Multiscale modeling of the dynamical conductivity of self-assembled nanoparticle networks: Numerical simulations vs analytical models

Abstract

Impedance spectroscopy experiments are able to reveal the fundamental charge transport properties of a wide variety of complex disordered and nano-structured materials provided that appropriate modeling tools are used. In this paper, we present a numerical simulation-based approach to model the dynamical conductivity of networks formed by self-assembled metal nanoparticles. Inter-particle nano-resistance and nano-capacitance are implemented at the nano-scale assuming inter-particle charge transfer and accumulation mechanisms that can be adapted depending on the nature of the nano-particles and the surrounding medium. The actual positions and spatial arrangements of the nanoparticles within the network are taken into consideration, allowing the attributes of percolating conducting routes to be extracted, classified, and compared in terms of path conductance and statistical distribution of path lengths. Our findings are contrasted to those obtained using analytic models, which are commonly used, but rely on strong assumptions about the electric properties of the conducting paths. We address these assumptions and show that in the case of weakly disordered systems, there is a general agreement between numerical simulations and analytic modeling-based approaches. In the case of disordered networks where the nano-particle size and position fluctuations are included, we show that the path length distribution is frequency-dependent and can differ significantly from the lognormal distribution usually assumed in the analytic models. The impedance of individual pathways may be extracted from the numerical simulations; we discovered that the conductance and susceptance of a specific path are frequency-dependent and inversely proportional to the path length only in ordered networks. Strong scattering of conductance values is caused by disorder effects. The developed numerical approach is generic and applies to most nano-devices where charge transport relies on percolation; it allows to bridge the gap between the nano-scale and micro-scale electric characteristics and, thus, permits a deeper understanding of the charge transport properties of nano-structured materials.