Complex permittivity based on equivalent circuit model for polymer/metal composite. Frequency dependence of permittivity as function of concentration

The frequency dependence of the complex permittivity of a binary composite system in which metal particles were randomly dispersed in a polymer was formulated for a wide range of particle concentrations (5 to 50%vol) by using a simple equivalent circuit model. A composite containing a small amount of particles has a unit structure in which polymer separates the metal particles. This indicates one type of channel for electric-flux running from one particle to the next one via the polymer. The complex permittivity ε˙_c, of this composite was found to be proportional to the complex permittivity ε˙_p of the polymer, independent of frequency ε˙_c=kε˙_p, where coefficient k increases with the particle concentration. In contrast, a composite containing a large amount of particles has a unit structure in which the metal particles directly touch. This indicates two types of channels running from particle to particle: one via the polymer and one via the particle boundaries. The complex permittivity ε˙_c, of this composite is expressed as the sum of two terms: ε˙_c=k₁ε˙_p+F₂ (f), where k₁ increases with the particle concentration and F˙₂(f) decreases with the frequency. Both formulas were verified experimentally by analyzing the relationship between composite permittivity ε˙_c, and polymer permittivity ε˙_p