# Nanomaterials' Influence on the Performance of Thermal Insulating Mortars--A Statistical Analysis
## 3 Results and Discussion
### Principal Components and Factor Analysis
#### 3.2.2 Discussion of the PCA and Factor Analysis  
The PCA found that three PCs would be considered the ideal number of dimensions. Then, with the factor analysis, it was possible to identify their latent structure. The first component, PC1, captured 47% of the total variance, displaying positive correlations between all variables. The higher loadings were associated with \(\lambda\), BD, and mechanical properties. This was a behaviour already expected and known [68; 106]. An increment in any of these variables leads to an increase in the other variables included in the same PC, probably being associated with the mortars' compacity and microstructural porosity [43], influencing their behaviour. Figure 3: Biplots of PC1, PC2, and PC3 (ind—industrial; lab—laboratory; semi—industrial manipulated in the laboratory). The second component, PC2, captured 15% of the total variance, displaying a high negative loading of the _fu_ correlated with both positive _Cons_ and _w/p_ ratio. This behaviour was already reported as a consequence of a more porous microstructure [108; 110], due to the increased needs of kneading water that leaves voids after water evaporation [111], fragilizing the microstructure. However, it was unexpected that _Cons_ and _w/p_ would relate so well with the decrease in _fu_. The third component, PC3, captured 9% of the total variance, presenting a positive correlation with both variables linked to water permeability, one to liquid (_TK_) and the other to vapour (\(\lambda\)). This is an interesting behaviour, somehow expected [109], that can be related to interconnected voids and capillaries present in the mortars' microstructure [112]. Therefore, with the loadings' distribution and the biplots, it was possible to try to interpret the latent factors on each PC: Factor 1--thermo-mechanical behaviour; Factor 2--internal cohesion and microstructural porosity behaviour; Factor 3--water permeability behaviour. Analysing the biplot of PC1 and PC2 (Figure 3a), it is observed that laboratory mortars (_lab_) tend to present lower thermo-mechanical properties and lower internal cohesion, being further apart from the other two types. For the mortars manipulated in the laboratory (_semi_), their PC1 behaviour is neutral, presenting values around the average. However, the cohesion presented higher variability, related with the insertion of thermal insulating nano aggregates (i.e., silica aerogel) in formulations initially designed considering other quantities, or materials, increasing their need for kneading water [107] and limiting their performance due to porosity increases. Finally, the industrial mortars (_ind_) present a distribution around the average of PC1 and PC2, being an expected behaviour due to the maturity of their development. For the biplot of PC1 and PC3 (Figure 3b), it is seen that the decrease in thermo-mechanical factors is associated with permeability increases. This is in line with the fact that the increase in voids and cracks leads to a more fragile matrix, with those voids then being filled with water, while also allowing water vapour circulation [110; 113]. The biplot representing PC2 and PC3 (Figure 3c) did not correspond to a significant improvement of the level of interpretation, due to a central distribution of the values. From the integrated analysis of all the biplots, it is seen that the current thermal insulation mortars with lower \(\lambda\) lose their mechanical resistance and cohesion, with an increased water permeability. This fact can be related with the fragility of the thermal insulating nano aggregates [25; 71] but also with the high need for kneading water that leaves capillaries and pores when it evaporates after the hydration reactions [114], indicating the need for further development. However, as shown by [PERSON] et al. [115], this can be overcome using multilayer protective systems.