Predicting effective permittivity of composites containing conductive inclusions at microwave frequencies

Abstract

A review and analysis of microwave absorption in polymer composites filled with carbonaceous particles Journal of Applied Physics 111, 061301 (2012) We predict the effective dielectric properties at microwave frequencies of composites containing various volume loadings of high conductivity (stainless steel or iron) spheres or flakes by adapting the semi-empirical method developed by McLachlan. Rather than the typical approach of fixing A (A = 1/v c -1, where v c is percolation threshold) for a given inclusion shape, we consider it as an unknown and fix one of the geometric exponents. We observe that A varies linearly with the inverse of volume loading with a higher slope for flakes than spheres. The exponent is consistently higher for spheres than flakes and for iron than stainless steel. We achieve good agreement between measured and calculated permittivity over a wide range of volume loadings, inclusion shapes, and materials from 3 to 20 GHz.

A semi-empirical approach for predicting the performance of multiphase composites at microwave frequencies

“…Our scenario more closely resembles the IRVM since we introduce conducting inclusions into an insulating matrix. Although the t calculated for SS flakes (t ~1.7 [47]) is slightly below the universal value, it falls within the range of values calculated for other inclusions [29]. Balberg [44] showed that t could take any value larger than t un by no longer assuming a uniform void size (x) as x → 0 and allowing a nonrandom distribution of voids.…”

“…We observed variations in t between materials [20,47], which could suggest material induced changes in inclusion dispersion.…”

“…We noted that t was a function of inclusion material and shape while A x was a function of inclusion material, shape, and volume loading [47]. Specifically, A x varied linearly with 1/v rather than the standard 1/v c noted above [20,47], although A x approaches a constant as the system began to percolate, suggesting that the 1/v behavior may occur only below percolation [20].…”

“…For instance, the consistently larger value of t for iron inclusions than SS could suggest less uniform dispersion for the iron inclusions, which could arise due to the extruding process or the magnetic characteristics of the iron impacting inclusion alignment [47]. Another possibility is that the presence of an oxide layer on the iron particles could result in an increased t by a combination of the geometric effects (such as through the RVM or IRVM model) with tunneling [49].…”

“…We solved the real and imaginary components of (1) and its magnetic analog for t and A x previously for stainless steel (SS) spheres, flakes, and fibers [20,47]. We noted that t was a function of inclusion material and shape while A x was a function of inclusion material, shape, and volume loading [47].…”