A Theoretical Consideration of Disorder in a Finite 1D Metal Cluster Chain in a Nanoporous Solid

Abstract

Green's function formalism was developed to study the physical properties of one-dimensional arrangements of ligand stabilized metal clusters intercalated into the channel structure of a nanoporous solid. This approach enables us to formulate the so called partial “solitary” problem of mesoscopic tunnel junctions similarly to the problem of the behavior of an electron in a one-dimensional tight-binding and in a set of vertically and horizontally random delta-function models. We analytically calculated the potential distribution, taking into account the effects of disorder, which influence the form of the charge soliton. Applied to a channel of a porous solid filled with metal clusters, we discuss that the inter cluster capacitance C as well as the self-capacitance C0 can fluctuate from site to site, i.e. “vertical” and “horizontal” disorder, respectively. It is shown that the knowledge of the potential distribution enables us, in principle to calculate the capacitances and by this the diameter as well as the spacing of the clusters.