Surface Thermodynamic Properties of Styrene–Divinylbenzene Copolymer Modified by Supramolecular Structure of Melamine Using Inverse Gas Chromatography

Abstract

The surface thermodynamic properties of polymers and copolymers modified by supramolecular structures are used in several industrial processes, such as selective adsorption, paints, coatings, colloids, and adhesion applications. Background: Inverse gas chromatography at infinite dilution was proved to be the best technique to determine the surface properties of solid surfaces by studying the adsorption of some model polar and non-polar organic molecules adsorbed on solid surfaces at different temperatures. Methods: The retention volume of adsorbed solvents is a valuable parameter that was used to obtain the London dispersive and polar free energies and the London dispersive surface energy of styrene–divinylbenzene copolymer modified by supramolecular structure of melamine using both the Hamieh thermal model and our new methodology consisting of the separation of the two polar molecules and the dispersive free energy of their interaction. This led to the determination of the polar acid and base surface energy, and the Lewis acid–base constants of the various solid materials. Results: Following our new methodology, all surface energetic properties of styrene–divinylbenzene copolymer modified by melamine at different percentages were determined as a function of temperature. Conclusions: It was observed that the styrene–divinylbenzene copolymer exhibited the highest London dispersive surface energy, which decreased when the melamine percentage increased. All materials presented higher Lewis basicity and this Lewis basicity increased with the percentage of melamine.

1. Introduction

Due to their important applications in the domain of molecular recognition and surface chemistry, in the last thirty years, several papers have been devoted to two-dimensional network supramolecular structures [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. When supported on solid surfaces, these heterocyclic compounds, such as melamine, cyanuric acid, and uracil and its derivatives, are likely to constitute supramolecular network structures capable of selectively adsorbing various molecules, including enantiomers [10].

In the case of formed supramolecular structures on the surface of inert supports and porous polymer sorbents, it has been shown that the properties of the resulting adsorbents depend on the polarity of the surface and porosity of the initial adsorbents [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. The effect of the amount of the supported modifier on the properties of the obtained adsorbents was studied by Sukhareva et al. [3] and Guskov et al. [10,11,12,13,14,15,16] using the inverse gas chromatography technique. They studied the specific interactions between the various polymer adsorbents and some model organic solvents, as well as the London dispersive energy of the various solid surfaces using the Dorris–Gray method [17]. It was proved in other works that the classic chromatographic methods, such as that proposed by Schultz et al. [18], and the Dorris-Gray method, cannot be used for an accurate evaluation of the London dispersive surface energy of solid materials, because these methods were based on the hypothesis of the constant surface area of organic solvents. In several studies [19,20,21,22,23], an important effect of temperature on the surface area of organic molecules was highlighted and more accurate values of the London dispersive and polar components of the surface energy, and the Lewis acid–base properties of various solid substrates were obtained using the Hamieh thermal model. Furthermore, the polar and dispersive interactions between the organic solvents and several solid surfaces were determined by applying the new method [24,25] using the London interaction equation [26].

In this paper, we were interested in the determination of the surface thermodynamic properties of some important porous polymers such as styrene–divinylbenzene copolymer modified by the supramolecular structure of melamine. Indeed, the highly porous structure, chemical stability, easier functionalization, and large surface area of this copolymer make it an excellent candidate for several applications such as biotechnology, environmental science, industrial chemistry, adsorption, and catalysis.

Inverse gas chromatography (IGC) at infinite dilution [27,28,29,30,31,32,33,34,35,36,37,38,39,40] was used in applying our new methodology, which consisted of the correction of the London dispersive surface energy and the correct determination of polar free energy of adsorption of some polar organic probes, as well as the Lewis acid–base parameters of the modified porous polymer.

2. Materials and Methods

2.1. Adsorbent and Materials

A porous polymer such as styrene–divinylbenzene copolymer (Dowex L-285, from Dow Chemical, Midland, MI, USA), was used as the initial adsorbent for modification. Its specific surface area was 800 m²/g, with particle sizes of 250–500 μm. The chosen surface modifier was melamine (from Vecton, St. Petersburg, Russia, 97%, CAS108-78-1), with percentage mass from 1% to 4%, impregnated into the adsorbent surface by evaporation of aqueous solutions at 60 °C. The amount of melamine necessary for coating the adsorbent surface with a monolayer was determined from the specific surface area of the sorbent and molecular dimensions of melamine. The surface area of the melamine molecule was previously determined and shown to be equal to 139.8 Ų [3]. This allowed us to determine the various melamine percentages needed for the formation of the planar layer of the supramolecular structure of melamine. The temperature choice was necessary to uniformly impregnate the modifier on the surface. Then, the resulting sample was washed with high-purity water to pH 7. Chemically pure organic solvents such as n-hexane, n-heptane, n-octane, benzene, cyclohexane, toluene, ethanol, n-propanol, n-butanol, i-propanol, i-butanol, n-pentanol, i-pentanol, dichloromethane, and ethyl acetate (Chimreactivsnab, Russia) were used as the probes.

2.2. Inverse Gas Chromatography

The experimental determination of the retention time of organic molecules adsorbed on Dowex L-285 was carried out using inverse gas chromatography at infinite dilution with the help of a Chromos GC-1000 chromatograph (from Chromos, Russia) equipped with a flame ionization detector (FID). The solid particles were packed into stainless steel columns of 30 cm length and 3 mm internal diameter. The temperature of the column was 200 °C and the temperatures of the injector and detector were 280°C. The flow rate of the nitrogen carrier gas was 30 mL/min. The mass of the sorbent packed into the column was equal to 1 g. All chromatographic columns were conditioned overnight at 200 °C to remove any residual impurities. The probes in the vapor phase were injected with microsyringes at different temperatures to realize the infinite dilution and to satisfy Henry’s law. The experiments were repeated three times and the error in the value of the retention volume did not exceed 2%.

2.3. Thermodynamic Methods

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

The chromatographic measurements led to the determination of the net retention volume $Vn$ of the different probes adsorbed on the solid surfaces. This allowed determination of the values of the free energy of adsorption $∆G_a^0$ of the adsorbed organic molecules as a function of temperature using the following equation:

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

(1)

where $T$ is the absolute temperature, $R$ the perfect constant gas, and $C\left(T\right)$ a constant depending on the temperature and the solvent–sorbent interaction.

In the case of non-polar probes such as n-alkanes, $∆G_a^0\left(T\right)$ is equivalent to the London dispersive energy $∆G_a^d\left(T\right)$ of adsorption for all temperatures:

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

(2)

When polar molecules are adsorbed on solid materials, $∆G_a^0\left(T\right)$ is written as follows:

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

(3)

where $∆G_a^{sp}\left(T\right)$ is the free polar energy of the polar solvents.

To separate the two dispersive and polar contributions of the free energy of adsorption, we applied the new methodology recently published [24,25] that used the London dispersion interaction energy Equation (4):

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

(4)

where $\mathcal{N}$ is the Avogadro number, ${\epsilon }_0$ the dielectric constant of vacuum, ${\alpha }_{0S}$ and ${\alpha }_{0X}$ are the respective deformation polarizabilities of the solid material denoted by S and the organic molecule denoted by X, separated by a distance $H$, and ${\epsilon }_S$ and ${\epsilon }_X$ are their corresponding ionization energies.

Previous equations led to Equation (5):

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

(5)

The new chosen chromatographic interaction parameter ${\mathcal{P}}_{SX}$ was given by

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

(6)

For non-polar molecules such as n-alkanes, the representation of $RTlnVn$ of these molecules is given by

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

(7)

where $A$ is the slope of the non-polar straight line.

Using the distance between the straight line of n-alkanes and the representative point of a polar molecule, it was possible to determine the free polar energy $∆G_a^p\left(polar\right)$ of the polar molecule, at any temperature:

$$∆G_a^p\left(T, polar\right)=RTlnVn \left(T, polar\right)-A\left[{\displaystyle \frac{3\mathcal{N}}{{2\left(4\pi {\epsilon }_0\right)}^2}}{\mathcal{P}}_{SX}\left(polar\right)\right]-C(T)$$

(8)

The polar enthalpy $\left(-∆H_a^p\right)$ and entropy $\left(-∆S_a^p\right)$ of polar probes adsorbed on porous polymers can be deduced from Equation (9) if the linearity of $∆G_a^p\left(T\right)$ is assured:

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

(9)

The Lewis acid–base properties of the solid substrates characterized by its enthalpic (K_A, K_D) and entropic (${\omega }_A$, ${\omega }_D$) acid–base constants are obtained:

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

(10)

where $D{N}^{\prime }$ and $A{N}^{\prime }$ are, respectively, the corrected electron donor and acceptor numbers of the polar molecule [41,42].

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

The London dispersive surface energy ${\gamma }_s^d\left(T\right)$ of the different sorbents was determined using the Fowkes relation [43] and applying the Hamieh thermal model that gave the surface area $a\left(T\right)$ of organic molecules as a function of the temperature [19,20,21,22,23]:

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

(11)

where $\beta \left(T\right)$ is a constant depending only on the temperature and the solid material.

The total surface energy of material is then given by

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

(12)

where ${\gamma }_s^p$ represents the total polar (or acid–base) contribution of the surface energy.

Using Van Oss et al.’s method [44], it was possible to determine ${\gamma }_s^p$ of the different polymers. This method consists of the determination of the Lewis acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of the solid particles. By choosing two monopolar solvents such as ethyl acetate (B) and dichloromethane (A), characterized by the following parameters:

$$\left\{\begin{array}{c}{\gamma }_A^{+}=5.2 \mathrm{mJ}/{\mathrm{m}}^2, {\gamma }_A^{-}=0 \\ {\gamma }_B^{+}=0 , {\gamma }_B^{-}=19.2 \mathrm{mJ}/{\mathrm{m}}^2\end{array}\right.$$

(13)

and using the expression of polar free energy $∆G_a^p\left(T\right)$ of the polar molecules, given by Equation (14):

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

(14)

the Lewis acid and base surface energies of the solid surfaces were deduced from Equation (15):

$$\left\{\begin{array}{c}\begin{array}{c}{\gamma }_s^{+}\left(\mathrm{T}\right) ={\displaystyle \frac{{\left[∆G_a^p\left(T\right)\left(B\right)\right]}^2}{{4\mathcal{N}}^2{\left[a_B\left(T\right)\right]}^2{\gamma }_B^{-}}} \end{array} \\ {\gamma }_s^{-}\left(\mathrm{T}\right)={\displaystyle \frac{{\left[∆G_a^p\left(T\right)\left(A\right)\right]}^2}{{4\mathcal{N}}^2{\left[a_A\left(T\right)\right]}^2{\gamma }_A^{+}}} \end{array}\right.$$

(15)

The polar (or acid–base) surface energy ${{\gamma }_s^{p }=\gamma }_s^{AB}$ and the total surface energy ${\gamma }_s^{tot.}$ of different materials were then obtained using Equation (16):

$$\left\{\begin{array}{c}{\gamma }_s^{AB}=2\sqrt{{\gamma }_s^{+}{\gamma }_s^{-}}\\ {\gamma }_s^{tot.}={{\gamma }_s^d+\gamma }_s^{AB}\end{array}\right.$$

(16)

3. Results

3.1. Variations in $RTln{V}_n\left(T\right)$ of Adsorbed Probes Against the Temperature

The experimental determination of the net retention volume $V_n$ of organic molecules adsorbed on Dowex L-285 modified by different percentages of melamine as a function of temperature $T$ led to the variations, with temperature, in $RTln{V}_n\left(T\right)$ for the various organic solvents (Table S1). Using the obtained results, Figure 1 shows the curves of $RTln{V}_n\left(T\right)$ of the different organic molecules at different temperatures, as well as the variations in $∆G_a$(-$C{H}_2$-) of n-alkanes adsorbed solid materials as a function of temperature.

• where

$$∆G_a(\text{-}C{H}_2\text{-})=RTln{\displaystyle \frac{V_n\left(C_{n+1}{H}_{2n+4}\right)}{V_n\left(C_n{H}_{2n+2}\right)}}$$

(17)

Figure 1. Effect of the percentage of melamine on the values of $RTln{V}_n\left(T\right)$ of different adsorbed organic solvents at various temperatures: T = 453.15 K (a), T = 463.15 K (b), T = 473.15 K (c), and variations in $∆G_a$(-$C{H}_2$-) of n-alkanes adsorbed on solid surfaces as a function of temperature (d).

Figure 1. Effect of the percentage of melamine on the values of $RTln{V}_n\left(T\right)$ of different adsorbed organic solvents at various temperatures: T = 453.15 K (a), T = 463.15 K (b), T = 473.15 K (c), and variations in $∆G_a$(-$C{H}_2$-) of n-alkanes adsorbed on solid surfaces as a function of temperature (d).

The curves presented in Figure 1 show an important variation in $RTln{V}_n\left(T\right)$ of the various organic solvents as a function of temperature and the percentage of melamine on the porous polymer Dowex L-285. It seems that these variations were stabilized after 3% of melamine. Figure 1d also shows a significant decrease in the values of $∆G_a$(-$C{H}_2$-) of n-alkanes for 1% and 4% of melamine; however, a slight decrease was observed in the two cases of 2% and 3% of melamine (Figure 1d). The deviation between these results was certainly due to the closer values of $RTln{V}_n\left(T\right)$ (Figure 1a–c) of the adsorbed n-alkane solvents for 2% and 3% of melamine that implied closer values of $∆G_a$(-$C{H}_2$-) at different temperatures. These observations show that 1% of melamine had a screening effect on the surface of the copolymer which gave constant values of $∆G_a$(-$C{H}_2$-) until a melamine percentage lower than 4%. An increase in the surface thermodynamic parameters was observed at 4% for the various temperatures, proving an important effect of the melamine on the surface properties of the copolymer.

However, the variations in $RTln{V}_n\left(T\right)$ of the different probes adsorbed on solid materials alone cannot describe the polar and dispersive free energies of adsorption. In the next sections, a new methodology was applied to better determine the London dispersive surface energy and the surface thermodynamic parameters of interaction of the examined porous polymers with the model organic molecules.

3.2. London Dispersive Surface Energy of Dowex L-285 with Different Melamine Percentages

The new expressions of the surface area $a\left(T\right)$ of organic solvents were obtained using the Hamieh thermal model [19,20,21,22,23]. The slopes of straight lines representing the variations in $RTln{V}_n\left(T\right)$ of n-alkanes adsorbed on Dowex L-285 with different percentages of melamine as a function of $2\mathcal{N}a(T){\left({\gamma }_l^d\right)}^{1/2}$ using the London dispersive surface energy ${\gamma }_l^d\left(T\right)$ of n-alkanes [19,20,21,22,23], gave the values of the London dispersive surface energy ${\gamma }_s^d\left(T\right)$ of the various porous polymers for the different temperatures. The variations in the London dispersive surface energy of materials when the temperature and the percentage of melamine varied are presented in Figure 2. A linear decrease in ${\gamma }_s^d\left(T\right)$ was observed for all materials when the temperature increased (Figure 2a). The highest values of ${\gamma }_s^d\left(T\right)$ were obtained for the copolymer Dowex L-285 without any addition of melamine. An important difference in the behavior of different materials was observed in

Table 1. Linear expressions of ${\gamma }_s^d\left(T\right)$ of Dowex L-285 modified by different percentages of melamine, 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 $T_{Max}$.

Solid Material	${\mathit{\gamma }}_{\mathit{s}}^{\mathit{d}}\left(\mathit{T}\right)$ (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)
Dowex L-285	${\gamma }_s^d\left(T\right)$ = −0.835 T + 482.43	0.9980	−0.835	482.43	233.47	577.8
1% Melamine	${\gamma }_s^d\left(T\right)$ = −0.907 T + 496.21	0.9972	−0.907	496.21	225.79	547.1
2% Melamine	${\gamma }_s^d\left(T\right)$ = −0.656 T + 341.59	0.9590	−0.656	341.59	146.12	521.0
3% Melamine	${\gamma }_s^d\left(T\right)$ = −0.827 T + 439.96	0.9608	−0.827	439.96	193.51	532.3
4% Melamine	${\gamma }_s^d\left(T\right)$ = −0.876 T + 473.64	0.9735	−0.876	473.64	212.40	540.6

, showing different values of ${\gamma }_s^d\left(T\right)$ of Dowex L-285 modified by melamine percentages, the London dispersive surface entropy ${\epsilon }_s^d$, the extrapolated values of London dispersive surface energy at 0 K and 298.15 K, and the temperature maximum $T_{Max}$.

A minimum in the different values of ${\epsilon }_s^d$, ${\gamma }_s^d(T=0\mathrm{K})$, ${\gamma }_s^d(T=298.15\mathrm{K})$, and $T_{Max}$ was obtained for 2% of melamine, proving that there was a change in the surface groups of the copolymer due to the effect of this minimum percentage on the different surface parameters of Dowex L-285. Figure 2b highlights the presence of such a minimum of melamine. The obtained curves of ${\gamma }_s^d$ of solid materials presented in Figure 2b at different temperatures clearly show a minimum of ${\gamma }_s^d$ corresponding to 2% of melamine.

The values of extrapolated London dispersive surface energy at room temperature were limited to 140 to 230 mJ/m² for the different melamine percentages. In a recent paper [45], ${\gamma }_s^d=290$ mJ/m² was obtained using the Dorris–Gray (DG) method and ${\gamma }_s^d=220$ mJ/m², applying the linear free-energy relationship (LFER) coupled with the Dorris–Gray calculation (DG–LFER) for the same copolymer Dowex L-285 modified with 1% melamine, while our new methodology gave ${\gamma }_s^d=225.8$ mJ/m². Our results were based on the use of the Hamieh thermal model to determine the London dispersive surface energy. This thermal model was proved to be the most accurate method, because it takes into consideration the effect of the temperature on the surface area of organic molecules needed for the evaluation of London dispersive surface energy. The deviation percentage of another method, X, was calculated using the following relation:

$$Deviation Percentage of method X={\displaystyle \frac{{\gamma }_s^d\left(Method X\right)-{\gamma }_s^d(Hamieh Method)}{{\gamma }_s^d(Hamieh Method)}}\times 100$$

(18)

Using the above relation, one can deduce a deviation, in the case of DG method, of 31.8%. This large deviation is due to the DG method used by Gustov that did not take into account the temperature effect on the surface area of methylene group. However, a deviation of 2.6% was obtained using DG–LFER method. The value obtained by our new method was very close to that obtained by Guskov et al. using the DG–LFER calculation. However, the advantage of the new methodology, using the Hamieh thermal model, is to give the expressions of ${\gamma }_s^d\left(T\right)$ for the different percentages of melamine. For Dowex L-285 modified by 1% of melamine, the following relation is obtained:

$${\gamma }_s^d\left(T\right) = -0.907 T + 496.21$$

(19)

The obtained values of ${\gamma }_s^d\left(T\right)$ of the styrene–divinylbenzene copolymer as a function of temperature were correlated with the thermal conductivity $K$ of this copolymer. Indeed, Yamamoto and Kambe [46] determined the thermal conductivity of this material by the following relation:

$$K \left(\mathrm{m}\mathrm{W}\times {\mathrm{K}}^{-1}{\mathrm{m}}^{-1}\right)=0.897T\left(\mathrm{K}\right)-155.28$$

(20)

The results in Table 1 and Equation (20) led to the expression of the thermal conductivity $K\left(T\right)$ as a function of ${\gamma }_s^d$:

$$K\left(\mathrm{m}\mathrm{W}\times {\mathrm{K}}^{-1}{\mathrm{m}}^{-1}\right)=-1.074 {\gamma }_s^d\left(\mathrm{m}\mathrm{J}\times {\mathrm{m}}^{-2}\right)+362.97$$

(21)

Equation (21) clearly shows that the thermal conductivity $K$ of Dowex L-285 decreased when the London dispersive surface energy increased or when the temperature decreased. This study confirmed the results, obtained in a recent paper [47], of the presence of a strong relationship between the thermal conductivity of some graphene and carbon materials and their London dispersive surface energy.

3.3. Polar Free Interaction Energy of Dowex L-285 Modified by Melamine with the Polar Probes

The free polar energy $-∆G_a^p\left(T\right)$ of adsorption of polar organic probes adsorbed on the different solid materials was determined, against temperature, using our new approach, Equations (5)–(8), and Table S1. The obtained results are presented in Table S2.

The curves of $-∆G_a^p\left(T\right)$ of the various polar organic probes adsorbed on Dowex L-285, drawn in Figure 3, as a function of temperature, show linear variations in the various melamine percentages. The obtained straight lines of the $-∆G_a^p\left(T\right)$ function of the temperature easily led to the polar enthalpy $(-∆H_a^p)$ and entropy $(-∆S_a^p)$ values of the adsorbed polar solvents.

Several conclusions can be deduced from the curves in Figure 3:

• The free polar energies, $-∆G_a^p\left(T\right),$ of interaction between the solids and the organic solvents can be globally classified in increasing order of interaction energy with the various polar probes at all temperatures: cyclohexane < benzene < toluene < ethyl acetate < i-butanol < n-butanol < ethanol < n-propanol < dichloromethane < i-propanol.
• The highest free interaction energy was obtained for 4% melamine on Dowex L-285 for the following polar molecules in increasing order: cyclohexane < benzene < toluene < n-butanol < ethanol < n-propanol.
• However, a maximum of free interaction energy was observed for 2% melamine on Dowex L-285 for the other polar solvents such as dichloromethane, i-propanol, and i-butanol.
• It was proved that the alcohol molecules exchanged the maximum free interaction energy with the various solid surfaces, and especially with 4% melamine, while the minimum interaction was observed in the case of adsorption on Dowex L-285.
• The above results show that the modification of the copolymer Dowex L-285 by melamine increased the polar free interaction.

The above results were confirmed by the curves of $-∆G_a^p$ presented in Figure 4 as a function of the percentage of melamine on Dowex L-285 at different temperatures, where the maximum of the free interaction energy is shown for all polar solvents. Different non-linear variations in the free interaction energy were observed for the various polar molecules when the melamine percentage increased, but with a global increasing tendency of $-∆G_a^p$.

In order to better understand the polar behavior of the different solid surfaces, it was necessary to determine the surface polar enthalpy and the entropy of adsorption, as well as the Lewis acid–base constants of the solid materials. This is developed in the next section.

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

The polar enthalpy ($-∆H_a^p)$ and entropy ($-∆S_a^p)$ of the polar solvents adsorbed on the copolymer Dowex L-285 modified by different melamine percentages, were deduced from the variations in $-∆G_a^p\left(T\right)$ using Table S2, Figure 3, and Equation (9). The curves in Figure 5 show that the approximate linear variations in $\left({\displaystyle \frac{-∆H_a^p}{{AN}^{\prime }}}\right)$ 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 different solid materials led to the values of the Lewis enthalpic $K_A$ and $K_D$ and entropic ${\omega }_A$ and ${\omega }_D$ acid–base constants of Dowex L-285 with different melamine percentages. The results are presented in

Table 2. 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 Dowex L-285, modified by different melamine percentages with the corresponding parameters S_K = K_A + K_D and S_K = ω_A + ω_D.

Material	KA	KD	KD/KA	KA + KD	R2	10−3ωA	10−3ωD	ωD/ωA	10−3 (ωA + ωD)	R2
Dowex L-285	0.550	0.844	1.53	1.393	0.999	1.05	0.55	0.5	1.59	0.9968
1% Melamine on Dowex L-285	0.164	1.455	8.85	1.620	0.9783	0.09	2.81	30.2	2.90	0.9316
2% Melamine on Dowex L-285	0.160	2.137	13.38	2.297	0.9989	0.22	4.00	18.5	4.21	0.9520
3% Melamine on Dowex L-285	0.193	3.263	16.90	3.456	0.9938	0.22	6.30	28.0	6.52	0.9695
4% Melamine on Dowex L-285	0.218	3.401	15.58	3.619	0.9276	0.34	5.00	14.8	5.34	0.9702

and clearly show an amphoteric behavior of the different solid surfaces with a Lewis basicity higher than their Lewis acidity for all solid substrates.

The values of the Lewis acid and base constants of different materials were obtained using Equation (10) and Figure 5. The slopes of straight lines of $\left({\displaystyle \frac{-∆H_a^p}{{AN}^{\prime }}}\right)$ and $\left({\displaystyle \frac{-∆S_a^p}{{AN}^{\prime }}}\right)$ against $\left({\displaystyle \frac{{DN}^{\prime }}{{AN}^{\prime }}}\right)$ determined the Lewis acid constants $K_A$ and ${\omega }_A$, while the ordinates at origin led to the Lewis base constants $K_D$ and ${\omega }_D$. The results in Table 2 show that Dowex L-285 exhibited the highest acid character, whereas the copolymer modified by 4% of melamine had the highest basicity. The results presented in Figure 6 show that the basicity of solid materials largely increased when the melamine percentage increased, while a brutal decrease in the acidity was observed when Dowex L-285 was modified by 1% of melamine. A slight increase in acidity was found when the melamine percentage passed from 2% to 4%. The same conclusions were observed for the entropic acid–base constants. The total acid–base parameters S_K = K_A + K_D and S_K = ω_A + ω_D are given in Table 2. It was proved that the total acidity–basicity increased when the melamine percentage increased. It seemed that this continued for all acid–base parameters of solid surfaces after 3% of melamine. In fact, the presence of six nitrogen atoms in the supramolecular structure of melamine increased its donor interaction of electrons when added to the structure of styrene–divinylbenzene copolymer. This increased the basicity of Dowex L-285 when the melamine percentage increased, while the Lewis acidity decreased because of the strong basic sites of melamine that certainly interacted with the acidic sites of the copolymer by decreasing the total acidity of the solid materials.

3.5. Polar Acid–Base Surface Energies of Dowex L-285 Modified by Melamine

The different polar surface energies, such as the polar acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of Dowex L-285 modified by different melamine percentages were determined using the method of Van Oss et al. [44]. To do that, the free polar energy $-∆G_a^{sp}\left(T\right)$ of the different polar molecules, given in

Table 3. 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 melamine percentages at different temperatures.

Dichloromethane
T(K)	Dowex L-285	1% Melamine	2% Melamine	3% Melamine	4% Melamine
453.15	15.274	15.609	24.349	9.737	16.294
458.15	15.239	15.559	24.294	9.352	16.452
463.15	15.204	15.509	24.239	8.967	16.012
468.15	15.169	15.459	24.184	8.582	15.989
473.15	15.134	15.409	24.129	8.197	12.318
Ethyl Acetate
T(K)	Dowex L-285	1% Melamine	2% Melamine	3% Melamine	4% Melamine
453.15	10.106	8.503	9.667	10.567	39.887
458.15	9.593	8.378	9.507	10.314	38.842
463.15	9.079	8.253	9.347	10.060	37.077
468.15	8.566	8.128	9.187	9.807	35.814
473.15	8.052	8.003	9.027	9.553	30.163

, was used to determine the values of ${\gamma }_s^{+}$ and ${\gamma }_s^{-}$ at different temperatures, knowing the values of the polar acid ${\gamma }_l^{+}$ and base ${\gamma }_l^{-}$ surface energies of two chosen polar solvents such as dichloromethane and ethyl acetate molecules.

Using Equations (13) and (15), the values of $-∆G_a^{sp}\left(T\right)$ in Table 3, and the Hamieh thermal model, we obtained the values of ${\gamma }_s^{+}$ and ${\gamma }_s^{-}$ of the various solid surfaces as a function of temperature. The polar acid–base surface energy ${\gamma }_s^{AB}={\gamma }_s^p$ was then deduced from the relation ${\gamma }_s^p=2\sqrt{{\gamma }_s^{+}{\gamma }_s^{-}}$. This led to the total surface energy ${\gamma }_s^{tot.}$ of the different solid surfaces using the relation ${\gamma }_s^{tot.}={{\gamma }_s^d+\gamma }_s^p$.

The variations in ${\gamma }_s^{+}\left(T\right)$, ${\gamma }_s^{-}\left(T\right)$, ${\gamma }_s^{AB}\left(T\right)$, ${\gamma }_s^d \left(T\right)$, and ${\gamma }_s^{tot.}\left(T\right)$ of Dowex L-285 with different percentages of melamine are given in Table S3. Figure 7 gives the linear variations in polar surface energy components of Dowex L-285 modified by different melamine percentages as a function of temperature. The results show that the highest polar surface energy values were obtained with the Lewis base surface energy for all materials, while the lowest values were highlighted with the Lewis acid surface energy, confirming the highest basic character of Dowex L-285 at different melamine percentages. Furthermore, the maximum values of the Lewis base surface energy and the polar acid–base surface energy were obtained when using Dowex L-285 modified by 2% of melamine, followed by that of 4% of melamine.

By applying the Hamieh thermal model to determine the values of the surface area of organic molecules adsorbed on the different solid surfaces as a function of temperature and the results in Table S3 and Figure 7, Figure 8 shows the variations in the polar surface energy of the adsorbed polar probes against the temperature using the Fowkes relation [43]. The highest values of the polar surface energy were obtained with dichloromethane and ethanol adsorbed on the various solid materials, whereas, the lowest values were obtained in the case of adsorption of cyclohexane and benzene. These results are in perfect agreement with the polarity of the above organic molecules.

3.6. Determination of the Average Separation Distance H

The separation distance $H$ between the organic molecules and the solid surfaces was determined as a function of the temperature, using Equations (7) and (8) and the previous experimental results. The obtained curves are plotted in Figure 9. It was observed that the separation distance $H$ increased when the temperature increased proving the effect of the thermal agitation on the separation distance between molecules and solid substrates. The results show that the separation distance was between 5.5 Å and 6.1 Å, with the highest value in the case of 2% of melamine.

4. Conclusions

The surface thermodynamic properties of styrene–divinylbenzene copolymer (Dowex L-285) modified by a supramolecular structure of melamine at different percentages were characterized using the inverse gas chromatography at infinite dilution. The new methodology based on the Hamieh thermal model was used for accurate determination of the London dispersive surface energy of the different materials as a function of the temperature and the melamine percentage. A linear decrease in ${\gamma }_s^d\left(T\right)$ in the London dispersive surface energy of materials was noticed when the temperature increased, with the highest value obtained for the copolymer Dowex L-285. The results show an important difference in the behavior of different materials when the melamine percentage varied. This study highlighted a linear correlation between the thermal conductivity of the styrene–divinylbenzene copolymer and its London dispersive surface energy, confirming similar relationships previously obtained with graphene and carbon materials.

The application of our new methodology using the London dispersion interaction on the styrene–divinylbenzene copolymer modified by melamine led to the determination of the polar free energy, enthalpy, and entropy of adsorption of polar solvents on the various solid surfaces, as well the Lewis acid–base constants. It was proved that all materials used exhibited basic behavior that was largely higher than their acid behavior and the basic character increased with the melamine percentage in good agreement with the increase in nitrogen atom number at the surface of solid materials. The determination of the various components of polar acid and base surface energies of the different materials led to the conclusion that the highest polar surface energy values were obtained with the Lewis base surface energy for all materials, while the lowest values were obtained with the Lewis acid surface energy, confirming the highest basic character of Dowex L-285 at different melamine percentages. It was also shown that the maximum values of the Lewis base surface energy and the polar acid–base surface energy were obtained when using Dowex L-285 modified by 2% of melamine, which showed the highest separation distance between surface materials and organic solvents.