*2.3.1 Percolation network by conductive filler reinforcement*

Percolation theory states that introducing conductive fillers into a non-conductive matrix above the percolation threshold leads to the formation of a continuous conductive path in the composite. It is a common observation that the conductive filler concentrations (e.g., carbon-based, metal-based fillers, etc.) in the matrix exhibit a conductivity profile that can be represented by an S-shaped curve (**Figure 3**). This behavior indicates a substantial increase in conductivity within a small range of filler loading. For an insulating elastic matrix, the percolation threshold for conductive nanofillers, such as carbon blacks (CBs) with spherical morphology, typically falls within the range of 10–20% by volume fraction. This range is consistent with the predictions of classical percolation theory [46, 47]. An epoxy hybrid system was created by introducing multi-wall carbon nanotubes (MWCNTs) and graphene nanosheets (GNs) in two specific filler quantities: less than 0.1 wt% and greater than 0.5 wt% [48]. This was done using different ratios of MWCNTs to GNs. These hybrid epoxy systems demonstrated outstanding electrical capabilities, credited to the interactions between the π–π bonds of the multi-wall carbon nanotubes and the dispersed graphene layers within the epoxy resin matrix. When using high loading of stiff nanofillers, challenges arise due to increased viscosities, and inferior mechanical performance resulting from nanofiller aggregation at higher concentrations. Therefore, achieving an effective reduction in the percolation threshold while preserving electrical

#### **Figure 3.**

*The effective electrical conductivity exhibits an S-shaped curve near the percolation threshold fc. This proximity to the threshold reveals notable phenomena of percolation theory and nonlinear changes in the transport properties of composites. The insets illustrate the geometric phase transition of fillers within the microstructures of the composites precisely at the percolation point. Reproduced from Ref. [45] with permission from the Royal Society of Chemistry.*

## *Electrically Conductive Self-Healing Epoxy Composites for Flexible Applications: A Review DOI: http://dx.doi.org/10.5772/intechopen.1003037*

properties becomes crucial for fabricating high-performance conductive composite materials. To achieve this objective, various parameters of conductive nanofillers can be tailored, including aspect ratio, dimensional size, size distribution, surface wettability, and contact resistance between individual nanofillers. This customization allows for fine-tuning the corresponding electrical properties to suit specific applications.

### *2.3.2 Segregated conductive filler network*

By strategically forming segregated filler networks within an epoxy matrix, conductive epoxy composites can achieve remarkably improved conductivity even at lower nanofiller concentrations. Instead of being dispersed randomly throughout the entire matrix, conductive nanofillers are intentionally positioned at the interfaces of epoxy matrix domains, leading to a significantly lowered percolation threshold compared to conventional percolation networks. The establishment of these segregated conductive networks depends on the fabrication approach used during the construction of the composites [49, 50].

Through the implementation of an interface engineering strategy, branched CNTs were skillfully coated on the surface of catalyst-infused epoxy waste particles. Subsequently, vitrimerized epoxy/CNT composites were created via compression molding [51]. This innovative approach resulted in the development of a segregated filler structure at the interfaces of "vitrimerized" epoxy particles, achieving two important objectives simultaneously. Firstly, it enabled the recycling of epoxy waste, contributing to sustainability efforts. Secondly, it significantly enhanced the mechanical and electrical properties of the recycled epoxy, even with low carbon nanofiller content (below 1 wt%). The successful incorporation of branched CNTs facilitated the fabrication of highly electrically conductive composites, which hold great promise for applications such as electromagnetic interference (EMI) shielding and strain sensing. Zhang et al. [52] successfully accomplished the controlled dispersion of multiwalled carbon nanotubes (MWCNTs) within the distinct network of hexagonal boron nitride (h-BN) in the epoxy vitrimer matrix using compression molding. This method facilitated the creation of interfacial bonds through dynamic transesterification involving small molecules, particularly at elevated temperatures. As a result of this process, the epoxy vitrimer composites demonstrated improved thermal conductivity and electrical insulation even with a low concentration of fillers. This improvement is attributed to the collaborative effect of the well-organized nanofiller network. In a composite containing 1 wt% MWCNTs and 8 wt% h-BN, the recorded thermal conductivity and electrical resistivity values were 0.83 W (m K)−1 and 1.92 × 1011 Ω cm, respectively. Furthermore, by increasing the portion of separated h-BN, it is possible to further enhance the electrical resistivity.
