Conducting Carbon Wires in Ordered, Nanometer-Sized Channels

The encapsulation of graphite-type carbon wires in the regular, 3-nanometer-wide hexagonal channels of the mesoporous host MCM-41 is reported. Acrylonitrile monomers are introduced through vapor or solution transfer and polymerized in the channels with external radical initiators. Pyrolysis of the intrachannel polyacrylonitrile results in filaments whose microwave conductivity is about 10 times that of bulk carbonized polyacrylonitrile. The MCM host plays a key role in ordering the carbon structure, most likely through the parallel alignment of the precursor polymer chains in the channels. The fabrication of stable carbon filaments in ordered, nanometer-sized channels represents an important step toward the development of nanometer electronics

From lattice Quantum Electrodynamics to the distribution of the algebraic areas enclosed by random walks on Z2Z^2

In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the algebraic areas over the set of loops that have fixed number of edges in the two directions. We show that these moments are the product of a combinatorial factor that counts the number of such loops, by a polynomial in the numbers of steps in each direction. Our approach leads to an algorithm for obtaining explicit formulas for the moments of low order.Comment: 21 pages, to appear in Annales de l'Institut Henri Poincar\'e