## 3 Results and Discussion
### Radius of Gyration Analysis  
A larger fluctuation in the radius of gyration indicates a greater degree of flexibility in the system, while a smaller fluctuation suggests a more rigid structure. The radius of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Interface Models** & **Value of Bulk** & **Value of Shear** & **Value of Young’s** & & \\
**Modulus (GPa)** & **Modulus (GPa)** & **Modulus (GPa)** & **Value of Poisson’s Ratio** & & \\ \hline \multirow{3}{*}{DGEBA–Sand} & 29.5767 ([PERSON]) & 17.7002 ([PERSON]) & 45.8205 (X) & 0.2803 (XY) & 0.1965 (YZ) \\  & 29.5878 ([PERSON]) & 18.6745 ([PERSON]) & 45.6388 (Y) & 0.1942 (XZ) & 0.2185 (ZX) \\  & 29.5823 & 18.1874 & & 51.5474 (Z) & 0.2792 (YX) & 0.2220 (ZY) \\  & 29.5140 ([PERSON]) & 17.6058 ([PERSON]) & 44.8274 (X) & 0.2807 (XY) & 0.1967 (YZ) \\  & 29.5247 ([PERSON]) & 18.6088 ([PERSON]) & 45.7942 (Y) & 0.1971 (XZ) & 0.2238 (ZX) \\  & 29.5194 ([PERSON]) & 18.1073 ([PERSON]) & 50.9026 (Z) & 0.2868 (YX) & 0.2186 (ZY) \\ \hline \multirow{3}{*}{AEOR–Sand} & 29.4350 ([PERSON]) & 17.7204 ([PERSON]) & 45.1663 (X) & 0.2830 (XY) & 0.1953 (YZ) \\  & 29.4597 ([PERSON]) & 18.7226 ([PERSON]) & 44.8343 (Y) & 0.1920 (XZ) & 0.2206 (ZX) \\ \cline{1-1}  & 29.4473 & 18.2215 & & 51.8890 (Z) & 0.2809 (YX) & 0.2260 (ZY) \\ \cline{1-1}  & (Hill) & 11.8890 (Z) & 0.2809 (YX) & 0.2260 (ZY) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The computed mechanical properties of the three interface models. gyration of DGEBA, DGEDDS, and AEOR in their lowest energy conformations is shown in Figure 8. The Rg of all three polymer molecules increased compared to their initial states. For DGEBA, the Rg increased rapidly at the beginning and then stabilized, consistent with observations from its simulation trajectories. The DGEBA molecule was more compact and rigid than AEOR due to the presence of the bisphenol-A group. This rigidity was reflected in the smaller Rg value, averaging around 0.8-0.9 nm. The relatively stable Rg value in Figure 8a indicated that the molecule experiences less conformational change over the simulation time. The DGEDDS molecule had a combination of rigid and flexible segments. The presence of the sulfur atoms within the molecule led to a greater conformational flexibility compared to that of DGEBA. The average Rg was between 0.8 and 1 nm. Figure 8b shows a more dynamic fluctuation of the Rg value for DGEDDS, suggesting a higher degree of conformational change compared to DGEBA. The AEOR molecule had a relatively linear structure with long alkyl chains. This linearity contributed to a larger Rg value compared to the other two epoxy resins. Figure 8c shows a relatively constant value of around 1.1-1.2 nm. The high Rg of AEOR suggests that its structure was less compact, allowing for more flexibility and movement within the molecule. The analysis of Rg values revealed distinct structural characteristics and flexibilities among the three epoxy resins (AEOR, DGEBA, and DGEDDS). AEOR, with its largest Rg, exhibited a more extended and flexible molecular conformation. In contrast, DGEBA, with a smaller and stable Rg, demonstrated a more compact and rigid structure. DGEDDS displayed an intermediate Rg value with significant fluctuations, indicating a mixed structure with both flexible and rigid segments. This dynamic nature of DGEDDS was evident in the  
Figure 8: The radius of gyration of the three epoxy resins on the sand surface: **(a)** the radius of gyration of DGEBA–Sand; **(b)** the radius of gyration of DGEDDS–Sand; **(c)** the radius of gyration of AEOR–Sand. step-like Rg pattern observed within the first 10 ns of the simulation, where the molecule initially adsorbed to the surface with one end, then progressively stretched out and stabilized with the attachment of the other end. In contrast, the rigid structure of AEOR resulted in a stable Rg. The curve of DGEDDS exhibited a step-like pattern, with the Rg increasing twice within the first 10 ns of the simulation.