## 3 Results and Discussion
### Thermal and Strength Performances of Composite Cement Paste Samples  
Figure 6 presents the \(F_{c}\) and \(k\), at 28 days of curing, of the composite cement paste samples that contained varying silica aerogel content. \(F_{c}\) decreased from 49.28 MPa to 42.89 MPa when the silica aerogel content per sample was increased from 0 wt.% to 2 wt.%. Conversely, a further addition of 2 wt.% of silica aerogel per sample, which was from 2 wt.% to 4 wt.%, led to the culmination of \(F_{c}\) at its highest value of 54.33 MPa. As the silica aerogel content was increased from 4 wt.% to 6 wt.% and then 8 wt.%, \(F_{c}\) was adversely affected, where \(F_{c}\) decreased from 54.33 MPa to 47.03 MPa and then its lowest value of 34.77 MPa, respectively. A similar trend of \(F_{c}\) was reported in [PERSON] et al. [56]. Furthermore, it can be projected that the adverse effect on \(F_{c}\) will extend as higher amounts of silica aerogel are incorporated, as revealed in [PERSON] et al. [57]. In essence, the incorporation of 8 wt.% of silica aerogel led to a loss of strength of 29.44%, where \(F_{c}\) decreased from 49.28 MPa to 34.77 MPa. On the other hand, the incorporation of silica aerogel led to a drop in \(k\) from 1.185 W/mK to 0.340 W/mK, 0.142 W/mK, 0.086 W/mK, and 0.076 W/mK when 2 wt.%, 4 wt.%, 6 wt.%, and 8 wt.% of silica aerogel were incorporated, respectively. Essentially, the incorporation of 8 wt.% of silica aerogel resulted in a decline in \(k\) of 93.59%, with a gradient that decreased as the silica aerogel content was increased. In view of the culmination of \(F_{c}\) at its highest value of 54.33 MPa that coincides with the conspicuous decrease in the gradient of \(k\) as it declined from 1.185 W/mK to 0.142 W/mK, it can be deduced that the silica aerogel content of 4 wt.% resulted in the optimum formulation of the silica-aerogel-incorporated composite cement paste.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Oxides** & **Content (wt.\%)** \\ \hline Silicon Dioxide (SiO\({}_{2}\)) & 74.48 \\ Sodium Oxide (Na\({}_{2}\)O) & 9.15 \\ Aluminium Oxide (Al\({}_{2}\)O\({}_{3}\)) & 0.05 \\ Calcium Oxide (CaO) & 0.05 \\ Iron (III) Oxide (Fe\({}_{2}\)O\({}_{3}\)) & 0.05 \\ Magnesium Oxide (MgO) & 0.01 \\ Manganese (II) Oxide (MnO) & 0.01 \\ Titanium (IV) Oxide (TiO\({}_{2}\)) & Below detection limit \\ \hline \hline \end{tabular}
\end{table}
Table 2: Composition of the silica aerogel sample obtained from the X-Ray Fluorescence (XRF) analysis.  
Figure 5: X-Ray Diffraction (XRD) pattern of the silica aerogel sample.  
Figure 7 shows that the increase in the silica aerogel content in the composite cement paste increased its \(\phi\), which was due to the nano-sized pore structure of silica aerogel. The \(\phi\) of the cement paste, without the incorporation of silica aerogel, was 0.128%. The incorporation of 2 wt.% of silica aerogel in the cement paste induced a rise in \(\phi\) from 0.128% to 0.160%. Further addition of silica aerogel from 2 wt.% to 4 wt.%, 6 wt.%, and 8 wt.% led to the increase in \(\phi\) to 0.220%, 0.216%, and 0.256%, respectively. The increase in the silica aerogel content beyond 4 wt.% led to the sharp decline in \(F_{c}\) from 54.33 MPa to 34.77 MPa due to the high \(\phi\) of 0.256%. However, when the silica aerogel content was increased from 2 wt.% to its optimum value of 4 wt.%, the \(F_{c}\) improved from 42.89 MPa to 54.33 MPa in spite of the increase in porosity from 0.160% to 0.220%.  
Figure 6: Compressive strength (\(F_{c}\)) and thermal conductivity (\(k\)) of the composite cement paste after 28 days of curing.  
Figure 7: Compressive strength (\(F_{c}\)) and permeable porosity (\(\phi\)) of the composite cement paste after 28 days of curing.