The ultra-broadband dielectric spectroscopy is particularly useful for studying dielectric–conductor nanocomposites, particularly near the electrical percolation threshold. Theoretically, we have studied the spectra of effective dielectric response of such composites using several models within the effective medium approximation .
It was shown that the divergence of the static permittivity at the percolation threshold is caused by a strong dielectric relaxation, which softens on approaching the threshold with changing the composition, passing through the whole frequency range from infrared down to zero.
Experimentally, we have studied e.g. nanocomposites of polymers with carbon nanotubes (CNTs) . A well electrically conducting CNT, due to its specific shape, enables processing composites with extremely low percolation threshold. Within our collaboration with Queen’s University in Belfast, who prepared well-dispersed composites of polyethylene terephthalate (PET) polymer with CNTs, we characterized them by broadband conductivity and dielectric spectroscopy, covering up to 17 orders of magnitude in frequency (10−4–1013 Hz) from room temperature down to 5 K. An extremely low percolation threshold of 0.07 vol% CNT was revealed as appearance of the low-frequency AC conductivity plateau corresponding to the DC conductivity, whose value increased with CNT concentration according to the power law with a high critical exponent of 4.3. Its semiconductor temperature dependence obeying the tunnelling law confirmed the model that each CNT in the percolating clusters is covered by a thin (~ 1 nm) layer of PET .
Our first results on other nanocomposites of similar type were reviewed in . Successful modelling of porosity in high-permittivity ceramics in infrared as well as low-frequency range using the Lichtenecker model was achieved for a classical relaxor PbMg1/3Nb2/3O3 (PMN) .
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 D. Nuzhnyy et al., Phys. Rev. B 89, 214307 (2014)