We report the results of effective direct current (dc) resistivities and alternating current (ac) complex permittivity measurements carried out on two series of polymer∕multiwalled (MW) carbon nanotube (CNT) composite samples as function of the CNTs volume fraction and temperature. The CNTs have typical aspect ratio over 100:1 and are quasiuniformly dispersed in two types of polymer host [epoxy and polystyrene (PS)-cobutyl acrylate latex] according transmission electron microscopy characterization. A percolation threshold occurs in the composites with the PS latex matrix when the CNT volume fraction is ≈0.012. In contrast, the set of resistivity data for samples containing epoxy resin as host matrix is not representative of an intrinsically percolation transition. Atomic force microscopy, coupled to the measurement of the local electric resistances, permits us to study the agglomerate distribution in both types of composites. The differences in morphology between the two series of polymer∕MWCNTs are attributed to interface effects between the elongated filler nanoparticles and the polymer chains. Comparison of the measured effective dc and ac resistivities, at temperatures ranging from 30to300K, with Sheng’s model supports the fact that charge transport in the composites follows a thermal fluctuation induced tunneling mechanism, in which the tunneling of the electrons through the thermally induced fluctuating potential barrier formed by a thin insulating polymer layer separating MWCNTs aggregates. The spectral behavior of permittivity is consistent with a power-law form. Several mixing laws were tested to represent the filler fraction dependence of the effective permittivity in the microwave range of frequencies; however, none of them is able to quantitatively describe the sets of data. The basic deficiency of these formulas is that they make no explicit reference to the internal length scales in the composite samples.

Multiple-walled carbon nanotube (CNT)-and carbon black (CB)-polymer composites have been fabricated by mechanical mixing with different loadings, the polymeric matrix being identical between the two series of samples. The main focus of this work is to report measurements of physical properties of these mixtures in ambient conditions and to discuss the origin of similarities and differences among them according the kind of carbonaceous filler. The uniform dispersion of the carbonaceous phase in the dielectric matrix was probed by high-resolution transmission electron microscopy. The good dispersibility of the filler particle is also reflected in the much lower conduction threshold observed for CNT-containing samples than in the CB composites. This is likely due to the high aspect ratio of the CNTs. Mechanical properties show that the storage modulus of the two kinds of samples is close to the modulus value of the neat styrene-butadiene rubber (SBR), independent of filler content over a wide range of compositions $\left(\varphi <0.1\right)$ encompassing the percolation threshold. Microwave measurements show that the real part of the effective permittivity exhibits a flat frequency response, with the exception of the sample containing $30\text{vol}\mathrm{\%}$ CB for which an inverse-power law is observed revealing a behavior that has been seen for many random heterogeneous soft materials. No resonant dielectric absorption is evidenced within the frequency range explored and for the filler concentrations investigated. The results were also compared with analytical effective (mean-field) models. The symmetric Bruggeman model is in very good agreement with the microwave effective permittivity once account is taken of the depolarization factor which is close to the value found for a three-dimensional (3D) random dispersion of monodisperse spherical conductive inclusions within a dielectric matrix. By combining microwave frequency-domain spectroscopy with uniaxial tension, we obtain the effective permittivity as a function of the elongation ratio. Our results indicate that the effective permittivity spectrum of the CNT-polymer samples and their CB-based counterparts is not very sensitive to the applied stress in the range of elongation ratios explored. For the sample containing $30\text{vol}\mathrm{\%}$ CB, the relative variation in the effective permittivity as a function of the elongation ratio is well described by the Gaussian molecular network model. The experimentally determined mechanical and microwave properties of these nanocomposites is related to the change in the mesostructure, formed by the heterogeneous 3D interconnected network of polymer and of aggregates (or agglomerates) of filler particles, as the composite is stretched. The results of this study provide another insight and opportunities to the comprehension of multifunctional materials, including novel nanoelectronic components, and carbon-based systems.

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 $0.1-3\text{GHz}$ 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.

The evolution of the frequency-dependent absorption spectra for plastoferrites and carbon black-filled ethylene butylacrylate copolymer composites subjected to a uniaxial tension is evaluated using a vector network analyzer as a function of the elongation ratio over the frequency range of 0.3–5 GHz and at room temperature. The absorption spectrum has a double-peaked structure with two broad and symmetrical components. The positions of the lower-frequency peak (1.5 GHz) and the higher-frequency $\left(\cong 4\pm 0.3\text{GHz}\right)$ do not change with extension over the considered range of strain, however, their relative absorption energy changes versus tensile stress can be explained in terms of a Gaussian molecular network model (affine behavior) provided that the elasticity network in the material occurs in a manner that is topologically similar to the elasticity network of a conventional rubber. The sensitivity of the microwave absorption to elongation ratio can be exploited to provide artificially structured materials with tunable electromagnetic properties.

The majority of industry using high-speed communication systems is shifting towards higher frequencies, namely the terahertz range, to meet demands of more effective data transfer. Due to the rising number of devices working in terahertz range, effective shielding of electromagnetic interference (EMI) is required, and thus the need for novel shielding materials to reduce the electromagnetic pollution. Here, we show a study on optical and electrical properties of a series of ethylene co-butyl acrylate/carbon black (EBA/CB) composites with various CB loading. We investigate the transmittance, reflectance, shielding efficiency, absorption coefficient, refractive index and complex dielectric permittivity of the fabricated composites. Finally, we report a material that exhibits superior shielding efficiency (SE)—80 dB at 0.9 THz (14.44 vol% CB loading, 1 mm thick)—which is one of the highest SE values among non-metallic composite materials reported in the literature thus far. Importantly, 99% of the incoming radiation is absorbed by the material, significantly increasing its applicability. The absorption coefficient (α) reaches ~100 cm⁻¹ for the samples with highest CB loading. The EBA/CB composites can be used as lightweight and flexible shielding packaging materials for electronics, as passive terahertz absorbers or as radiation shields for stealth applications.

Using a home-built experimental setup, we investigate the carbon black (CB) volume fraction-resolved, time-resolved, and frequency-resolved spectra of the room temperature (well above the glass transition temperature of the matrix) effective complex permittivity of well characterized CB filled ethylene butylacrylate copolymer samples that are submitted to a uniaxial tension. We focus here on three samples with CB volume fraction less, near, and well away the percolation threshold at about $8\text{vol}\%$ . Our primary observation is that the temporal evolution of the real and imaginary parts of the effective permittivity is distinctly different for samples containing a CB volume fraction below and above percolation threshold. For samples containing a CB volume fraction below and close to the percolation threshold, and at a given frequency, ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ remain constant over the time scale of our measurements. For the sample containing a CB volume fraction above the percolation threshold the evolution of ${\epsilon }^{\prime }$ and ${\epsilon }^{″}$ is different in the low and high elongation ratio regimes. At low strain, the temporal evolution of permittivity during aging under stress shows a logarithmic growth phase followed by a logarithmic decay phase, whereas for sufficiently large strain the permittivity behaviors coincide with those observed below the percolation threshold. To explain the issues involved, we argue that the phenomenology for physical aging in these materials is related to the change in the mesostructure, formed by the heterogeneous three-dimensional interconnected network of polymer and of aggregates (or agglomerates) of CB particles, as the composite is stretched. Indeed, it is possible to argue qualitatively that below the percolation threshold the time-independent permittivity behavior is reminiscent to the elasticity network properties of the polymeric matrix. The reorientation and breakdown of the CB aggregates are believed to be crucial for the physical aging understanding above the percolation threshold and low strain. An examination of the surface and volume morphological evolutions of these materials under the action of a mechanical stress at the microscale by scanning electron microscopy and atomic force microscopy indicates that aging during a few hundreds of hours, even at a moderate strain, generates voids and cracks that are aligned along the stretching direction. The overall behavior is compared to what occurs in another type of filled polymer system, i.e., plastoferrites, for which it was recently discovered that two characteristic time scales are required to describe physical aging.