|Title||Controlled Formation of Nanostructures with Desired Geometries. 1. Robust Static Structures|
|Publication Type||Journal Article|
|Year of Publication||2010|
|Authors||Solis, E. O. P., P. I. Barton, and G. Stephanopoulos|
|Journal||Industrial & Engineeering Chemistry Research|
|Pagination||7728 - 7745|
An essential requirement for the fabrication of future electronic, magnetic, optical, and biologically based devices, composed of constituents at the nanometer length scale, is the precise positioning of constituents in the system’s physical domain. The desired nanostructure must be locally stable to a desired level of robustness, which is the basis for the static design problem described in this paper: systematic use of externally imposed controls, realized through point conditions that introduce attractive or repulsive interaction terms in the system potential energy, to ensure a robust desired structure. The locations of the point conditions are found through the solution of a minimum tiling problem. Given these locations, the point condition strengths are found through the solution of combinatorially constrained optimization problems. System ergodicity must be broken to isolate the desired structure from all competing structures in phase space. We illustrate these static problem solution methods with 1- and 2-dimensional example lattice model systems.