## 5 Experimental Results  
### PTR Results  
Figure 8 shows the amplitude and phase characteristics of the PTR signal collected for a series of PBMA-siloxane samples annealed at temperatures of 25, 90, 120, 150, and 180 \({}^{\circ}\)C.  
The next two figures (Figures 9 and 10) present the fits of the theoretical curves to the experimental results for two samples annealed at two extreme temperatures: 25 \({}^{\circ}\)C and 180 \({}^{\circ}\)C.  
Figure 8: The experimental amplitude and phase characteristics of the PTR signal obtained for a series of PBMA–siloxane samples annealed at different temperatures. Figure 10: Theoretical (lines) and experimental (circles) PTR amplitude and phase frequency characteristics. They were obtained for the PBMA–siloxane coating annealed at 180 \({}^{\circ}\)C. Characteristics shown with the solid green line were computed for (\(\alpha_{\rm c}\), \(\lambda_{\rm c}\)), those with the solid blue line were computed for (3-\(\alpha_{\rm c}\), 3-\(\lambda_{\rm c}\)), and those with the solid red line were computed for (\(\alpha_{\rm c}\)/3, \(\lambda_{\rm c}\)/3). Figure 9: Theoretical (lines) and experimental (circles) PTR amplitude and phase frequency characteristics. They were obtained for the PBMA–siloxane coating annealed at 25 \({}^{\circ}\)C. Characteristics shown with the solid green line were computed for (\(\alpha_{\rm c}\), \(\lambda_{\rm c}\)), those with the solid blue line were computed for (\(\alpha_{\rm c}\)/3, \(\lambda_{\rm c}\)/3). The best fit of theoretical characteristics to experimental data was obtained for the following values of thermal parameters: \(\alpha_{\rm c}=2.524\cdot 10^{-3}\) cm\({}^{2}\)/s and \(\lambda_{\rm c}=3.02\cdot 10^{-3}\) W/cm\(\cdot\)K.  
The best fit of theoretical characteristics to experimental data was obtained for the following values of thermal parameters: \(\alpha_{\rm c}=2.785\cdot 10^{-3}\) cm\({}^{2}\)/s and \(\lambda_{\rm c}=3.489\cdot 10^{-3}\) W/cm\(\cdot\)K.  
The obtained thermal parameters of PBMA-siloxane coatings (thermal diffusivity, thermal conductivity, and thermal effusivity) annealed at different temperatures (25, 90, 120, 150, 180 \({}^{\circ}\)C) were determined (Table 1) using the least-squares fitting procedure for theoretical dependence, obtained by Equation (4), to the normalized experimental data. The fitted parameters were the thermal conductivity \(\lambda\) and the diffusivity \(\alpha\) of the PBMA-siloxane coating. The best fit was found when the samples' thermal parameters were within the relative expanded uncertainty of a 94.45% (\(\pm 2\sigma\)) confidence level (CL) [42; 43]. The thermal effusivity was calculated by Equation (23). \[e_{c}=\frac{\lambda_{c}}{\sqrt{\alpha}_{c}} \tag{23}\]  
It is seen that all the thermal parameters show a general trend of increasing with the increase in the value of the annealing temperature (Figures 11-13). This behavior reflects the changes in material properties that occur as a result of its annealing. The increase in the temperature of the material during sol-gel synthesis causes the breaking of double bonds, thus making the whole material more compact, which also increases its thermal properties [44]. The increase in annealing temperature from 25 \({}^{\circ}\)C to 180 \({}^{\circ}\)C results in about a 10% increase in the Si-PBMA coating's thermal properties, reaching values of 2.785\(\cdot 10^{-3}\) cm\({}^{2}\cdot\)s\({}^{-1}\), 3.489\(\cdot 10^{-3}\) W\(\cdot\)cm\({}^{-1}\cdot\)K\({}^{-1}\), and 6.61\(\cdot 10^{-2}\) W\(\cdot\)s\({}^{1/2}\) cm\({}^{-2}\cdot\)K