## 1 Introduction  
Polymer nanocomposites are prepared by including a nanofiller (carbon, ceramic, metal/metal oxide, and/or others) in a polymer matrix in order to alter (or improve) its properties, such as mechanical, electrical, and optical properties, barrier properties, flame resistance, etc. [1]. Recently, a great deal of interest has been focused on carbon nanofillers and, in particular, graphene. Graphene is a two-dimensional (2-D) nanomaterial consisting of sheets of carbon atoms bonded by sp\({}^{2}\) bonds in a hexagonal configuration: Its unique mechanical, electrical, thermal, and optical properties have been extensively studied [2]. These properties have been leveraged in the development of a wide range of different graphene-polymer nanocomposites [3] using a variety of fabrication methods and polymer types for numerous structural and functional applications [4], including, e.g., biomedical devices [5], biosensing [6], and gas barrier membranes [7]. The key distinguishing feature of nano-fillers, as compared with microscale or conventional fillers, is the very high surface-to-volume ratio inherent in their nanoscale size. Therefore, nano-fillers can have an increased interfacial interaction with the polymer matrix, despite being present at very low concentrations (<5 wt%). In this context, along with the size, the dispersion of the nanofiller in the matrix plays a central role in governing the resulting nanocomposite properties [8]. Generally, it is advantageous for a nanofiller to be well dispersed within the polymer matrix; however, in the case of carbon nanofillers, graphene, and graphite nanoplatelets in particular, obtaining high-quality dispersions without aggregation is a major challenge and limitation [4]. Further, control over the dispersion--to obtain ordered or hierarchical organization of the nanofiller within the polymer matrix--holds breakthrough potential [8]. At present, electron microscopy--transmission electron microscopy (TEM) in particular--remains the gold standard for assessing the dispersion of a nanofiller, because it gives a direct nanofiller image of the dispersion and morphology and can offer density quantification [9]. This approach is limited, however, by the fact that it presents only very local information from select fields of view that are always 2-D. As a result, other methods are being investigated, such as x-ray diffraction and small-angle scattering [10], modulated temperature differential scanning calorimetry [11], ultrasonic dynamic mechanical analysis [12], or dynamic rheological analysis [13]. While each of these methods has distinct advantages, none of them can be used on an object or component of a device because they all require dedicated sample preparation and are often destructive. As a result, these methods cannot be used to assess a nanocomposite after it has been processed into its application state without alteration. However, polymer processing methods--and especially industrially and economically viable methods, such as injection or compression molding--have a definite impact on the properties of a given nanocomposite [14], including the dispersion of a nanofiller. Terahertz time-domain spectroscopy (THz-TDS) offers an alternative as a non-destructive method suitable for testing even relatively large specimens. THz-TDS has already demonstrated its potential for materials characterization [15], including non-destructive testing (NDT) of both polymers [16] and other composite materials [17]. For example, it has been used to assess damage or detect defects in aeronautic components [18; 19]. Further, several groups have proposed using this approach to analyze carbon nanotube and/or graphene-polymer nanocomposites to assess the level of dispersion of the nanofiller [20; 21; 22; 23; 24]. Here, we report the use of a THz-TDS technique to characterize graphene nanofiller dispersion within multi-block copolyester nanocomposite materials.