*3.3. Swelling Behavior*

Figure 11 shows the variation of the swelling degree of pHEMA and pHPMA film samples versus time, and Table 2 collects the deducted swelling degree at equilibrium.

**Figure 11.** Variation of the swelling degree of (**A**) pHEMA, (**B**) pHPMA film samples versus time at 37 ◦C.


**Table 2.** Swelling capacity of pHEMA and pHPMA film samples in different pH of medium.

The comparison of the swelling degree values of these two polymer samples reveals that the absorption capacity of the pHEMA film is approximately double that of pHPMA, regardless of the pH of absorbed medium. This seems to be obvious and can be explained quite simply by the more hydrophilic character of the hydroxyethyl substitute belonging to the HEMA units, with regard to that of the hydroxypropyl of pHPMA, which contains an additional methyl. These results also reveal that, for both samples, the swelling capacity increased slightly when the pH medium decreased. This is probably due to the protonation of the oxygen of certain hydroxyl or carbonyl groups belonging to the monomeric units, thus increasing the hydrophilicity of the polymer. Generally, the swelling kinetics are used to investigate the diffusion of small molecules such as water through polymeric materials when immersed in a penetrating medium during a certain time. According to Comyn [46], the kinetics that govern the diffusion of small molecules through a polymer material are given by Equation (6)

$$\frac{m\_t}{m\_{\text{max}}} = 1 - \sum\_{n=0}^{\infty} \frac{8}{\left(2n+1\right)^2 \pi^2} \exp\left[\frac{-D\left(2n+1\right)^2 \pi^2 t}{l^2}\right],\tag{6}$$

where *mt* and *mmax* are the masses of the absorbed molecules during *t* time and at the maximum absorption (equilibrium), respectively. *D* and *l* are the diffusion coefficient with regard to the small molecules and the film thickness, respectively. For the short times of the initial stage of diffusion and when the *mt/mmax* ratio is lower than 0.5, Equation (6) above takes the following expression:

$$\frac{m\_{\rm fl}}{m\_{\rm max}} = 2 \times \left(\frac{D \times t}{\pi \times l^2}\right)^{1/2} \text{ .} \tag{7}$$

in which, *D* can be deduced from the slope of the linear portion of the curve corresponding to the variation of *mt/mmax* versus square root of time.

The fundamental equation of mass uptake by a polymer material is given by Equation (8) [47]:

$$\frac{m\_t}{m\_{\max}} = k \times t^n,\tag{8}$$

where *n* exponent is the type of diffusion mechanism and *k* is the constant that depends on the diffusion coefficient and the film thickness. By analogy with Equation (7), *k* takes the following expression:

$$k = \frac{2}{l} \left(\frac{D}{\pi}\right)^n,\tag{9}$$

Equation (8) can be linearized by entering the logarithm of its two members as follows:

$$
\ln\left(\frac{m\_t}{m\_{\max}}\right) = \ln k + n \ln t\_\prime \tag{10}
$$

The variation of ln(*mt*/*mmax*) versus ln*t* for pHEMA and pHPMA materials is plotted in Figures 12 and 13, respectively. Straight lines were obtained, indicating that the diffusion of water molecules through these polymer materials obeys the Fick's model as long as their temperature in media (37 ◦C) is well above Tg (80 ◦C for pHEMA and 87 ◦C for pHPMA). This condition also indicates that the diffusion of water through the polymer film is purely and simply governed by a mechanical process and non-disturbed by a probable esterification reaction, which can occur in acidic media between the hydroxyl group contained in these polymers and the carboxylic group of Naproxen. The data of *n*, *D,* and *k* values deducted from these linear curves are gathered in Table 3. These results reveal, for both systems, an increase of the diffusion rate of water molecules when the pH of the medium increased. This property is highly valued in the field of drug delivery because this carrier is able to swell sufficiently and therefore delivers an appropriate amount of drug directly into the target organ (intestines, neutral pH medium).

**Figure 12.** Variation of ln (*mt/mmax*) versus ln (*t*) for the pHEMA material.

**Figure 13.** Variation of the ln (*mt/mmax*) versus ln (*t*) for the pHPMA material.

As can be seen from these data, practically no change in the order of the water diffusion through each polymer material is observed, regardless the pH of medium, which is close to 0.40. The diffusion coefficient attributed to pHEMA material is higher than that of pHPMA, except those experimented in medium at neutral pH, which are both close to 0.80 mm2·h−1. This is probably due to the decrease of the affinity between pHPMA and water caused by the hydropropyl group of the substitute (less hydrophilic) compared to that of hydroxyethyl group of pHEMA (more hydrophilic). These data also reveal that, for the pHEMA material, the *D* value decreased when the pH of the medium increased. In this same pH order, this parameter increased for the pHPMA.


**Table 3.** Diffusion parameters of water at different pHs through pHEMA and pHPMA materials.

#### *3.4. Drug–Polymer Interactions*

The drug–polymer Flory–Huggins interaction parameter denoted *χd*,*<sup>p</sup>* gives an important idea on the chemical affinity and the magnitude of the adhesion force between the drug and the polymer carrier through its sign and its absolute value, respectively. According to the Flory–Huggins theory [48], a negative value of *χd*,*<sup>p</sup>* indicates miscibility of a drug carrier system, and a positive value indicates its immiscibility. The *χd*,*<sup>p</sup>* values of the drug carrier systems involving NPX and pHEMA on the one hand and NPX and pHPMA on the other hand were estimated using the data of Table 4 and Equation (11) [49]:

$$\frac{\Delta H\_f}{R} \left( \frac{1}{T\_f} - \frac{1}{T} \right) = \ln v\_d + \left( 1 - \frac{1}{\lambda} \right) v\_p + \chi\_{d,p} v\_{p\prime}^2 \tag{11}$$

where Δ*Hf* and *Tf* are the enthalpy of fusion of Naproxen and the melting temperature of the pure drug. *R* is the gas constant, and *T* is the measured solubility temperature for a volume fraction *v* with subscripts *d* and *p* denoting drug and polymer, respectively. *λ* is the ratio of the molar volumes of the drug and polymer. *χd*,*<sup>p</sup>* is the drug–polymer Flory–Huggins interaction parameter. The results obtained are gathered for comparison in Table 5.



<sup>a</sup> Ref. [50]; <sup>b</sup> Ref. [34]; <sup>c</sup> Ref. [51].

**Table 5.** Comparative values of the Flory–Huggins parameters of the NPX/pHEMA and NPX/pHPMA drug carrier systems determined at 25 ◦C using Equation (9).


As it can be seen from these results, the values of *χd*,*<sup>p</sup>* are all negative regardless of the drug carrier system and its composition. According to the Flory–Huggins theory, a negative value of *χd*,*<sup>p</sup>* indicates the miscibility of the drug carrier system. These data also reveal that the values of *χd*,*<sup>p</sup>* increase with the NPX loading incorporated into the polymer. This means an increase in the affinity of NPX molecules with regard to the polymer when the drug loaded in the drug carrier system increased. This seems to be obvious because the density of hydrogen bonds between the hydroxyl groups of pHEMA or pHPMA and the carbonyl of the carboxyl group of NPX increases with the drug load in the drug carrier system. This leads to an increase of the attraction forces between these two components.

The comparison of the values *χd*,*<sup>p</sup>* of the NPX/pHPMA system with those of the NPX/pHEMA system indicates a slight increase in the interactions between NPX and pHPMA compared to those between NPX and pHEMA, whatever the composition of the mixture studied. These results also reveal that the more the amount of NPX increases in the drug carrier system, the greater the absolute value of the difference between the Flory– Huggins interaction parameters of the NPX/pHEMA and NPX/pHPMA drug systems, Δ *χd*,*<sup>p</sup>* also increases.
