# Thermal Investigations on Carbon Nanotubes by Spectroscopic Techniques
## 3 Results and Discussion
### Wavelet Cross-Correlation Analysis  
From the value of \(r_{XWT}\), by means of Equation (5), for each investigated temperature of the registered IR and Raman spectra, it emerges that the values arrange themselves in decreasing sigmoidal behavior. In this case, a curve fit model based on Equation (2) was also employed for the two profiles and an inflection point at 206.19 \({}^{\circ}\)C for the IR spectra and an inflection point at 206.15 \({}^{\circ}\)C for the Raman spectra were obtained. Figure 4a,b reports the trend of XWT versus temperature for CNTs, respectively of the recorded IR and Raman spectra, in the temperature interval from 25 \({}^{\circ}\)C to 450 \({}^{\circ}\)C together with the model fit of Equation (2) (blue line). This approach, like the previous one, provides the same value of inflection point for both the spectroscopic techniques employed.  
From the performed SD analysis, both for the IR and Raman obtained spectra, it emerges that the obtained relaxation temperature values, i.e., the \(T_{0}\) value of Equation (2), are very close for the two techniques. This value detects the decay of the mechanical properties and coincides with the oxidation of amorphous carbonate. Furthermore, one should also take into account that the tubes begin to oxidize at 200 \({}^{\circ}\)C under partial oxygen and that a greater quantity of oxygen increases the reaction rate at lower temperatures and causes oxidation of amorphous carbon at 200 \({}^{\circ}\)C.  
Although the obtained relaxation temperature values are similar, the SD fit curve rises to \(\sim\)2.3 in Figure 3a, while to \(\sim\)3.5 in Figure 3b. A specular behavior is registered in Figure 4, where the fit curve drops to \(\sim\)0.2 in Figure 4a, while to \(\sim\)0.4 in Figure 4b. The amplitude difference can be attributed to the different technique sensitivities; in particular IR and Raman techniques couple with a different system quantity, i.e., dipole moment and polarizability tensor, respectively.  
Figure 3: (**a**) Spectral Distance (SD) behavior with respect to temperature for CNTs, for the recorded IR spectra, together with the fit of the model (brown line); (**b**) Spectral Distance behavior with respect to temperature for CNTs, for the recorded IR spectra, together with the fit of the model (brown line) in the temperature range from 25 \({}^{\circ}\)C to 450 \({}^{\circ}\)C.  
In this experimental work, the investigation of thermal behavior for CNTs was evaluated by means of Fourier Transform Infrared analysis and then continued by means of two innovative approaches, i.e., SD and XWT. From both techniques, a relaxation temperature value of about T = 206 \({}^{\circ}\)C was obtained, corresponding to the inflection point of the curves. Such a value was obtained both for the IR and Raman data. This relaxation temperature can be linked to the same relaxation phenomenon, which generally occurs in fiber CNTs. This relaxation process is connected with decay of the mechanical properties and is due to a decrease in the alignment and compaction of the fibers. Furthermore, the value obtained coincided with the oxidation of the tubes that occurred at 200 \({}^{\circ}\)C. This took place because the amount of oxygen present allowed the speed rate to be increased at the lowest temperature, thus causing oxidation of the amorphous carbonate at 200 \({}^{\circ}\)C even though the greatest loss occurred above 420 \({}^{\circ}\)C.