Percolation In Nanoporous Gold And The Principle Of Universality For Two-dimensional Tornhyperdimensional Networks

摘要

Percolation in nanoporous gold can be achieved with as little as 8% by volume of gold. Samples of nanoporous gold of various morphologies are analyzed with a combination of electrical and optical data. Growing thin films and complex multiply connected three-dimensional networks both display nonuniversal character. Growing films have two-dimensional morphology but a three-dimensional percolation threshold and nonuniversal critical coefficients, yet similar silver films percolate as expected with universal coefficients. Growing gold however regresses to two-dimensional resistive behavior between 65% to 100% gold, and this regime lies along a single power-law curve shared by the hyperdimensional networks of gold, suggesting underlying symmetry governed by diffusion-limited aggregation. Models of data imply either hyperdimension-ality or major internal property changes as density shifts. The distinctive flat spectral signature found near the percolation threshold is common to all highly porous samples and is explained quantitatively in terms of effective plasmonic response. Parameters from fits of effective medium models to optical and resistivity data are in close agreement, especially at the highest porosities. They imply an effective dimension which increases continuously as porosity grows via the increased branching needed for structural integrity.