_Article_  
_Terahertz Time-Domain Spectroscopy of Graphene_  
_Nanoflakes Embedded in Polymer Matrix_  
**[PERSON] 1,\({}^{\dagger}\), [PERSON] 2, [PERSON] 3, [PERSON] 3, [PERSON] 4, [PERSON] 4, [PERSON] 4,\({}^{\spadesuit}\), [PERSON] 5, [PERSON] 5, [PERSON] 6 and [PERSON] 1,2,5,\({}^{\spadesuit}\)**  
1 Department of Electrical and Computer Engineering and the Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627-0231, USA; [EMAIL_ADDRESS]  
2 Materials Science Program and the Laboratory for Laser Energetics, University of Rochester, Rochester, NY 14627, USA; [EMAIL_ADDRESS]  
3 The Institute of Optics, University of Rochester, Rochester, NY 14627, USA; [EMAIL_ADDRESS] (K.M.G. ); [EMAIL_ADDRESS] (A.N.V.) 4 Polymer Institute, West Pomeranian University of Technology, PL-70322 Szczecin, Poland; [EMAIL_ADDRESS] (Z.S. ); [EMAIL_ADDRESS] (P.S.) 5 Institute of Electron Technology, PL-02668 Warszawa, Poland; [EMAIL_ADDRESS] (A.L. ); [EMAIL_ADDRESS] (A.C.)  
6 Chemical Engineering, University of Iceland, IS-107 Reykjavik, Iceland; [EMAIL_ADDRESS]  
* Correspondence: [EMAIL_ADDRESS] (M.E.F. ); [EMAIL_ADDRESS] (R.S. ); Tel. : +48-91-449-4828 (M.E.F. ); +1-585-275-1551 (R.S.) 7 Current address: Center for Physical Sciences and Technology, LT-10257 Vilnius, Lithuania. Received: 29 November 2018; Accepted: 14 January 2019; Published: 23 January 2019  
**Featured Application: We describe the use of terahertz (THz) time-domain spectroscopy to characterize the dispersion of graphene nanoflakes, within a multiblock copolymer matrix. This method probes the dielectric properties of the sample in an almost cm2 cross-section beam path, thereby providing \"global\" information regarding the dispersion of graphene and its in-situ electronic quality. Because it is a non-destructive testing method, THz time-domain spectroscopy holds great potential for monitoring any nanofiller dispersion in a polymer matrix throughout the product development chain: After polymer nanocomposite synthesis, following processing into a given prototype, and even after product testing. **  
**Abstract: 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 dilinoate) (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. Usingthe Clausius-Mossotti relation, we also managed to estimate the graphene effective dielectric constant to be equal to ~7 \(\pm\) 2.