# Nanomaterials' Influence on the Performance of Thermal Insulating Mortars--A Statistical Analysis
## 3 Results and Discussion
### Uni and Bivariate Analysis
#### 3.1.3 Discussion of the Uni and Bivariate Analysis
These results also show that for the average thermal insulation mortar, although presenting higher mechanical performance than required by the EN 998-1 [7] (fc \(\geq\) 0.40 MPa), the associated thermal conductivities are also high (classified as a T2, according to the same standard), even more so if \(\lambda\) is compared with EPS (\(\lambda\) \(\sim\) 0.032 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)[30]). From this analysis, it was verified that these mortars still have a high margin of development if the objective is to decrease their \(\lambda\) and \(W\) while maintaining high \(\Lambda\) and mechanical behaviour. However, the use of formulations incorporating nanomaterials significantly reduced their thermal conductivities, allowing us to obtain mortars with \(\lambda\) below classic thermal insulating materials. In the bivariate analysis and using the matrices of linear correlation and of scatterplots, it was observed how the different variables relate to each other. The linear correlation coefficients ranged from \(\sim\) 0 (_fu_ and \(\Lambda\)) to \(|1|\) (\(\lambda_{10^{\circ}C,28 days}\), and \(\lambda_{10^{\circ}C,dry}\)) and, in most cases, with \(p\)-value \(<\) 0.05, increasing the confidence in accepting the observed result as representative of all thermal insulating mortars, indicating that independently of the insulation aggregate, nanomaterial or not, the correlations were maintained. The bivariate analysis showed interesting correlations: _BDh_ presents a high correlation (0.91) with _BDf_, this being somehow expected, as it was also verified by [PERSON] [68]. However, some other significant correlations were also identified: for the \(\lambda_{10^{\circ}C,28 days}\), high correlations (\(\geq\) 0.80) were found with _BDf_, _BDh_, _Ed_, and _ft_, which is an interesting behaviour. Although, for the bulk density values, this was a known fact [68; 103; 104], it is a new finding that _Ed_ and _ft_ also showed high correlations. This can be related to a less porous microstructure that better conducts the heat-flux [105], increasing the thermal conductivity. This behaviour was also verified for other types of mortars by [PERSON] et al. [106] and is something to consider when designing new formulations. For the dry state (\(\lambda_{10^{\circ}C,dry}\)), the correlation with _BDh_ and _BDf_ was also high, but it was higher with \(\lambda_{10^{\circ}C,28 days}\). So, despite the drying process in which the free water lost is unpredictable, a very high correlation was found between \(\lambda_{10^{\circ}C,dry}\) and \(\lambda_{10^{\circ}C,28 days}\). The behaviour of the variable _w/p_ was expected (inverse with other variables). This fact agrees with what is known, since the increase of _w/p_, to improve the workability, reduces _fc_, _ft_, and _BDH_, because of the increase in voids, capillaries, and pores in the microstructure, when the free water evaporates [107; 108]. This would be expected to correlate well with a decrease in the thermal conductivity values (due to the low thermal conductivity of the air), but that was not verified. Some correlation between \(W\) and \(\Lambda\) was also expected, due to the presence of capillaries, as well as between _fc_ and _ft_, as a result of the internal cohesion, but that was not verified. As for _fc_, it was correlated with _Ed_ and _ft_, as expected [109], since the increment of one increases the others. Figure 1 complemented the matrix of linear correlation, allowing us to visualise the values' dispersion for all formulations. This way, it was possible to see that all pairs of variables did not show distribution patterns other than linear, and that outlier behaviours were not significant. With this analysis, it was verified that the use of nanomaterials in thermal insulating mortars leads to a significant lowering of _BDf_, _BDh_, \(\lambda_{10^{\circ}Cdry}\), and \(\lambda_{10^{\circ}C,28 days}\), however, it also lowered _fc_ and _ft_.