## 3 Results and Discussion
### Evaluation of Self-Healing Performance as a Function of Temperature and pH  
#### 3.2.1 Volume Change in Cracked Section  
To observe the progression of self-healing inside a crack, the crack interior in a test body was monitored using microfocus X-ray CT scans. An X-ray of 40 \(\upmu\)A at 180 kV was employed, and the screen analysis domain for the X-ray CT scans was set as shown in Figure 8. The three-dimensional (3D) images obtained for each test body were composed of voxels, and the crack width and volume of the cracked section were calculated by using these voxels (Figure 8) [28] (While a pixel (short for \"picture element\") is defined by a two-dimensional (2D) coordinate and the value of a data point (e.g., luminance, color) at that coordinate, a voxel (short for \"volume element\") is defined by a 3D coordinate and the value of a data point (e.g., luminance, color) at that coordinate). A conceptual histogram of the luminance and frequency of the 3D screen is shown in Figure 9, where the boundary in luminance between a void and the material (cement matrix) is clearly differentiated by the normal distribution of each peak. The total volume of the pores could be calculated because the cracked section before self-healing had the same density as that of the void. The volume changes of the voids in the cracked section before and after self-healing were compared and evaluated by calculating the difference between the density of the section with voids and that of the section filled by precipitates. Figure 6: Cracked surface after self-healing. Note: CM: Ca(OH)\({}_{2}\) + microbubbles; CN: Ca(OH)\({}_{2}\) + nanobubbles; 20: Temperature of self-healing (\({}^{\circ}\)C). Figure 7: Raman spectroscopy analysis: (**a**) experimental setup; (**b**) Raman spectra of self-healing substances generated in test bodies (CM-20, CN-20). The volume change recorded in the section with voids before and after self-healing in each test body are shown in Figure 10 as a function of the self-healing temperature (20, 40, and 60 \({}^{\circ}\)C) at a constant pH of 9.0. A comparison of the volume after step B with the volume after step A shows that the volume of the section with voids decreased in both test bodies after self-healing at 20 \({}^{\circ}\)C, dropping by about 50% (from 1.11% to 0.56%) in CM-20 and by about 60% (from 1.60% to 0.71%) in CN-20. When self-healing took place at 40 \({}^{\circ}\)C, the section with voids also decreased in volume by about 65% (from 2.41% to 0.89%) in CM-40 and by about 85% (from 2.42% to 0.39%) in CN-40. After self-healing at 60 \({}^{\circ}\)C, the volume of the section with voids decreased by about 40% (from 2.1% to 1.11%) in CM-60 and by about 60% (from 1.25% to 0.53%) in CN-60. These results show that the volume of the section with voids experienced 15%-20% more reduction in the CN series than in the CM series, and the reduction rate of the volume of the section with voids decreased with a self-healing temperature in the order of 40 \(>\) 20 \(>\) 60 for all series. Therefore, the supply of nanobubbles was more advantageous for self-healing (CN series) than the supply of microbubbles (CM series), and the self-healing temperature of 40 \({}^{\circ}\)C was more advantageous than the temperatures of 20 and 60 \({}^{\circ}\)C.  
Figure 11 shows the volume change in the section with voids as a function of the pH (9.0, 10.5, and 12.0) before and after self-healing at a constant temperature of 40 \({}^{\circ}\)C. The volume changed by about 60% (from 2.41% to 0.89%) in CM-9.0 and by about 85% (from 2.42% to 0.39%) in CN-9.0 when the pH was set at 9.0. When self-healing took place at a pH of 10.5, the volume of the section with voids decreased by about 40% (from 2.22% to 1.34%) in CM-10.5 and by about 60% (from 1.5% to 0.56%) in CN-10.5. When the pH was set at 12.0, the volume of the section with voids decreased by about 45% (from 2.21% to 1.18%) in CM-12.0 and by about 80% (from 0.92% to 0.2%) in CN-12.0.