# Nanomaterials' Influence on the Performance of Thermal Insulating Mortars--A Statistical Analysis
## 1 Introduction  
With the increasing importance of indoor comfort and energy efficiency in buildings [1; 2; 3; 4], the thermal performance of facades' coating materials, such as thermal insulating mortars, has been a growing research area [5; 6]. According to EN 998-1 [7], a thermal insulating mortar must present \(\lambda\leq 0.200\) W\(\cdot\)m\({}^{-1}\).K\({}^{-1}\) to be classified as T2, or \(\lambda\leq 0.100\) W\(\cdot\)m\({}^{-1}\).K\({}^{-1}\) to be classified as T1. Thermal insulating mortars have been used as an alternative to conventional thermal insulating materials [8], making use of the introduction of EPS (expanded polystyrene) granules and other materials, such as cork granulate, perlite, or natural fibres [9; 10; 11; 12], to lower their thermal conductivities [9; 13]. Although their performance being still lower than that of ETICS (External Thermal Insulation Composite System) solutions incorporating traditional thermal insulation materials [14], they present several advantages over those materials, such as [15; 16]: the possibility of smoothing complex areas; improved fire reaction; and easiness of application. To improve the performance of construction materials, several studies have included nanomaterials [17; 18]. One of the nanomaterials recently used and studied as a thermal insulator is the silica aerogel [19; 20]. This material is produced by a bottom-up approach through the sol-gel process, presenting only a small fraction of solid silica [21]. Although it can be classified as a 3-D nanomaterial (with all dimensions above the nanoscale), its inner structure is within the nanoscale [21; 22]. The silica aerogel is nanostructured and presents a very high quantity of pores with a reduced dimension (~10 to 100 nm) [21; 23], supported by a nanoparticle structure (with particle diameters-2 to 5 nm) of silica (SiO\({}_{2}\)), that are interconnected, forming a porous grid. It has an open pore network, with densities between 1.9 and 500 kg\(\cdot\)m\({}^{-3}\)[24; 25; 26]. As a consequence of its nanostructure and highly tortuous paths, the silica aerogel presents high thermal insulation due to the limitation of heat transport by radiation, convection, and conduction [27; 28; 29]. Therefore, the silica aerogel presents thermal conductivities between 0.012 and 0.021 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\), which is lower than that of air at ambient pressure (0.026 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)), but it is also significantly lower than those of EPS (0.032 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) [8; 30] and cork granules (0.045 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) [14]. With the inclusion of this nanomaterial in mortars, first done in 2012 by [PERSON] [31], it started being possible to significantly decrease the thermal conductivity of mortars (\(<\)0.060 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\)) [32; 33; 34], leading to the development and market reach of high-performance thermal insulating mortars [20; 35; 36; 37; 38; 39]. In order to analyse, compare, and optimise new products, different approaches have been used [40; 41], with one of these approaches being related to the use of multivariate statistical techniques [42; 43; 44; 45]. These techniques have also been used to study cement-based products [46; 47], allowing for the simplification of the interpretation of their performance, with particular emphasis on cluster analysis and Principal Components Analysis (PCA) [43; 44; 48; 49]. This approach allows us to reduce data dimension, visualise results, and identify possible correlations that would otherwise not be found [50].