## 1 Introduction  
Since their discovery by [PERSON] in 1909, epoxy resins have found a wide range of applications [1]. Due to their exceptional mechanical properties, which include high adhesive strength, high electrical insulation and good heat resistance, epoxy resins are used as coatings, adhesives and matrices for fiber-reinforced polymer (FRP) composites in demanding engineering fields such as the aerospace, naval, and automotive industries, etc. [2; 3; 4; 5]. Despite the exceptional mechanical and physical properties of epoxy resins, their highly dielectric character creates a barrier to the addition of functionalities such as strain sensing and Structural Health Monitoring (SHM), where electrical conductivity of the material is demanded [6; 7; 8; 9; 10; 11]. It is well known that the addition of a nano- or micro-scaled conductive phase inside the insulating epoxy matrix is capable of increasing the electrical and thermal conductivity, as well as improving the mechanical properties [12]. According to various studies, some of the most promising carbonaceous nano-fillers include carbon nanotubes (CNTs), due to their unique 1D character and extremely high aspect ratio (L/d), and graphene; meanwhile, short carbon fibers and Carbon Black (CB) are the most widely used micro-scale fillers [12; 13; 14]. Polymer nanocomposites are attractive materials due to their ease of production, relatively low cost, environmentally benign characteristics, flexibility, and high specific properties [15; 16; 17; 18; 19]. The introduction of CNTs in engineering thermosetting, thermoplastic and elastomer polymer-based matrices has resulted in electrically conductive nanocomposites [20; 21; 22; 23]. Specifically, the CNT networks in a polymer matrix allow electron transport by a tunneling or a hopping mechanism when junctions are separated by an insulating polymeric film [24]. Fundamental to the attainment of these properties is the concentration of the filler exceeding a critical concentration, called the percolation threshold. Above this concentration, the formation of a network of the nano- or the micro-filler occurs, and this network is responsible for the charge carrier transport phenomena, which impart electrical conductivity to the matrix [12; 25]. A positive side-effect of the introduction of carbonaceous fillers in epoxies is the improved mechanical properties that can be also achieved [12; 13]. Such fillers include CB [26; 27], and single-, double- or multi-walled carbon nanotubes (SWCNTs, DWCNTs, MWCNTs respectively) [28], and can impart significantly enhanced mechanical properties like flexural strength, factor toughness, adhesion strength, etc. [14; 29; 30], to epoxy matrices. The magnitude of improvement in material properties is highly dependent on the dispersion efficiency of the fillers in the epoxy resins and parameters like the employed dispersion method, duration or intensity, the filler type and weight content can greatly affect the resulting composite performance [31]. The most important parameter for the deployment of electrical and mechanical properties of CNTs in a CNT polymer nanocomposite is the dispersion process, to achieve an optimum nano-scale CNT disentangled network with extended CNT junctions. As such, the high quality of CNT dispersion can facilitate the full exploitation of the electrical, mechanical, thermal, etc., properties of the CNT nanoparticle additives, while at the same time preserving an ultra-low percolation threshold. Namely, for epoxy/CNT nanocomposites it is crucial to optimize the time and shear conditions for the shear assisted dispersion of CNTs, while for thermoplastic/CNT nanocomposites, the appropriate melt-mixing conditions and temperature to facilitate polymer infiltration through the CNT macro- and micro- aggregates without degrading the polymer matrix are of utmost importance [12].