# Process of Facilitated Extraction of Vanadium Ions through Supported Liquid Membranes: Parameters and Mechanism

Authors: O. Kamal; T. Eljaddi; El H. El Atmani; I. Touarssi; I. Mourtah; L. Lebrun; M. Hlaïbi
Journal: Advances in Materials Science and Engineering
 (2017)

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## Abstract

To conduct experiments related to the facilitated extraction phenomenon of vanadium ions (VO2+), three supported liquid membranes (SLMs) were prepared, each containing 0.01 M of methyl cholate (MC), resorcinarene (RESO), or trioctylamine (TOA) as extractive agents. Kinetic and thermodynamic models were developed, based on the interaction of the substrate (VO2+) with the extractive agentT and the diffusion of the formed entity (TS) through the membrane. The experimental results verify the models, and to determine, macroscopic parameters, permeabilities (P) and initial fluxes (J0), and microscopic parameters, association constants (Kass) and apparent diffusion coefficients (D⁎) related to formed entities (TS) and their diffusion through the membrane organic phase. The experimental results indicate that the mechanism on the migration of the VO2+ ions through the membrane organic phase is based on the successive jumps of substrate, from one site to another of the extractive agent. To explain these results and understand the mechanism, we studied influence of temperature factor, and we determined activation parameters (Ea, ΔH≠, and ΔS≠). The results show that this extraction phenomenon is governed by a structural term. Therefore, the membrane performance changes according to nature and structure of the association site presented by each of extractive agents.


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## Body

## 1. Introduction

Conventional industrial techniques of extraction and separation by distillation or crystallization have a high cost, since they require large amounts of energy and use polluting organic solvents. The technique of liquid-liquid extraction is cheaper, but it requires large amounts of volatile organic solvents, often considered pollutants to the environment, which limits its use. Membrane processes for separation and recovery are more economical because they can operate at standard temperature and pressure and with very small amounts of organic solvents [1, 2].The supported liquid membranes (SLMs) are part of these membrane processes types; they have a major economic and environmental interest, since they are necessary for the treatment of liquid mediums, contaminated with metal ions or organic compounds. These membrane types (SLMs) are prepared from inert polymer support; in fact, an organic solution containing a hydrophobic extractive agent is incorporated usually by immersion of this polymeric support. Polypropylene remains a widely used polymer support, for its high porosity, which generates large fluxes of metal ions through these membrane types. The supported liquid membrane processes have several advantages compared to the liquid-liquid extraction phenomenon. In particular, a very low uses of organic solvents, which today an important criterion for the protection of the environment and the treatment of toxic effluents. These processes permit continuous operation in a single step, since the two steps extraction and reextraction are so coupled to the two interfaces. Indeed, the membranes are thin films that separate two fluids; an essential property of membranes is their permeability and therefore their ability to allow the passage of only certain species from one environment to another, while acting as a barrier to other species.Studies based on the use of supported liquid membranes for removing some toxic metal ions from concentrated acid solutions are very numerous; the interest in this study was focused on the phenomenon of facilitated transport and extraction ofVO2+ ions. Indeed, vanadium is often present as an impurity during the process of manufacturing industrial phosphoric acid by the wet process, in which sulfuric acid is used to dissolve the phosphate ores. The obtained liquor is a complex solution composed of organic and inorganic impurities. Among these impurities, vanadium ions in high concentrations around 600 mg L−1, this is a potential source of vanadium element [3].In the present work, we try to use the SLMs technique for the facilitated extraction of vanadium ions (VO2+) from acid environments. This technique is based on work carried out by the principle of substrate transport by membrane processes, such as facilitated transport through liquid membranes. The used supported liquid membranes consist of a microporous inert polymeric support polyvinylidene difluoride (PVDF), a thickness of 100 μm, and a porosity of 60% with pores of 0.45 μm in diameter. For each of the prepared membranes, this support will be impregnated with organic solution toluene in 0.01 M concentration for each following carrier agents: methyl cholate (MC), resorcinarene (RESO), or trioctylamine (TOA). Kinetic and mechanistic models have been developed and tested to the facilitated extraction phenomenon of VO2+ ions from acid solutions. The macroscopic parameters, permeabilities P, and initial fluxes J0 were determined and related to the microscopic parameters, the apparent diffusion coefficient D∗ and the association constant Kass characteristics of the formation of entity “Extractive agent-Substrate” (TS) and its diffusion across organic phase [4–7]. For a better understanding of this phenomenon, the explanation of the results and the identification of the mechanism for this process, we studied the temperature factor influence on the evolution of the parameters P,J0,D∗, and Kass, as well as the performance of adopted SLMs. Similarly, we determined the activation parameters, energy Ea, enthalpy ΔH≠, and entropy ΔS≠, in order to know the factor that governs the movement of VO2+ ions during their passage through the membrane organic phase.


## 2. Material and Methods

### 2.1. Description and Operating Principle of a SLM

The SLMs consist of an organic solvent immobilized by capillary forces in the pores of a polymeric support, separating the source and the receiving phases. The support of these membranes is generally an hydrophobic inert polymer which is characterized by a small thickness of 25 to 100μm and pore diameters of 0.12 to 1 μm [3, 4]. The diffusion of chemical species through these membranes is an interfacial phenomenon; the use of a support having a high porosity is necessary to increase the contact area and the selectivity to the diffusion of species and very important to operate in the best conditions of extraction and separation through the SLMs [4]. To improve the separation process, the researchers added to the organic phases of SLMs mobile extractive agents, which accelerate and facilitate the extraction of species, while increasing the selectivity of these membrane types [8–11]. In addition, the technical SLM approach is widely used for the extraction and enrichment of metal ions and some organic compounds [12–14]. Indeed, this technique has been used to study the facilitated transport and apply it to the selective extraction and enrichment of varied organic compounds, such as amino acids [15, 16], amino-aromatic phosphates [17], sugars [18–20], herbicides [21, 22], and organic acids [23, 24].This method, which is called facilitated transport or extraction through supported liquid membranes, is based on the recognition of a substrate (S) by a extractive agent molecule (T). This process involves the mobility within the membrane organic phase of a complex (ST) produced by a reversible forming reaction, between the agent (T) and the transported substrate (S), which takes place at membrane interfaces with the source and receiving phases. This facilitated extraction phenomenon through the SLMs is a cyclical process which is based on the five following successive steps:(1)
Diffusion of the substrate (S) in the feed phase to the membrane interface(2)
Formation of substrate-carrier complex (ST) at the interface source phase membrane(3)
Diffusion of entity (ST) through the membrane organic phase to the interface membrane-receiving phase(4)
Dissociation of entity (ST) at the interface membrane receiving phase(5)
Diffusion of free substrate (S) in the receiving phase and the extractive agent (T) in the membrane organic phase to perform a new cycle(interaction-diffusion-dissociation)These five steps are represented by the diagram in Figure 1 and constitute the mechanism of facilitated extraction through a SLM, in which step (3) is the rate-determining step.Figure 1
Facilitated transport and extraction mechanism through a SLM.


### 2.2. Cell for the Facilitated Extraction

Experiments on the transport of these ions were performed in the cell represented by the scheme in Figure2. This cell consists of two glass compartments of equal volumes (175 mL), separated by the microporous membrane (M). The cell is immersed in a water bath (TB), and a multiagitator allows continuous stirring solutions in both compartments.Figure 2
Scheme on the transport cell: M: SLM, F: feed source, R: receiving phase. TB: thermostated bath, and MS: multimagnetic stirrer.


### 2.3. Experimental Section

All chemicals, reagents, and solvents were pure commercial products (Aldrich, Fluka) of analytical grade. The used solutions of vanadium ionsVO2+ are obtained by acid hydrolysis of ammonium metavanadate NH4VO3. The support is a microporous polymeric film of polyvinylidene difluoride (PVDF), a thickness of 100 μm, a porosity of 60%, and a pore diameter of 0.45 μm. Liquid solutions adopted for the SLM preparation consist of toluene organic phase containing 0.01 M of one of the following extractive agents: MC, RESO, or TOA (Figures 3, 4, and 5). The three used membranes were prepared by impregnation for a 5-to-6-hour period, each of three polymer supports by one of the previous organic phases. Acidic solutions (0.10 to 0.0125 M) of VO2+ ions are prepared in pure distilled water from stock solutions. Before being used, each of the prepared MLSs was treated in a conditioning step by pure water for 20 hours [6, 19], to remove a long induction period preceding the facilitated extraction process of a substrate by a SLM. Each used SLM was placed for a period of about 20 hours between the two compartments of the used cell for this facilitated transport process (Figure 2), filled with bidistilled pure water solution.Figure 3
Methyl cholate structure (MC).Figure 4
Resorcinarene structure (RESO).Figure 5
Tri-n-octylamine structure (TOA).For experiments relating to the facilitated extraction ofVO2+ ions, the feed phase is a fixed acidity solution of nitric acid containing a known concentration of VO2+ ions, and the receiving phase is a hydrochloric acid solution to same acidity. The two compartment solutions are maintained at the same agitation and kinetic study on the evolution of the VO2+ ions concentration Cr is done by regular sampling from the receiving phase at known time intervals. These samples were analyzed by UV-visible spectroscopy, and Cr concentration values in the receiving phase were calculated at the different time intervals as well as the term.ln
⁡
(
C
0
-
2
C
r
) versus time. Table 1 includes an example of results for facilitated extraction of VO2+ ions from a concentrated acid medium.Table 1
Results for the facilitated extraction phenomenon ofVO2+ ions by SLM containing resorcinarene extractive agent.
t (mn)
Absorbance
C
r (mol L−1)
-
ln
⁡
(
C
0
-
2
C
r
)
0
0.978
0
2.303
30
0.039
0.00398
2.386
60
0.052
0.00531
2.415
90
0.085
0.00869
2.494
120
0.114
0.01165
2.568
C
0 = [VO2+]0 = 0.1 M, [H3O+] = 1 M, [RESO] = 0.01 M, and T = 293 K.


## 2.1. Description and Operating Principle of a SLM

The SLMs consist of an organic solvent immobilized by capillary forces in the pores of a polymeric support, separating the source and the receiving phases. The support of these membranes is generally an hydrophobic inert polymer which is characterized by a small thickness of 25 to 100μm and pore diameters of 0.12 to 1 μm [3, 4]. The diffusion of chemical species through these membranes is an interfacial phenomenon; the use of a support having a high porosity is necessary to increase the contact area and the selectivity to the diffusion of species and very important to operate in the best conditions of extraction and separation through the SLMs [4]. To improve the separation process, the researchers added to the organic phases of SLMs mobile extractive agents, which accelerate and facilitate the extraction of species, while increasing the selectivity of these membrane types [8–11]. In addition, the technical SLM approach is widely used for the extraction and enrichment of metal ions and some organic compounds [12–14]. Indeed, this technique has been used to study the facilitated transport and apply it to the selective extraction and enrichment of varied organic compounds, such as amino acids [15, 16], amino-aromatic phosphates [17], sugars [18–20], herbicides [21, 22], and organic acids [23, 24].This method, which is called facilitated transport or extraction through supported liquid membranes, is based on the recognition of a substrate (S) by a extractive agent molecule (T). This process involves the mobility within the membrane organic phase of a complex (ST) produced by a reversible forming reaction, between the agent (T) and the transported substrate (S), which takes place at membrane interfaces with the source and receiving phases. This facilitated extraction phenomenon through the SLMs is a cyclical process which is based on the five following successive steps:(1)
Diffusion of the substrate (S) in the feed phase to the membrane interface(2)
Formation of substrate-carrier complex (ST) at the interface source phase membrane(3)
Diffusion of entity (ST) through the membrane organic phase to the interface membrane-receiving phase(4)
Dissociation of entity (ST) at the interface membrane receiving phase(5)
Diffusion of free substrate (S) in the receiving phase and the extractive agent (T) in the membrane organic phase to perform a new cycle(interaction-diffusion-dissociation)These five steps are represented by the diagram in Figure 1 and constitute the mechanism of facilitated extraction through a SLM, in which step (3) is the rate-determining step.Figure 1
Facilitated transport and extraction mechanism through a SLM.


## 2.2. Cell for the Facilitated Extraction

Experiments on the transport of these ions were performed in the cell represented by the scheme in Figure2. This cell consists of two glass compartments of equal volumes (175 mL), separated by the microporous membrane (M). The cell is immersed in a water bath (TB), and a multiagitator allows continuous stirring solutions in both compartments.Figure 2
Scheme on the transport cell: M: SLM, F: feed source, R: receiving phase. TB: thermostated bath, and MS: multimagnetic stirrer.


## 2.3. Experimental Section

All chemicals, reagents, and solvents were pure commercial products (Aldrich, Fluka) of analytical grade. The used solutions of vanadium ionsVO2+ are obtained by acid hydrolysis of ammonium metavanadate NH4VO3. The support is a microporous polymeric film of polyvinylidene difluoride (PVDF), a thickness of 100 μm, a porosity of 60%, and a pore diameter of 0.45 μm. Liquid solutions adopted for the SLM preparation consist of toluene organic phase containing 0.01 M of one of the following extractive agents: MC, RESO, or TOA (Figures 3, 4, and 5). The three used membranes were prepared by impregnation for a 5-to-6-hour period, each of three polymer supports by one of the previous organic phases. Acidic solutions (0.10 to 0.0125 M) of VO2+ ions are prepared in pure distilled water from stock solutions. Before being used, each of the prepared MLSs was treated in a conditioning step by pure water for 20 hours [6, 19], to remove a long induction period preceding the facilitated extraction process of a substrate by a SLM. Each used SLM was placed for a period of about 20 hours between the two compartments of the used cell for this facilitated transport process (Figure 2), filled with bidistilled pure water solution.Figure 3
Methyl cholate structure (MC).Figure 4
Resorcinarene structure (RESO).Figure 5
Tri-n-octylamine structure (TOA).For experiments relating to the facilitated extraction ofVO2+ ions, the feed phase is a fixed acidity solution of nitric acid containing a known concentration of VO2+ ions, and the receiving phase is a hydrochloric acid solution to same acidity. The two compartment solutions are maintained at the same agitation and kinetic study on the evolution of the VO2+ ions concentration Cr is done by regular sampling from the receiving phase at known time intervals. These samples were analyzed by UV-visible spectroscopy, and Cr concentration values in the receiving phase were calculated at the different time intervals as well as the term.ln
⁡
(
C
0
-
2
C
r
) versus time. Table 1 includes an example of results for facilitated extraction of VO2+ ions from a concentrated acid medium.Table 1
Results for the facilitated extraction phenomenon ofVO2+ ions by SLM containing resorcinarene extractive agent.
t (mn)
Absorbance
C
r (mol L−1)
-
ln
⁡
(
C
0
-
2
C
r
)
0
0.978
0
2.303
30
0.039
0.00398
2.386
60
0.052
0.00531
2.415
90
0.085
0.00869
2.494
120
0.114
0.01165
2.568
C
0 = [VO2+]0 = 0.1 M, [H3O+] = 1 M, [RESO] = 0.01 M, and T = 293 K.


## 3. Theoretical Models and Calculations

### 3.1. Kinetic Model and Calculation of Permeability (P) and Initial Flux (J0)

The membrane is placed between the two compartments; in source compartment, a known volume of the substrate solution (S) with C0 concentration, is introduced, and the same volume of water is placed in the receiving compartment. We carry several samples from the receiving phase at known time intervals, we note Cr substrate concentration in this phase at time t, and the substrate concentration in the source phase at this time is Cs=C0-Cr (used support is very thin).The equation that relates the fluxJ to the Cr concentration of the substrate S is given by the relationship:(1)dCrdt=J∗SV,where S is membrane area in contact with the aqueous solutions and V is the receiving phase volume.For a quasi-static state, the flux is related to the difference in concentrations of the two compartments ΔC = Cs-Cr, by Fick’s first law:(2)J=P∗ΔCl,where P is membrane permeability and l is the membrane thicknessKnowing that the membrane is very thin, thenCs=C0-Cr and (3)ΔC=Cs-Cr=C0-2Cr.Combining (1), (2), and (3), we have(4)Pdt=l∗V/SdCrC0-2Cr.After integration,(5)Pt-tL=l∗V2Sln⁡C0C0-2Cr.This equation shows that, after an induction period (tL), which can reach several hours, the term -ln⁡(C0-2Cr) should be a linear function of time t.The slope (a) of this line allows calculating the permeability, using(6)P=a×Vl2S.The initial flux J0 can be calculated from the permeability P according to the following:(7)J0=P×C0l.The experience end is achieved when a dynamic equilibrium is established between the two compartments, with Cs = Cr = C0/2 and diffusion rates being equal in both directions.


### 3.2. Thermodynamic Model and Determination of Microscopic Parameters

Transport of a substrateS depends on the formation and dissociation of the complex carrier-substrate (TS) at solution-membrane interfaces. It should be noted that the carrier T is insoluble in aqueous phases and the substrate S is insoluble in the membrane organic phase. The formation-dissociation equilibrium of the complex (TS) is(8)Torg+Saq⟺TSorg, where org and aq are, respectively, the membrane organic phase and the aqueous source and receiving phases. Concentration TSi of complex at the membrane interface is governed by the law of mass action according to the following:(9)TSi=KassTiSi,where Kass is the association constant on the complex (TS) and is the equilibrium constant of this heterogeneous reaction at the interface feed phase-membrane; Ti is the carrier concentration at the interface membrane-feed phase; and Si is the substrate concentration in the source phase at the membrane interface.In the rate-determining step, the fluxJ is determined by (10), derived from Fick’s first law, which assumes that the complex concentration [ST] is almost zero at the interface membrane-receiving phase (dissociation of the complex):(10)J=D∗l×TSi.where D∗ is the apparent diffusion coefficient and l is the membrane thickness.However, at the interface source phase-membrane,TSi≪Si (excess of substrate relative to the carrier) and the concentration Si is equal to the substrate concentration St at time t and thus Si=St. The total carrier concentration T0 immobilized in the membrane is constant, and it is equal to the sum of the concentrations Ti and TSi.(11)T0=Ti+TSi=TSi·1+Kass·SiKass·Si,(12)TSi=T0·Kass·Si1+Kass·Si.But, in the initial conditions, we operate with an excess of substrate relative to the carrier and at the interface feed phase-membrane, Si=S0=C0. This allows to write the expression for the initial flux J0 according to T0 and C0 ((10) and (12)):(13)J=D∗l×T0·Kass·Si1+Kass·Si.or(14)J0=D∗l×T0·Kass·C01+Kass·C0This expression is used to calculate the membrane permeability P according to T0, C0, and constant Kass:(15)P=J0·lC0=D∗×T0·Kass1+Kass·C0.These relationships indicate that the evolution of macroscopic parameters J0 and P is proportional to the initial substrate concentration C0 and it is of Michaelis-Menten type, since, at high substrate concentrations, these two parameters are the limit values by saturation phenomenon of the carrier.To determine the microscopic parametersD∗ and Kass, we linearized the expression in (16) as Lineweaver-Burk straights 1/J0=f(1/C0).(16)1J0=lD∗×1T0·Kass·1C0+1T0and therefore (17)Kass=interceptOOslopep,D∗=lOO·1T0.


### 3.3. Determination of Activation Parameters

Studies relating to the facilitated extraction process of ions across membranes [25, 26] indicate that the initial flux is related to temperature factor by Arrhenius law, according to the following relationship:(18)JiT=Ajexp⁡-EaRT,whereR is the gas constant (8.314 J·mol−1·K−1), Aj is a constant (preexponential factor), and Ea is the transition state activation energy on the formation-dissociation reaction of entity (TS) at the membrane interfaces and in the SLM organic phase, during the migration of the substrate through the membrane, which is the rate-determining step relative to the apparent diffusion of the complex (TS). After linearization, we get(19)ln⁡Ji=-EaR×1T+ln⁡Aj.Thus the terms of activation energy (Ea) and preexponential factor (Aj) are determined from the slope and intercept for the linear function ln⁡(Ji) versus (1/T). According to the activated complex theory (Eyring theory), we can calculate the activation parameters, enthalpy ΔH≠, and entropy ΔS≠, according to the expressions in(20)ΔH≠=Ea-2500J·mol-1,ΔS≠=Rln⁡Aj-30,46J·K-1·mol-1at298K°.


## 3.1. Kinetic Model and Calculation of Permeability (P) and Initial Flux (J0)

The membrane is placed between the two compartments; in source compartment, a known volume of the substrate solution (S) with C0 concentration, is introduced, and the same volume of water is placed in the receiving compartment. We carry several samples from the receiving phase at known time intervals, we note Cr substrate concentration in this phase at time t, and the substrate concentration in the source phase at this time is Cs=C0-Cr (used support is very thin).The equation that relates the fluxJ to the Cr concentration of the substrate S is given by the relationship:(1)dCrdt=J∗SV,where S is membrane area in contact with the aqueous solutions and V is the receiving phase volume.For a quasi-static state, the flux is related to the difference in concentrations of the two compartments ΔC = Cs-Cr, by Fick’s first law:(2)J=P∗ΔCl,where P is membrane permeability and l is the membrane thicknessKnowing that the membrane is very thin, thenCs=C0-Cr and (3)ΔC=Cs-Cr=C0-2Cr.Combining (1), (2), and (3), we have(4)Pdt=l∗V/SdCrC0-2Cr.After integration,(5)Pt-tL=l∗V2Sln⁡C0C0-2Cr.This equation shows that, after an induction period (tL), which can reach several hours, the term -ln⁡(C0-2Cr) should be a linear function of time t.The slope (a) of this line allows calculating the permeability, using(6)P=a×Vl2S.The initial flux J0 can be calculated from the permeability P according to the following:(7)J0=P×C0l.The experience end is achieved when a dynamic equilibrium is established between the two compartments, with Cs = Cr = C0/2 and diffusion rates being equal in both directions.


## 3.2. Thermodynamic Model and Determination of Microscopic Parameters

Transport of a substrateS depends on the formation and dissociation of the complex carrier-substrate (TS) at solution-membrane interfaces. It should be noted that the carrier T is insoluble in aqueous phases and the substrate S is insoluble in the membrane organic phase. The formation-dissociation equilibrium of the complex (TS) is(8)Torg+Saq⟺TSorg, where org and aq are, respectively, the membrane organic phase and the aqueous source and receiving phases. Concentration TSi of complex at the membrane interface is governed by the law of mass action according to the following:(9)TSi=KassTiSi,where Kass is the association constant on the complex (TS) and is the equilibrium constant of this heterogeneous reaction at the interface feed phase-membrane; Ti is the carrier concentration at the interface membrane-feed phase; and Si is the substrate concentration in the source phase at the membrane interface.In the rate-determining step, the fluxJ is determined by (10), derived from Fick’s first law, which assumes that the complex concentration [ST] is almost zero at the interface membrane-receiving phase (dissociation of the complex):(10)J=D∗l×TSi.where D∗ is the apparent diffusion coefficient and l is the membrane thickness.However, at the interface source phase-membrane,TSi≪Si (excess of substrate relative to the carrier) and the concentration Si is equal to the substrate concentration St at time t and thus Si=St. The total carrier concentration T0 immobilized in the membrane is constant, and it is equal to the sum of the concentrations Ti and TSi.(11)T0=Ti+TSi=TSi·1+Kass·SiKass·Si,(12)TSi=T0·Kass·Si1+Kass·Si.But, in the initial conditions, we operate with an excess of substrate relative to the carrier and at the interface feed phase-membrane, Si=S0=C0. This allows to write the expression for the initial flux J0 according to T0 and C0 ((10) and (12)):(13)J=D∗l×T0·Kass·Si1+Kass·Si.or(14)J0=D∗l×T0·Kass·C01+Kass·C0This expression is used to calculate the membrane permeability P according to T0, C0, and constant Kass:(15)P=J0·lC0=D∗×T0·Kass1+Kass·C0.These relationships indicate that the evolution of macroscopic parameters J0 and P is proportional to the initial substrate concentration C0 and it is of Michaelis-Menten type, since, at high substrate concentrations, these two parameters are the limit values by saturation phenomenon of the carrier.To determine the microscopic parametersD∗ and Kass, we linearized the expression in (16) as Lineweaver-Burk straights 1/J0=f(1/C0).(16)1J0=lD∗×1T0·Kass·1C0+1T0and therefore (17)Kass=interceptOOslopep,D∗=lOO·1T0.


## 3.3. Determination of Activation Parameters

Studies relating to the facilitated extraction process of ions across membranes [25, 26] indicate that the initial flux is related to temperature factor by Arrhenius law, according to the following relationship:(18)JiT=Ajexp⁡-EaRT,whereR is the gas constant (8.314 J·mol−1·K−1), Aj is a constant (preexponential factor), and Ea is the transition state activation energy on the formation-dissociation reaction of entity (TS) at the membrane interfaces and in the SLM organic phase, during the migration of the substrate through the membrane, which is the rate-determining step relative to the apparent diffusion of the complex (TS). After linearization, we get(19)ln⁡Ji=-EaR×1T+ln⁡Aj.Thus the terms of activation energy (Ea) and preexponential factor (Aj) are determined from the slope and intercept for the linear function ln⁡(Ji) versus (1/T). According to the activated complex theory (Eyring theory), we can calculate the activation parameters, enthalpy ΔH≠, and entropy ΔS≠, according to the expressions in(20)ΔH≠=Ea-2500J·mol-1,ΔS≠=Rln⁡Aj-30,46J·K-1·mol-1at298K°.


## 4. Results and Discussion

### 4.1. Macroscopic ParametersP and J0

In the same experimental conditions, using each of the three prepared membranes (MLSs) with one of the agents MC, RESO, or TOA in the same concentration (T0 = 0.01 M) facilitated extraction of VO2+ ions that was carried out for different initial concentrations C0 (0.0125–0.100 M) at the same temperature 293 K. Proposed kinetic model for this phenomenon in which the diffusion of the complex carrier-substrate (TS) is considered the rate-determining step indicates that the evolution of the term -ln⁡(C0-2Cr) must be linear in function of time (see (5)). Indeed, the experimental results verify the model and allow obtaining the straight line segments shown by graphs of Figures 6 and 7.Figure 6
Evolution of the term −ln⁡(C0-2Cr) versus time for facilitated extraction of VO2+ ions by SLM containing extractive agent RESO. [H3O+] = 1 M, [RESO] = 10−2M, andT = 293 K.Figure 7
Evolution of the term −ln⁡(C0-2Cr) versus time for facilitated extraction of VO2+ ions by SLM containing extractive agent TOA. [H3O+] = 1 M, [TOA] = 10−2M, andT = 293 K.The slopes calculated from these lines are used to determine the permeability values (P) of the used membranes with respect to VO2+ ions for different tested solutions (see (6)), while the initial flux values (J0) of the substrate through the used SLMs are calculated using (7). Table 2 summarizes all results for the three membranes at temperature 293 K.Table 2
The values of macroscopic parameters (P and J0) on the facilitated extraction of VO2+ ions by the three developed SLMs.
C
0 concentration (mol L−1)
PermeabilityP (107 cm2 s−1)
Initial FluxJ0 (105 mmol s−1 cm−2)
RESO
MC
TOA
RESO
MC
TOA
0.1
13.37
17.28
23.56
1.33
1.72
2.35
0.05
14.64
18.22
24.84
0.73
0.91
1.24
0.025
15.92
20.27
26.11
0.39
0.50
0.65
0.0125
17.19
21.29
27.38
0.21
0.26
0.34
[RESO] = [MC] = [TOA] = 10−2 M [H3O+] = 1 M, and T = 293 K.All these experimental results indicate that the permeabilityP of the used SLM varies inversely with the initial concentration C0 of VO2+ ions, and an increase in substrate concentration results in a decrease in permeability. However, the initial flux values J0 of these ions through each of studied SLMs increase as the initial concentration C0 of the substrate [27–29]. On the other hand, we observe that the values of permeabilities P and initial fluxes J0 relative facilitated extraction of VO2+ ions, using both SLMs containing, respectively, methyl cholate (MC) and resorcinarene (RESO) as extractive agents are slightly near, while the use of the SLM containing trioctylamine (TOA) as extractive agent provides relatively high values for these two parameters P and J0, in the same experimental conditions and the same temperature.


### 4.2. Microscopic ParametersD∗ and Kass

To verify the proposed mechanism for this facilitated extraction phenomenon of theVO2+ ions by prepared SLMs and determine themicroscopic parameters, apparent coefficients D∗, and association constants Kass, we traced the Lineweaver-Burk lines (1/J0=f(1/C0)) provided by (16), from the experimental results for the three used SLMs. The obtained line segments are shown by the graph in Figure 8.Figure 8
The Lineweaver-Burk representation1/J0=f(1/C0) for facilitated extraction of VO2+ ions by adopted SLMs. [RESO] = [MC] = [TOA] = 10−2M, [H3O+] = 1 M, and T = 293 K.The obtained straight lines clearly indicate that the proposed mechanism for this phenomenon is verified, and there is formation entity (ST) of composition (1/1), by association “substrate-extractive agent” in the organic phase of used SLM. The migration of this entity through this phase is the rate-determining step of the mechanism for the facilitated extraction of VO2+ ions. Slopes (p) and intercepts (OO) were calculated from these lines and using the expressions in (16); the apparent coefficients D∗ and the association constants Kass were determined. The obtained results for the used membranes are summarized in Table 3 and the histogram in Figure 9 shows that these twomicroscopic parameters vary inversely. This result indicates that a high stability of entity (ST) formed in the SLM organic phase results in a low diffusion of this entity and conversely.Table 3
Values of microscopic parameters (D∗ and Kass) for facilitated extraction of VO2+ ions.
Extractive agent
RESO
MC
TOA
D
∗ 105 (cm2⋅s−1)
4.19
6.15
11.50
K
a
s
s (L⋅ mol−1)
4.29
3.60
2.48
[RESO] = [MC] = [TOA] = 10−2 M, [H3O+] = 1 M, and T = 293 K.Figure 9
Microscopic parameters evolution for facilitated extraction phenomenon ofVO2+ ions.The values of permeabilityP, initial flux J0, (Table 2), association constant Kass, and apparent diffusion coefficient D∗ (Table 3), relating to this facilitated extraction phenomenon of VO2+ ions, clearly show that, for the same concentration of the extractive agent (0.01 M) and at the same temperature (293 K), the facilitated extraction of the substrate (VO2+) is more efficient through SLM containing trioctylamine (TOA) as extractive agent, compared with two other investigated membranes, containing, respectively, methyl cholate (MC) and resorcinarene (RESO). These results clearly show that the value of association constant Kass depends on the nature of association site carried by each of the extractive agents, as well as the reverse evolution of Kass and D∗ parameters, indicates that the movement of VO2+ ions in the membrane organic phase cannot be a pure diffusion movement, but it takes place by successive jumps of the substrate (VO2+) from one site to another of the extractive agent in successive and reversible reactions (association/dissociation).


### 4.3. Influence of the Temperature Factor

Under the same experimental conditions and using membranes, respectively. MLS-RESO, SLM-MC, and SLM-TOA, we performed experiments to the facilitated extraction ofVO2+ ions in solutions of C0 concentrations ranging from 0.0125 to 0.1 M and at temperatures 293, 298, and 303°K. Graphs in Figures 10 and 11 represent the straight lines relating to the evolution of the term -ln⁡(C0-2Cr) with time provided by kinetic model, for different studied temperatures, at C0 = 0.10 M, and for adopted membranes SLM-TOA and SLM-RESO.Figure 10
-
ln
⁡
(
C
0
-
2
C
r
) term evolution versus temperature for the facilitated extraction of VO2+ ions through membrane SLM-TOA. [H3O+] = 1 M, [TOA] = 10−2M, [VO2+] = 0.1 M.Figure 11
Temperature effect on-ln⁡(C0-2Cr) term evolution versus time, for the facilitated extraction of VO2+ ions by membrane SLM-RESO. [H3O+] = 1 M, [RESO] = 10−2M [VO2+] = 0.1 M.The slopes calculated from obtained lines for the different experiments were used to calculate according to the expressions in (6) and (7), the values of permeabilities P, and initial fluxes J0, relative to this facilitated extraction phenomenon of VO2+ ions through the adopted membranes. For the different studied temperatures, all obtained results are summarized in Table 4.Table 4
Temperature factor influence on the evolution of macroscopic parametersP and J0.
Extractive agent
C
0 mol L−1
P
⋅
107 cm2 s−1
J
0
⋅
105 mmol s−1 cm−2
293 K
298 K
303 K
293 K
298 K
303 K
RESO
0.1
13.37
15.92
20.38
1.33
1.59
2.03
0.05
14.64
17.19
21.65
0.73
0.85
1.08
0.025
15.92
18.47
22.92
0.39
0.46
0.57
0.0125
17.19
19.74
24.20
0.21
0.24
0.30
288 K
293 K
303 K
288 K
293 K
303 K
MC
0.1
14.43
17.28
24.71
1.44
1.72
2.47
0.05
16.47
18.22
25.95
0.82
0.91
1.29
0.025
17.57
20.27
28.43
0.43
0.50
0.71
0.0125
18.66
21.29
29.89
0.23
0.26
0.37
293 K
298 K
303 K
293 K
298 K
303 K
TOA
0.1
23.56
26.75
29.30
2.35
2.67
2.92
0.05
24.84
28.02
30.57
1.24
1.40
1.52
0.025
26.11
28.62
31.84
0.65
0.71
0.79
0.0125
27.38
30.57
33.12
0.34
0.38
0.41
[RESO] = [MC] = [TOA] = 10−2 M.These results confirm that the permeabilityP and the initial flux J0 parameters vary inversely and with the initial concentration C0 of VO2+ ions [18, 19]. They indicate clear influence of temperature factor on the values of these parameters and therefore an increase in the membrane performances, with an excellent performance of SLM-TOA membrane relative to other adopted SLMs.To confirm the previous results and to study temperature factor influence on the evolution of microscopic parametersD∗ and Kass, we traced the Lineweaver-Burk lines, 1/J0 = f(1/C0), and the obtained line segments are represented by the graphs in Figures 12 and 13, for two adopted membranes SLM-RESO and SLM-MC.Figure 12
Lineweaver-Burk lines for the facilitated extraction ofVO2+ ions by SLM-RESO membrane, for different values of temperature. [H3O+] = 1 M, [RESO] = 10−2M.Figure 13
Lineweaver-Burk straight lines relating to the influence of temperature on the microscopic parameters for extractingVO2+ ions by SLM-MC membrane. [H3O+] = 1 M, [MC] = 10−2M.Slopes (p) and intercepts (oo) determined from different Lineweaver-Burk straight lines (Figures 12 and 13) were used to calculate the values of parameters D∗ and Kass according to the terms in (16). The obtained results are summarized in Table 5 and confirm the inverse evolution of these microscopic parameters, and the temperature factor influence, in fact, an increase in the temperature causes a decrease in the value of Kass and increased the coefficient D∗ and therefore an improvement of the adopted membrane performance.Table 5
Temperature factor influence on the values ofKass and D∗ for the facilitated extraction phenomenon of VO2+ ions.
Extractive agent
T (K)
D
∗
⋅
105 (cm2⋅s−1)
K
a
s
s (L⋅mol−1)
RESO
293
4.19
4.29
298
5.67
3.61
303
8.80
2.83
MC
288
5.19
3.75
293
6.15
3.60
303
9.42
3.29
TOA
293
11.50
2.48
298
14.08
2.29
303
17.24
1.97
[Extractive agent] = 0.01 M and [H3O+] = 1 M.For the three adopted membranes, the results indicate a clear influence of temperature factor on the evolution ofKass and D∗ parameters, and an increase in temperature results in a weak association of substrate (VO2+) with the extractive agent, so fast jumps of substrate from one site to another of extractive agent, and a good substrate diffusion through the membrane. These results also show that microscopic parameters Kass and D∗ are specific for the pair (substrate, extractive agent), and SLM-TOA membrane remains the most effective for this facilitated extraction process of VO2+ ions.


### 4.4. Activation ParametersEa, ΔH≠, and ΔS≠

To examine the influence of energetic and associative terms on the mechanism for the facilitated extraction process ofVO2+ ions, we plotted the function ln⁡(J0moy)=f(1/T) provided by Arrhenius relationship (see (19)). For adopted SLMs, the line segments obtained at studied temperatures are represented by the graph in Figure 14.Figure 14
The representation ofln⁡(J0moy) = f(1/T) function on the facilitated extraction phenomenon of VO2+ ions by three membranes: SLM-RESO (-MC) and (-TOA).The slopes (p) and intercepts (oo) calculated from straight lines represented by the graph in Figure 14 were used to determine according to the expressions in (20) and the values of activation parameters, energy Ea, enthalpy ΔH≠, and entropy ΔS≠, related to the transition states of association/dissociation reactions of substrate (VO2+) with each of extractive agents (TOA, MC, or RESO). All obtained results for these parameters are summarized in Table 6,Table 6
All values of microscopic parametersKass and D∗ and activation parameters Ea,ΔH≠, and ΔS≠ for facilitated extraction process of VO2+ ions.
Extractive agent
T (K)
D
∗
⋅
105 (cm2⋅s−1)
K
a
s
s (L⋅mol−1)
E
a  (J⋅mol−1)
ΔH≠ (J⋅mol−1)
ΔS≠ (J⋅K−1⋅mol−1)
RESO
293
4.19
4.29
28767.57
26291.19
−232.85
298
5.67
3.61
303
8.80
2.83
MC
288
5.19
3.75
24469.63
21969.63
−235.84
293
6.15
3.60
303
9.42
3.29
TOA
293
11.50
2.48
15531.39
13055.01
−275.39
298
14.08
2.29
303
17.24
1.97
[RESO] = [MC] = [TOA] = 10−2 M.These results clearly indicate that the transition states related to association/dissociation reactions of substrate with the extractive agent are highly ordered states and require small amounts of energy. The analysis of the results shows that the facilitated extraction processVO2+ ions is a phenomenon governed by a structural term related to the nature and the structure of the interaction site of each extractive agents; then the influence of energetic term is negligible. On the other hand, recent studies [5, 6, 30, 31] and this analysis confirm previous results which indicate that the substrate movement across each of the developed membranes cannot be a pure diffusion movement (way A), but it takes place by successive jumps of one site to an another of used extractive agent, via interaction reactions of VO2+ ions with the extractive agent according tothe way B indicated by the diagram in Figure 15.Figure 15
Possible movements of substrate across the organic phases of SLM membranes: (A) pure diffusion movement (low values ofD∗), (B) movement in successive jumps (high values of D∗).


## 4.1. Macroscopic ParametersP and J0

In the same experimental conditions, using each of the three prepared membranes (MLSs) with one of the agents MC, RESO, or TOA in the same concentration (T0 = 0.01 M) facilitated extraction of VO2+ ions that was carried out for different initial concentrations C0 (0.0125–0.100 M) at the same temperature 293 K. Proposed kinetic model for this phenomenon in which the diffusion of the complex carrier-substrate (TS) is considered the rate-determining step indicates that the evolution of the term -ln⁡(C0-2Cr) must be linear in function of time (see (5)). Indeed, the experimental results verify the model and allow obtaining the straight line segments shown by graphs of Figures 6 and 7.Figure 6
Evolution of the term −ln⁡(C0-2Cr) versus time for facilitated extraction of VO2+ ions by SLM containing extractive agent RESO. [H3O+] = 1 M, [RESO] = 10−2M, andT = 293 K.Figure 7
Evolution of the term −ln⁡(C0-2Cr) versus time for facilitated extraction of VO2+ ions by SLM containing extractive agent TOA. [H3O+] = 1 M, [TOA] = 10−2M, andT = 293 K.The slopes calculated from these lines are used to determine the permeability values (P) of the used membranes with respect to VO2+ ions for different tested solutions (see (6)), while the initial flux values (J0) of the substrate through the used SLMs are calculated using (7). Table 2 summarizes all results for the three membranes at temperature 293 K.Table 2
The values of macroscopic parameters (P and J0) on the facilitated extraction of VO2+ ions by the three developed SLMs.
C
0 concentration (mol L−1)
PermeabilityP (107 cm2 s−1)
Initial FluxJ0 (105 mmol s−1 cm−2)
RESO
MC
TOA
RESO
MC
TOA
0.1
13.37
17.28
23.56
1.33
1.72
2.35
0.05
14.64
18.22
24.84
0.73
0.91
1.24
0.025
15.92
20.27
26.11
0.39
0.50
0.65
0.0125
17.19
21.29
27.38
0.21
0.26
0.34
[RESO] = [MC] = [TOA] = 10−2 M [H3O+] = 1 M, and T = 293 K.All these experimental results indicate that the permeabilityP of the used SLM varies inversely with the initial concentration C0 of VO2+ ions, and an increase in substrate concentration results in a decrease in permeability. However, the initial flux values J0 of these ions through each of studied SLMs increase as the initial concentration C0 of the substrate [27–29]. On the other hand, we observe that the values of permeabilities P and initial fluxes J0 relative facilitated extraction of VO2+ ions, using both SLMs containing, respectively, methyl cholate (MC) and resorcinarene (RESO) as extractive agents are slightly near, while the use of the SLM containing trioctylamine (TOA) as extractive agent provides relatively high values for these two parameters P and J0, in the same experimental conditions and the same temperature.


## 4.2. Microscopic ParametersD∗ and Kass

To verify the proposed mechanism for this facilitated extraction phenomenon of theVO2+ ions by prepared SLMs and determine themicroscopic parameters, apparent coefficients D∗, and association constants Kass, we traced the Lineweaver-Burk lines (1/J0=f(1/C0)) provided by (16), from the experimental results for the three used SLMs. The obtained line segments are shown by the graph in Figure 8.Figure 8
The Lineweaver-Burk representation1/J0=f(1/C0) for facilitated extraction of VO2+ ions by adopted SLMs. [RESO] = [MC] = [TOA] = 10−2M, [H3O+] = 1 M, and T = 293 K.The obtained straight lines clearly indicate that the proposed mechanism for this phenomenon is verified, and there is formation entity (ST) of composition (1/1), by association “substrate-extractive agent” in the organic phase of used SLM. The migration of this entity through this phase is the rate-determining step of the mechanism for the facilitated extraction of VO2+ ions. Slopes (p) and intercepts (OO) were calculated from these lines and using the expressions in (16); the apparent coefficients D∗ and the association constants Kass were determined. The obtained results for the used membranes are summarized in Table 3 and the histogram in Figure 9 shows that these twomicroscopic parameters vary inversely. This result indicates that a high stability of entity (ST) formed in the SLM organic phase results in a low diffusion of this entity and conversely.Table 3
Values of microscopic parameters (D∗ and Kass) for facilitated extraction of VO2+ ions.
Extractive agent
RESO
MC
TOA
D
∗ 105 (cm2⋅s−1)
4.19
6.15
11.50
K
a
s
s (L⋅ mol−1)
4.29
3.60
2.48
[RESO] = [MC] = [TOA] = 10−2 M, [H3O+] = 1 M, and T = 293 K.Figure 9
Microscopic parameters evolution for facilitated extraction phenomenon ofVO2+ ions.The values of permeabilityP, initial flux J0, (Table 2), association constant Kass, and apparent diffusion coefficient D∗ (Table 3), relating to this facilitated extraction phenomenon of VO2+ ions, clearly show that, for the same concentration of the extractive agent (0.01 M) and at the same temperature (293 K), the facilitated extraction of the substrate (VO2+) is more efficient through SLM containing trioctylamine (TOA) as extractive agent, compared with two other investigated membranes, containing, respectively, methyl cholate (MC) and resorcinarene (RESO). These results clearly show that the value of association constant Kass depends on the nature of association site carried by each of the extractive agents, as well as the reverse evolution of Kass and D∗ parameters, indicates that the movement of VO2+ ions in the membrane organic phase cannot be a pure diffusion movement, but it takes place by successive jumps of the substrate (VO2+) from one site to another of the extractive agent in successive and reversible reactions (association/dissociation).


## 4.3. Influence of the Temperature Factor

Under the same experimental conditions and using membranes, respectively. MLS-RESO, SLM-MC, and SLM-TOA, we performed experiments to the facilitated extraction ofVO2+ ions in solutions of C0 concentrations ranging from 0.0125 to 0.1 M and at temperatures 293, 298, and 303°K. Graphs in Figures 10 and 11 represent the straight lines relating to the evolution of the term -ln⁡(C0-2Cr) with time provided by kinetic model, for different studied temperatures, at C0 = 0.10 M, and for adopted membranes SLM-TOA and SLM-RESO.Figure 10
-
ln
⁡
(
C
0
-
2
C
r
) term evolution versus temperature for the facilitated extraction of VO2+ ions through membrane SLM-TOA. [H3O+] = 1 M, [TOA] = 10−2M, [VO2+] = 0.1 M.Figure 11
Temperature effect on-ln⁡(C0-2Cr) term evolution versus time, for the facilitated extraction of VO2+ ions by membrane SLM-RESO. [H3O+] = 1 M, [RESO] = 10−2M [VO2+] = 0.1 M.The slopes calculated from obtained lines for the different experiments were used to calculate according to the expressions in (6) and (7), the values of permeabilities P, and initial fluxes J0, relative to this facilitated extraction phenomenon of VO2+ ions through the adopted membranes. For the different studied temperatures, all obtained results are summarized in Table 4.Table 4
Temperature factor influence on the evolution of macroscopic parametersP and J0.
Extractive agent
C
0 mol L−1
P
⋅
107 cm2 s−1
J
0
⋅
105 mmol s−1 cm−2
293 K
298 K
303 K
293 K
298 K
303 K
RESO
0.1
13.37
15.92
20.38
1.33
1.59
2.03
0.05
14.64
17.19
21.65
0.73
0.85
1.08
0.025
15.92
18.47
22.92
0.39
0.46
0.57
0.0125
17.19
19.74
24.20
0.21
0.24
0.30
288 K
293 K
303 K
288 K
293 K
303 K
MC
0.1
14.43
17.28
24.71
1.44
1.72
2.47
0.05
16.47
18.22
25.95
0.82
0.91
1.29
0.025
17.57
20.27
28.43
0.43
0.50
0.71
0.0125
18.66
21.29
29.89
0.23
0.26
0.37
293 K
298 K
303 K
293 K
298 K
303 K
TOA
0.1
23.56
26.75
29.30
2.35
2.67
2.92
0.05
24.84
28.02
30.57
1.24
1.40
1.52
0.025
26.11
28.62
31.84
0.65
0.71
0.79
0.0125
27.38
30.57
33.12
0.34
0.38
0.41
[RESO] = [MC] = [TOA] = 10−2 M.These results confirm that the permeabilityP and the initial flux J0 parameters vary inversely and with the initial concentration C0 of VO2+ ions [18, 19]. They indicate clear influence of temperature factor on the values of these parameters and therefore an increase in the membrane performances, with an excellent performance of SLM-TOA membrane relative to other adopted SLMs.To confirm the previous results and to study temperature factor influence on the evolution of microscopic parametersD∗ and Kass, we traced the Lineweaver-Burk lines, 1/J0 = f(1/C0), and the obtained line segments are represented by the graphs in Figures 12 and 13, for two adopted membranes SLM-RESO and SLM-MC.Figure 12
Lineweaver-Burk lines for the facilitated extraction ofVO2+ ions by SLM-RESO membrane, for different values of temperature. [H3O+] = 1 M, [RESO] = 10−2M.Figure 13
Lineweaver-Burk straight lines relating to the influence of temperature on the microscopic parameters for extractingVO2+ ions by SLM-MC membrane. [H3O+] = 1 M, [MC] = 10−2M.Slopes (p) and intercepts (oo) determined from different Lineweaver-Burk straight lines (Figures 12 and 13) were used to calculate the values of parameters D∗ and Kass according to the terms in (16). The obtained results are summarized in Table 5 and confirm the inverse evolution of these microscopic parameters, and the temperature factor influence, in fact, an increase in the temperature causes a decrease in the value of Kass and increased the coefficient D∗ and therefore an improvement of the adopted membrane performance.Table 5
Temperature factor influence on the values ofKass and D∗ for the facilitated extraction phenomenon of VO2+ ions.
Extractive agent
T (K)
D
∗
⋅
105 (cm2⋅s−1)
K
a
s
s (L⋅mol−1)
RESO
293
4.19
4.29
298
5.67
3.61
303
8.80
2.83
MC
288
5.19
3.75
293
6.15
3.60
303
9.42
3.29
TOA
293
11.50
2.48
298
14.08
2.29
303
17.24
1.97
[Extractive agent] = 0.01 M and [H3O+] = 1 M.For the three adopted membranes, the results indicate a clear influence of temperature factor on the evolution ofKass and D∗ parameters, and an increase in temperature results in a weak association of substrate (VO2+) with the extractive agent, so fast jumps of substrate from one site to another of extractive agent, and a good substrate diffusion through the membrane. These results also show that microscopic parameters Kass and D∗ are specific for the pair (substrate, extractive agent), and SLM-TOA membrane remains the most effective for this facilitated extraction process of VO2+ ions.


## 4.4. Activation ParametersEa, ΔH≠, and ΔS≠

To examine the influence of energetic and associative terms on the mechanism for the facilitated extraction process ofVO2+ ions, we plotted the function ln⁡(J0moy)=f(1/T) provided by Arrhenius relationship (see (19)). For adopted SLMs, the line segments obtained at studied temperatures are represented by the graph in Figure 14.Figure 14
The representation ofln⁡(J0moy) = f(1/T) function on the facilitated extraction phenomenon of VO2+ ions by three membranes: SLM-RESO (-MC) and (-TOA).The slopes (p) and intercepts (oo) calculated from straight lines represented by the graph in Figure 14 were used to determine according to the expressions in (20) and the values of activation parameters, energy Ea, enthalpy ΔH≠, and entropy ΔS≠, related to the transition states of association/dissociation reactions of substrate (VO2+) with each of extractive agents (TOA, MC, or RESO). All obtained results for these parameters are summarized in Table 6,Table 6
All values of microscopic parametersKass and D∗ and activation parameters Ea,ΔH≠, and ΔS≠ for facilitated extraction process of VO2+ ions.
Extractive agent
T (K)
D
∗
⋅
105 (cm2⋅s−1)
K
a
s
s (L⋅mol−1)
E
a  (J⋅mol−1)
ΔH≠ (J⋅mol−1)
ΔS≠ (J⋅K−1⋅mol−1)
RESO
293
4.19
4.29
28767.57
26291.19
−232.85
298
5.67
3.61
303
8.80
2.83
MC
288
5.19
3.75
24469.63
21969.63
−235.84
293
6.15
3.60
303
9.42
3.29
TOA
293
11.50
2.48
15531.39
13055.01
−275.39
298
14.08
2.29
303
17.24
1.97
[RESO] = [MC] = [TOA] = 10−2 M.These results clearly indicate that the transition states related to association/dissociation reactions of substrate with the extractive agent are highly ordered states and require small amounts of energy. The analysis of the results shows that the facilitated extraction processVO2+ ions is a phenomenon governed by a structural term related to the nature and the structure of the interaction site of each extractive agents; then the influence of energetic term is negligible. On the other hand, recent studies [5, 6, 30, 31] and this analysis confirm previous results which indicate that the substrate movement across each of the developed membranes cannot be a pure diffusion movement (way A), but it takes place by successive jumps of one site to an another of used extractive agent, via interaction reactions of VO2+ ions with the extractive agent according tothe way B indicated by the diagram in Figure 15.Figure 15
Possible movements of substrate across the organic phases of SLM membranes: (A) pure diffusion movement (low values ofD∗), (B) movement in successive jumps (high values of D∗).


## 5. Conclusion

Three supported liquid membranes (SLMs) were prepared with same polymer support (PVDF), same organic phase (toluene), and three different extractive agents (TOA, MC, and RESO). These three SLMs were adopted for the facilitated extraction process ofVO2+ ions from concentrated acidic environments. All experimental results verify the proposed kinetic model, which was used to determine themacroscopic parameters permeability P and initial flux J0 relating to each adopted membranes. The obtained results show that prepared SLMs are highly permeable for the extraction process of VO2+ ions. To better understand this facilitated extraction phenomenon by this liquid membrane type, we developed a thermodynamic model based on the formation of an entity (ST) by association of substrate with the extractive agent at membrane interface and the migration of this formed entity through membrane organic phase. This model was verified by experimental results, which helped to determine themicroscopic parameters, association constant Kass, and apparent diffusion coefficient D∗, related to the formation of the entity (ST) and its diffusion through membrane organic phase. The low values of association constants Kass and the high values of apparent coefficients D∗ perfectly explain the large permeabilities and high fluxes obtained for this facilitated extraction process of VO2+ ions by prepared SLMs. Indeed, the parameters Kass and D∗ vary inversely, and the results indicate that very low values of constant Kass result in higher values of apparent coefficients D∗; this important result shows that these high values of coefficients D∗ certainly do not reflect a pure diffusion movement of the entity (ST) through adopted SLM organic phase. Some recent studies on the facilitated extraction process of metal ions or organic molecules by the same type of membranes clearly confirm the high values of the coefficients D∗ and explain this result by the movement nature of the substrateS during its passage from the source aqueous phase to the receiving aqueous phase, through the membrane organic phase. Indeed, the results clearly show that the mechanism for this facilitated extraction process of VO2+ ions is a mechanism performed by successive jumps of substrateS from one site to another of extractive agent movable in the membrane organic phase. On the other hand, studies on the temperature factor influence indicated a clear evolution of all parameters for this phenomenon, and an increase in temperature results in a decrease in the association constant values (Kass) and an increase in parameter values of D∗,P, and J0 and improved performance of the adopted SLMs. The results confirmed the proposed mechanism for this facilitated extraction process, and an increase in the temperature factor disadvantage interactions between substrateS and the used extractive agentT (Kass decreases) facilitates the phenomenon of substrate jumps from one site to another and therefore rapid passage (D∗ increases) of VO2+ ions through the membrane organic phase.



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*Source: 3425419-2017-03-26.xml*