Random Resistor-capacitor Network Research Articles

Investigation of the dielectric response of binary disordered systems modelled as random resistor–capacitor networks

In this paper, we investigate the dielectric response of binary disordered systems, which are widely modelled by random resistor–capacitor networks (RRCN). Our results show the existence of a scaling law connecting the standard deviation of conductivity to the network size and capacitors proportion. In addition, we have studied the effect of using lossy capacitors on the dielectric response of RRCN. We found that lossy capacitors may introduce substantial effects of the dielectric loss, especially at low frequencies.

AC Conduction in Polyaniline Emeraldine Salt-Graphite Pellets

The conduction characteristics of Polyaniline emeraldine salt-Graphite (PAni-ES/Gr) pellets were characterized using an impedance analyzer. The pellets were prepared with varying mass fractions of PAni-ES and Gr. FTIR spectra have the stretching vibrations for PAni-ES and absence of peaks for Gr. PAni-ES showed aggregated particles while Gr appeared as sheets and flaky structures. The composition of the pellets was differentiated in the AC conductivity values. The critical frequency representing the transition from frequency-independent to frequency-dependent conductivity decreases with increasing Gr content. Lastly, the frequency-dependent conductivity behavior follows power-law behavior reflecting possible hopping mechanisms and random resistor-capacitor network.

Understanding the anomalous frequency responses of composite materials using very large random resistor-capacitor networks

In this paper large resistor-capacitor (RC) networks that consist of randomly distributed conductive and capacitive elements which are much larger than those previously explored are studied using an efficient algorithm. We investigate the emergent power-law scaling of the conductance and the percolation and saturation limits of the networks at the high and low frequency bounds in order to compare with a modification of the classical Effective Medium Approximation (EMA) that enables its extension to finite network sizes. It is shown that the new formula provides a simple analytical description of the network response that accurately predicts the effects of finite network size and composition and it agrees well with the new numerical calculations on large networks and is a significant improvement on earlier EMA formulae. Avenues for future improvement and explanation of the formula are highlighted. Finally, the statistical variation of network conductivity with network size is observed and explained. This work provides a deeper insight into the response of large resistor-capacitor networks to understand the AC electrical properties, size effects, composition effects and statistical variation of properties of a range of heterogeneous materials and composite systems.

From capacitive to tunnelling conduction through annealing in metal-insulating granular films: the role of ultra-small particles

In situ transmission electron microscopy (TEM) during annealing of metal-insulating granular thin films reveals significant microstructural changes: nucleation of ultra-small particles and growth of those already existing. Radio frequency impedance spectroscopy shows that by subsequent annealing, tunnelling conductance becomes more important at the expense of the decrease of capacitive contributions, giving place to an almost frequency-independent conduction, although being very far from physical percolation. These results are simulated assuming a random resistor–capacitor network, which represents the competing conduction channels between particles through thermally assisted tunnelling and capacitive conductance. The physical parameters derived from this simple model agree well with the microstructural changes observed by TEM through annealing, and evidence the increase of tunnelling conduction paths mediated by segregated ultra-small glue particles in between bigger ones. Those glue particles grow with further annealing and account for the correlation of the microstructural changes to the ac transport properties.

Ac conductance in granular insulatingCo-ZrO2thin films: A universal response

The ac conductance in granular insulating Co-ZrO2 thin films prepared by pulsed laser deposition is systematically studied as a function of the Co volume content x. An absorption phenomenon at low frequencies that mimics the universal response of disordered dielectric materials is observed in the range of metal content below the Co percolation threshold xp 0.35 in the so-called dielectric regime. The temperature and frequency dependences of this absorption phenomenon are successfully analyzed in terms of random competing conduction channels between Co particles through thermally assisted tunneling and capacitive conductance. The ac conductance is well correlated with the nanostructure of the samples obtained by the transmission electron microscopy and perfectly matches the calculated ac response for a random resistor-capacitor network. We also show the occurrence of fractional power-law dependences on the frequency of the ac conductance taking place at very low frequencies as compared to the typical ranges at which dispersive behavior is observed in classicaldisordered dielectric materials.

Effective nonlinear optical properties in compositionally graded films: Analytical and numerical calculations

Effective nonlinear optical properties of compositionally graded films, in which the volume fraction of nonlinear metal particles varies along the direction perpendicular to the films, are theoretically and numerically investigated. Theoretically, we first adopt effective medium approximation to derive equivalent linear dielectric constant and third-order nonlinear susceptibility in a $z$-slice. Then, the formulas for effective nonlinear optical properties of the graded film are established, if we regard the graded film as a multilayer one. Numerically, random resistor-capacitor networks are used to simulate our system. We find that the surface plasmon resonant bands and the optical nonlinearity enhancement magnitude for compositional graded profile become broader and larger than those in the nongraded case. Moreover, for a graded profile $p(z)=a{z}^{m}$, increasing $a$ (or decreasing $m$) is helpful to broaden the resonant bands. To one's interest, there exist two enhancement peaks in the frequency region $0.4{\ensuremath{\omega}}_{p}\ensuremath{\leqslant}\ensuremath{\omega}\ensuremath{\leqslant}0.6{\ensuremath{\omega}}_{p}$, which are not predicted by our approximate theory. Otherwise, our theoretical results are found to be in good agreement with numerical simulation data.

Numerical study of effective optical nonlinear properties in composites with anomalous distribution

We investigate the nonlinear optical response of random composites consisting of nonlinear conductors and linear conductors with an anomalous distribution. Random resistor–capacitor networks are used to simulate our model, in which the nonlinear component with the fraction p is taken as i = g 1 v + χ 1 | v | 2 v and the linear component with the fraction 1 − p obeys an anomalous distribution h ( g 2 ) ∼ g 2 − α , where 0 < g 2 < 1 . We find that the distribution exponent α plays an important role in the effective linear and nonlinear optical response. As α decreases, the enhancement of optical nonlinear χ e can be achieved. Moreover, the effective nonlinear optical response exhibits a sharp peak at a moderate volume fraction, dependent on α. The effective medium approximation is found to be in good agreement with linear response of numerical simulation, and describes nonlinear response of our numerical results qualitatively.

Complex magnetoimpedance analysis of interparticle boundaries in Fe3O4 powder compact

Recent experimental results of Fe3O4 in polycrystalline film, powder compact, and single crystal form have indicated that boundaries play an important role in magnetoresistance effect. In this paper, the complex impedance analysis is used to evaluate the contribution of particle boundary to conduction process in Fe3O4 powders. Considering particle boundaries with different thicknesses, we developed a random resistor-capacitor network model to investigate the influence of magnetic field on impedance behaviors. The fitting results to experimental data indicated that two kinds of conduction mechanisms, spin-dependent tunneling and spin-independent hopping, dominate the transport process in particle boundaries. The capacitive transport through particles with a size of 10–20nm may yield negative magnetoreactance. It is also found that magnetic field has little influence not only on the competition between resistive and capacitive path, but also phase angle Φ(f). Finally, it can be deducted that the magnetoreactance effect could be enhanced in this granular sample if the particle size is less than 10–20nm.

The ‘emergent scaling’ phenomenon and the dielectric properties of randomresistor–capacitor networks

An efficient algorithm, based on the Frank–Lobb reduction scheme, for calculatingthe equivalent dielectric properties of very large random resistor–capacitor (R–C)networks has been developed. It has been used to investigate the network size andcomposition dependence of dielectric properties and their statistical variability.The dielectric properties of 256 samples of random networks containing: 512,2048, 8192 and 32 768 components distributed randomly in the ratios 60% R–40%C, 50% R–50% C and 40% R–60% C have been computed. It has been found thatthese properties exhibit the anomalous power law dependences on frequencyknown as the ‘universal dielectric response’ (UDR). Attention is drawn to thecontrast between frequency ranges across which percolation determinesdielectric response, where considerable variability is found amongst thesamples, and those across which power laws define response where verylittle variability is found between samples. It is concluded that the powerlaw UDRs are emergent properties of large random R–C networks.

Random resistor-capacitor network model of island metal films and three-dimensional metal-insulator composites

Abstract A new random resistor-capacitor network model for the study of the a.c. properties of island metal films and three-dimensional metal-insulator composites is proposed. The model is a generalization of the random resistor network model (which is used in the study of the variable-range hopping conductivity): randomly placed sites representing metallic particles are interlinked by parallel R-C circuits. The a.c. response of this random impedance network is calculated using methods of percolation theory and a novel highly efficient algorithm for the network simplification. The correspondence between the frequency dependence of the real part of the network impedance and the distribution of time constants of R-C circuits in the backbone of the percolating cluster is established. The role played by the self-similar nature of the backbone and by its bottlenecks is also discussed.

Numerical study of transport properties in continuum percolation

The authors present numerical simulations of AC conductance for a random resistor-capacitor network. The conductance obeys a probability density function p(g) varies as g- alpha (0( alpha (1). They use a highly efficient propagation algorithm to calculate the effective conductance of a long strip of a lattice. At low frequencies, they find that for the concentration p of conducting bonds less than the percolation threshold pc, the imaginary part of conductance is proportional to frequency Im(geff) approximately= omega and the real part of conductance shows an anomalous frequency dependence Re(geff) approximately= omega 2- alpha . The results of simulations in such a continuum system are in agreement with the predictions of the effective medium and the Maxwell-Garnett approximation. They also calculate the non-universal DC conductivity exponents in continuum percolation; the results are consistent with earlier theoretical predictions and numerical calculations.

Anomalous transport in random resistor-capacitor network: Application to composite materials

Kirkpatrick's effective medium approximation is extended to deal with a random resistor-capacitor network in which the conductance (with a fraction p) obeys an anomalous distribution of the form h( g)≈ g −α (0<α<1). In the limit of small concentration p and low frequencies, the results are in good accord with previous calculations via the Maxwell-Garnett formula. The ac conductivity is also calculated near the percolation threshold. As one increases the frequency, both the real and imaginary parts of the conductivity cross over to the same high-frequency behavior g eff ≈ω 1 (2−α . Corrections to the leading behavior are obtained at the percolation threshold.