Modelisation of electrical intergrain contacts at high frequencies

A 3-D numerical simulation of AC electrical properties of short fiber composites

“…Resistor and capacitor values are usually, in the RC model, chosen either to be constant 10 or to follow a given distribution. 11 In the present approach, their value reflects the local geometry. Thus, by defining the distance between two nodes i and j as D ij , the values of the resistors were calculated from:…”

“…9 Improvement of this RC model, namely R-RC 8,10 and RLC 11 models, have been proposed to correlate the optical properties of conductor-insulator mixtures with the local conduction mechanisms. For example, Clerc et al 8,11 showed that resonant phenomenon in the optical properties of composites can be accounted for by numerical simulations using an RLC model. As already mentioned, these simulations were developed on incompletely connected networks in which the bonds (or sites) are active with a given probability.…”

Modelling of impedance spectroscopy of composites by electrical networks

“…This situation was explained by the existence of either a quantum tunnelling current or a thermal activation due to the contact between grains, which is the subject of this investigation. Further measurements on the impedance spectra of such mixtures showed an inductive behaviour of the system at low frequencies [10], attributed to inter-grain contact rather than the grains themselves. We use here a Gaussian intergrain distance distribution to compare with the uniform one and extend the calculations to sizes as large as 400 × 400 in order to examine the scaling behaviour of the impedance and its characteristic frequencies.…”

“…where x i,j (the same parameter as in equation ( 3)) is a random variable distributed within the interval {0, 1} and R 0 is the minimum value of R and λ (here λ = λ(p) log(e) and e is the Napierian constant) the width of the distribution (R i,j and L i,j vary by a factor 10 λ ) and characterizes the doping of the system (since it depends on p). From experimental data, there is a constant ratio between R i,j and L i,j [10]. The conductivity of each contact (bond) is…”

“…However, due to the complex structure of experimental spectra, numerical simulations become inevitable for understanding the data. One such simulation was done previously to explain the results from mixtures of glass beads (insulator) and silver-coated glass beads (conductor) [10]. By choosing a uniform distribution of the inter-grain distance, it was found that the conductance depends exponentially on this distance.…”