. At an appropriate pH large dipoles are found in the flexible part of the headgroups, leading to attractive interactions between them, while the rigid parts participate in the formation of an effective parallel beta sheet due to hydrogen bonding oriented in the same direction as the large dipoles, and stabilizing the self-assembly in that direction. Molecular dynamics simulations on the self-assembled amphiphiles are performed with periodic boundary conditions in two dimensions. The tendency of the nanostructure to curve around an axis parallel to the dipoles and the beta sheet is revealed by removing the periodic boundary conditions, one direction at a time, leading to the conclusion that a cylindrical micelle would be the most stable one.