Kinetic control concept for the diffusion processes of Paracetamol active molecules across affinity polymer membranes

Background: Paracetamol compound remains the most used pharmaceutical as an analgesic and antipyretic for pain and fever. It has been detected in aquatic environments. The recovery of this compound from wastewater is one of the important operations carried out by modern industries. Its recovery is especially important for environmental protection. Currently, research is focused on membrane technology that has gained considerable interest over the last decades due to the various advantages that it presents. Result: Our work reports the selective extraction of paracetamol from liquid solution using two types of affinity polymer membranes: (i) polymer inclusion membrane (PIM) and (ii) grafted polymer membrane (GPM). The same extractive agent, gluconic acid (GA), is used for both. After total characterization, the developed membranes were adopted. Kinetic and thermodynamic models have been used to determine the values of various macroscopic parameters, permeability (P), and initial flux (J0), to understand the membrane performance. The same techniques have been used to determine the values of different microscopic parameters, association constant (Kass), and apparent diffusion coefficient (D*) that determine the interaction between the paracetamol substrates and the extractive agent, necessary for the diffusion of paracetamol molecules through the membrane. Similarly, the effects of initial concentration (C0), acidity (pH), and temperature were examined. Conclusion: The experimental results allow the determination of values of activation and thermodynamic parameters (Ea, ΔH # , ΔS #, ΔH # dis, and ΔH # th). The results explain the membrane performances and confirm that the energetic or kinetic aspects control the mechanisms related to the oriented processes. The results also indicate that it is possible to recycle wastewater and eliminate contaminants such as paracetamol.


Introduction
In the last few decades, increasing attention has been paid to pharmaceutical industries that generate liquid wastes containing several pollutants and toxic substances [1][2][3][4][5]. These pollutants induce undesirable effects on the ecosystem and can potentially cause unexpected consequences and unintended effects on living organisms [5][6][7][8][9]. Consequently, the treatment of these wastes becomes a major environmental issue for modern pharmaceutical industries and scientific research institutions.
New technologies for the extraction, separation, and elimination of organic or inorganic substances and the recovery of several value-added molecules for evaluating these releases must be developed [10][11][12][13] to minimize and reduce the rate of formation of toxic products [14].
Paracetamol, also known as acetaminophen or para-acetyl aminophenol, is one of the major active pharmaceutical ingredients used in many medicines as an analgesic and antipyretic. It is used (alone or in combination with other analgesics) to treat mild-to-moderate pain or fever [15][16][17], and it is one of the drugs used widely without prescription. This compound is currently a drug of choice (after acetylsalicylic) for numerous people worldwide [18]. It is one of the components of numerous pharmaceutical products. Due to these commercial and medical uses, modern industries use special methods to develop this active ingredient, which is not effectively removed by conventional methods during wastewater treatment. Thus they remain in municipal effluents. Different concentrations of paracetamol have been detected in various parts of the world [19,20]. Long-term exposure to drugs containing this active pharmaceutical ingredient can cause serious damage to humans and other animals [21][22][23][24]. Paracetamol presents some strange and life-threatening effects like liver damage, which leads to fulminant liver failure (with a high rate of morbidity and mortality) [25]. Therefore, its recovery and extraction from industrial liquid waste is the need of the hour. Paracetamol is an acylated aromatic amide [26] that belongs to the family of anilides (derivatives of aniline) (Additional file 1: Figure S1).
Paracetamol, (C 8 H 9 NO 2 ) is a fat-soluble weak organic acid (pKa = 9.5) that is found in its ionized form in the stomach and small intestine where it is absorbed. Its maximum absorption in the UV region is at 244 nm in an acidic solution. Today various industrial synthesis methods are used to produce paracetamol. However, most of the synthetic route involves acylation of para-aminophenol in the presence of acetic anhydride.
In recent years, various membrane processes have been reported for various applications [27][28][29] (such as removal, purification, recovery, and extraction of organic compounds present in liquid wastewater). Membrane-based technology has become immensely important and has attracted much attention as a valuable technology for many industries. It is an environmentally friendly alternative that considerably reduces the volume of used chemical products, and minimal energy is consumed during the process. These methods are successfully applied in several fields, such as environment, energy, health, water treatment, cosmetic, food, chemical, and pharmaceutical industries. Depending on their structure, composition, and morphology, a wide range of membranes (including organic polymer membranes) can be developed for use in different fields. These favorable properties and functionalities exhibit clear and important advantages compared to other separation and extraction techniques such as resin separation, liquid-liquid extraction (ELL), solid-phase extraction (EPS), and chromatography [30][31][32][33][34]. These properties help in determining the selectivity parameters in particular.
In general, the extraction mechanism through a membrane is based on facilitated diffusion. These oriented membranes that promote facilitated extraction are now the subject of several studies. The studied membranes include the affinity membranes (for purification and recovery of organic molecules from aqueous solutions), supported liquid membranes (SLMs), polymer inclusion membranes (PIMs), and grafted polymer membranes (GPMs) [35][36][37][38]. This technology combines extraction and stripping operations in a single step. Due to the simple preparation steps, stability, better mechanical properties, good chemical resistance, better mechanical properties, and particularly, stable integration of the extractive agent into the polymer support, special attention is paid to PIMs and GPMs [39][40][41][42].
We aimed to improve the treatment process in the pharmaceutical industry. Accordingly, in our laboratory, experiments related to the facilitated extraction process of paracetamol, which is used here as a model drug to evaluate the extraction capabilities of the membrane process, were carried out to extract the active substances from the liquid solution. Our challenge was to determine the proper and selective extractive agent for the fabrication of a stable and efficient membrane for extracting paracetamol. We also aimed to evaluate the parameters to achieve high recovery, high throughput, and low consumption time. This extraction process was performed using PIM and GPM containing gluconic acid (GA) (Additional file 1: Figure S2) as the extractive agent. The prepared membranes were characterized by two spectroscopic techniques: (i) Fourier transform infrared spectroscopy (FTIR) and (ii) scanning electron microscopy (SEM) techniques to confirm the presence of the extractive agent in the polymeric support. The developed membranes were used to perform oriented processes for facilitated extraction and to recover paracetamol substrates under the influence of initial substrate concentration, acidity, and temperature of the medium. The dynamics of mass transfer and the effect of the different factors on the process of extracting the paracetamol substrate were discussed. The kinetically determining step, which controls the rate of paracetamol extraction when PIMs and GPMs are used, has been elucidated by analyzing the kinetic data.
The paracetamol concentration (C R ) in the receiving phase was measured (ƛ max = 244 nm) using a UV−visible spectrophotometer. A single-beam type monochromator, Helios γ Rayleigh U.V.-2601) was used to analyze the solutions. An Infrared spectrophotometer (AVATAR 360 FTIR ESP) was used to plot the FTIR spectra to identify the presence of extractive agents in the polymer matrix.
Similarly, the SEM technique (ZEISS EVO40 EP) was used to produce different micrographs and study the morphology and porosity of the developed membranes.

Membrane preparation
To conduct the oriented processes of the facilitated extraction of paracetamol, we have prepared two types of polymer membranes PIM and GPM, based on polyvinyl alcohol and polysulfone as polymer supports with the same extractive agent (GA). The adopted GPM was developed according to the following experimental protocol [43]: A precise amount (3 g) of polysulfone polymer dissolved in 13 mL of dimethylformamide (DMF) was introduced into a closed bottle to isolate the mixture from the air. The system was stirred for 12 h until polysulfone was completely solubilized. Next, a 0.625 g of polyvinylpyrrolidone (PVP) was added to this homogeneous solution, followed by slow addition of the weighed mass of the extractive agent. The mixture was stirred for 3 to four days to completely solubilize the extractive agent to produce a homogeneous phase. The resulting phase was cast on a glass plate and then spread with a ruler. This glass plate was rapidly immersed in a bath containing distilled water. The solvent DMF leaves the membrane matrix and a rigid membrane in the form of a paper (phase inversion method) was obtained [44,45]. After this operation, the GPM membrane was dried, its mass (0.030 g) and thickness (l = 162 µm) were determined. Its total surface area (10 cm 2 ) was measured and the concentration of the extractive agent [T] 0 = 0.20 mol L -1 was calculated.
PIM [46] was prepared by dissolving 10 g of polyvinyl alcohol (PVA) in a mixture of 20 mL of DMSO and 80 mL of distilled water. The mixture was stirred for 24 h at a temperature of 120 °C to dissolve the PVA in the solution. In this homogeneous solution, a precise amount of the extractive agent (GA) was added slowly under a condition of constant stirring to avoid polymer aggregation.
The resulting solution was poured carefully into a Petri dish, placed on a stove at a temperature in the range of 70 to 80 °C to completely evaporate the solvent. The PIM obtained by this experimental protocol (heat vulcanization method) was homogenous, transparent, flexible, and mechanically strong. Its thickness was measured (l = 228 µm) and the extractive agent concentration was calculated ([T] 0 = 0.30 mole.L -1 ).

Experimental methods and adopted materials
(Additional file 1: Figure S3) shows the experimental cell used for carrying out the facilitated extraction processes for extracting paracetamol. It consists of two compartments of identical volume separated by the developed membrane. The feed phase (F) contained the paracetamol solution in the concentration range of 0.01 M to 0.08 M, and the receiving phase (R) contained distilled water. The aqueous phase volume was 70 mL in each compartment. The system was immersed in a thermostatic bath (TB) containing water to maintain a constant temperature throughout the experimental procedure. Homogeneity was ensured by using a multi-station magnetic stirrer.
Samples were collected from the receiving phase every 30 min and were measured at a wavelength of 244 nm using an ultraviolet-visible (UV-visible) spectrophotometer to determine C R in the receiving phase. The acidities of the aqueous solutions (feed phase and receiving phase) were measured using a pH meter (HANNA Instruments HI 8519N). The pH was adjusted with an analytical grade solution of hydrochloric acid. The thicknesses of the developed membranes, which were specified in the preceding paragraph, were measured using an electronic micrometer (Mitutoyo). A knowledge of these values is necessary to calculate the membrane volume to determine the fixed concentration [T] 0 of GA in the membrane phase.

Theoretical models for quantification of processes
The facilitated extraction processes for substrate S was conducted using an affinity polymer membrane. The process depends on the formation and the dissociation of the substrate-extractive agent entity (ST) at the membrane-solution interfaces and in the membrane phase during the diffusion of the substrate. To quantify the processes carried out and to study the performances of the adopted membranes, kinetic and thermodynamic models based on the first and second Fick's laws and a saturation law of the extractive agent (T) by the substrate (S) have been developed in the laboratory [43,[46][47][48][49]. The following relationships were established.

Determination of macroscopic parameters P and J 0
If the kinetic model is verified, after an induction time (t I ), the function (-Ln (C 0− 2C R ) versus time) evolves linearly. The slope (a) of the obtained straight line allows the determination of the permeability parameter P according to the following equation [50,51].

(3)
The initial flux J 0 can be calculated from the permeability coefficient P by the following equation:

Determination of microscopic parameters D* and K ass
To determine the nature of the movement of the substrate S during its diffusion through the membrane phase and to elucidate the mechanism that governs the studied processes, it is necessary to determine the values of the microscopic parameters D* and K ass . We used the Lineweaver-Burk method (L-B) to linearize the expression in equation 2, according to the following equation [52,53]:

Determination of activation and thermodynamic parameters
The initial flux is related to the temperature factor by the Arrhenius law [54,55], according to the following equation: On the other hand, according to the transition state theory, for an elementary reaction, this important thermodynamic parameter is related to the activation enthalpies, association ΔH ≠ ass , and dissociation ΔH ≠ dis (Kj.mol -1 ) by the following relation:

Fourier Transform-Infrared (FTIR) Analysis
After drying the sample for 48 h to remove traces of residual water and solvent, the obtained membranes (PSU-PVP) and (PSU-PVP-AG) were characterized by the IRTF-spectroscopy technique to record the vibration bands corresponding to the membrane components. FTIR spectra (Figure 1) were plotted and recorded using an Avatar 360 FT-IR ESP spectrometer. The analysis of the ATR-FTIR spectrum of the prepared membrane reveals the presence (at around 3350 cm -1 ) of a characteristic broad absorption band corresponding to the alcohol (OH) group. A peak at 1720 cm −1 was also observed, which was attributed to the vibration of the C =O group of GA. This result proved that the extractive agent was successfully grafted onto the surface of the PSU membrane.

Figure 2. SEM micrographs: a) support polymer surface and cross-section (PSU/PVP), b), and c) membrane cross-section (PSU/PVP-GA)
The PIM was analyzed and characterized using the spectroscopic techniques used for characterizing the membrane described in the previous section. The results indicated and proved that the extractive agent was trapped in the polymer matrix of the membrane whose porosity increased with the concentration of the extractive agent.

Influence of the initial substrate concentration (C 0 ) on the performance of the fabricated membranes
In this section, we have examined the effect of C 0 on the evolution of macroscopic parameters  Table 1. Analysis of the results grouped in Table 1 demonstrates that the used membranes are effective extractors of paracetamol. The PIM membrane was more efficient than the GPM membrane.
However, it was noticed that permeability P increases, and initial flux J 0 and C 0 decrease.

Acidity factor influence the evolution of paracetamol extraction processes
To investigate the effect of acidity (feed and receiving aqueous solutions) on the efficiency of extraction through the adopted membranes, a series of experiments were performed at different pH (1, 2, and 3). Different substrate concentrations (0.01 M -0.08 M) were used for the experiments. The values of the macroscopic parameters P and J 0 were determined at each pH value ( Table 2). The Lineweaver-Burk (L-B) representation 1/J 0 = f (1/C 0 ) was plotted using the values of initial fluxes.
The slopes and intercepts of the straight lines are shown in Figure 4. The D * and K ass values (microscopic parameters) were estimated. The results are presented as histograms in Figure 5. According to the results grouped in Table 2, it is clear that the pH of the aqueous solutions does not significantly influence the extraction oriented processes followed for the extraction of paracetamol. On the other hand, it has been confirmed that the performance of the PIM membrane is better than that of the GPM membrane.

Temperature influence on the evolution of oriented extraction processes of paracetamol
The values of the macroscopic parameters (P) and (J 0 ) were determined at different temperatures (298, 303, and 308 K) to assess the influence of temperature on the facilitated extraction processes. The experiments were conducted at pH=1. C 0 was varied in the range of 0.08 M to 0.01 M. This study is very important to explain the performances of developed membranes and to elucidate the mechanisms related to these oriented processes. The values of macroscopic parameters P and J 0 have been summarized in Table 3. The data reveals the impact of temperature on the facilitated extraction processes employed for isolating paracetamol. In addition, an increase in temperature leads to an increase in membrane performance. It was noted that the permeability through the PIM membrane was higher than the permeability of the GPM membrane at all temperatures. To complete our study, we plotted the L-B curve ( Figure S4).
The scheme in ( Additional file 1: Figure S4) describes the mechanism of successive jumps and explains the good performances of these polymer membranes during the extraction of paracetamol.
Several models have been used to elucidate the mechanisms of extraction of organic and metal ions. Theories derived from these models are important for interpreting the results obtained for the current systems. These can help in designing more efficient and selective systems. Indeed, the literature reports several studies on the application of extraction procedures of various compounds that have been used as anti-inflammatories and analgesics and are found in wastewater. T. Razo-Lazcano et al. [56][57][58] examined the structure and the effect of pharmaceuticals on different types of extraction processes.
The reviews and papers published by Hlaibi et al. [59,60] have indicated that the interaction between the substrate and the extractive agent assists the migration of organic compounds through a membrane. The formation of a "substrate-extractive agent," the stabilities of which depend on the structure of the compounds and the nature of interaction sites, was observed. On the other hand, a jumping mechanism [61,62], in which the substrate moves while binding successively to several fixed carriers (considered as a complexation site), similar to the case of an ion-exchange membrane, was studied. Reversible association-dissociation reactions leading to the formation and decomposition of an unstable "host-guest" complex were carried out. The jumping mechanism, frequently seen for cases when PIM is used [63,64], is characterized by a percolation threshold, which corresponds to the minimal concentration of the carrier required to produce a measurable flux.
The existence of a percolation threshold is highlighted when the influence of the concentration of the carrier on the permeability of the membrane is studied.

Activation and thermodynamic parameters for the extraction studied processes
To confirm the results, to elucidate the energetic or kinetic aspect that controls the mechanism of the studied processes, and to explain the performances of the fabricated membranes, it is necessary to determine the values of the activation and thermodynamic parameters (E a , ΔH ≠ ass , ΔS ≠ , ΔH ≠ diss , and ΔH th ) corresponding to the transition state of the substrate diffusion step across each organic membrane phase. For this, we have studied Arrhenius and Van't Hoff relationships (Eqs. 8 and 10) for the extraction-oriented processes. The J 0 and K ass values were determined, and the straight line segments were plotted (Figure 8). The slopes and intercepts calculated from these straight line segments were used to determine the values of the activation parameters E a and A j . The thermodynamic parameter ΔH th was also studied. The activation enthalpies ΔH ≠ ass and ΔH ≠ dis and the activation entropy ΔS ≠ were calculated following equations 9 and 11. Table 4 presents the values of all the activation and thermodynamic parameters. Analysis of the activation parameters indicates that the transition state corresponding to the diffusion step requires little energy (E a and ΔH ♯ ). On the other hand, the negative activation entropy (ΔS ♯ ) indicates a late transition state, and the transition state depends on the structures of the substrate and extractive agent. It also depends on the orientation of their interaction sites. The evolution of these parameters is described by the table 4. The results indicate that a favorable orientation of the interaction sites is required to achieve a good association between the paracetamol molecules and GA in the transition state with the bidentate sites (ΔS ♯ = -300 J.mol -1 .K -1 ) (Additional file 1: Figure S5 and Figure S6). On the other hand, the low values of the important parameters (ΔH ≠ ass and ΔH ≠ dis ) reveal the kinetic control aspect of the mechanisms of the oriented processes leading to good membrane performances even at low temperatures. This kinetic control aspect for the diffusion of paracetamol molecules through affinity polymer membranes can be ascribed to the structure of the molecules and the pharmacological and biological activities of these molecules that diffuse through cell membranes at a constant temperature.

Conclusion
The results described in this work are very interesting and can help elucidate and understand the different parameters and steps necessary for the realization of membrane oriented processes performed for extracting paracetamol (through two types of affinity polymer membranes). Indeed, two types of polymer membranes (PIM and GPM) were developed following the heat vulcanization and phase inversion methods using the same extractive agent (GA). Different techniques have been used to characterize the composition, morphology, and porosity of the developed membranes and the concentration of the extractive agent included and immobilized in the membrane phases. Detailed studies have been carried out with these two membranes to determine the optimal experimental and technical conditions required for the oriented processes employed for extracting high-value paracetamol. Several kinetic, thermodynamic, and activation parameters were determined under different experimental conditions. The evolution of all these parameters with C 0 of paracetamol, acidity (pH), and temperature (T) of the aqueous phases was studied, and the membrane performance was quantified. The mechanisms of the oriented processes were also determined.
Finally, original ideas regarding the kinetic and energetic control aspects that help elucidate the mechanism of the oriented processes (through affinity polymer membranes) have been presented in this work. The kinetic control affected the mechanism of extraction of this biologically active compound (paracetamol) through the two developed membranes. Good membrane performance was observed even at low temperatures. In fact, the paracetamol molecules can potentially diffuse through the cell walls having well-adapted structures at a constant temperature. Consequently, the kinetic control of the extraction processes of paracetamol is an original idea, and the studies produced logical results. It can be correlated to the molecular structures of paracetamol and the extractive agent. The effect of temperature on the diffusion of paracetamol molecules through the membrane phases was not significant. Figure S1. Structure of gluconic acid. Figure S2. 1-hydroxy-4-acetaminobenzene (paracetamol). Figure S3. Representation of the facilitated extraction cell. Figure S4. Mechanism of successive jumps on fixed sites during the facilitated extraction process followed for extracting paracetamol through the PIM-GA membrane Figure S5. Possible interaction sites between paracetamol and gluconic acid. Figure S6. Interaction sites between paracetamol and gluconic acid (Chemdrew).

Authors´ contributions
ST did most of the experiment and wrote the manuscript. RL and El-H did the preparation and characterization of the membrane. MH helped in editing the English language beside adding some paragraphs to the text. All authors read and approved the final manuscript.