## 3 Results and Discussion
### Vibrational and Thermodynamic Characterization  
In silico investigations were conducted to describe the theoretical characteristics of the four molecules under study, including their vibrational and thermodynamic modes. These characteristics are essential for characterizing the combined polymer/drug systems that will form the nanocapsules. Figure 6 presents the theoretical spectra obtained from the in silico studies in the region from 500 to 4000 cm\({}^{-1}\). The spectra obtained experimentally are presented in Figure 7. By comparing the two sets of spectra, it can be observed that they are very similar, highlighting some vibrational peaks, as explained in Table 3.  
In both the theoretical and experimental IR spectra, it is evident that PMMA, PCL, and PLGA display characteristic peaks of C=O stretching vibrations at 1726 cm\({}^{-1}\). The calculated C=O stretching vibrations in the region of 1797 cm\({}^{-1}\) show a shift of 71 cm\({}^{-1}\), which is in good agreement with experimental assignments in the regions of 1720 to 1740 cm\({}^{-1}\), as referenced by CH\({}_{2}\) bending modes at 1361, 1397, and 1473 cm\({}^{-1}\) and CH\({}_{2}\) asymmetric stretching at 2942 and symmetric stretching at 2862 cm\({}^{-1}\) are observed. The C=O=C stretching vibrations yield peaks at 1042, 1107, and 1233 cm\({}^{-1}\).  
The FTIR spectra of QPhNO\({}_{2}\) clearly show the formation of urethane groups (from isocyanate segments). The symmetric and asymmetric stretching vibrations of N-H correspond to the broad absorption bands near 3329-3337 cm\({}^{-1}\), while the medium-strong peak at 1530-1535 cm\({}^{-1}\) confirms the in-plane bending vibration of N-H. Strong absorption peaks at 1665-1720 cm\({}^{-1}\) and 1221 cm\({}^{-1}\) are typical for the stretching vibration of esters  
Figure 6: Theoretical FTIR spectra of PMMA, PCL, PLGA, and QPhNO\({}_{2}\), respectively, obtained by computer simulation.  
CO and the asymmetric stretching vibration of C-O (from N-CO-O), respectively. The weak peak near 916 cm\({}^{-1}\) is due to the N-CO-O symmetric stretching vibration. The 1601 cm\({}^{-1}\) absorption peak is caused by the vibration of C-C in benzene. These values show good agreement with theoretical calculations.  
Thermodynamic data were obtained and can be used to calculate additional thermodynamic properties, such as energies and reaction directions, based on correlations between thermodynamic functions. These analyses provide insights into the stability and reactivity of the polymer/drug systems, contributing to a better understanding of their behavior under different conditions. Thermodynamic parameters, such as entropy (S), enthalpy (H), and heat capacity (Cv), are essential for characterizing complex systems composed of two or more molecular components. These parameters, calculated for the PMMA, PCL, PLGA polymers, and the QPhNO\({}_{2}\) drug, were determined using the DFT/B3 LYP/6-3 11++G method at 298.15 K (room temperature) and are shown in Table 4. Additionally, these parameters were computed across a temperature range from 100 K to 500 K. It should be noted from the results that these thermodynamic parameters depend on temperature, as does the way in which the vibrational intensities of molecules increase with temperature. A quadratic polynomial function was used to fit the equations relating temperatures to entropy, heat capacity, and enthalpy, as well as the corresponding adjustment factors (R\({}^{2}\)).  
Figure 8 shows the correlation graphs of these thermodynamic functions. The corresponding adjustment equations for enthalpy, heat capacity, and the entropy of PMMA, PCL, PLGA, and QPhNO\({}_{2}\) are shown in Table 5. All parameters show increasing behavior with temperature, except for enthalpy.  
These data can be used to compute other thermodynamic energies based on the relationships between thermodynamic functions and to estimate the directions of chemical reactions in accordance with the second law of thermodynamics within the thermochemical field.