Microwave dielectric properties of carbon black filled polymers under uniaxial tension

Broadband microwave spectroscopy is commonly employed in the determination of the wave transport properties in mesostructured polymers with embedded carbon black particles. However, very little is known on how uniaxial stress affects the effective permittivity of these percolative materials. In this work we carry out a comprehensive study of the complex permittivity spectra of carbon black filled ethylene butylacrylate copolymer which is submitted to a tensile stress up to 45% over the 0.1-3 GHz frequency range and at room temperature. Permittivity measurements indicated large decreases in the real and imaginary parts of the effective permittivity of the axially elongated samples. This set of experiments illustrates that these microwave permittivity data scale as a power law in frequency, where the exponent is strongly sensitive to stress. In addition, we show that our effective permittivity measurements under stress can be explained in terms of the Gaussian molecular network model in the limit of low stress. The observed variation of the effective permittivity is consistent with that reported for related materials, i.e., carbon black filled cross-linked rubber. Our analysis points out to the importance of local properties, i.e., properties associated with specific subsystems (e.g., aggregates of carbon black particles) in understanding the effective dielectric properties of these "macroscopic homogeneous" materials. Improved reliability through real-time monitoring of strain and material parameters (permittivity and permeability) simultaneously will result in significant benefits to the community in many areas, such as aerospace, power, and automotive industries.