London Dispersive and Polar Surface Properties of Styrene–Divinylbenzene Copolymer Modified by 5-Hydroxy-6-Methyluracil Using Inverse Gas Chromatography

Abstract

The London dispersive and polar surface properties of solid materials are very important in many chemical processes, such as adsorption, coatings, catalysis, colloids, and mechanical engineering. One of the materials, a styrene–divinylbenzene copolymer modified with 5-hydroxy-6-methyluracil at different percentages, has not been deeply characterized in the literature, and it isparticularly crucial to determine its London dispersive and polar properties. Recent research in the inverse gas chromatography (IGC) technique allowed a full determination of the surface properties of a styrene–divinylbenzene copolymer modified with 5-hydroxy-6-methyluracil by using well-known polar and non-polar organic solvents and varying the temperature. Applying the IGC technique at infinite dilution resulted in the retention volume of adsorbed molecules on styrene–divinylbenzene copolymer modified with 5-hydroxy-6-methyluracil at different percentages, using the Hamieh thermal model and our recent results on the separation of the two polar and dispersive contributions to the free energy of interaction. The surface properties of these materials, such as the surface free energy of adsorption, the polar acid and base surface energy, and the Lewis acid–base parameters, were obtained as a function of temperature and for different percentages of 5-hydroxy-6-methyluracil. The obtained results proved that the polar free energy of adsorption on styrene–divinylbenzene copolymer increased when the percentage of 5-hydroxy-6-methyluracil (HMU) increased. However, a decrease in the London dispersive surface energy of the copolymer was observed for higher percentages of 5-hydroxy-6-methyluracil. A Lewis amphoteric character was shown for the copolymer with the highest acidity, while the basicity linearly increased when the percentage of HMU increased.

1. Introduction

Styrene–divinylbenzene (S-DVB) copolymers are widely employed in various applications due to their chemical robustness, thermal stability, and tunable porosity. These crosslinked polymers serve as versatile platforms for ion exchange resins, adsorbents, and catalysts, particularly in fields such as water purification, chromatography, and catalysis [1,2,3]. However, the intrinsic hydrophobicity and limited functional diversity of the base S-DVB matrix often necessitate chemical modification to enhance selectivity, reactivity, and biocompatibility [4]. Incorporating biologically active or heterocyclic compounds into S-DVB matrices has proven effective in enhancing their physicochemical properties. Among such modifiers, 5-hydroxy-6-methyluracil (HMU)—a derivative of uracil—is of particular interest due to its hydrogen-bonding capability, antioxidant activity, and nucleobase-like structural features. These properties open avenues for molecular recognition, metal ion coordination, and biological interfacing [5,6,7]. The functionalization of S-DVB with HMU is expected to introduce hydrophilic groups and aromatic nitrogen heterocycles, thereby altering the surface chemistry and potentially the sorption characteristics, swelling behavior, and thermal stability of the polymer matrix. Previous work has shown that nucleobase-modified polymers exhibit enhanced metal-binding capacities and increased interaction with biomolecules [8,9], suggesting that similar enhancements may be observed upon HMU grafting.

Other researchers have been interested in studying two-dimensional network supramolecular structures [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. The use of HMU modifying the S-DVB copolymer at different percentages of the supported modifier is very important to constitute supramolecular network structures used for selective adsorption of several molecules [14,15,16].

Knowing that the surface properties of polymeric materials are of paramount importance in applications ranging from chromatography and sorption technologies to biomedical and catalytic systems [17,18,19,20,21,22,23,24,25,26,27,28,29,30], it is therefore crucial to determine these properties, such as the surface energy components, particularly the London dispersive (γ^d) and specific polar (γ^s) contributions, that govern a material’s interactions with gases, liquids, and biological species [30,31,32,33,34,35,36]. Precise characterization of these components is essential for understanding interfacial phenomena, such as adhesion, wettability, sorption behavior, and chemical reactivity [37,38,39,40,41].

Inverse gas chromatography (IGC) has emerged as a powerful and sensitive technique for assessing the thermodynamic surface properties of solids, especially polymers, in their native dry state. Unlike traditional techniques such as contact angle measurements, IGC enables the evaluation of surface energy under well-controlled and reproducible gas–solid interaction conditions, even for porous, irregular, or finely powdered materials [42,43,44,45,46,47,48,49,50,51].

In this study, we investigated the London dispersive and specific polar components of the surface energy of a styrene–divinylbenzene (S-DVB) copolymer modified by 5-hydroxy-6-methyluracil at different percentages. Using inverse gas chromatography at infinite dilution (IGC-ID), by applying our new methodology [40,41,52,53,54,55], we determined the surface free energy parameters, assessed the acid–base character of the surfaces, and examined how HMU grafting affects the thermodynamic affinity of the polymer toward various probe molecules. This analysis provided critical insight into the physicochemical transformation of S-DVB surfaces following functionalization and their potential suitability for selective adsorption, separation, or biomedical applications.

2. Materials and Methods

2.1. Adsorbent and Materials

The S-DVB copolymer, the different n-alkanes, and the polar solvents used in this study were the same as those used in a previous work [56]. The chosen surface modifier was 5-hydroxy-6-methyluracil (from Vecton, St. Petersburg, Russia, 97%), with varying percentages of mass from 1% to 10%, impregnated into the adsorbent surface by evaporation of aqueous solutions at 70 °C.

2.2. Inverse Gas Chromatography

The net retention time of adsorbed organic molecules on S-DVB copolymer modified by HMU was determined using the IGC technique at infinite dilution. The same chromatograph and experimental procedure developed in previous research [56] were applied to this study, using the same chromatographic conditions.

2.3. Thermodynamic Methods

2.3.1. Dispersive and Polar Energies and Lewis Acid–Base Parameters

The determination of the free energy of adsorption $∆G_a^0$ of the solvents on S-DVB/HMU was carried out from the retention volume measurements $Vn$ using Equation (1):

$$∆G_a^0\left(T\right)=-RTlnVn+C\left(T\right)$$

(1)

where $T$ is the absolute temperature, $R$ is the perfect gas constant, and $C\left(T\right)$ is a characteristic of interaction.

The expression of $∆G_a^0\left(T\right)$ of organic solvents is composed of the summation of the dispersive component $∆G_a^d\left(T\right)$ and the polar component $∆G_a^{sp}\left(T\right)$ of adsorption by varying the temperature:

$$∆G_a^0\left(T\right)=∆G_a^d\left(T\right)+∆G_a^p\left(T\right)$$

(2)

Hamieh [37,38] gave a new expression of $∆G_a^d\left(T\right)$:

$$∆G_a^d\left(T\right)=-{\displaystyle \frac{{\alpha }_{0S} }{ H^6}}\left[{\displaystyle \frac{3\mathcal{N}}{{2\left(4\pi {\epsilon }_0\right)}^2}}\left({\displaystyle \frac{{\epsilon }_S {\epsilon }_X}{\left({\epsilon }_S+{\epsilon }_X\right)}}{\alpha }_{0X}\right)\right]$$

(3)

where ${\epsilon }_0$ is the dielectric constant of vacuum, ${\alpha }_0$represents the deformation polarizability relative to the solid (S) and the solvent (X), $\epsilon$ is the ionization energy, and $H$ is the separation distance between the solid substrate and the adsorbed molecule.

The combination of Equations (1) and (3) allowed writing Equation (4):

$$RTlnVn={\displaystyle \frac{{\alpha }_{0S} }{ H^6}}\left[{\displaystyle \frac{3\mathcal{N}}{{2\left(4\pi {\epsilon }_0\right)}^2}}\left({\displaystyle \frac{{\epsilon }_S {\epsilon }_X}{\left({\epsilon }_S+{\epsilon }_X\right)}}{\alpha }_{0X}\right)\right]-∆G_a^p\left(T\right)+C\left(T\right)$$

(4)

The interaction parameter ${\mathcal{P}}_{SX}$ used as a chromatographic index was given by Equation (5):

$${\mathcal{P}}_{SX}={\displaystyle \frac{{\epsilon }_S {\epsilon }_X}{\left({\epsilon }_S+{\epsilon }_X\right)}}{\alpha }_{0X}$$

(5)

For n-alkanes, $RTlnVn$ can be written as:

$$\left\{\begin{array}{c}RTlnVn\left(n-alkane\right)=A(T)\left[{\displaystyle \frac{3\mathcal{N}}{{2\left(4\pi {\epsilon }_0\right)}^2}}{\mathcal{P}}_{SX}\left(nn-alkane\right)\right]+C(T)\\ A(T)={\displaystyle \frac{{\alpha }_{0S} }{ {\left[H\left(T\right)\right]}^6}} \end{array}\right.$$

(6)

where $A\left(T\right)$ is a constant depending on ${\alpha }_{0S}$ and $H\left(T\right)$.

The values of $∆G_a^p\left(polar\right)$ of adsorption were obtained from Equation (7):

$$∆G_a^p\left(T, polar\right)=RTlnVn \left(T, polar\right)-RTlnVn \left(T, X_{n.p.}\right)$$

(7)

where $X_{n.p.}$ is the geometric point obtained from the projection of the polar point intersecting the straight line of n-alkanes.

While the values of $\left(-∆H_a^p\right)$ and $\left(-∆S_a^p\right)$ of adsorbed polar solvents were deduced from Relation (8) when the linearity of $∆G_a^p\left(T\right)$ was confirmed:

$$∆G_a^p\left(T\right)=∆H_a^p-T∆S_a^p$$

(8)

The following Equation (9) allowed obtaining the Lewis enthalpic (K_A, K_D) and entropic (${\omega }_A$, ${\omega }_D$) Lewis acid–base constants:

$$\left\{\begin{array}{c}\left(-∆H^p\right)= K_A\times D{N}^{\prime }+K_D\times A{N}^{\prime } \\ \left(-∆S_a^p\right)={\omega }_A\times {DN}^{\prime }+{\omega }_D\times {AN}^{\prime }\end{array}\right.$$

(9)

where $D{N}^{\prime }$ and $A{N}^{\prime }$ are, respectively, the corrected electron donor and acceptor numbers of the polar molecule [56,57].

2.3.2. London Dispersive Surface Energy and Lewis Acid–Base Surface Energies

Denoting, ${\gamma }_l^d\left(T\right)$ and ${\gamma }_s^d\left(T\right)$ the respective dispersive components of the surface energy of the organic molecule and the solid surface, and applying the Fowkes relation [58,59] and the Hamieh thermal model [40,41,52,53,54,55] to determine the value ${\gamma }_s^d\left(T\right)$ of the modified copolymer using the following relation:

$$RTln{V}_n=2\mathcal{N}a\left(T\right){\left[{\gamma }_l^d\left(T\right){\gamma }_s^d\left(T\right)\right]}^{1/2}+\beta \left(T\right)$$

(10)

where $a\left(T\right)$ is the surface area of solvents given by Hamieh [40] versus the temperature, and $\beta \left(T\right)$ is a parameter of the adsorption function of temperature.

The total surface energy ${\gamma }_s^{tot.}$of a solid material is equal to the summation of the London dispersive component ${\gamma }_s^d$ and the polar component ${\gamma }_s^p$ of the surface energy. Equation (11) can be then written as follows:

$${\gamma }_s^{tot.}={\gamma }_s^d+{\gamma }_s^p$$

(11)

The values of ${\gamma }_s^p$ and the Lewis acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of solid copolymers were obtained using the method of Van Oss et al. [60] and applying Equation (12):

$$∆G_a^p\left(T\right)=2\mathcal{N}a\left(T\right)\left(\sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right)$$

(12)

This allowed obtaining the polar (or acid–base) surface energy ${\gamma }_s^{AB}$ of the modified copolymers using Equation (13):

$${\gamma }_s^{AB}={\gamma }_s^{p }=2\sqrt{{\gamma }_s^{+}{\gamma }_s^{-}}$$

(13)

The determination of the polar (or acid–base) surface energy and the London dispersive surface energy of copolymers allowed obtaining the total surface energy ${\gamma }_s^{tot.}$of all solid surfaces.

3. Results

3.1. Variations of the Free Energy of Adsorption

The evolution of the free energy or $RTln{V}_n\left(T\right)$ of different adsorbed organic solvents at various temperatures for different HMU percentages modifying the styrene–divinylbenzene copolymer was represented in Figure 1.

The curves given in Figure 1 show an important effect of organic solvents as a function of temperature and a significant effect of the HMU percentage on the porous copolymer S-DVB-L285. Figure 1 also shows a linear decrease of $RTln{V}_n\left(T\right)$ when the temperature increases. The highest values of $RTln{V}_n\left(T\right)$ were obtained for 10% HMU. Therefore, the increase in the modifier percentage led to an increase in the free energy of adsorption.

To better describe the dispersive and polar interactions, it is important to determine both the London dispersive surface energy and the surface acid-base interactions, as variations in the free energy of interaction versus the temperature alone cannot give the required information. This will be developed in the next sections.

3.2. 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 $a\left(T\right)$ of organic molecules. Equation (10) was used to draw the variations of $RTln{V}_n\left(T\right)$ of n-alkanes adsorbed on S-DVB-L285 for different HMU percentages, as a function of $2\mathcal{N}a\left(T\right){\left({\gamma }_l^d\right)}^{1/2}$ (the expressions of ${\gamma }_l^d\left(T\right)$ of n-alkanes were taken from the Hamieh works [40,41]). The values of ${\gamma }_s^d\left(T\right)$ of the various porous copolymers for different temperatures were obtained from the slope of $RTln{V}_n\left(T\right)$ of n-alkane-straight lines.

Figure 2 gives the variations of ${\gamma }_s^d\left(T\right)$ of different copolymer surfaces as a function of the temperature (Figure 2a) and the HMU percentage (Figure 2b). An excellent linearity in ${\gamma }_s^d\left(T\right)$ was shown with a decrease in ${\gamma }_s^d\left(T\right)$ as the temperature increased (Figure 2a). However, a slight increase in the London dispersive surface energy was observed for 1% HMU, followed by an important decrease in ${\gamma }_s^d\left(T\right)$ as the modifier percentage increased for all temperatures (Figure 2b).

To better understand the thermodynamic behavior differences in the modified copolymers,

Table 1. Equations of ${\gamma }_s^d\left(T\right)$ of S-DVB-L-285 varying the HMU percentage, the linear regression coefficients R², the London dispersive surface entropy ${\epsilon }_s^d$, the values of London dispersive surface energy extrapolated at 0 K and 298.15 K, and the temperature maximum $T_{Max}$, using the Hamieh thermal model.

Copolymer	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}\left(\mathit{T}\right)$ (mJ/m2)	R2	${\mathit{\epsilon }}_{\mathit{s}}^{\mathit{d}}={\mathit{d}\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}/\mathit{d}\mathit{T}$ (mJ m−2 K−1)	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}(\mathit{T}=0 \mathbf{K})$ (mJ/m2)	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}(\mathit{T}=298.15 \mathbf{K})$ (mJ/m2)	${\mathit{T}}_{\mathit{M}\mathit{a}\mathit{x}}$ (K)
S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = −0.835 T + 482.43	0.9980	−0.835	482.43	233.47	577.8
1% HMU/S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = −0.874 T + 444.68	0.9837	−0.874	444.68	184.16	508.9
3.5% HMU/S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = −1.096 T + 544.23	0.9886	−1.096	544.23	217.52	496.7
10% HMU/S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = −1.198 T + 582.13	0.9973	−1.198	582.13	224.95	485.9

summarizes the different values for ${\gamma }_s^d\left(T\right)$ 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 −${\epsilon }_s^d$, ${\gamma }_s^d(T=0 \mathrm{K})$, and ${\gamma }_s^d(T=298.15 \mathrm{K})$ 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 ${\gamma }_s^d\left(T\right)$ for higher temperatures.

The above results obtained using the Hamieh thermal model are very different from those obtained by applying the classical Dorris-Gray method [61]. Indeed, Dorris and Gray determined the values ${\gamma }_s^d$of a solid by defining the increment $∆G_{-CH2-}^0$ (Relation (14)):

$$∆G_{-CH2-}^0=∆G^0\left(C_{n+1}{H}_{2(n+2)}\right)-∆G^0\left(C_n{H}_{2(n+1)}\right)$$

(14)

where $C_n{H}_{2(n+1)}$ and $C_n{H}_{2(n+1)}$ represents the formulas of two consecutive n-alkanes. ${\gamma }_s^d\left(T\right)$ was then determined by Equation (15):

$${\gamma }_s^d={\displaystyle \frac{{\left[RTln\left[\frac{V_n\left(C_{n+1}{H}_{2(n+2)}\right)}{V_n\left(C_n{H}_{2(n+1)}\right)}\right]\right]}^2}{4{\mathcal{N}}^2{a}_{-CH2-}^2{\gamma }_{-CH2-}}}$$

(15)

Dorris and Gray [61] supposed the surface area of the methylene group $a_{-CH2-}$ equal to 6 Ų and the surface energy of $-CH2-$ given by Equation (16)

$${\gamma }_{-CH2-}\left(\mathrm{i}\mathrm{n} \mathrm{m}\mathrm{J}/{\mathrm{m}}^2\right)=52.603-0.058 T\left(in K\right)$$

(16)

Applying the Dorris-Gray method, it was possible to give the results in

Table 2. Linear expressions of ${\gamma }_s^d\left(T\right)$ of S-DVB-L-285 modified by different HMU percentages, regression coefficients, London dispersive surface entropy ${\epsilon }_s^d$, extrapolated values of London dispersive surface energy at 0 K and 298.15 K, and the temperature maximum $T_{Max}$, using the Dorris-Gray method.

Copolymer	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}\left(\mathit{T}\right)$ (mJ/m2)	R2	${\mathit{\epsilon }}_{\mathit{s}}^{\mathit{d}}={\mathit{d}\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}/\mathit{d}\mathit{T}$ (mJ m−2 K−1)	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}(\mathit{T}=0 \mathbf{K})$ (mJ/m2)	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}(\mathit{T}=298.15 \mathbf{K})$ (mJ/m2)	${\mathit{T}}_{\mathit{M}\mathit{a}\mathit{x}}$ (K)
S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = −3.250 T + 1610.5	0.9037	−3.25	1610.5	641.51	495.54
1% HMU/S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = 1.065 T − 416.4	0.9855	1.065	−416.4	−98.87	390.99
3.5% HMU/S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = 1.091 T − 421.2	0.9493	1.091	−421.2	−95.92	386.07
10% HMU/S-DVB-L-285	${\gamma }_s^d\left(T\right)$ = 1.474 T − 600.3	0.9413	1.474	−600.3	−160.83	407.26

.

The comparison between Table 1 and Table 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 Hamieh recently proved that this surface area strongly depends on the temperature. This explained the errors obtained by the Dorris–Gray method, which showed negative values for the extrapolated London dispersive surface energy at both room temperature and 0 K. The thermal model was proven to be the most accurate method, correcting the errors in the values of ${\gamma }_s^d\left(T\right)$ committed by the Dorris–Gray method, which exceeded 100% in several cases.

3.3. Polar Free Interaction Energy of S-DVB Copolymer Modified by HMU with the Polar Probes

Applying Equations (4) to (7), it was easy to determine the values of $-∆G_a^p\left(T\right)$ of adsorbed polar molecules on the copolymer surfaces with the temperature. The obtained values were given in Table S1.

The variations of $-∆G_a^p\left(T\right)$ for polar molecules adsorbed on copolymer surfaces were plotted in Figure 3 versus temperature for various HMU percentages. Linear variations were obtained, allowing the values of polar enthalpy ($-∆H_a^p)$ and entropy ($-∆S_a^p)$ of adsorption. Table S1 and Figure 3 showed that the highest interaction was obtained with the highest HMU percentage (10%), showing that the polar free energy increased with the modifier percentage for all polar solvents. The lowest interaction was obtained with the S-DVB copolymer, meaning that the addition of HMU on the copolymer certainly increased the interaction capacity of the copolymer with the polar molecules. It can also be deduced that the lowest interaction for all materials was obtained with benzene and toluene solvents, whereas the highest adsorption was shown in Table S1 and Figure 3 for i-pentanol and i-butanol solvents, thus proving the highest effect of the hydroxyl group on the free polar interaction.

These conclusions can be obviously shown by Figure 4, which shows the variations of $-∆G_a^p$ presented as a function of the HMU percentage in the copolymer at different temperatures. The maximum of the free interaction energy is shown for all polar solvents. The effect of the modifier percentage, as shown in Figure 4, demonstrates non-linear variations in the polar free energy of adsorption, with an evident increase in the polar interaction energy as the HMU percentage increases.

The determination of the polar enthalpy and entropy of adsorption for the different copolymers was obtained using Equation (8). The obtained results allowed determining the surface polar enthalpy and the entropy of adsorption, as well as the Lewis acid–base constants of the solid materials, as shown in the next section.

3.4. Polar Enthalpy and Entropy of Adsorption, and Lewis Acid–Base Parameters of Dowex L-285 Modified by HMU

The variations of $-∆G_a^p\left(T\right)$ given in Table S1 and Figure 3, against temperature, allowed the values of ($-∆H_a^p)$ and ($-∆S_a^p)$ of the adsorbed polar solvents for the different modifier percentages, using Equation (9). The representation of the variations of $\left({\displaystyle \frac{-∆H_a^p}{{AN}^{\prime }}}\right)$ and $\left({\displaystyle \frac{-∆S_a^p}{{AN}^{\prime }}}\right)$ versus $\left({\displaystyle \frac{{DN}^{\prime }}{{AN}^{\prime }}}\right)$ of the polar solvents adsorbed on the various surfaces (Figure 5) led to the values of the Lewis acid–base parameters $K_A$, $K_D$, ${\omega }_A$, and ${\omega }_D$ relative to S-DVB-L-285 with different HMU percentages (from 1% to 10%). The obtained values are given in

Table 3. Values of the Lewis acid–base constants $K_A$, $K_D$, ${\omega }_A$, and ${\omega }_D;$ the acid–base ratios; and the linear regression coefficient R² relative to S-DVB-L-285, modified by different HMU percentages with the corresponding parameters ${S_K=K}_A+K_D$ and ${{S\prime }_K=\omega }_A+{\omega }_D$.

Material	${\mathit{K}}_{\mathit{D}}$	${\mathit{K}}_{\mathit{A}}$	${\mathit{K}}_{\mathit{D}}/{\mathit{K}}_{\mathit{A}}$	${\mathit{K}}_{\mathit{A}}+{\mathit{K}}_{\mathit{D}}$	R2	${10}^{-3}{\mathit{\omega }}_{\mathit{D}}$	${10}^{-3}{\mathit{\omega }}_{\mathit{A}}$	${\mathit{\omega }}_{\mathit{D}}$$/{\mathit{\omega }}_{\mathit{A}}$	${10}^{-3} ({\mathit{\omega }}_{\mathit{A}}+{\mathit{\omega }}_{\mathit{D}}$)	R2
S-DVB-L-285	0.283	0.786	0.36	1.069	0.886	0.43	1.41	0.30	1.83	0.871
1% HMU on S-DVB-L-285	0.459	0.696	0.66	1.155	0.9561	1.64	0.81	2.02	2.45	0.975
3.5% HMU on S-DVB-L-285	1.265	0.75	1.69	2.015	0.994	2.07	0.82	2.52	2.89	0.9806
10% HMU on S-DVB-L-285	2.425	0.451	5.38	2.876	0.9397	2.25	0.46	4.89	2.71	0.9277

. The results proved the amphoteric character of the various copolymers. A stronger Lewis acidity than the Lewis basicity was observed in the case of the S-DVB copolymer, for a modifier percentage equal to 1%. However, this tendency was inverted for an HMU percentage higher than 3% where the Lewis basicity was shown to be two times higher than their Lewis acidity.

Table 3 clearly shows that the basicity of the copolymer linearly increased with the HMU percentage from $K_D=0.28$ to $K_D=0.24$ (about 10 times higher for 10% HMU on the copolymer). However, the acidity of S-DVB-copolymer gradually decreased from $K_A=0.79$ to $K_A=0.45,$ showing a decrease of about 60% for 10% HMU on S-DVB copolymer. The same conclusions were confirmed for the entropic Lewis acid–base parameters ${\omega }_A$ and ${\omega }_D$. Table 3 showed that total Lewis acid–base parameters $S_K$ and ${S\prime }_K$ highlighted an important increase when the HMU percentage increased, also confirming the previous conclusion relative to the stronger polar interaction for higher HMU percentage.

From the previous results, it was possible to give in

Table 4. Equations of Lewis acid—base parameters as a function of %HMU with the corresponding linear regression coefficients.

Parameter	Equation	R2
Basic constant $K_D$	$K_D$ = 0.22%HMU + 0.33	0.9839
Acid constant $K_A$	$K_A$ = −0.031%HMU + 0.784	0.8638
Ratio $K_D/K_A$	$K_D/K_A$ = 0.51%HMU + 0.17	0.9926
Ratio ${\omega }_D$/${\omega }_A$	${\omega }_D$/${\omega }_A$ = 0.40%HMU + 0.97	0.9165
Parameter $S_K$	$S_K$ = 0.18%HMU + 1.11	0.9561

the different equations of Lewis acid–base constants for the different HMU percentages with the corresponding values of R².

The excellent linear regression coefficients given in Table 4 and shown in Figure 6 highlighted the large effect of the HMU percentage on the Lewis acid–base character of the S-DVB copolymer.

3.5. Polar Acid–Base Surface Energies of S-DVB Copolymer Modified by HMU

Using Equations (11) to (13), the polar acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of S-DVB copolymer modified by different HMU percentages were determined with the help of the values of the free polar energy $-∆G_a^{sp}\left(T\right)$ of dichloromethane and ethyl acetate polar solvents given in

Table 5. Values of $-∆G_a^p\left(T\right) (\mathrm{i}\mathrm{n} \mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l})$ for dichloromethane and ethyl acetate adsorbed on Dowex L-285 modified with different HMU percentages at different temperatures.

Dichloromethane
T(K)	Dowex L-285	3.5% HMU/Dowex L-285	1% HMU/Dowex L-285	10% HMU/Dowex L-285
453.15	15.274	15.609	24.349	9.737
458.15	15.239	15.559	24.294	9.352
463.15	15.204	15.509	24.239	8.967
468.15	15.169	15.459	24.184	8.582
Ethyl Acetate
T(K)	Dowex L-285	3.5% HMU/Dowex L-285	1% HMU/Dowex L-285	10% HMU/Dowex L-285
453.15	10.106	8.503	9.667	10.567
458.15	9.593	8.378	9.507	10.314
463.15	9.079	8.253	9.347	10.06
468.15	8.566	8.128	9.187	9.807

.

The obtained results were plotted in Figure 7.

The values of ${\gamma }_s^p$ were obtained using Equation (11), while the total surface energy ${\gamma }_s^{tot.}$ was determined from Equation (13) as a function of temperature. The surface polar parameters such as ${\gamma }_s^{+}\left(T\right)$, ${\gamma }_s^{-}\left(T\right)$, ${\gamma }_s^{AB}\left(T\right)$, ${\gamma }_s^d \left(T\right)$, and ${\gamma }_s^{tot.}\left(T\right)$ of the modified copolymer were given in Table S2. The variations of the different surface polar parameters were plotted in Figure 7 against the temperature. Linear variations of the different polar surface energies versus temperature are shown in Figure 7. The results show that the highest polar surface energy values were obtained for the highest HMU percentage, again confirming the important role of the modifier in increasing the polarity of the copolymer and consequently its use in many industrial applications such as catalysis and selective adsorption of several organic molecules.

The results given in Table S2 and Figure 7 allowed the drawing of the polar surface energy of the adsorbed polar probes against temperature in Figure 8, using the Fowkes relation and the Hamieh thermal model. It seems that the adsorbed ethanol and i-propanol polar solvents exhibit the highest values of polar surface energy. In contrast, the lowest values were obtained for the adsorption of toluene and benzene. Identical results were obtained when the S-DVB copolymer was modified by melamine in a previous study [56].

3.6. Determination of the Average Separation Distance H

Our new methodology was applied to determine the separation distance $H$ between the organic molecules and the modified copolymer as a function of temperature. The results were represented in Figure 9. It was shown that a certain effect of the HMU percentage on the separation distance between solvents and copolymer. A net difference in the values of H between the S-DVB copolymer and the corresponding modified copolymer.

4. Conclusions

This study constituted a new advance on the determination of the London dispersive surface energy, the polar surface energy and Lewis acid–base properties of styrene–divinylbenzene copolymer (S-DVB) modified by HMU at different percentages from 1% to 10%, using the IGC technique at infinite dilution and applying our new methodology allowing a net separation between the dispersive and polar contributions of the interaction between the polar solvents and the copolymer. The determination of ${\gamma }_s^d\left(T\right)$ for different solid surfaces showed a linear decrease in ${\gamma }_s^d\left(T\right)$ as the temperature increased and proved that the modification of the copolymer by HMU led to a net decrease in the values of ${\gamma }_s^d$. The application of the Hamieh thermal model using the London dispersion interaction allowed an accurate determination of the Lewis acid–base parameters of the modified copolymer. An amphoteric character of the different copolymers was highlighted with a more acidic character for the copolymer and for 1%HMU, and a stronger basicity when the percentage of the modifier is higher than 3%. The highest basicity was observed for 10% HMU. An important effect of the modifier percentage on the dispersive and polar surface energy of S-DVB copolymer was highlighted, with the highest values of the different surface parameters for the copolymer modified by 10% HMU.