## 3 Results
### Microstructure of Mortar/SAPs Specimens  
#### 3.2.1 Microstructure Analysis  
In this work, the effect of SAPs incorporation on the mortar microstructure in means of porosity and phase segmentation was examined via microCT. In cementitious materials, porosity affects greatly key properties such as mechanical and transport properties [46]. Moreover, the dispersion quality of SAPs in the cementitious matrix can be evaluated through porosity determination. The porosity of cementitious materials is usually divided into gel pores (ranging from a few nanometers to 0.2 \(\upmu\)m), capillary pores (ranging from  
Figure 5: Maximum values of loads for mortar specimens at 28 days of age (**a**), compressive strength of mortar specimens at 28 days of age (**b**), optical image of specimen after compressive test (**c**).  
Figure 6: Relationship between compressive and flexural strength of mortar-based materials.  
0.2 to 10 \(\upmu\)m), and air voids (above 10 \(\upmu\)m) [50,55,56]. In this work, the pore analysis from micro-CT applies only to the pores with diameters larger than 9 \(\upmu\)m. The specimen size dictates the minimum distance that can be reached from the X-ray source during scanning and consequently the accuracy of the method. Therefore, the pore analysis from micro-CT scans includes partially capillary pores and the air voids. Air voids are mainly of interest in this work, as in literature, it is reported that the incorporation of SAPs in cementitious matrixes creates air voids around them as a result of the water absorption/desorption by them combined with their poor dispersion in cement and therefore the formation of large SAPs agglomerates [9,10,15,21,31,35,38]. The statistical pore analysis of mortar specimens and the corresponding pore size distribution are exhibited in Table 3 and Figure 7, respectively. The statistical pore analysis parameters calculated are delineated as follows.  
* \"Volume of closed porosity\" (mm\({}^{3}\)) is the total volume of all closed pores within the Volume of Interest (VOI), when a closed pore in 3D is a connected assemblage of space (black) voxels that is fully surrounded on all sides in 3D by solid (white) voxels.
* \"Closed porosity\" (%) is the volume of closed pores (as defined above) as a percent of the total of solid plus closed pore volume, within the VOI.
* \"Volume of open porosity\" (mm\({}^{3}\)) is the total volume of all open pores within the VOI. An open pore is defined as any space located within a solid object or between solid objects, which has any connection in 3D to the space outside the object or objects.  
Figure 7: Pore size distribution in mortar-reference, mortar-SAPs-1 and mortar-SAPs-2.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Property** & **Unit** & **Mortar-Reference** & **Mortar-SAPs-1** & **Mortar-SAPs-2** \\ \hline Volume of closed porosity & mm\({}^{3}\) & 10.60 & 1.87 & 1.18 \\ Closed porosity & \% & 2.440 & 1.800 & 0.341 \\ Volume of open porosity & mm\({}^{3}\) & 5.43 & 1.49 & 2.54 \\ Open porosity & \% & 1.230 & 1.420 & 0.725 \\ Volume of total porosity & mm\({}^{3}\) & 16.10 & 3.36 & 3.72 \\ Total porosity & \% & 3.64 & 3.19 & 1.06 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical pore analysis of mortar specimens.  
* \"Open porosity\" (%) is the volume of open pores (as defined above) as a percent of the total VOI volume
* \"Volume of total porosity\" (mm\({}^{3}\)) is the total volume of all open and closed pores within the VOI
* \"Total porosity\" (%) is the volume of all open plus closed pores (as defined above) as a percent of the total VOI volume.