Kinetics of Chromium(VI) Transport from Mineral Acids across

For transport experiments, the polymer inclusion membranes (PIMs) were ... of polymer inclusion membrane systems that contain amines, crown ethers, an...
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Ind. Eng. Chem. Res. 2007, 46, 5420-5428

Kinetics of Chromium(VI) Transport from Mineral Acids across Cellulose Triacetate (CTA) Plasticized Membranes Immobilized by Tri-n-octylamine Cezary A. Kozłowski* Institute of Chemistry and EnVironment Protection, Jan Dlugosz UniVersity of Czestochowa, 42-201 Czestochowa, Armii Krajowej 13 Street, Poland

The extraction of chromium(VI) from an aqueous acidic solution into a coexisting organic phase that contained tri-n-octylamine (TOA) and solvent (o-nitrophenyl pentyl ether) was studied. The calculated logarithm of the extraction constant (log Kex) value for this extraction system was 6.03 ( 0.03. For transport experiments, the polymer inclusion membranes (PIMs) were prepared by physical immobilization of TOA as the carrier and o-nitrophenyl pentyl ether in cellulose triacetate as the polymer matrix. The competitive transport of Cr(VI) ions from mineral acid solutions (chloride, sulfate, nitrate) media through a PIM with TOA was investigated. The selectivity of the process is described by the sequence of ions removed from the source phase: HCrO4> NO3- > Cl- > SO42-. This order of permeability limits seems to correlate with the molar Gibbs energy of hydration of transported anions. An activation energy of 30.5 kJ/mol was also determined for Cr(VI) permeability across a PIM with TOA, which suggests that the transport of Cr(VI) ions is controlled by a membrane diffusion mechanism. A presented model describes the transport mechanism, which involves diffusion via a fast interfacial chemical reaction, as well as diffusion of a carrier and its metal complex through the plasticized membrane. The diffusion coefficients of the Cr(VI) complex were calculated as a function of the carrier concentration and membrane thickness; their values were 2.34 × 10-9 and 1.22 × 10-10 cm2/s, respectively. 1. Introduction Currently, the application of extraction techniques for the removal and recovery of metals is very significant. Increased demand for metal production has led to research on more efficient and economical methods of purification that are required by industry. Membrane technology has become an important alternative to normal processes applied for wastewater treatments, as well as for the separation and recovery of target metals. Selective transport across liquid membranes and solvent extraction of metal ions has been widely reviewed.1-4 These membranes include bulk liquid membranes (BLMs), emulsion liquid membranes (ELMs), and supported liquid membranes (SLMs).5 Recently, a remarkable increase in the applications of liquid membranes, especially those of a new type (i.e., polymer inclusion membranes, PIMs), in separation processes of metal ions and small organic compounds has been observed. PIMs are formed by casting using as a support cellulose triacetate (CTA) or poly(vinyl chloride) (PVC) from an organic solution to form a thin, stable film. This casting solution also contains an ion carrier and a membrane plasticizer (mostly o-nitrophenyl alkyl ethers). The resulting membrane is used to separate the source and receiving phases.6 Chromium(VI) is one of major toxic elements present in the environment and generated by galvanic plant and mine waters. Chromium(VI) compounds are toxic to bacteria, plants, animals, and people. Human toxicity includes lung cancer as well as kidney, liver, and gastric damage.7 The use of the organic membrane solutions of the liquid membranes for chromium removal and recovery may be realized not only in laboratory experiments but also in the technology field.8-10 Several results of the concentration and separation of chromium(VI) with the ELM process with tertiary amines (such as * To whom correspondence should be addressed. Tel./Fax: +48 34 3665322. E-mail address: [email protected].

tri-n-dodecylamine11 and tributyl phosphate12) also have been reported. Quaternary ammonium salt (i.e., Aliquat 336) was also applied as an ion carrier in ELMs.13-15 The applications of SLMs for chromium(VI) concentration and separation with tertiary amines and quaternary ammonium salts as the most widely used ionic carriers have been shown in a few papers.16-18 Alguacil et al. reported the use of a commercially available phosphine oxide (i.e., Cyanex 923)19 A common problem for SLMs is the loss of membrane solvent and/or carrier to both aqueous phases, and, as a result, the SLM-based processes have not been exploited industrially, because of their poor durability. Many studies have been made on the chromium(VI) transport across ELMs20 and SLMs.21,22 Recently, we have been involved in the design and preparation of polymer inclusion membrane systems that contain amines, crown ethers, and phosphine oxide for the selective and efficient transport of a variety of metal ions, such as Cr(VI), and Cr(III),23 as well as Cr(VI), Zn(II), and Cd(II).24,25 In another study, Wionczyk et al.26 have described the transport of Cr(VI) ions from a sulfuric acid solution into 0.1 M NaOH across a PIM similar to that used by Walkowiak et al.27 but containing tridecyl(pyridine) oxide (TDPNO) as the ion carrier. The actual membrane composition was 20 wt % CTA, 70 wt % onitrophenyl pentyl ether (ONPPE), and 10 wt % TDPNO (0.5 M based on the plasticizer volume). It was observed that the initial flux attained a maximum value for 0.3 M sulfuric acid. Choi and Moon28 found that the transport of Cr(VI) ions through the PIM (0.0735 g poly(vinyl) chloride, 0.1471 cm3 o-nitrophenyl octyl ether (ONPOE), and 5.43 × 10-5 mol Aliquat 336) was dominated by membrane diffusion and that the Aliquat 336 in the membrane had a key role in the selective transport of Cr(VI) ions, whereas ONPOE gave an assisting mobility of the ion-carrier complex in the membrane. The maximum recovery of Cr(VI) ions in the test solution that contained Cr(III) ions was 93.2%. Scindia et al.29 investigated three different classes of anionexchange membranes for Cr(VI) recovery from aqueous solu-

10.1021/ie070215i CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007

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tions. The comparison of permeability coefficients and selfdiffusion coefficients of Cr(VI) ions across a pore-filled membrane (PFM), SLM, and PIM indicated that the hydrophobicity of the membrane, membrane architecture, and chemical form of the Cr(VI) complex have an important role in Cr(VI) diffusion across these membranes. The permeability coefficients of Cr(VI) ions in these membrane decreased in the following order:

at pH 8: PFM > SLM ≈ PIM and

at pH 2: PFM ≈ SLM > PIM The PIM was an effective membrane for the recovery of Cr(VI) ions from seawater. The transport through PIMs was determined to be an effective and selective method of Cr(VI) ion removal from acidic chloride aqueous solutions. The optimal PIM content was as follows: 41 wt % of cellulose triacetate as the support, 23 wt % of trin-octylamine (TOA) as the ionic carrier, and 36 wt % of o-nitrophenyl pentyl ether as a plasticizer. The transport of Cr(VI) ions through PIMs reduces the concentration of Cr(VI) ions in source aqueous phase from 1.0 mg/dm3 to 0.0028 mg/ dm3, which is below the permissible limit in drinking water in Poland. Competitive transport of chromium(VI), cadmium(II), zinc(II), and iron(III) from acidic aqueous solutions across PIMs was determined to be efficient for chromium(VI) (99%) and cadmium(II) (99%).30 In our previous work, we have shown comparisons of the facilitated chromium(VI) transport across SLMs and PIMs with tertiary amines and a quaternary ammonium salt (Aliquat 336) from acidic chloride aqueous solutions to 0.10 M NaOH.31 A linear decrease of initial flux of chromium(VI) with the increasing logarithm of the n-octanol/water partition coefficient for R3N amines was observed. The transport of chromate ions across PIM with PVC was slower than that PIM with CTA as a support. The Cr(VI) initial flux values decrease in the following order of plasticizers:

o-nitrophenyl pentyl ether > bis(2-ethylhexyl) adipate > dibutyl phtalate In the experiments, the long-term integrity of PIM was observed.31 In the past, many researchers had reported the application of PIMs with LIX 84-I,32 D2EHPA and di-(2-ethylhexyl) dithiophosphoric acid,33-35 hydrophobic β-cyclodextrin polymer,36 and Lasalocid A37 as ion carriers for the carrier-mediated transport of transition-metal ions such as Zn(II), Cd(II), Pb(II), Cu(II), Co(II), and Ni(II). In the present work, we analyze kinetics and mechanism of the competitive transport of chromium(VI) from mineral acid solutions through a PIM consisting of CTA as a polymer matrix, ONPPE as a solvent, and TOA as a carrier. Determining methods of transport parameters values such as the diffusion coefficient are described, and the dependence of the initial flux on the experimental conditions is calculated. For polymeric membranes, the influence of the temperature in chromium(VI) transport, as well as the effect of the thickness of plasticized CTA membranes, and carrier concentration have been evaluated. 2. Materials and Methods 2.1. Chemicals. Organic compounds, such as TOA, ONPPE, CTA (number-average molecular weight of Mn ) 72 000-

74 000), and dichloromethane, were purchased from Fluka and used without further purification. Inorganic compounds (such as potassium dichromate, sodium hydroxide, and hydrochloric acid, nitric acid, and sulfuric acid solutions) were prepared from analytical-grade reagents (POCh, Gliwice, Poland). The gamma radioactive isotope, Cr-51, was used as K2Cr2O7 in HCl aqueous solution. This isotope had a specific activity that was sufficiently high to neglect the effect of carrier concentration (4.5 GBq/g), and it was obtained from the Atomic Energy Institute (Swierk, Poland). A capillary electrophoresis system with an ultraviolet (UV) detector (Capel-105, Russia) was used to determine the concentrations of the sulfate, nitrate, and chloride anions. The electrophoretic buffer consisted of 5.0 × 10-3 mol/dm3 chromium(VI) oxide (CrO3), 2 × 10-2 mol/dm3 diethanolamine, and 1.65 × 10-3 mol/dm3 cetyltetraammonium bromide (from Fluka), at a voltage of 17 kV. The resulting detection limits in this method for the Cl- , NO3-, and SO42- anions were 0.10, 0.15, and 0.20 mg/dm,3 respectively. 2.2. Polymer Inclusion Membrane Preparation. A solution of the support (CTA), the ion carrier, and the plasticizer in dichloromethane was prepared. A portion of this solution was poured into a membrane mold that consisted of a 9.0-cm glass ring attached to glass plate with CTA-dichloromethane glue. The organic solvent was allowed to evaporate overnight, and the resultant membrane was separated from the glass plate by immersion in cold water. The membrane was soaked in an aqueous solution of 0.1 M HCl for 12 h and stored in distilled water. The details of PIM preparation are described in ref 31. The thickness of the PIM samples was measured using a digital micrometer (Mitutoy) with an accuracy of 0.0001 mm. The thickness of the membrane was measured 10 times for each case and is shown in the Results section as an average value of these measurements with a standard deviation of Cl > SO4

2-

The selectivity coefficients, which are defined as permeability ratios HCrO4-/NO3-, HCrO4-/Cl-, and HCrO4-/SO42- for this membrane system, are 8.6, 12.5, and 171, respectively. Other kinetic parameters of the transport of NO3-, Cl-, SO42-, and Cr(VI) ions are shown in Table 1. This behavior of PIM toward Cr(VI) ions seems to be based on two factors: (i) The hydrophobicity and nucleophilicity of the extractant present in the PIM (TOA) leads to an increase in quaternary ammonium-monovalent anion complex stability,40 and (ii) The solubility of anions in the hydrophobic organic medium of PIM is dependent on the hydration of anions.41 The selectivity of this membrane system is defined by not only the local extraction constant but also by the degree of hydratation of the transported anions. The linear correlation of permeability coefficients versus the Gibbs free energy hydration free ions in water in log-log coordinates suggests the aforementioned observation (Figure 4). This order of permeability limits seems to correlate with the molar Gibbs free energy of hydration for free ions in water,42 which is given in Figure 4 and is described by eq 29:

log P ) -4.18∆Gh + 10.06

(29)

As the literature states,43,44 in most cases, the order of simple inorganic anions follows the order of the hydration energy of these anions. The more easily the anion is to be dehydrated, the more readily it can be transported. The transport properties of metal ions are dependent on the composition of the membrane phase (i.e., the type and concentration of ion carrier, the type and amount of plasticizer, and the type of matrix used). This investigation was made by transporting chromate ions at a concentration of 0.0010 mol/

Figure 2. Relationship between log Y and log[TOA] during the solvent extraction of Cr(VI) by TOA solution in ONPPE. The diagrams show the confidence intervals of obtained results from five independent measurements.

Figure 3. Relationship between ln(c/c0) and transport time of Cr(VI) ions in aqueous solution containing HNO3, H2SO4, and HCl across the PIM. The source phase is a 0.10 mol/dm3 solution of mineral acids; the receiving phase is 0.10 mol/dm3 NaOH; the membrane is comprised of 0.8 cm3 ONPOE/1.0 g CTA, 1.0 mol/dm3 TOA. Table 1. Rate Constants, Permeability Coefficients, and Selectivity Order for the Transport of Chloride, Nitrate, and Sulfate Anions across a Polymer Inclusion Membrane (PIM) Containing Tri-n-octylamine (TOA)a Value parameter (h-1)

rate constant, k permeability coefficient, P (mm/s) -∆Gh (kJ/mol)b selectivity order a

Cl-

SO42-

NO3-

HCrO4-

0.001141 340

0.000857 1080

0.01699 300

0.1464 184

0.32

0.0024 0.47 3.99 HCrO4- > NO3- > Cl- . SO42-

Transport conditions are as given in Figure 3. b Data taken from ref

45.

dm3 from a 0.010 mol/dm3 HCl solution across a PIM of the following composition: 1.6 cm3 ONPPE/1.0 g CTA, 0.50 mol/ dm3 TOA into 0.010 mol/dm3 NaOH solution as a receiving phase. Increasing the amount of plasticizer in the matrix and increasing the TOA concentration (Figure 5) does not reduce the efficiency of the membrane system. Under these conditions, the sequence of metal-ion transport was determined by the selectivity order Cr(VI) > Cl-. The membrane obtained in this way effectively removed chromate ions: the RF values after the 12-h process were, for the Cr(VI) ions and Cl- anions, 96% and 16%, respectively (see Table 2). 3.3. Influence of Temperature on Cr(VI) Transport. The activation energy of transport across the PIM was determined using the Arrhenius equation. For this purpose, the measurements of Cr(VI) transport across the PIM with 1.28 mol/dm3 TOA were made, changing the temperature from 293 K to 338 K.

Ind. Eng. Chem. Res., Vol. 46, No. 16, 2007 5425 Table 3. Initial Fluxes of Chromium Transport across PIMs Obtained at Various Temperaturesa temperature, T (K)

1/T (× 103 K-1)

initial flux of Cr(VI) (µmol/(m2 s))

293 298 313 323 328 338

3.41 3.35 3.19 3.09 3.05 2.95

4.87 6.00 9.77 16.18 16.45 27.04

a Source aqueous phase: 0.0020 mol/dm3 Cr(VI) in 0.1 mol/dm3 HCl. Receiving phase: 0.10 mol/dm3 HCl solution; PIM: 0.80 cm3 ONOPE/1.0 g CTA, 1.28 mol/dm3 TOA.

Figure 4. Plot of permeability coefficients versus -∆Gh transported anions ((1) HCrO4-, (2) NO3-, (3) Cl-, and (4) SO42-) across the PIM, on a loglog scale. Conditions are as given in Figure 3. Experimental and calculated (based on the Marcus model) molar Gibbs energy of hydration of ions (-∆Gh) taken from ref 45.

Figure 6. Dependence of Cr(VI) fluxes on temperature obtained in transport across the PIM. The bar diagrams show standard deviations from three independent measurements.

enables calculation of the activation energy from the Arrhenius equation: Figure 5. Kinetics of Cr(VI) ions transport from HCl solution. Source aqueous phase is 0.0010 mol/dm3 Cr(VI) in 0.010 mol/dm3 HCl; receiving aqueous phase is 0.10 mol/dm3 NaOH; PIM is comprised of 1.6 cm3 ONPOE/1.0 g CTA; 0.50 mol/dm3 TOA. Table 2. Rate Constants, Permeability Coefficients, Initial Fluxes, and Recovery Coefficients Obtained during of Cr(VI) Transport across PIM with TOAa Value parameter

Cl-

Cr(VI)

rate constant, k (h-1) permeability coefficient, P (µm/s) initial flux, Ji (µmol/(m2 s)) recovery coefficient, RF (%)

0.02592 0.72 7.2 18

0.135 3.75 3.75 96

a

Transport conditions are as given in Figure 5.

The flux of ions transport in liquid membranes is dependent on numerous factors that are associated with the experimental conditions (i.e., temperature, viscosity of membrane phase, carrier concentration, pH, and metal concentration in source phase) and may be described by the equation17

log J ) A + log T - log η + log[H+] + log[TOA] + log cCr(VI) (30) where η is the viscosity of the organic phase in the membrane (given in centipoise), cCr(VI) the chromium concentration in the source phase (expressed in terms of molal), T the temperature of the process (expressed in Kelvin), and A an empirical constant. Under the given conditions of composition of the aqueous source phase, receiving phase, and membrane, the flux of metalion transport is dependent only on temperature. Therefore, the measurement of the initial transport flux at different temperatures

log Ji )

-Ea +B 2.303RT

(31)

where Ea is the activation energy (given in units of kJ/mol), R the gas constant (8.314 kJ/(mol K)), and B a constant. The results obtained are shown in Table 3 and are depicted graphically in Figure 6. As the data given in Table 3 show, the initial fluxes of Cr(VI) ions transport are strongly dependent on temperature. The temperature increase results in a larger value of the initial flux. Figure 6 shows that this flux decreases linearly with the higher inverse of temperature; this fact is confirmed by the very high determination coefficients (r2 ) 0.9881). Therefore, in accordance with eq 31, the activation energy may be determined if the slope of the straight line for the function log Ji ) f(1/T) is known. The activation energy determined in the temperature range of 20-65 °C is Ea ) 30.5 kJ/mol. This value is almost identical to the activation energy determined for Cr(VI) transport across a SLM that contains TOA in the temperature range of 25-45 °C (Ea ) 30.64 kJ/mol).17 Both membrane processes (i.e., transport across SLM and PIM) are controlled by the diffusion of chromium complexes in the membrane, and are not dependent on reactions that occur at the aqueous phase/membrane interface. The flux of Cr(VI) ions transport across the PIMs increased with higher temperature; therefore, this process is controlled by diffusion kinetics. 3.4. Diffusion of Chromium Complex across PIMs. The diffusion of the metal-ion complex across the membrane may be described by several simultaneously occurring transport steps (i.e., chemical reaction of complexation and decomplexation of metal ions with a carrier, and diffusion of a complex or a carrier in the membrane).

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Figure 7. Relationship between [Me]0 - [Me]t and time of Cr(VI) ions transport across the PIM. Source aqueous phase is 0.10 mol/dm3 HCl solution and 0.0020 mol/dm3 Cr(VI); receiving aqueous phase is 0.10 mol/ dm3 NaOH; PIM is comprised of 0.90 mol/dm3 TOA and 0.80 cm3 ONPPE/ 1.0 g CTA.

Figure 8. Changes of mole fractions of Cr(VI) ions in three phases during the transport across the PIM. Source phase is 0.10 mol/dm3 HCl solution and 0.0020 mol/dm3 Cr(VI); receiving phase is 0.10 mol/dm3 NaOH, PIM is comprised of 1.28 mol/dm3 TOA and 0.80 cm3 ONPPE/1.0 g CTA.

Table 4. Diffusion Coefficients of Cr(VI) Complexes for the Transport across PIMs Containing Different TOA Concentrationsa

a

TOA concentration in the membrane (mol/dm3)

diffusion coefficient (× 109 cm2/s)

0.34 0.69 0.90 1.28

3.10 2.00 2.47 1.77

Transport conditions are as given in Figure 7.

In the present work, diffusion coefficients for Cr(VI) ions have been determined using the method given in the experimental section, using the dependence of the carrier (TOA) concentration and the membrane thickness. The Cr(VI) complex diffusion coefficients were determined using the measurement data shown in Figure 7; the relation [Cr(VI)]0 - [Cr(VI)]t, as a function of the time of Cr(VI) transport across a membrane containing 0.90 mol/dm3 TOA, is shown. The [Cr(VI)]0 - [Cr(VI)]t relationship, as a function of the time of the process, is linear, and its slope (eq 19) allows one to calculate the diffusional resistances of the membrane (∆0). Knowing the diffusional resistances of the membrane and its thickness (d0 ) 28 µm), the diffusion coefficients of the Cr(VI) complex for various TOA concentrations in the membrane have been calculated (see Table 4). Moreover, based on the concentration measurements in the source and receiving phases, performed via the method described in Section 2.4, the changes of chromium concentration in membrane have been calculated. In Figure 8, the mole fractions of chromium(VI) in the source and receiving aqueous phases, and in the membrane, are shown. From eq 1, the flux of the Cr(VI) complex in the membrane has been calculated to be 24.1 µmol/(m2 s). Assuming the Cr(VI) concentration in the membrane to be 8.2 × 10-5 mol/dm3 and d0 ) 28 µm, from eq 22, the diffusion coefficient of the complex (TOAH)HCrO4 was calculated to be 8.1 × 10-9 cm2/s. However, this result is incorrect, and the gross error is due to the fact that the Cr(VI) concentration in the membrane after achieving the maximum has a tendency toward a continuous decrease; as a result, the diffusion is no more controlled by a concentration gradient at the interface and the rate of complexing and decomplexing begins to have an important role. The transport of Cr(VI) ions across PIMs of a different thickness, but with an identical TOA concentration in the membrane equal to 1.28 mol/dm3, has been also investigated. The prepared membranes had thicknesses of 27, 29, 39, and 54 µm.

Figure 9. Dependence of permeability coefficient on the thickness of PIMs (d0) during Cr(VI) transport across the PIM. Source aqueous phase is 0.0020 mol/dm3 Cr(VI) in 0.10 mol/dm3 HCl; receiving phase is 0.10 mol/dm3 NaOH solution.

The removal of metal ions from an aqueous source phase, which contained 0.0020 mol/dm3 Cr(VI) and 0.10 mol/dm3 HCl, into an aqueous receiving phase that contained 0.10 mol/dm3 NaOH was performed for 10 h, with on-line measurement of the Cr(VI) concentration in the source and receiving phases. The determined values of the permeability coefficients (P) and measured thickness of membranes for particular experiments served to help calculate the diffusion coefficient (D0) of the chromium complex. From the linear relation P vs 1/d0, described by eq 21 and shown in Figure 9, the slope (D0[TOA]Kex) was calculated to be 1.7 × 10-8. Knowing the carrier concentration ([TOA] ) 1.28 mol/dm3) in the membrane and the value of the extraction constant Kex, the diffusion coefficient was calculated to be 1.22 × 10-10 cm2/s. The transport of Cr(VI) ions across the PIM happens under diffusion kinetic control, because its rate increases as the temperature increases, according to eq 31. The diffusion coefficient of the Cr(VI) complex with TOA is dependent, to a small extent, on the carrier concentration in the membrane, and the determined average value of D0 in the range of TOA concentrations studied is 2.34 × 10-9 cm2/s (see Table 4). This value corresponds with the determined diffusion coefficients of the Cr(VI) complex with Aliquat 336 for SLM and PIM transport (i.e., in the range of 10-8-10-9 cm2/s).29 Because only a few reports have concerned the investigation of the diffusion of Cr(VI) ions across SLM, a comparison of both types of membranes is difficult. Alonso and Pantlides45 reported that the D0 value for the Cr(VI)-Aliquat 336 complex determined in the organic solvent was equal to 2.5 × 10-7 cm2/ s. The value of this diffusion coefficient does not take into

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account the diffusional resistances of the membrane, which are associated with diffusion across the polymer film of a given tortuosity and porosity. The high viscosity of the plasticizer (ONPPE), 7.58 cP,46 causes the decrease in D0 values, but simultaneously helps in the improvement of the stability of the system studied. As it was established, the transport of the Cr(VI) complex is under the control of its diffusion across the PIM; however, differences in D0 values (10-9-10-10 cm2/s) may suggest a slight tendency toward the formation of polyoxochromate complexes in the organic phase. This process does not remarkably slow the transport, because it is not dependent on carrier concentration, and it is only slightly dependent on the diffusion route (this observation is reflected in the one-order-lower value of the diffusion coefficient). However, Harrington and Stevens47 suggested that, at high Cr(VI) concentrations in the membrane, the chromium organic complex form was determined to be (R3N)(R3NH)HCrO4, because of aggregation in the organic phase. In this report, which they obtained at 20 °C, the low values of the diffusion coefficients for R3N and the Cr(VI) organic complex were 1.90 × 10-10 and 2.43 × 10-10 m2/s, respectively.48 In addition, de Gyves et al.32 achieved, in the membrane phase, the value of the diffusion coefficient for a Cu(II)- LIX 84-I complex (D0 ) 10-12.2 m2/s), and, based on the transport profiles, they proposed a carrier-diffusion mechanism of ion transport through the PIM. The step that limits the process rate in membranes of the type SLM and PIM is the diffusion of the metal complex in the membrane phase. Sometimes, this process may be slower, because of the reaction that occurs at the interface of the source phase and the membrane, as well as because of the formation of polymeric associated metal complexes in the organic phase of the membrane. Based on the determined values of the diffusion coefficient from the dependence on the carrier concentration (only a slight decrease of their values with the higher TOA concentration), as well as on the membrane thickness, it may be established that the transport is under the control of mixed kinetics (i.e., of the diffusion of the metal complex and, to a small extent, of the chemical reaction that occurs in the liquid phase of the membrane). 4. Conclusions Competitive transport experiments demonstrated the ability of polymer inclusion membranes (PIMs) to extract chromium(VI) from a mineral acids solution, using a commercial carrier (i.e., tri-n-octylamine, TOA). Based on the present kinetic model for Cr(VI) permeation, it can be inferred that the permeation process is controlled by the diffusion of the metal carrier complex across the PIM. The role of membrane diffusion becomes dominant under the conditions of low pH and low carrier concentrations in the membrane phase. The organic resistances values, together with the value found for the apparent activation energy, as well as the metal profile curves of the permeability versus process time, indicate that the facilitated transport of Cr(VI) species across the PIM proceeds via a carriermediated mechanism. In this mechanism, the diffusion of metal species across the membrane phase is the rate-controlling step in the experimental conditions that have been applied. Acknowledgment Financial support of this work was provided by Polish Science Foundation (Grant 4T09C030 32). The author gratefully ac-

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ReceiVed for reView February 6, 2007 ReVised manuscript receiVed May 8, 2007 Accepted May 30, 2007 IE070215I