Physics Colloquium - Friday, Nov. 9th, 2007, 4:00 P.M.

E300 Math/Science Center; Refreshments at 3:30 P.M. in Room E200

Mark A. Novotny
Mississippi State University Department of Physics and Astronomy and Center for Computational Sciences of the High Performance Computing Collaboratory

Are Small-World Nanomaterials Possible?

The central question to be addressed is whether nanomaterials can effectively be in dimensions other than one, two, or three. Recently there has been renewed interest in the behavior of complex networks, including Small-World networks. These networks mainly originate in areas in technology, or the social sciences. Models for materials, including atomistic and magnetic and quantum models, have been studied on such unphysical networks, and it has been found that the properties of all models on Small-World networks are governed by a mean-field (infinite dimensional) fixed point. The question to be addressed in this talk is whether or not actual nanomaterials based on physical Small-World networks are possible. Physical constraints, such as uniform bond lengths and node sizes, and that the network must be embedded in three dimensions, are the new features added to Small-World networks to make them physical. We provide an introduction to small-world networks. We show that small-world nanomaterials are not possible, but that in analogy to the existence of pseudo-one-dimensional materials that pseudo-small-world nanomaterial may be possible. We will discuss condensed matter models on physical Small-World networks to explore whether the materials properties are also governed by a mean-field fixed point. The electronic transport through such (pseudo) small-world nanomaterials will be briefly described. Density functional theory calculations of pure carbon molecules which should have this (pseudo) small-world property will be introduced and NMR and vibrational spectra presented.