## 3 Results and Discussion
### Drug-Polymer Interaction
The binding energies calculated for PMMA/QPhNO\({}_{2}\), PCL/QPhNO\({}_{2}\), and PLGA/QPhNO\({}_{2}\) fall within typical ranges observed for non-covalent interactions in drug-polymer systems, generally reported between \(-1\) and \(-6\) kcal/mol [38; 45; 46; 47]. Lower (more negative) binding energy values suggest stronger molecular affinity, while less negative values indicate weaker but still relevant interactions for encapsulation purposes. These findings are consistent with results from similar studies investigating molecular docking for drug delivery applications [38; 47]. Non-covalent interactions, such as Van der Waals forces and hydrogen bonds, are essential for the efficacy of drug delivery systems, directly affecting encapsulation efficiency and release profiles [52; 53]. These weaker interactions facilitate  
Figure 8: Thermodynamic parameters of PMMA, PCL, PLGA, and QPhNO\({}_{2}\) molecules: entropy, heat capacity, and enthalpy. The lines are the theoretical adjustments described in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Functional Form**} & \multicolumn{5}{c}{_a + b T + c T\({}^{2}\)_} \\ \cline{2-6}  & & \(a\) & \(b\) & \(c\) & \(\mathbf{R^{2}}\) \\ \hline \multirow{5}{*}{Enthalpy} & PMMA & \(-345.66\) & \(1.10\times 10^{-5}\) & \(5.00\times 10^{-8}\) & \(0.99535\) \\ \cline{2-6}  & PCL & \(-464.72\) & \(1.71\times 10^{-5}\) & \(7.14\times 10^{-8}\) & \(0.99591\) \\ \cline{2-6}  & PLGA & \(-571.33\) & \(2.62\times 10^{-5}\) & \(4.24\times 10^{-8}\) & \(0.96821\) \\ \cline{2-6}  & QPhNO\({}_{2}\) & \(-1241.54\) & \(2.10\times 10^{-5}\) & \(15.0\times 10^{-8}\) & \(0.99969\) \\ \hline \multirow{5}{*}{Entropy} & PMMA & \(218.44\) & \(0.53\) & \(-3.29\times 10^{-4}\) & \(0.99673\) \\ \cline{2-6}  & PCL & \(262.22\) & \(0.61\) & \(-3.06\times 10^{-4}\) & \(0.99616\) \\ \cline{2-6}  & PLGA & \(240.35\) & \(0.62\) & \(-3.43\times 10^{-4}\) & \(0.99833\) \\ \cline{2-6}  & QPhNO\({}_{2}\) & \(292.66\) & \(0.90\) & \(-1.30\times 10^{-4}\) & \(0.99938\) \\ \hline \multirow{5}{*}{Heat capacity} & PMMA & \(30.10\) & \(0.16\) & \(9.31\times 10^{-5}\) & \(0.99980\) \\ \cline{2-6}  & PCL & \(48.88\) & \(0.20\) & \(2.70\times 10^{-5}\) & \(0.99937\) \\ \cline{2-6}  & PLGA & \(31.14\) & \(0.31\) & \(-8.29\times 10^{-5}\) & \(0.99991\) \\ \cline{1-1} \cline{2-6}  & QPhNO\({}_{2}\) & \(17.76\) & \(0.85\) & \(-21.31\times 10^{-5}\) & \(0.99980\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Thermodynamic parameters H, S, and C\({}_{v}\) obtained through theoretical adjustments using a second-order polynomial equation as a function of temperature T.  
controlled drug release, allowing factors like diffusion, polymer degradation, and surfactants to influence the release profile. By correlating binding energies, polymer properties, and encapsulation dynamics, we conclude that the observed interactions are sufficient to ensure encapsulation stability and effective controlled release of QPhNO\({}_{2}\) across different applications. Together, these data validate our methodology and provide confidence in the accuracy of the computational predictions presented in this work. Figure 9: Simulations of the molecular interactions among (**A**) PMMA/QPhNO\({}_{2}\), (**B**) PCL/QPhNO\({}_{2}\), and (**C**) PLGA/QPhNO\({}_{2}\). QPhNO\({}_{2}\) is highlighted in yellow. The distances between interacting groups are also shown (in angstroms). Figure 9A illustrates the interaction between PMMA and QPhNO\({}_{2}\). Using Discovery Studio, five favorable interactions were identified, involving pi-sigma, pi-alkyl interactions (hydrophobic interaction), and a non-classical hydrogen bond. One of the pi-sigma interactions occur between the PMMA carbon atom and the aromatic ring of the QPhNO\({}_{2}\) molecule. The other pi-sigma interaction involves the same carbon atom and another ring containing two double carbon bonds. Non-covalent interactions involving pi systems are critical for biological processes, such as protein-ligand recognition [1].