Percolation in nanoporous gold and the principle of universality for two-dimensional to hyperdimensional networks

Abstract

Percolation in nanoporous gold can be achieved with as little as 8% by volume of gold. Samples of nanoporous gold of various morphologies are analysed with a combination of electrical and optical data. Growing thin films and complex multiply-connected 3-dimensional networks both display non-universal character. Growing films have 2-dimensional morphology but a 3-dimensional percolation threshold and non-universal critical coefficients, yet similar silver films percolate as expected with universal coefficients. Growing gold however regresses to 2-dimensional resistive behaviour between 65% to 100% gold, and this regime lies along a single power law curve shared by the hyper-dimensional networks of gold, suggesting underlying symmetry governed by diffusion limited aggregation. Models of data imply either hyperdimensionality 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.

Optimum plasmon hybridization at percolation threshold of silver films near metallic surfaces

“…The result is then compared with localized surface plasmon interactions for more clarification. The spectra are dominated by a highly symmetric localized surface plasmon peak that can be fitted extremely well by the classical Fano equation in term of absorbance, which describes the interaction between localized and delocalized surface plasmons such unique plasmonic properties favorable and open new platform for a range of potential applications using such interesting region, such as sensors, medical, filters, metamaterials and other plasmonic devices especially if we consider using more complicated nanostructures [30].…”

Evolution of plasmonic response in growing silver thin films with pre-percolation non-local conduction and emittance drop

“…Volume fractions f which vary with t should be found from high resolution images. Past attempts to model the percolation transition in growing metal films as an effective medium approximation (EMA) usually relied on a two phase Bruggeman (Br) model [6,7,19] because it allowed for formation of a touching network of nanoparticles to form at a critical concentration, for example at f c = 0.33 for gold spheres. A phenomenological modification to the Br model has been introduced [20] in which component dc conductivity's dependence on (f -f c ) is exponential with critical coefficients.…”

“…The dc electrical response across this growth domain is well characterised by classical percolation/phase change theory [3,6,7] with conductivity under-going a sharp phase change which varies as ( f − f c ) ±α ± with f metal volume fraction. The critical co-efficients α ± are not independent of the critical concentration f c [6,7] but at large enough scales both quantities are insensitive to local variations in nanostructure. They instead involve averages which can be expressed in terms of a dimensionality or connectivity d of the network [8].…”

“…It clearly differs in growing Ag and Au. This in turn is linked to differences in atomic diffusivity [6].…”

“…They instead involve averages which can be expressed in terms of a dimensionality or connectivity d of the network [8]. Parameters d, α, and f c are thus not independent and vary with average connectivity which is hyper-dimensional when d > 3 [6]. Growing thin films involving islands linking up are usually allocated d = 2 for silver or d = 3 for gold.…”