Effect of Temperature on Adhesion Work of Model Organic Molecules on Modified Styrene– Divinylbenzene Copolymer Using Inverse Gas Chromatography

2. Materials and Methods

2.1. Materials and Technique

The different organic solvents, modifiers, the S-DVB copolymer, and their origins were described in previous papers [35,36,37]. The chromatographic measurements of the retention volume of the various organic adsorbed on the modified S-DVB, as well as the IGC technique, and the experimental procedure were the same as those given in previous works [35,36,37].

2.2. Thermodynamic Methods

2.2.1. Surface Energy Parameters of Modified Copolymers

The application of the Hamieh thermal model allowed obtaining the correct London dispersive surface energy ${\gamma }_s^d\left(T\right)$ of the S-DVB copolymer respectively modified by melamine [35], 5-hydroxy-6-methyluracil [36], and 5-fluouracil [37], for percentages varying from 1% to 10% and the temperature from 443.15 K to 473.15 K. Whereas, the new applied methodology led to the separation between the dispersive free energy $∆G_a^0\left(T\right)$ and the polar free energy $∆G_a^p\left(T\right)$ of adsorption of the various organic adsorbed on the modified S-DVB copolymer at different temperatures.

Denoting ${\gamma }_s^p\left(T\right)$ the polar surface energy of the modified copolymer, the total surface energy ${\gamma }_s\left(T\right)$ can be written as follows:

$${\gamma }_s\left(T\right)={\gamma }_s^d\left(T\right)+{\gamma }_s^p\left(T\right)$$

(1)

Applying the Van Oss et al.’s method [11] to the modified copolymers, it was possible to obtain the different values of the Lewis acid ${\gamma }_s^{+}$, and base ${\gamma }_s^{-}$ surface energies using the following expression of $∆G_a^p\left(T\right)$ and the well-known surface parameters of two polar solvents such as ethyl acetate and dichloromethane:

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

(2)

Equation (2) led to the values of the acid-base surface energy ${\gamma }_s^{AB}$ or ${\gamma }_s^p$ of the solid surfaces with the help of Relation (3):

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

(3)

2.2.2. Surface Energy and Work of Adhesion

Considering a liquid of known surface tension ${\mathit{\gamma }}_{\mathit{l}}$ in contact with a simple solid, smooth, homogeneous, non-deformable and isotropic surface, the corresponding work of adhesion ${\mathit{W}}_{\mathit{a}}$ can be then written as:

$${{\mathit{W}}_{\mathit{a}}=\mathit{\gamma }}_{\mathit{s}}+{\mathit{\gamma }}_{\mathit{l}}-{\mathit{\gamma }}_{\mathit{s}\mathit{l}}$$

(4)

Where ${\mathit{\gamma }}_{\mathit{s}\mathit{l}}$ is the solid/liquid interface tension.

Young [38] proposed the following equation:

$${{\mathit{\gamma }}_{\mathit{l}}\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }=\mathit{\gamma }}_{\mathit{s}}-{\mathit{\gamma }}_{\mathit{s}\mathit{l}}$$

(5)

by defining the concept of the contact angle $\mathit{\theta }$ formed between the liquid drop and the plan solid surface.

Whereas, Dupré [7] used the Young’s equation and expressed the work of adhesion by Equation (6):

$${\mathit{W}}_{\mathit{a}}={\mathit{\gamma }}_{\mathit{l}}\left(1+\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }\right)$$

(6)

Fowkes [8] applied the geometric mean of the dispersive components of the solid and liquid and proposed a new expression of the work of adhesion:

$${\mathit{W}}_{\mathit{a}}={\mathit{\gamma }}_{\mathit{l}}\left(1+\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }\right)=2\sqrt{{\mathit{\gamma }}_{\mathit{s}}^{\mathbf{d}}{\mathit{\gamma }}_{\mathit{l}}^{\mathbf{d}}}$$

(7)

where Equation (7) is only valid for dispersive interactions.

Later, the Fowkes’s equation [8] was extended to an approach taking into account the polar contribution (hydrogen bonding) [9] in the expression of the work adhesion:

$${\mathit{W}}_{\mathit{a}}=2\sqrt{{\mathit{\gamma }}_{\mathit{s}}^{\mathbf{d}}{\mathit{\gamma }}_{\mathit{l}}^{\mathbf{d}}}+2\sqrt{{\mathit{\gamma }}_{\mathit{s}}^{\mathbf{p}}{\mathit{\gamma }}_{\mathit{l}}^{\mathbf{p}}}$$

(8)

The values of ${\gamma }_s^p$ and the Lewis acid ${\gamma }_s^{+}$, and base ${\gamma }_s^{-}$ surface energies of solid copolymers were obtained using Van Oss et al.’s method [10] and applying Equation (9):

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

(9)

This allowed obtaining the polar (or acid–base) surface energy ${\gamma }_s^{AB}$ of the modified copolymers using Equation (10):

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

(10)

Therefore, the work of adhesion can be expressed as follows:

$$W_a=2\left[\sqrt{{\gamma }_s^{\mathrm{d}}{\gamma }_l^{\mathrm{d}}}+\sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right]$$

(11)

The different surface energy components of the modified copolymers were previously determined, it was then possible to calculate the work of adhesion with the help of Equations (11).

Furthermore, the dispersive $W_a^{\mathrm{d}}\left(T\right)$ and polar $W_a^{\mathrm{p}}\left(T\right)$ contributions of the work of adhesion can be written as follows:

$$\left\{\begin{array}{c}{W}_a\left(T\right)=W_a^{\mathrm{d}}\left(T\right)+W_a^{\mathrm{p}}\left(T\right) \\ W_a^{\mathrm{d}}\left(T\right)=2 \sqrt{{\gamma }_s^{\mathrm{d}}{\left(T\right)\gamma }_l^{\mathrm{d}}\left(T\right)} \\ W_a^{\mathrm{p}}\left(T\right)=2 \left[ \sqrt{{\gamma }_l^{-}{\gamma }_s^{+}}+\sqrt{{\gamma }_l^{+}{\gamma }_s^{-}}\right]=2 \sqrt{{\gamma }_l^{\mathrm{p}}\left(T\right){\gamma }_s^{\mathrm{p}}\left(T\right)}\end{array}\right.$$

(12)

3. Results

3.1. London Dispersive Surface Energy of Modified Copolymers

Based on the Hamieh thermal model [22,24] and the Fowkes’s equation [8], the representation of the variations of $RTln{V}_n\left(T\right)$ of n-alkanes adsorbed on the modified copolymers as a function of $2\mathcal{N}a\left(T\right){\left({\gamma }_l^d\left(T\right)\right)}^{1/2}$ led to ${\gamma }_s^d\left(T\right)$ of the various copolymers against the temperatures [H1-H3]. The results were plotted in Figure 1 where a decrease of ${\gamma }_s^d\left(T\right)$ was observed as the temperature increased. The highest London dispersive surface energy was obtained with 1% melamine / S-DVB closest to ${\gamma }_s^d\left(T\right)$ of the copolymer alone, while the lowest values were shown with 10% 5-HMU / S-DVB. An important difference in ${\gamma }_s^d\left(T\right)$ of the copolymer behavior was found affected both by the modifier and its percentage. Figure 1 clearly showed a decrease in the values of ${\gamma }_s^d\left(T\right)$ of S-DVB when it was modified by 5-HMU or 5-FU certainly due to the morphology change in the copolymer structure.

The different linear equations of ${\gamma }_s^d\left(T\right)$ function of the temperature, were given in Table 1 with the values of the surface entropy and the maximum temperature of the various modified copolymers. The results in Table 1 proved a difference in the various surface thermodynamic variables of the modified copolymers. Furthermore, the abnormally high values of the London dispersive surface extrapolated at 298.15K observed in Table 1 are mainly due to the nonlinear variations of ${\gamma }_s^d\left(T\right)$ of the solid surfaces for lower temperatures resulted in the important change in the surface groups of the copolymers when the temperature undergoes severe variations from 475.15K to 298.15K.

Table 1 showed 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 percentage of 5-hydroxy-6-methyluracil 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 $T_{Max}$ when the modifier percentage increased certainly due to the decrease of ${\gamma }_s^d\left(T\right)$ for higher temperatures.

3.2. Polar (Lewis Acid–Base) Surface Energy of Modified Copolymers

First, the polar acid ${\gamma }_s^{+}$ and base ${\gamma }_s^{-}$ surface energies of modified copolymers were obtained using the method of van Oss et al. [10]. This led to the values of the polar surface energy ${\gamma }_s^p$ and consequently to those of the total surface energy ${\gamma }_s^{tot.}$ obtained as a function of temperature using the previous equations and the results of ${\gamma }_s^d\left(T\right)$. The values of ${\gamma }_s^p\left(T\right)$ of the copolymers were given in Table 2. They showed that the modifier 2% melamine on S-DVB copolymer exhibited the highest polar surface energy followed by 5% 5-Fu / S-DVB. Whereas the lowest ${\gamma }_s^p\left(T\right)$ was observed with 1% 5-Fu / S-DVB. The results in Table 2 clearly showed the large effect of the temperature and the modifier on the polar surface energy.

To highlight the effect of the modifier percentage on ${\gamma }_s^p$ of the different modified copolymers, the curves of ${\gamma }_s^p$ of solid surfaces were drawn in Figure 2 as a function of the modifier percentage. The variations of ${\gamma }_s^p$ for all used modifiers are not linear when the modifier percentage varies. A maximum of ${\gamma }_s^p$ was observed at 2% melamine / S-DVB and a minimum at 3% of melamine for all temperatures with a pallier after 4% melamine (Figure 2a). However, a minimum of ${\gamma }_s^p$ was observed at 1% of 5-HMU (Figure 2b.) and 5-FU (Figure 2c.) for the different temperatures and a pallier shown in Figure 2 after 4% of modifier on S-DVB copolymer. The results thus proved that the polar surface energy is strongly affected not only by the temperature but also by both the nature and the percentage of the modifier as it was shown in Figure 3. It seems that the S-DVB copolymer modified by melamine gives the highest ${\gamma }_s^p$ at 2% melamine, while the 5-Fu on S-DVB exhibits the highest ${\gamma }_s^p$ after 4% 5-Fu.

3.3. Polar Surface Energy of Organic Solvents

The polar free energy $-∆G_a^p\left(T\right)$ of adsorption of solvents on the various copolymers can be also written as:

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

(13)

Where ${\gamma }_l^{\mathrm{p}}\left(T\right)$ is the polar surface energy of the solvents depending on temperature.

The variations of $-∆G_a^p\left(T\right)$ of the various polar solvents versus the temperature were previously determined [35,36,37]. Knowing the values of ${\gamma }_s^{\mathrm{p}}\left(T\right)$ of the various copolymers and those of the surface area of the different organic molecules [16,17,18,19,20,21,22,23], the variations of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ were directly obtained using Equation (13). The results were plotted in Figure S1. The curves in Figure S1 showed linear variations of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ of the different polar solvents versus the temperature. The different equations of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ were given in Table 3.

Results in Figure S1 and Table 3 highlighted the important dependence of ${\gamma }_l^{\mathrm{p}}\left(T\right)$ both on the temperature and the modifier percentage. It was shown that the polar surface energy of ethanol, propanol, i-propanol, and n-butanol, i-butanol and n-pentanol gave the highest values whereas cyclohexane, benzene, and toluene exhibited the lowest ${\gamma }_l^{\mathrm{p}}\left(T\right)$. Of course, the presence of hydroxyl group in these solvents strengthens their polarity relative to other polar molecules.

3.4. Work of Adhesion of Organic Solvents on Modified Copolymer

The determination of the London dispersive and polar surface energies of the various modified copolymers as well as the values of polar surface energy of adsorbed solvents led using the Equations (12) to the values of dispersive $W_a^{\mathrm{d}}\left(T\right)$, polar $W_a^{\mathrm{p}}\left(T\right)$, and total work $W_a\left(T\right)$ of adhesion between solvents and the various solid surfaces by varying the temperature, the modifier, and its percentage. The variations of $W_a^{\mathrm{d}}\left(T\right)$ were plotted in Figures S2 as a function of temperature for all copolymers and modifiers at different percentages. Whereas the evolution of $W_a^{\mathrm{p}}\left(T\right)$ versus the temperature was drawn in Figures 3. An excellent linearity of the curves $W_a^{\mathrm{d}}\left(T\right)$ and $W_a^{\mathrm{p}}\left(T\right)$ was observed in Figures S2 and Figure 2 for all solvents and solid materials. A general decrease was noticed against the temperature for the two dispersive and polar works of adhesion with different behaviors depending on the modifier nature and its percentage. It was shown in Figure 3 that the polar adhesion work of ethanol on S-DVB modified by melamine was the highest while that of benzene and toluene was the lowest where a minimum of polar adhesion has been noticed confirming the lowest values obtained in adsorption of these solvents on the modified copolymer. However, in the case of the modification of S-DVB by 5-HMU, the polar work of adhesion $W_a^{\mathrm{p}}\left(T\right)$ of ethyl acetate was the highest for 1% and 3.5% of 5-HMU, while that of i-propanol gave the highest $W_a^{\mathrm{p}}\left(T\right)$ for 10% 5-HMU, 1% 5-FU and 5% 5-FU. Furthermore, the comparison between the various modifiers led to conclude using Figure S3 that the maximum of adhesion work was obtained with 5-FU.

The sum of the two dispersive and polar contributions of the adhesion work allowed the determination of the total work of adhesion of the various solvents on the different modified copolymers. The obtained results were given in Table 4 in the form of the equations $W_a\left(T\right)$ functions of temperature, the modifier and its percentage. Two new thermodynamic parameters were defined. The first one is the surface entropy $∆S_S$ of adhesion work and the second term is relative to the surface enthalpy $∆H_S$ of adhesion work. The general equation of $W_a\left(T\right)$ can be then written as:

$$W_a\left(T\right)=∆H_S-T∆S_S$$

14

The values of $∆H_S$ and $∆S_S$ of the different organic solvents given in Table 4 for the modified copolymers at different modifier percentages led to linear relations between these surface parameters and the corresponding percentage ($q$) of melamine (noted Mela), 5-HMU, and 5-FU. The equations of $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ relative to the work of adhesion on the modified copolymers were given in Table 5 with the linear regression coefficients. The results in Table 5 led to the following general equations:

$$∆H_S\left(q\right)=aq+b$$

(15)

$$∆S_S\left(q\right)=cq+d$$

(16)

Where $a$, $b$, $c$, and $d$ given in Table 5 are constant coefficients depending on the work of adhesion of the solvents on the modified S-DVB.

The combination of Equations (14) to (16) led to a universal equation giving the work of adhesion $W_a(T,q)$ of organic solvent on a copolymer modified by a modifier percentage $q$:

${\mathit{W}}_{\mathit{a}}\left(\mathit{T},\mathit{q}\right)=a\mathit{q}+b-\mathit{T}(c\mathit{q}+d)$ (17)

$W_a(T,q)$ given by Equation (17) is a function of two variables $T$ and $q$.

The above equation represents a quantification of the work of adhesion knowing the temperature and the modifier percentage. This result is similar to that obtained in previous studies during the study of the adsorption of PMMA on silica and alumina at different recovery fractions where the polar free energy of adsorption was correlated to the two thermodynamic variables such as the temperature and the percentage of adsorption.

Another interesting result was obtained from Table 5 by drawing the variations of $∆H_S$ and $∆S_S$ of the different modified copolymers. Linear relation of the surface enthalpy of adhesion work $∆H_S(∆S_S)$ was obtained versus the surface entropy for the different copolymers and a new surface temperature $T_S$ was defined. This new variable constitutes a real characteristic of the copolymer. The linear equations were given in table 6.

The various equations presented in Table 6 can be generally described by the following equation for all materials:

$$∆{\mathit{H}}_{\mathit{S}}=\mathit{\alpha }∆{\mathit{S}}_{\mathit{S}}+\mathit{\beta }$$

(18)

where the slope $\mathit{\alpha }$ represents an isokinetic surface temperature $T_S$ ($T_S=\mathit{\alpha }$) at which all processes in series of organic solvents proceed with the same work of adhesion here given by the constant parameter $\mathit{\beta }$. This interesting equation traduces the surface enthalpy – surface entropy compensation with excellent linear regression coefficient for all studied copolymers.

4. Conclusions

A new method was proposed to determine the variations of the work of adhesion $W_a\left(T\right)$ of model organic solvents on S-DVB copolymer modified by melamine, 5-HMU, and 5-FU at different percentages by varying the temperature. The surface properties of modified copolymers such as the dispersive and polar free energy of adsorption, the London dispersive and polar surface energies of copolymers were used to determine the dispersive $W_a^{\mathrm{d}}\left(T\right)$ and polar $W_a^{\mathrm{p}}\left(T\right)$ works of adhesion of the various organic model solvents on S-DVB copolymer as a function of temperature and modifier percentage. Results showed an excellent linearity of $W_a^{\mathrm{d}}\left(T\right)$ and $W_a^{\mathrm{p}}\left(T\right)$ as a function of temperature for all solvents and copolymers with a decrease against the temperature depending on the modifier nature and its percentage. The highest polar adhesion work was obtained with ethanol on S-DVB modified by melamine while the values of $W_a^{\mathrm{p}}\left(T\right)$ of benzene and toluene were the lowest. The comparison between the various modifiers led to conclude that the maximum of adhesion work was obtained with 5-FU on S-DVB copolymer. The work of adhesion was correlated to the surface enthalpy $∆H_S$ and entropy $∆S_S$ of organic solvents adsorbed on copolymers at different modifier percentages ($q)$ via the following equation:

$$W_a\left(T,q\right)=∆H_S\left(q\right)-T∆S_S\left(q\right)$$

It was proved that $∆H_S\left(q\right)$ and $∆S_S\left(q\right)$ linearly varied as a function of the modifier percentage ($q)$ as follows: The results in Table 5 led to the following general equations:

$$∆H_S\left(q\right)=aq+b∆S_S\left(q\right)=cq+d$$

A new relation of the work of adhesion $W_a(T,q)$ function of the two variables $T$ and $q$ was therefore proposed:

$$W_a\left(T,q\right)=aq+b-T(cq+d)$$

Furthermore, linear relations of the surface enthalpy of adhesion work $∆H_S$ as a function of the surface entropy of adhesion were obtained and a new surface temperature $T_S$ representing an isokinetic surface temperature was defined.