## 3 Results
### London Dispersive Surface Energy of the System S-DVB-L285 with Different HMU Percentages  
The Hamieh thermal model [40; 41] gave the variations in the surface area \(a(T)\) of organic molecules. Equation (10) was used to draw the variations of \(RTInV_{n}(T)\) of n-alkanes adsorbed on S-DVB-L285 for different HMU percentages, as a function of \(2\mathcal{N}a(T)\Big{(}\gamma_{l}^{d}\Big{)}^{1/2}\) (the expressions of \(\gamma_{l}^{d}(T)\) of n-alkanes were taken from the [PERSON] works [40; 41]). The values of \(\gamma_{s}^{d}(T)\) of the various porous copolymers for different temperatures were obtained from the slope of \(RTInV_{n}(T)\) of n-alkane-straight lines. Figure 2 gives the variations of \(\gamma_{s}^{d}(T)\) of different copolymer surfaces as a function of the temperature (Figure 2a) and the HMU percentage (Figure 2b). An excellent linearity in \(\gamma_{s}^{d}(T)\) was shown with a decrease in \(\gamma_{s}^{d}(T)\) as the temperature increased (Figure 2a). Figure 1: Effect of the HMU percentage modifying the styrene–divinylbenzene copolymer, on the values of \(RTInV_{n}(T)\) of different adsorbed organic solvents at various temperatures: porous copolymer S-DVB-L285 (**a**), 1% HMU (**b**), 3.5% HMU (**c**), and 10% HMU (**d**). However, a slight increase in the London dispersive surface energy was observed for 1% HMU, followed by an important decrease in \(\gamma_{s}^{d}(T)\) as the modifier percentage increased for all temperatures (Figure 2b). To better understand the thermodynamic behavior differences in the modified copolymers, Table 1 summarizes the different values for \(\gamma_{s}^{d}(T)\) of S-DVB-L-285 modified by various HMU percentages, with other surface thermodynamic parameters of adsorption. Table 1 shows that the different values of \(-\)\(\epsilon_{s}^{d}\), \(\gamma_{s}^{d}(T=0\) K), and \(\gamma_{s}^{d}(T=298.15\) K) increased when the HMU percentage increased. This also showed an important effect of the surface groups of the copolymer on the London dispersive surface parameters. However, a decrease was observed in the values of \(T_{Max}\) as the modifier percentage increased, certainly due to the decrease in \(\gamma_{s}^{d}(T)\) for higher temperatures. Figure 2: Variations in the London dispersive surface energy of materials as a function of the temperature (**a**) and the HMU percentage (**b**). The above results obtained using the Hamieh thermal model are very different from those obtained by applying the classical Dorris-Gray method [61]. Indeed, [PERSON] and [PERSON] determined the values \(\gamma_{s}^{d}\) of a solid by defining the increment \(\Delta G_{-CH2-}^{0}\) (Relation (14)):  
\[\Delta G_{-CH2-}^{0}=\Delta G^{0}\Big{(}C_{n+1}H_{2(n+2)}\Big{)}-\Delta G^{0} \Big{(}C_{n}H_{2(n+1)}\Big{)} \tag{14}\]  
where \(C_{n}H_{2(n+1)}\) and \(C_{n}H_{2(n+1)}\) represents the formulas of two consecutive n-alkanes. \(\gamma_{s}^{d}(T)\) was then determined by Equation (15):  
\[\gamma_{s}^{d}=\frac{\left[RTln\left[\frac{V_{n}\big{(}C_{n+1}H_{2(n+2)}\big{)} }{V_{n}\big{(}C_{n}H_{2(n+1)}\big{)}}\right]\right]^{2}}{4\mathcal{N}^{2}a_{- CH2-}^{2}\mathcal{T}_{-CH2-}^{2}} \tag{15}\]  
[PERSON] and [PERSON] [61] supposed the surface area of the methylene group \(a_{-CH2-}\) equal to 6 A\({}^{2}\) and the surface energy of \(-CH2-\) given by Equation (16)  
\[\gamma_{-CH2-}\Big{(}\mathrm{in\;mJ/m^{2}}\Big{)}=52.603-0.058\;T(in\;K) \tag{16}\]  
Applying the Dorris-Gray method, it was possible to give the results in Table 2.  
The comparison between Tables 1 and 2 clearly shows the superiority of the Hamieh thermal model over the Dorris-Gray method. Indeed, the Dorris-Gray method was based on the hypothesis supposing the surface area of the methylene group did not depend on the temperature, while [PERSON] recently proved that this surface area strongly depends on the temperature.