The metal-filled polymer nanocomposites are being widely used as conducting materials over last years. As a result there exists a problem to forecast the effective properties of such composites. Nowadays, there is no model adequate to describe real nanocomposites, and there are no methods for the calculation of the effective electrical conductivity of nanocomposite polymers filled with metal powders that take into account the clusterization (aggregation) of the filler particles and the contact electrical conductivity between the metal filler particles.

The effective electrical conductivity of the metal-filled polymers depends on the conductivity of filler particles chains. In order to define the contact conductivity between the filler particles we consider the electron passage in the contact zone between the particles and the existing in this region image forces. The average contact conductivity in the aggregate (cluster) consisting of the filler particles was defined as:

σ_k=2e²σ_f/πRεε₀φ_M

where φ_M- the work function of the electron from metal; e – the charge of the electron; ε -the relative permittivity of the contact, ε₀ – the dielectric constant, R – the radius of the filler particle, σ_f- the electrical conductivity of the filler.

The fractal model was introduced in order to describe the chaotic structure of the nanocomposite. The filled polymeric composite is presented as a chaotic mix of two sorts of polyhedrons: the polyhedrons with the conductivity and the polyhedrons with the conductivity of the polymer. The effective conductivity of a composite with chaotic structure was determined using an iterative averaging method. The comparison between the calculation of the effective conductivity of the nanocomposites and experimental data demonstrates their close agreement.

The above fractal model of the chaotic structure and the calculation method allow us to determine the effective conductivity of nanocomposites, without resort to insertion of fitting parameters.

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1. Thermal conductivity of the nanocomposites with chaotic structure