The terahertz time-domain spectroscopy (THz-TDS) technique has been used to obtain transmission THz-radiation spectra of polymer nanocomposites containing a controlled amount of exfoliated graphene. Graphene nanocomposites (1 wt%) that were used in this work were based on poly(ethylene terephthalate-ethylene dilinoleate) (PET-DLA) matrix and were prepared via a kilo-scale (suitable for research and development, and prototyping) in-situ polymerization. This was followed by compression molding into 0.3-mm-thick and 0.9-mm-thick foils. Transmission electron microscopy (TEM) and Raman studies were used to confirm that the graphene nanoflakes dispersed in a polymer matrix consisted of a few-layer graphene. The THz-radiation transients were generated and detected using a low-temperature–grown GaAs photoconductive emitter and detector, both excited by 100-fs-wide, 800-nm-wavelength optical pulses, generated at a 76-MHz repetition rate by a Ti:Sapphire laser. Time-domain signals transmitted through the nitrogen, neat polymer reference, and 1-wt% graphene-polymer nanocomposite samples were recorded and subsequently converted into the spectral domain by means of a fast Fourier transformation. The spectral range of our spectrometer was up to 4 THz, and measurements were taken at room temperature in a dry nitrogen environment. We collected a family of spectra and, based on Fresnel equations, performed a numerical analysis, that allowed us to extract the THz-frequency-range refractive index and absorption coefficient and their dependences on the sample composition and graphene content. Using the Clausius-Mossotti relation, we also managed to estimate the graphene effective dielectric constant to be equal to ~7 ± 2. Finally, we extracted from our experimental data complex conductivity spectra of graphene nanocomposites and successfully fitted them to the Drude-Smith model, demonstrating that our graphene nanoflakes were isolated in their polymer matrix and exhibited highly localized electron backscattering with a femtosecond relaxation time. Our results shed new light on how the incorporation of exfoliated graphene nanoflakes modifies polymer electrical properties in the THz-frequency range. Importantly, they demonstrate that the complex conductivity analysis is a very efficient, macroscopic and non-destructive (contrary to TEM) tool for the characterization of the dispersion of a graphene nanofiller within a copolyester matrix.
A Comparison of Time-Domain Implementation Methods for Fractional-Order Battery Impedance Models