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<p>The intricate interplay between complex permittivity and permeability constitutes the cornerstone of electromagnetic (EM) applications, enabling precise customization for various uses. This study employed silver-epoxy nano-composites to exemplify a conductor-insulator composite, leveraging silver’s exceptional attributes, such as high conductivity and low reactivity. The determination of complex permittivity and permeability was conducted via the transmission/reflection method. At lower concentrations of dispersed silver particles, these nanoparticles within the epoxy resin act as modest dipoles, augmenting permittivity. This regime aligns closely with the effective medium theory (EMT) and comprises the focus of much research. However, nearing the percolation threshold, a percolation effect emerges, drastically accelerating enhancement rates beyond the predictions of EMT. Simultaneously, long-wavelength electromagnetic waves induce diamagnetic currents within loops formed by metal grains. This diamagnetic effect intensifies with increasing volume fraction, leading to a reduction in permeability. Here we report the first simultaneous extraction of complex permittivity and permeability for a metal–polymer system inside the microwave percolation window (8.2 ~ 12.4&#xa0;GHz). We observe a record-high <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{\epsilon\:}^{\prime}\approx496\)</EquationSource> </InlineEquation> co-existing with a record-low <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:{\mu\:}^{\prime}\approx0.31\)</EquationSource> </InlineEquation>, and we show that both quantities obey 2D percolation scaling. The results constitute the first experimental verification of the Bowman–Stroud diamagnetic-loop model at GHz frequencies.</p>

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Percolation effect induced significant changes in the complex permittivity and permeability of silver-epoxy nano-composites

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  • 发表日期：

    2025年12月13日

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  • Bo-Wei Tseng,
  • Tsun-Hsu Chang

摘要

The intricate interplay between complex permittivity and permeability constitutes the cornerstone of electromagnetic (EM) applications, enabling precise customization for various uses. This study employed silver-epoxy nano-composites to exemplify a conductor-insulator composite, leveraging silver’s exceptional attributes, such as high conductivity and low reactivity. The determination of complex permittivity and permeability was conducted via the transmission/reflection method. At lower concentrations of dispersed silver particles, these nanoparticles within the epoxy resin act as modest dipoles, augmenting permittivity. This regime aligns closely with the effective medium theory (EMT) and comprises the focus of much research. However, nearing the percolation threshold, a percolation effect emerges, drastically accelerating enhancement rates beyond the predictions of EMT. Simultaneously, long-wavelength electromagnetic waves induce diamagnetic currents within loops formed by metal grains. This diamagnetic effect intensifies with increasing volume fraction, leading to a reduction in permeability. Here we report the first simultaneous extraction of complex permittivity and permeability for a metal–polymer system inside the microwave percolation window (8.2 ~ 12.4 GHz). We observe a record-high \(\:{\epsilon\:}^{\prime}\approx496\) co-existing with a record-low \(\:{\mu\:}^{\prime}\approx0.31\) , and we show that both quantities obey 2D percolation scaling. The results constitute the first experimental verification of the Bowman–Stroud diamagnetic-loop model at GHz frequencies.