## 2 Experimental Design
### Dispersion of MWCNTs and GNPs  
An additional experimental variable is whether MWCNTs andSNPs were functionalized. Owing to their hydrophobic properties, CBNs have difficulty securing dispersibility, even when mixed in water. The cohesion between the carbon particles of MWCNTs and GNPs by the strong van der Waals force results in the agglomeration of CBNs, leading to the formation of clusters and bundles when dispersed in a solution. To avoid such aggregation and uniformly disperse CBNs without breakage, a combination of chemical and physical methods must be implemented [33]. That is, a physical method of separating CBNs individually by applying ultrasonic energy and a chemical treatment method that involves modifying and functionalizing the surface of CBNs to prevent re-agglomeration following ultrasonication should be performed simultaneously. This study investigated the effect of securing dispersibility through functionalization on conductivity. The MWCNTs and GNPs were noncovalent functionalized using the process proposed by [PERSON] et al. [30]. The functionalization process performed in this study is shown in Figure 1. First, CBNs were mixed with melamine in a 1:1 ratio and ultrasonicated in dimethylformamide (DMF, a polar solvent) for 1 h to produce the mixture (Figure 1a). The ultrasonication-treated mixed solution was poured into a polypropylene bottle containing stainless steel balls, and ball milling was performed for 24 h (Figure 1b). After the synthesis of CBNs and melamine  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specific Surface Area** & **Bulk Density** & **Purity** & **Diameter** \\
**(m2/g)** & **(g/cm3)** & **(\%)** & **(\%)** \\ \hline
30–60 & 0.03–0.1 & \textgreater{}95 & 7–25 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties of graphene nanoplatelets (GNPs).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mix ID.** & **Dispersion** & **MWCNTs** & **GNPs** \\
**(wt\%)** & **(wt\%)** & **(wt\%)** \\ \hline MWCNT & & 0.06 & - \\  & & 0.12 & - \\  & & 0.30 & - \\  & & 0.60 & - \\  & & 1.20 & - \\ \hline  & & & - & 0.06 \\ GNP & & & - & 0.30 \\  & & & - & 0.60 \\  & & & - & 1.20 \\ \hline Hybrid & & 0.06 & 0.06 \\  & & 0.30 & 0.30 \\  & & 0.60 & 0.60 \\ \hline  & & & 0.06 & - \\  & & 0.12 & - \\ f-MWCNT & & 0.30 & - \\  & & 0.60 & - \\  & & 1.20 & - \\ \hline  & Noncovalent & & - & 0.06 \\  & functionalization & + & - & 0.12 \\ f-GNP & ultrasonication & - & 0.30 \\  & & - & 0.60 \\  & & - & 1.20 \\ \hline  & & 0.06 & 0.06 \\ f-Hybrid & & 0.30 & 0.30 \\  & & 0.60 & 0.60 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental variables.  
via ball milling, the DMF was washed through filtration using ethanol and distilled water (Figure 1c). It was then dried in a vacuum oven for 24 h to produce functionalized MWCNTs and GNPs. To produce the specimens, functionalized MWCNTs or GNPs were added to the mixed water, underwent ultrasonication for 30 min, and was then mixed with the cement for 10 min at 300 rpm using a mortar mixer. The control group did not go through the functionalization and underwent ultrasonication for 30 min and mortar mixing for only 10 min.