The development of new supported liquid membranes (SLMs) with agents: Methyl cholate and resorcinarene as carriers for the removal of dichromate ions (Cr2O72-)

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The development of new supported liquid membranes (SLMs) with agents:

Methyl cholate and resorcinarene as carriers for the removal of dichromate ions (Cr 2 O 7 2

)

Abdelkhalek Benjjar

^a,b

, Tarik Eljaddi

^a

, Oussama Kamal

^a,b

, Khalifa Touaj

^a

, Laurent Lebrun

^b

, Miloudi Hlaibi

^a,b,

*

aLaboratoire Interface Mate´riaux et Environnement (LIME), Universite´ Hassan II, Faculte´ des Sciences Aı¨n Chock, B.P. 5366, Maaˆrif, 20101 Casablanca, Morocco

bLaboratoire des Polyme`res, Biopolyme`res, Surfaces, UMR 6270 du CNRS, Universite´ de Rouen, Faculte´ des Sciences et Techniques, F-76821 Mont-Saint-Aignan, France

Introduction

Currently, different membrane types are used for many industrial applications, to recover or separate the constituents of a mixture, or to selectively control the exchange of material between different media. The use of membrane technology has recently rapidly grown, particularly because of the increasing application areas. This development should be increased because of its good performance (low energy and use simple techniques), offered by membrane processes and due to the emerging needs of environmental protection (effluent treatment, clean processes, and so on). Meanwhile, these different applications, a research increasingly pushed to better understand the functioning of these membrane processes, create and develop more efficient or more specific and new methods to access new applications [1–6].

Today, it is necessary and certainly required to develop highly selective systems that are essential, for separations and recoveries of very harmful metal ions to the environment (mainly radioactive

species). For this purpose, the liquid–liquid separation technique was ﬁrst widely used, with more or less suitable agents, for the recovery of metal ions from complex and loaded aqueous media.

This technique involves the use of complexing agents, and large amounts of organic solvents which are often expensive and toxic [7–10]. It includes an extracting step by phase transfer, followed by re-extraction step and these steps are consumers of organic solvents, particularly when volatile solvents are involved. A stylish alternative to liquid–liquid extraction is the development of artificial membrane systems that mimic the process of facilitated transport across bio-membranes (by mobile carriers and more by ion channels). Liquid membranes incorporating specific complex- ing agents are artificial systems of choice for the treatment of liquid media charged with metal ions [4,5].

Our work will be limited to the supported liquid membranes (SLMs), made of a polymer ﬁlm, inert, micro porous polyvinylidene diﬂuoride (PVDF), a thickness of 100 m m and 69% porosity with pores of 0.45 m m in diameter, containing one of the following amphiphilic carriers (Fig. S1): methyl cholate or resorcinarene, soluble in toluene phase [5,6]. A kinetic model as well as a transport mechanism have been developed and tested for the facilitated transport of Cr

2

O

72

ions from different solutions. The macroscopic parameters, permeabilities P and initial ﬂuxes J

₀

were determined and related to microscopic parameters, the association constant K

ass

,

Journal of Environmental Chemical Engineering 2 (2014) 503–509

A R T I C L E I N F O

Article history:

Received 18 March 2013

Received in revised form 1 October 2013 Accepted 5 October 2013

Keywords:

Supported liquid membrane Facilitated transport Flux

Association constant Apparent diffusion coefﬁcient

A B S T R A C T

The technique of SLMs was used to achieve the facilitated extraction of Cr

2

O

72

ions, using methyl cholate and resorcinarene as carriers, widely used for facilitated transport of carbohydrates. For our SLMs, toluene as organic phase and microporous ﬁlm of PVDF as support. Permeability

P

and initial ﬂux

J0

were determined for different temperatures and the prepared membranes are highly permeable. The results indicate that values of the parameter

J0

depend on the temperature according to the Arrhenius equation. The activation parameters, (Ea, D

H^6¼

and D

S^6¼

) for transition state on the association reaction substrate–carrier were determined. The mechanism based on the complexation of the substrate by the carrier and the diffusion of the complex (ST) was developed. Results are used to determine the parameters, association constant

Kass

and apparent diffusion coefﬁcient

D*. All studies show that

parameters

Kass

and

D*

are changing signiﬁcantly with temperature factor, and better extraction of Cr

2

O

72

ions is possible.

ß

2013 Elsevier Ltd. All rights reserved.

* Corresponding author at: Laboratoire Interface Mate´riaux-chimie de l’Envir- onnement (LIME), Universite´ Hassan II, Faculte´ des Sciences Aı¨n Chock, B.P. 5366, Maaˆrif, Casablanca, Morocco. Tel.: +212 5 22 23 06 80; fax: +212 5 22 23 06 74.

E-mail address:miloudi58@hotmail.com(M. Hlaibi).

Contents lists available at ScienceDirect

Journal of Environmental Chemical Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j e c e

http://dx.doi.org/10.1016/j.jece.2013.10.003

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and apparent diffusion coefficient D*, relating to the stability of the complex substrate–carrier (ST), formed at the membrane interface, and its diffusion through the SLM organic phase. Detailed studies on the influence of temperature factor were performed and the results clearly show that these macroscopic and microscopic parameters vary depending on the medium temperature. An increase in temperature allows obtaining larger, permeabilities, initial fluxes and apparent diffusion coefficients, therefore, highly permeable membranes, more efficient extraction of transported substrate, and low stability complexes, with small values for the association constants (substrate–carrier). These results are important and will determine the movement nature of Cr

2

O

72

ions across organic phase of studied SLM, and explain the high permeability of such membranes for facilitated transport of these species.

Materials and methods

Description and operating principle of the SLMs

The supported liquid membrane (SLM) is made of an organic solvent, immobilized by capillary forces in the pores of a microporous support, separating the source phase and the receiving phase. The support of these membranes is generally an inert hydrophobic micro porous polymer, which is character- ized by a low thickness (25–100 m m) and pore diameter from 0.12 to 1 m m [11,12]. Since the chemical species passage through this type of membranes is an interfacial phenomenon, the use of a support with high porosity is necessary to increase the contact area and the favourability of the passage of species, and able to ensure the best transport and separation conditions through these membranes (SLMs) [13]. To improve the separation process, the researchers added to the SLM organic phase mobile carriers to accelerate and facilitate the transport of species, while increasing the selectivity of the membranes [5,14]. The MLS technique is an approach widely used for the extraction and enrichment of metal ions and organic compounds [15–17].

Indeed, this technique has been used to study the transport and apply it to the selective extraction and enrichment of varied organic compounds, such as amino acids [18,19], the aromatic aminophosphates [20], sugars [21–25], herbicides and some organic acids [26,27].

This method which is called facilitated transport through supported liquid membranes is based on the recognition of a substance (S) by a carrier molecule (T). This process involves mobility within the membrane of a complex (ST) produced by a reversible forming reaction between the carrier (T) and trans- ported species (S), at the membrane interfaces with the source and receiving phases. This phenomenon of facilitated transport through the SLMs is a cyclical process that involves ﬁve consecutive steps:

(1) Diffusion of free substrate (S) in the source phase to the membrane interface.

(2) Formation of the complex substrate–carrier (ST) at the source phase–membrane interface.

(3) Diffusion of the complex (ST) through the membrane organic phase to the membrane–receiving phase interface.

(4) Dissociation of the complex (ST) at the membrane–receiving phase interface.

(5) Diffusion of free substrate (S) in the receiving phase and the carrier (T) in the membrane organic phase to resume a new cycle.

These ﬁve steps are considered the mechanism of facilitated transport through SLM, with the diffusion step of the substrate–

carrier complex (3), as the rate-determining step.

Experimental

For this facilitated extraction process, the experiments were performed in the cell described in previous studies [4,24].

All chemicals reagents and solvents used were pure commer- cial products of analytical grade (Sigma–Aldrich, Fluka and Merck). The dichromate ion solutions used are obtained by hydrolysis of K

2

Cr

2

O

7

salt. The support is a micro porous polymer ﬁlm, polyvinylidene diﬂuoride (PVDF), of thickness 100 m m, porosity 69%, and pore diameter of 0.45 m m. The membrane liquid solution consists of the organic phase toluene, containing 0.01 M of carrier (methyl cholate or resorcinarene). Cr

2

O

72

ions solutions (0.20–0.025 M) were prepared from a stock solution in doubly distilled pure water. After conditioning the prepared SLM [2,4,24], it is placed between two compartments of the transport cell, in the feed phase, the Cr

2

O

72

ions solution with C

0

concentration, at pH 1, 2 or 3 and in the receiving phase KCl solution at pH 6. The two phases are subjected to the same agitation, and kinetic study on the transport of Cr

2

O

72

ions is performed by regular sampling of a small amount from receiving phase at known time intervals. These samples were analysed by UV–visible spectrophotometer ( l

max

= 260 nm), C

r

concentra- tions of Cr

₂

O

₇²

ions in the receiving phase are calculated, and the evolution of the term ln(C

0

2C

r

) versus time was studied. Table S1 represents an example of results on the Cr

2

O

72

ions transport from a source phase of pH 2 (pH is adjusted with hydrochloric acid).

Theoretical models and calculations

Determination of the macroscopic parameters: permeability P and ﬂux J

0

At time t, C

r

is the substrate concentration in the receiving phase, and the concentration of substrate in the source phase at Nomenclature

a slope of the plot ln(C

0

2C

r

) = f(t)

C

0

initial concentration of chromate ions in the feed phase (mol L

¹

)

C

r

concentration of transported chromate ions in the receiving phase (mol L

¹

)

C

_s

concentration of chromate ions in the feed phase (mol L

¹

)

P the permeability of the SLM for chromate ions (cm

²

s

¹

)

J

0

initial ﬂux on the facilitated transport of substrate (mmol cm

²

s

¹

)

D* apparent diffusion coefﬁcient of the complex (TS) (cm

²

s

¹

)

K

ass

association constant on the formation of the complex (TS)

l the membrane thickness (mm or m m) S the membrane area (cm

²

)

[T]

0

concentration of carrier in the membrane (mol L

¹

) [TS] concentration of the complex in the organic phase

(mol L

¹

)

T temperature (K or 8C)

t time (s)

V volume of the receiving compartment (cm

³

)

A. Benjjar et al. / Journal of Environmental Chemical Engineering 2 (2014) 503–509 504

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this time is C

s

= C

0

C

r

. C

0

is the substrate initial concentration. In experimental conditions with an excess of substrate S relative to the carrier T, recent studies show the equation relating perme- ability P to C

r

concentration of substrate S, is given by the relationship [6,24,25]:

Pðt t

L

Þ ¼ l V 2S

ln C

0

C

0

2C

r

(1) S is the membrane surface in contact with the source phase solution, V is the receiving phase volume and l is the membrane thickness.

For a quasi-static state applying Fick’s ﬁrst law:

J ¼ P D C

l (2)

and

P ¼ a V l

2S (3)

With, a is the slope experimental value of the line ln(C

₀

2C

r

) = f(t), the initial ﬂux J

0

can be calculated as follows:

J

0

¼ P C

0

l (4)

Modelling and calculations of microscopic parameters K

ass

and D*

The association of substrate and carrier, at the feed phase–

membrane interface, is written in the heterogeneous equilibrium:

S

aq

þ T

org

@ TS

org

org and aq represent the membrane organic phase and the aqueous solution of the feed phase, respectively. Similar studies [6,24,25], show the parameters, initial ﬂux J

0

, association constant K

ass

, and apparent diffusion coefﬁcient D* are related to initial concentrations, C

0

of substrate S and [T]

0

of carrier T by the relations:

J ¼ D l

½TS (5)

1 J

0

¼ l

D

1 ½T

₀

1 K

ass

1 C

0

þ 1

½T

₀

(6) With:

K

ass

¼ intercept ðOOÞ

slope ð pÞ and D ¼ l OO

1 ½T

₀

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Determination of activation parameters

Several factors can inﬂuence the evolution of J

0

parameter, especially the feed phase temperature. Some studies [28–30]

indicate that the values of this parameter vary with the temperature factor according to Arrhenius equation:

J

₀

ðT Þ ¼ A

j

exp Ea RT

(8) A

j

is a constant (pre-exponential factor) whose value is propor- tional to the number of favourable interaction faces between the substrate and carrier, and E

_a

is the transition state activation energy on the formation–dissociation reaction of complex (TS).

LnðJ

0

Þ ¼ Ea

RT þ LnðA

j

Þ (9)

On the other hand, according to the activated complex theory [31,32]), E

a

is related to the activation enthalpy ( D H

^#

) by the relation:

D H ¼ ðEa 2500Þ J mol

¹

at 298K (10) and the activation entropy ( D S

^#

), is related to A

j

constant by the equation:

D S ¼ Rðln A

J

30:46Þ J mol

¹

K

¹

at 298 K (11)

Results and discussion

Inﬂuence of the source phase acidity

Under the same experimental conditions, using the same SLM with the same carrier (methyl cholate), Cr

2

O

72

ions transport was performed at different C

0

concentrations of source phase, and for three different acidities, pH 1, 2 or 3 (HCl). The experimental results verify the proposed kinetic model for this facilitated transport process, and the segments of lines, represented by the graph in Fig. S2, show the linear evolution of ln(C

0

2C

r

) = f(t) function provided by this model.

The slopes calculated from these lines, according to Eq. (3), allow determining the permeability values (P) of the SLM to the transported substrate (Cr

2

O

72

ions), for the different studied solutions, while the Cr

2

O

72

ions initial ﬂuxes (J

0

) through this SLM are calculated using Eq. (4). Studies conducted on the facilitated transport of dichromate ions, to the three acidity pH 1, 2 and 3, were used to determine the results grouped in Table 1.

These results clearly show the SLM permeability parameter (P) varies inversely with the Cr

2

O

72

ions concentration in feed phase, and an increase in substrate concentration causes a decrease in this parameter. However, the Cr

2

O

72

ions initial ﬂux J

0

increases with C

0

substrate concentration in the source phase [23,24]. To verify the proposed mechanism for the facilitated transport of Cr

2

O

72

ions, and to determine the parameters K

ass

and D*, according to the Lineweaver–Burk method, we have drawn the lines 1/J

₀

= f(1/C

₀

), provided by Eq. (6). For the three studied acidity, the obtained straight segments are represented by the graph in Fig. 1.

The linear evolution of functions 1/J

0

= f(1/C

0

) (Fig. 1) clearly indicates that proposed mechanism is veriﬁed, and the interaction substrate–carrier allows the formation of complex (ST) with the composition (1/1) in the SLM organic phase, and migration of this complex across this phase is the rate-determining step of the mechanism for facilitated extraction of Cr

2

O

72

ions. From these straight segments (Fig. 1), slopes (p) and intercepts (oo) were calculated and using the expressions in Eq. (7), the apparent diffusion coefﬁcients D* and the association constants K

ass

were determined. The obtained results summarized in Table 2, show that microscopic parameters D* and K

_ass

vary with the medium acidity, and the formed complex (ST) is of low stability, while its diffusion through the SLM organic phase is important, and the apparent coefﬁcient D* varies inversely with the association constant K

ass

.

Table 1

Facilitated transport example of Cr2O72

ions.

T(min) Absorbance Cr(M) ln(C02Cr)

30 0.189 0.009 2.511

60 0.282 0.014 2.632

90 0.370 0.018 2.763

120 0.437 0.021 2.875

150 0.502 0.025 2.997

C0= [Cr2O72

]0= 0.10 M, pH 2, [MC] = 0.01 M andT= 298 K.

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Various studies show that characteristics nature and structure of the carrier are two important and decisive factors for the facilitated transport of metal ions and organic molecules through the SLMs [6,23,24,33,34]. To complement our results and examine the inﬂuence of the carrier nature, we conducted the same experiments under the same conditions with a new SLM contain- ing resorcinarene as a carrier. Kinetic model and mechanism for the facilitated transport of Cr

2

O

72

ions have been veriﬁed. The values of permeability (P) and initial ﬂux (J

0

) on the facilitated transport of these ions by this new SLM have been determined and are summarized in Table S2.

These results conﬁrm that the macroscopic parameters J

0

and P depend on the Cr

2

O

72

ions initial concentration (C

0

) and that methyl cholate is a better carrier than resorcinarene in the facilitated extraction of these oxygen anions from concentrated acidic media. The histogram in Fig. S3 shows the evolution of permeability P depending on the carrier nature and the source phase acidity.

From data in Table S2, the plots 1/J

0

= f(1/C

0

) were drawn according to Eq. (6), where linear segments were obtained for the three studied acidities (Fig. 2).

Slopes (p) and intercepts (OO) calculated from these linear segments, were used in the expressions of Eq. (7), and the apparent diffusion coefﬁcients D* and association constants K

ass

were determined for these three acidities. The obtained results summarized in Table S3 conﬁrm that the microscopic parameters

D* and K

ass

are inversely correlated and that the association constant K

ass

increases with the source phase acidity. The obtained values for these parameters D* and K

ass

, show that for this new SLM, stability and diffusion of the complex (TS) formed in the organic phase are lower than those of the obtained complex for the previous SLM. This result clearly indicates, the carrier nature is essential for better facilitated extraction. The results for both studied SLMs. show that this membrane type is very effective for the facilitated transport of dichromate ions, while the carrier nature and the medium acidity greatly inﬂuence the evolution of microscopic parameters D* and K

ass

. The histogram in Fig. S4 shows there is a clear relationship between K

ass

and D*, the methyl cholate agent is a best carrier and the medium acidity is a determining factor for the facilitated transport and extraction of Cr

2

O

72

ions by SLMs.

On the other hand, high values of apparent diffusion coefﬁcients D*, indicate that the migration of the complex (substrate–carrier) through the organic phase is not a pure diffusion movement.

Therefore, further studies are needed to elucidate the real movement of this complex through the SLM.

Inﬂuence of temperature factor

To study the temperature inﬂuence on all parameters related to this facilitated extraction of the substrate through the SLMs, we performed the same experiments using the most efﬁcient membrane, with the performance conditions ([MC] = 0.01 M and pH 2), The graph in Fig. S5 shows the evolution of some lines on the representation of the function ln(C

0

2C

r

) = f(t), and with different studied temperatures. We ﬁnd that the kinetic model established for the facilitated transport of dichromate ions, for which we consider the diffusion of substrate–carrier complex (TS) is the rate-determining step, is well veriﬁed for all tested temperatures. Table S4 includes all values for macroscopic parameters P and J

0

, determined for temperatures ranging 288–

303 K. Data in Table S4 show that the temperature factor is essential for the facilitated transport of substrate across these membranes type (SLMs), and an increase in temperature from 288 to 303 K, the permeability value have almost doubled.

This important inﬂuence of temperature is related certainly to increase reaction rates for formation and dissociation substrate–

carrier complex (ST), hence a decrease in the stability of this complex in the SLM organic phase. To determine the inﬂuence of this factor on the evolution of parameters K

ass

and D*, we plotted the functions 1/J

0

= f(1/C

0

) (Eq. (6)), for various studied tempera- tures. The lines in Fig. 3 clearly show that the experimental results verify the proposed mechanism, there is a clear inﬂuence of temperature factor on the evolution of these microscopic parameters K

_ass

and D*, and an increase in temperature resulted in a decrease of the complex stability (K

ass

), and consequently a large increase in the apparent diffusion coefﬁcient (D*), concerning

[(Fig._1)TD$FIG]

Fig. 1.The Lineweaver–Burk plots for the facilitated transport of Cr2O72

ions through the used SLM, [MC] = 0.01 M, toluene phase andT= 298 K.

Table 2

Inﬂuence of the source phase acidity on the macroscopic parametersPandJ0. pH C0= [Cr2O72

] M 10⁷P(cm²s¹) 10⁵J0(mmol cm²s¹)

1 0.2 26.250 5.250

0.1 29.895 2.989

0.05 32.812 1.640

2 0.2 28.437 5.687

0.1 30.625 3.062

0.05 32.083 1.604

3 0.2 29.166 5.833

0.1 31.354 3.135

0.05 33.541 1.677

[MC] = 0.01 M, toluene phase andT= 298 K.

[(Fig._2)TD$FIG]

Fig. 2.The Lineweaver–Burk plots for the transport of Cr2O72ions through the new SLM [RES] = 0.01 M, toluene phase andT= 298 K.

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the movement of this complex through the organic phase of the used SLM.

Slopes (p) and intercepts (OO) calculated from these linear segments were used in the expressions of Eq. (7), and the apparent diffusion coefﬁcients D* and association constants K

ass

were determined for all studied temperatures. Data in Table 3 conﬁrm that the microscopic parameters D* and K

ass

are inversely correlated and the association constant K

_ass

decreases slightly when the temperature varies from 288 to 303 K. For the same change of this factor (temperature), apparent diffusion coefﬁcient value (D*) has doubled.

The evolution of the apparent diffusion coefﬁcient D*, in the temperature factor (Fig. S6), and the activation parameter values determined in subsequent experiments, allows to specify the movement nature of the substrate through the SLM organic phase, and to explain the high permeability of such membranes for facilitated extraction of these ions. Indeed, these activation parameters values are related to the formation–dissociation equilibrium on the substrate–carrier complex (ST), especially at the interfaces and within the organic phase of the studied SLM (Tables 4–7).

Experimental determination of activation parameters

The ﬂux of ions transport in liquid membranes is dependent on numerous factors that are associated with the experimental conditions (temperature of membrane phase, carrier concentra- tion, pH, and metal concentration in source phase). Under the same experimental conditions of the source and receiving aqueous phases and the membrane ([MC] = 0.01 M, pH 2 and [Cr

2

O

72

]

0

= 0.20 M), metal ion ﬂux for the facilitated transport is dependent only on temperature. However, recent studies [35,36]

have shown that the determination of the initial ﬂux values at different temperatures, allows the calculation of the activation energy from the Arrhenius equation according to Eq. (9). All results obtained for the temperatures 288, 293, 298 and 303 K are shown in Table S4 and are depicted graphically in Fig. 4.

The data in Table S4 show that the parameters P and J

0

on facilitated extraction of Cr(VI) ions are strongly dependent on temperature. Indeed, these results show that the variation of the temperature factor causes a large change in values of the initial ﬂuxes. The graph in Fig. 4 indicates the linear evolution of the term ln(J

0

) with the inverse of temperature; this fact is conﬁrmed by the very high determination coefﬁcient (r

²

= 0.99). Therefore, in accordance with Eq. (9), the activation energy may be determined if the slope of the straight line of the function ln(J

0

) = f(1/T) is known. The activation energy is determined E

a

= 27.35 kJ mol

¹

, and the constant A

j

= 18.54 mol m

²

s

¹

in temperature interval

[(Fig._3)TD$FIG]

Fig. 3.The temperature inﬂuence on the Lineweaver–Burk plots for the transport of Cr2O72

ions [MC] = 0.01 M, pH 2 and [Cr2O72

]0= 0.20 M.

Table 3

The source phase acidity inﬂuence on the parametersD*andKass.

pH Kass(L mol¹) 10⁵D* (cm²s¹)

1 4.23 10.08

2 2.47 15.08

3 1.69 21.83

[MC] = 0.01 M, toluene phase andT= 298 K.

Table 4

Evolution of the parametersPandJ0with the source phase acidity.

pH C0= [Cr2O72

] M 10⁷P(cm²s¹) 10⁵J0(mmol cm²s¹)

1 0.200 17.500 3.500

0.100 18.958 1.895

0.050 21.145 1.057

2 0.200 13.854 2.770

0.100 16.041 1.604

0.050 16.770 0.838

3 0.200 16.770 3.354

0.100 18.229 1.822

0.050 18.958 0.947

[RES] = 0.01 M, toluene phase andT= 298 K.

Table 5

Evolution of the microscopic parametersD*andKasswith the source phase acidity.

pH Kass(L mol¹) 10⁵D* (cm²s¹)

1 3.23 7.95

2 2.08 9.16

3 1.31 15.67

[RES] = 0.01 M, toluene phase andT= 298 K.

Table 6

Temperature effect on the macroscopic parameters for the facilitated transport of Cr2O72

ions.

T(K) C0= [Cr2O72

] M P10⁷(cm²s¹) J010⁵(mmol cm²s¹)

288 0.2 20.41 4.08

0.1 21.14 2.113

0.05 22.60 1.13

0.025 23.40 0.58

293 0.2 26.25 5.25

0.1 27.70 2.77

0.05 29.16 1.45

0.025 30.26 0.75

298 0.2 30.62 6.12

0.1 32.08 3.20

0.05 33.54 1.67

0.025 34.92 0.87

303 0.2 37.04 7.40

0.1 37.62 3.76

0.05 38.71 1.93

0.025 40.90 1.02

[MC] = 0.01 M, toluene phase and pH 2.

Table 7

Temperature inﬂuence on the parametersD*andKassfor Cr2O72ions transport.

T(K) D*10⁵(cm²s¹) Kass(L mol¹)

288 21.06 1.14

293 28.57 1.09

298 33.89 1.05

303 41.73 0.99

[MC] = 0.01 M, toluene phase and pH 2.

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288–303 K. It is known that the membrane process of the facilitated transport through the SLM is controlled by a diffusion of substrate–carrier complex (ST) through the membrane, and does not depend on reactions that occur at interfaces (aqueous phases/

membrane). The ﬂux on the transport of Cr(VI) ions through this studied SLM, increased with a higher temperature, therefore, this process is controlled by the substrate movement kinetics across the SLM phase. To obtain our results, we calculated the activation parameters D H

^#

and D S

^#

, related to the activation energy E

a

and the constant A

j

, by the relations of the Eqs. (10) and (11).

D H

^#

= E

a

2.50 = +24.85 kJ mol

¹

and D S

^#

= R(ln A

j

30.46) = 228.86 J mol

¹

K

¹

at 298 K. These low values of E

a

and D H

^#

indicate that the transition state in the reaction formation–

dissociation of the complex (ST) requires little energy, while a negative value of D S

^#

expresses a gain of order and therefore a real association between substrate and the carrier in this transition state.

The results of the facilitated transport of Cr(VI) ions, by these prepared SLMs, especially the very high values of apparent diffusion coefﬁcients (D*) and the low value of the activation energy E

a

, clearly indicate that the substrate movement within the membrane is not a simple diffusion phenomenon controlled by a concentration gradient at the SLM interfaces. Therefore, the movement associated with the passage of Cr

2

O

72

ions through the SLM, is conducted using a series of reactions (formation/dissociation), and successive jumps of the substrate from one carrier to another. Various studies [34,37–41] show that the supported liquid membranes are very efﬁcient for the facilitated transport of some organic compounds (sugars, organic acids) and can be fully operational for the separation of these compound mixtures. Indeed, the parameters K

_ass

and D*

evolve in reverse and very low values of the constantK

ass

, correspond to high values of coefficients D, this important result shows that these high values of the apparent diffusion coefficients D do not certainly reflect a pure diffusion movement of the complex (TS) through the SLM organic phase. On the other hand, recent studies [42–46] on the facilitated transport of metal ions or organic molecules on this type of membranes, clearly confirm these high values of the coefficients D*and explain this result by the movement nature of the substrate S across SLM organic phase during its migration from source phase to receiving phase.

Conclusion

Two supported liquid membranes were prepared with the same polymer support (PVDF), the same organic phase (toluene) and two

different carriers (methyl cholate and resorcinarene). These membranes were used with the facilitated extraction of Cr

2

O

72

ions from concentrated acidic environments. The experimental results verify the proposed kinetic model, which was used to determine the macroscopic parameters, permeabilities P and the initial ﬂuxes J

0

of both prepared membranes (SLMs). The results show that used SLMs are very permeable, and can perform the facilitated transport and extraction of Cr

2

O

72

ions, with large ﬂuxes. To understand this phenomenon of facilitated extraction of substrates through these liquid membrane types, we developed a mechanism based on the formation by interaction of an entity substrate–carrier at the feed phase–membrane interface, and the migration of this entity through SLM organic phase. This mechanism has been veriﬁed and it was used to determine the microscopic parameters, association constants K

ass

and apparent diffusion coefﬁcients D*, related to the formation of complex (ST), and its diffusion across the SLM. The low values of the constants K

ass

and large values of the coefficients D* determined, may explain the significant permeabilities and large fluxes, obtained from facilitated extraction of Cr

2

O

72

ions by this type of membranes.

Changing values of the parameters K

ass

and D*, clearly indicates that the stability and the diffusion of the substrate–carrier complex (ST) are closely related to the movement nature of Cr

2

O

72

ions in the membrane organic phase. The study of the temperature factor inﬂuence showed a clear evolution of these parameters, an increase of temperature factor, leads to the increase of coefﬁcients D* and the decrease of constants K

ass

, and a membrane becomes more permeable to large ﬂuxes. These studies have identiﬁed the activation parameters (E

a

, D H

^#

and D S

^#

), for the transition state of formation and dissociation reactions of the complex (ST) at the interfaces. The obtained values conﬁrm the high permeability of prepared membranes; allow the identiﬁcation of mechanism type and movement nature of the substrate across membrane organic phase. The overall results show that agent methyl cholate is a suitable carrier for the preparation of highly permeable SLMs, for facilitated extraction of dichromate ions.

Acknowledgements

All authors are thankful to the Francophonie University Agency (Agence Universitaire de la Francophonie (AUF)) for ﬁnancial support (PCSI 59113PS014), and Professor Mohamed AJMANI for his valuable and indispensable discussions, and necessary correc- tions.

Appendix A:. Supplementary data

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jece.2013.10.003.

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