Anal. Chem. 1999, 71, 819-826
Mechanism and Kinetics of Copper(II) Transport through Diaza-crown Ether-Fatty Acid-Supported Liquid Membrane Franc¸ ois Guyon, Nalini Parthasarathy, and Jacques Buffle*
CABE, Department of Inorganic, Analytical and Applied Chemistry, University of Geneva, 30 quai E. Ansermet, CH-1211 Geneva 4, Switzerland
The mechanism of macrocycle-mediated Cu(II) transport through a supported liquid membrane containing 1,10didecyl-1,10-diaza-18-crown-6 ether-fatty acid in toluene/ phenylhexane solvent mixture has been investigated. The mechanism was elucidated by studying the effects of parameters such as stirring speed, membrane thickness, and temperature on Cu(II) flux. The results showed that a countercation transport is controlled by a sodium gradient. The rate-limiting step of Cu(II) transport in the system has been found to be diffusion of metal-carrier complex in the membrane. But, depending on the hydrodynamic conditions and cell geometry, diffusion of metal in the stagnant aqueous Nernst layer is found to be rate limiting. In addition, a linear Cu(II) gradient in the membrane was found by performing Cu(II) transport experiments in a stack of eight membranes and analyzing the copper(II) concentration in each of the membranes separately, supporting diffusion-limited steady-state transport. Comparative studies at optimum operational conditions have been done with two types of supports, Celgard 2500 and Accurel, differing in their pore size and porosity. From lag time measurements, the effective diffusion coefficient, D h m, of the metal-carrier complex in the membrane was evaluated and the values were found to be 5.2 × 10-8 and 2.55 × 10-7 cm2 s-1 for Celgard and Accurel membranes, respectively. These differences in D hm between the two membranes has been interpreted in terms of molecular diffusion of the complex in the solvent, Dm, and of the equilibrium constant for its adsorption on the pore wall of the membrane.
Facilitated transport of target element species using supported liquid membranes (SLMs) has a wide field of applications both industrial and analytical including separation, preconcentration of target species, removal of analytes from ground- and wastewater, water treatment, and extraction of analytes from biomedical samples.1-9 Few studies have been made on their application to (1) Danesi, P. R. Sep. Sci. Technol. 1984-85, 19, 857. (2) Jonsson, J. A.; Mathiasson, L. Trends Anal. Chem. 1992, 11, 106. (3) van Straaten-Nijenhuis, W. F.; de Jong, F.; Reinhoudt, D. N. Recl. Trav. Chim. Pays-Bas 1993, 112, 317. 10.1021/ac9804947 CCC: $18.00 Published on Web 01/20/1999
© 1999 American Chemical Society
trace metal element analysis in natural water10 and still fewer studies for metal speciation studies under natural water conditions.11,12 The attractive features of SLMs are high selectivity and simultaneous separation and preconcentration of elements, and it can be used for a broad spectrum of elements by proper choice of the carrier.13 It is a separation method in which an organic solvent immiscible in water containing a complexing agent, selective toward the target analyte, is immobilized in a thin macroporous hydrophobic membrane and interposed between two aqueous phases (source and strip solutions). The uphill transport may be aided by proton countercation gradient or co-anion gradient.1,14,15 Most of the studies have been made using a proton countergradient. Recently, for the purpose of applying SLM to trace metal speciation studies in natural water conditions, a countercation-aided system was designed containing a neutral carrier, 1,10-didecyl-1,10-diaza-18-crown-6 ether (22DD), and laurate as counteranion (Figure 1) in toluene/phenylhexane solvent. Since 22DD contains both oxygen and nitrogen donor atoms, it can transport transition and IIb metals as well as alcali metal ions.16,17 At neutral pH, these latter may thus serve as countercation countergradient. For improving the flux of metal transport and designing SLMs exhibiting high selectivity and stability for (4) Noble, R. D. In Membrane separation technology; Sterm, S. A., Ed.; Elsevier: New York, 1995. (5) Tsukube, H. In Liquid membrane application; Arachi, T., Tsukube, H., Eds.; CRC Press: Boca Raton, FL, 1990. (6) Cox, J. A. Talanta 1990, 37, 1037. (7) Chiarizia, R.; Horwitz, E. P.; Rickert, P. G.; Hodgson, K. M. Sep. Sci. Technol. 1990, 25, 1571. (8) Wijers, M. C.; Bargeman, D.; Van den Boomgaard, Th. Annu. Hydrometall, Meeting 24th 1994, 137. (9) Bartsch, R. A.; Way, J. D. In Chemical separation with liquid membranes: an overview; Bartsch, R. A., Way, J. D., Eds.; ACS Symposium Series 642; American Chemical Society: Washington, DC, 1996; Chapter 1. (10) Djane, N. K.; Ndung’u, K.; Malcus, F.; Johansonn, G.; Mathiasson, L. Fresenius J. Anal. Chem. 1997, 358, 822. (11) Parthasarathy, N.; Buffle, J. Anal. Chim. Acta 1991, 254, 1. (12) Parthasarathy, N.; Buffle, J. Anal. Chim. Acta 1991, 254, 9. (13) Izatt, R. M.; Lindh, G. C.; Bruening, R. L.; Bradshaw, J. S.; Lamb, J. D.; Christensen, J. J. Pure Appl. Chem. 1986, 58, 1453. (14) Fyles, T. M.; Malik-Diemer, V. A.; McGavin, C. A.; Whitfield, D. M. Can. J. Chem. 1982, 60, 2259. (15) Reichwein-Buitenhuis, E. G.; Visser, H. C.; de Jong, F.; Reinhoudt, D. N. J. Am. Chem. Soc. 1995, 117, 3913. (16) Parthasarathy, N.; Buffle, J. Anal. Chim. Acta 1994, 284, 649. (17) Parthasarathy, N.; Pelletier, M.; Buffle, J. Anal. Chim. Acta 1997, 350, 183.
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Figure 1. Schematic representation of 1,10 didecyl-1,10-diaza-18crown-6 (22DD) and lauric acid (LA).
long-term continuous use for metal ion monitoring in water, an insight into the transport mechanism in a given system is required. For this purpose, the exact nature of back-transported countercation, the transport rate-limiting step of the overall flux of the species of interest, and the type of metal-carrier complex formed in the organic solvent must be determined. A literature survey on metal transport mechanisms reveals that, depending on the SLM system, the rate-limiting step is either the uptake or release of metal at the membrane/aqueous solution interface or the diffusion of metal-carrier complex across the membrane. In this paper, the role of the stirring rate in the aqueous compartments, temperature, and membrane thickness and the nature of copper(II) concentration profiles in the membrane have been investigated, to determine the transport rate-limiting step of Cu(II) through 22DD/lauric acid (LA)/toluene/phenylhexane SLM. Combination of these results with extraction data allowed us to discriminate the relative contributions of true diffusion of the complex in the membrane liquid phase and its adsorption on the solid polymeric membrane phase.
MATERIALS AND METHODS Reagents, Membrane, and Apparatus. All the reagents used for transport experiments were of analytical-reagent grade unless otherwise stated; i.e., 2-(N-morpholino)ethanesulfonic acid (MES, Sigma), trans-1,2-diaminocyclohexane-N,N,N′,N′-tetraacetic acid monohydrate (CDTA, Fluka), sodium hydroxide and lithium hydroxide (Merck), lauric acid (LA, Fluka), 1,10-didecyl-1,10-diaza18-crown-6 ether (Kryptofix 22DD, Merck). The solvents, toluene, phenylhexane, phenyldecane, and 2-nitrophenyl octyl ether (NPOE), were Fluka products. Celgard 2500 (Celanese Plastic, Charlotte, NC) polypropylene hydrophobic membrane (porosity, Θ ) 0.45; thickness, l ) 25 µm, pore diameter, 0.04 µm) was used as the flat sheet support. Some experiments were done with an Accurel 1E-PP (Akzo; Θ ) 0.75, l ) 100 µm; pore diameter, 0.1 µm) for comparison purpose. The copper concentrations were measured by flame atomic absorption spectrometry (AAS) using a Pye Unicam SP9 spectrophotometer. MilliQ water was used for preparing all the aqueous solutions. Transport Experiments. The Celgard 2500 membrane was impregnated with a 1/1 (v/v) mixture of toluene/phenylhexane containing 10-1 M 22DD-LA (1/1). After rinsing it with water to remove the solvent excess, the membrane was placed between two identical compartments (solution volume 80 cm3) of the 820 Analytical Chemistry, Vol. 71, No. 4, February 15, 1999
Figure 2. Diagram of the diffusion cell used for performing transport experiments.
transport cell (Figure 2). The effective membrane area was 7.2 cm2. The source compartment was filled with 80 mL of 5 10-5 M copper(II) nitrate in 10-2 M MES buffer (pH 6, adjusted with LiOH); 80 mL of 10-3 M CDTA (pH 6, adjusted with NaOH) was used as the strip solution. Aqueous solutions were stirred, and aliquots of source and strip solutions were periodically withdrawn and analyzed by AAS. The initial concentrations were determined before the two aqueous solutions were put in the transport cell. The same protocol was used in all experiments, unless otherwise stated. To study the role of sodium as countercation, sodium transport from the strip to the source solution through a single Celgard membrane was also determined simultaneously with copper(II) transport. Transport experiments were also performed using different solvent mixtures, toluene/phenyldecane (1/1) and toluene/ NPOE (1/1), in order to check the effect of the solvent viscosity on Cu(II) transport across a single membrane at maximum stirring rate. The effect of stirring rate on the rate of Cu(II) transport was done with a single membrane. The stirring rates of the solutions was determined with a stroboscope (Digistrob RDS 10, Reglomat AG). The effect of temperature on the rate of Cu(II) transport was studied using a single membrane as well as a stack of eight membranes (see below). The Plexiglas diffusion cell, the source, and the strip solutions were all thermostated using a thermostat Thermomix M with a precision of (0.4 °C. Effect of Membrane Thickness. Lag Time Determination. Several 25-µm membranes were stacked together and then impregnated with the carrier solution. The membranes stick well together, probably because of electrostatic attractions. Whereas a single impregnated membrane is transparent, stacked membranes appear translucent; the more membranes there are in the stack, the more translucent it appears. The excess of solvent was removed from the stack of membranes by rinsing it with water. The stack of membrane was then placed in the diffusion cell as shown in Figure 2. The lag time (tlag, Figure 3b) corresponds to the time required to establish a stationary concentration gradient in the membrane, i.e., a constant flux through it. The effective diffusion coefficient of metal/carrier complex D h m through the membrane can be computed from lag time value determined
Figure 4. Relation between sodium concentration in the source compartment and Cu(II) concentration in the source and strip compartments at different times (ranging between 10 and 190 mn) during copper(II) transport experiment. [Cu2+]source (b) and [Cu2+]strip (9) vs [Na+]source. Conditions used are the same as those given for Figure 3a.
Figure 3. Cu(II) transport through SLM containing 22DD/LA as carrier in toluene/phenylhexane: typical plots of copper(II) concentration, [Cu2+], vs time. Conditions used: initial source solution, 5 × 10-5 mol L-1 Cu2+ in 10-2 mol L-1 MES/LiOH buffer (pH 6.0); strip solution, 10-3 mol L-1 CDTA (pH 6.2); carrier, 0.1 mol L-1 22DD and 0.1 mol L-1 LA in phenylhexane/toluene (v/v 1/1). b, [Cu2+] in source solution; 9, [Cu2+] in strip solution; 2, sum of source and strip Cu2+ concentrations. Transport experiments were done with (a) one membrane and (b) a stack of eight membranes.
experimentally, as follows:18,19 2
D h m ) l Θ/6tlag
(1)
where l is the membrane thickness, Θ the porosity, and tlag the lag time. Determination of Metal Concentration Profiles in the Membrane. Measurements were done with eight stacked membranes. After assembling the cell with the membrane, source and strip solutions were placed in the two compartments and stirred (maximum stirring rate) for preset times (typically 5, 10, 15, 30, and 60 min). Samples of source and strip solutions were then withdrawn for analysis, the two compartments were emptied, and then the stacked membrane was removed and rinsed with water. The eight membranes were separated from each other (the whole operation took ∼90 s) and immersed in tubes containing aqueous CDTA solution (10-3 M, pH 6.1) to back extract the metal from each of the membrane. After shaking the tubes for 2 h, the copper concentrations in the extracts were determined by AAS. An average concentration of copper in each membrane was then determined. (18) Crank, J. In The mathematics of diffusion, 2nd ed.; Oxford University Press Inc.: New York, 1975. (19) Yi, J. Korean J. Chem. Eng. 1995, 12, 391.
Determination of the Distribution Coefficient of Cu(II) between the Source Solution and the Membrane. A single membrane impregnated with carrier was dipped in an aqueous solution containing 5 × 10-5 M Cu2+ in 10-2 M MES (pH 6.1 adjusted with LiOH) placed in a beaker and gently agitated overnight on a shaker to ensure equilibrium. Then the membrane was rinsed with water and dipped in 10-3 M CDTA solution (pH 6.2 adjusted with NaOH) to extract the metal from the membrane. The equilibrium values of total copper(II) concentration extracted in the membrane, [Cu2+]t,m, and copper concentration in the aqueous solution, [Cu2+]aq, were determined by AAS. The distribution coefficient, KD, was calculated using the following equation:
KD ) [Cu2+]t,m/[Cu2+]aq
(2)
The partition coefficient, Kp, was determined using a classical liquid/liquid extraction method: 2 mL of 5 × 10-2 mol L-1 22DD and LA in a mixture of phenylhexane and toluene (1/1 v/v), placed in a glass bottle, and 2 mL of 5 × 10-5 mol L-1 Cu(II) nitrate in 10-2 mol L-1 MES (pH 6.1, adjusted with LiOH) were vigorously agitated with a shaker. The mixture was then centrifuged (4000 rpm for 30 min). The aqueous solution was withdrawn and the copper(II) concentration determined as described before. Kp was computed using eq 2, where [Cu2+]t,m is replaced by the total Cu(II) concentration in the solvent, [Cu2+]t,s. RESULTS Nature of the Countercation. The variations of Cu(II) concentration in the source and strip phases and that of Na(I) in the source phase with time are shown in Figure 4. Na+ concentrations vs time in the strip phase are not shown as the variation of sodium concentration were negligible compared to the initial total sodium concentration. As can be seen, sodium concentration in the source increases with time whereas Cu(II) concentration decreases. A plot of [Cu2+] (in source and strip solution) vs [Na+] in the source solution shows a linear relation, and the slope of the line was found to be 0.50 ( 0.02, indicating that two sodium ions are exchanged for one copper(II) ion. Determination of D h m, KD, and δ. A typical concentration vs time profile for Cu(II) transport is shown in Figure 3a. The mass Analytical Chemistry, Vol. 71, No. 4, February 15, 1999
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balance of copper(II) in the source and strip phase was obeyed at all times, t, indicating that there is no accumulation of Cu(II) in or on the membrane. Copper concentration in the strip phase varies linearly with time up to 25 min. Assuming that copper(II) transport is diffusion limited, the flux can be determined from the initial slope using the following general flux equation,1 based on Fick’s law, valid for dilute source solutions ( 450 rpm. This behavior is similar to that observed for convective diffusion at electrode surface where flux is found to be proportional to a fractional power of ω.20 A plot of J vs ω1/2 indeed yields a straight line. In subsequent studies, the maximum usable stirring speed (920 rpm) was used to minimize and maintain the thickness of the Nernst layer constant. Under this condition, the flux was found to be (1.43 ( 0.14) × 10-10 mol cm-2 s-1. A typical concentration vs time profile for copper(II) transport obtained with eight stacked 25-µm membranes is shown in Figure (20) Levich, V. G. Physiochemical hydrodynamics; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1962.
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no. of J D hm stacked thickness, l (10-10 mol P (10-3 tlag (10-8 -2 -1 -1 2 membranes (µm) cm s ) cm s ) (mn) cm s-1) KDa
(4)
where P is the permeability of copper(II). Combining eqs 3 and 4 and integrating the equation between t ) 0 and t ) t, one obtains
C0so - Cst
Table 1. Influence of Membrane Thickness on Cu(II) Flux, Diffusion, and Extraction Parameters for Celgard and Accurel Membranes
3b. J and P, determined from the initial slope of the curve after the time lag (if any), were found to decrease with increasing membrane thickness (Table 1). A plot of 1/P vs l yields a straight line (Figure 5) as expected for diffusion-controlled processes (eq 4). The effective diffusion coefficient, D h m, was computed from the lag time by using eq 1. D h m was found to be (5.2 ( 0.5) × 10-8 cm2 s-1 (Table 1). The aqueous Nernst layer thickness, δ, and the distribution coefficient, KD, of Cu2+ between the source phase and the membrane can also be evaluated from the slope of the plot in Figure 5, by substituting the experimentally values of D hm and Daq (7.8 × 10-6 cm2 s-1). The value of KD was thus found to be 1200 ( 180, and the thickness of the aqueous diffusion layer was found to be 15 ( 2 µm at 920 rpm, which is in accordance with other results.21 Some experiments were performed using an Accurel membrane (same chemical nature but different porosity and pore sizes) to determine the influence of the membrane structure on the metal complex diffusion coefficient. Transport experiments were done by stacking two 100-µm Accurel membrane (total l ) 200 µm). Under these conditions, and compared to the results of a stack of eight Celgard membranes (i.e., for the same thickness), a higher flux was observed (J ) (1.38 ( 0.14) × 10-10 mol cm-2 s-1) corresponding to a higher value of D h m ((2.5 ( 0.3) × 10-7 2 -1 cm s , Table 1). Moreover, a KD value of 620 ( 93 was found for Accurel membrane. (21) Paugam, M. F.; Buffle, J. J. Membr. Sci. 1998, 147, 207.
Table 2. Effect of Temperature on Cu(II) Flux (J), Permeability (P), and Effective Diffusion Coefficient, D h ma T (K)
J (10-10 mol cm-2 s-1)
P (10-3 cm s-1)
294.3 301.8 309.5 315.5
1.43 1.70 2.23 2.39
3.9 4.1 5.3 5.7
T (K)
tlag (mn)
D h m (10-8 cm2 s-1)
J (10-10 mol cm-2 s-1)
P (10-3 cm s-1)
294.3 311.0 316.3
9.6 6.3 5.8
5.2 7.9 8.6
0.89 1.40 1.63
1.9 3.5 4.7
a Transport experiments done with (top) a single Celgard membrane and (bottom) a stack of eight Celgard membranes.
Figure 6. Effect of the temperature, T, on the Cu(II) flux. Experiments were done with one membrane (9) and with a stack of eight membranes ([). Conditions used are the same as those described in Figure 3.
Effect of Temperature. The effect of temperature, T, on J was studied to check whether diffusion of Cu(II) in the membrane was indeed the rate-limiting step. Both chemical reaction kinetics and diffusion are temperature dependent, but the effect of T is usually much stronger on chemical kinetics than on diffusion processes. A discrimination between the two limiting cases can be made by determining the corresponding activation energy, ∆E*. The Stokes-Einstein equation shows that the molecular diffusion coefficient, Dm, of the species in solution is related to temperature by
Dm ) kBT/6πηr
(6)
where the viscosity, η, is given by η ) η0 exp(∆E*/RT). Since the temperature dependence of solvent viscosity is predominant in eq 6, an Arrhenius-type behavior should be observed for Dm. In our case, the measured flux does not depend directly on the molecular diffusion coefficient, Dm, but on the effective diffusion coefficient, D h m. The difference between these two parameters is explained in the Discussion section, where it will be shown that their temperature dependence is similar. Experimentally, the flux and effective diffusion coefficient were found to increase with the temperature (Table 2) according to an Arrhenius plot (Figure 6). The activation energies ∆E* for one and eight stacked membranes obtained from the slope of the lines were found to be nearly the
Figure 7. Copper(II) concentration profiles in the membrane at various transport times. Experiments performed with eight membranes stacked together: 9, 15 min; [, 30 min; 2, 60 min.
same i.e., 20 ( 6 and 21 ( 6 kJ mol-1 respectively, i.e., within the activation energy range for diffusion processes.15,22,23 Determination of Metal Concentration Profile in the Membrane. Another way to assess that diffusion in the membrane is the limiting step is to determine the concentration gradient in the membrane as a function of time. The advantage of stacking eight membranes is that it can be considered as a single thick membrane of 200 µm for the transport, while simultaneously the copper(II) concentration can be determined in each individual membrane, at any time. To our knowledge, it is the first time that the Cu(II) concentration profiles have been measured in this way in macrocycle-mediated transport in a supported liquid membrane. The copper(II) concentration measured in each single membrane of the stack is an average value since there is also a concentration gradient in each membrane. The transport experiments were done as described before; after prescribed times, the membranes were separated and Cu(II) in the membranes was analyzed. In all the experiments, the sum of the number of moles of Cu(II) in the source, the strip phases, and in membranes corresponded to the total number of moles of copper initially used in the source solution. Typical plots of the number of moles of Cu(II), nCu, in the membrane as a function of the membrane distance are shown in Figure 7. The Cu(II) concentration gradient decreases with time from 15 to 60 min as expected because the concentration in the source phase also decreases with time. During this period, in the last membrane (which is in contact with the strip side), low but constant values of nCu within experimental errors were observed. The fact that nCu does not extrapolate to zero at l ) 200 µm is most likely due to contaminations arising from experimental difficulties during membrane separation before analysis. Nevertheless, the fact that nCu in this membrane is always low and constant, as well as the fact that linear Cu(II) concentration profiles are observed in the membrane after 15 min (Figure 7), suggests that Cu(II) transfer from the membrane to the strip solution is fast, confirming that membrane diffusion is the limiting step. The Cu(II) concentration gradients in the membrane were also measured at 5 and 10 min, i.e., a period of time in which Cu(II) concentration in the source solution was quasi-constant. During this period, the average concentration gradient across the whole membrane increases to reach a maximum value at 15 min. Due (22) Kobya, M.; Topc¸ u, N.; Demircioglu, N. J. Membr. Sci. 1997, 130, 7. (23) Lazarova, Z.; Boyadzhiev, L. J. Membr. Sci. 1993, 78, 239.
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to experimental difficulties, more precise data could not be obtained. But these results are in good agreement with the observation that a lag time of 10 min is necessary to reach the steady-state gradient for a stack of eight membranes. During this lag time the total number of moles of Cu(II) in the membrane increases. DISCUSSION Countercation/Countergradient. In most SLM systems used, the proton serves as a countercation gradient.1,14,15 In our case, however, in order not to perturb the test sample, transport experiments are done at constant pH values close to that found in natural waters in both the source and strip compartments. The countercation thus is not H+ but Na+. Indeed, Figure 4 shows that two sodium ions are exchanged for one Cu2+. This confirms that this SLM system is suitable for in situ metal speciation in natural water, for which pH change of the test medium is not acceptable. Diffusion vs Chemical Reaction Limited Kinetics. All the Cu(II) transport experiment results suggest that in the 22DD/ LA/toluene/phenylhexane SLM system, diffusion of the metal complex across the membrane possibly coupled to diffusion of metal ion in the aqueous Nernst layer is the rate-limiting steps. Indeed, (a) the flux, J, was found to be directly proportional to the square root of the stirring rate, a relation commonly found for convective diffusion-controlled processes in solution;20 (b) at maximum stirring rate (920 rpm), 1/P (and 1/J) was found to vary linearly with l (Figure 5) as expected for diffusion-controlled transport in the membrane;15,22,23 (c) the temperature dependence of transport supports a diffusion process irrespective of membrane thickness (Figure 6); and (d) a steady-state linear concentration gradient was found within the membranes. Since no metal accumulation was found either in the first or eighth membrane, complexation and decomplexation must be fast. Furthermore, transport experiments performed using various solvent mixtures show that P decreases with increasing viscosity. However, the decrease is much less than that expected from the change in only the diffusion coefficient.24 This is because P depends on both D h m and KD (eq 4). The preliminary experiments suggest that the viscosity and solvent properties modify D h m and KD, but no systematic study of the solvent effects was done as this was not the goal of this paper. The effective diffusion coefficient in the membrane, D h m, evaluated from the time lag measurements (eq 1) was found to be (5.2 ( 0.5) × 10-8 and (2.5 ( 0.3) × 10-7 cm2 s-1 for Celgard and Accurel flat sheet membranes, respectively. D h m was also estimated by combining the flux value measured using eight stacked Celgard membranes and the corresponding concentration gradient computed from the concentration profile (Figure 7); it was found to be (8 ( 4) × 10-8 cm2 s-1 for Celgard membrane. This higher D h m value (compared with 5.2 × 10-8 cm2 s-1) stems from the fact that accurate determination of D h m values in this way is made difficult by a lot of sample handling involved in the determination of the concentration profile. Nevertheless, the two values are of the same order of magnitude, confirming the validity of the interpretation. Thus, all the results lead to the conclusion that the rate-limiting step is the diffusion of metal through the membrane and possibly (24) Visser, H. C.; de Jong, F.; Reinhoudt, D. N. J. Membr. Sci. 1995, 107, 267.
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the aqueous Nernst layer, depending on conditions. From Figure 5, one can deduce that the resistance to transport due to diffusion through the aqueous Nernst layer (first term in brackets, eq 4) is of the same order of magnitude as that through the membrane (second term in brackets, eq 4) when the membrane thickness is 130 µm. This observation is important to choose the right membrane thickness in trace metal speciation studies since the determination of metal fluxes under varying rate-limiting conditions such as the diffusion in the aqueous Nernst layer or through the membrane will allow one to discriminate between the free metal ions and labile or inert metal complexes.25 Values of δ, KD, D h m, and Dm. The flux was found to increase linearly with the square root of the stirring rates (up to ω < 920 rpm) as opposed to the observations reported in the literature where the flux becomes independent of ω for ω g 400 rpm.14,15,26 This deviation is probably due to the much higher metal/carrier concentration ratio used in the literature studies compared to that used here. At large concentration ratio, the carrier at the source/ membrane interface may become saturated with metal ions and hence the Cu(II) transport across the membrane may become rate limiting. Alternatively the cell geometry plays a role to achieve a constant Nernst layer thickness. At the maximum stirring rate used here (920 rpm), the aqueous Nernst layer thickness, δ, is 15 ( 2 µm, which is of the same order of magnitude as that reported by other workers.1,21 KD values of 1200 ( 180 and 620 ( 93 were found for Celgard and Accurel membranes, respectively. These values are very high compared to the partition coefficient value, Kp ) 10 ( 1, found by classical liquid/liquid extraction. Direct determination of KD by dipping the Celgard membrane impregnated with the solvent and carrier in a Cu(II) aqueous solution yielded KD ) 1127 ( 60, confirming the higher KD in polypropylene membranes. An additional interesting feature is that KD values decrease whereas D h m values increase when passing from Celgard to Accurel membranes (Table 1). The only differences between these two membranes are their porosity, Θ, and pore diameter. All the above observations can be interpreted by assuming that the metalcarrier complex is adsorbed on the polymers of the polypropylene membrane, as shown schematically in Figure 8. The adsorption constant can be defined as (see Appendix)
K′ads )
KD - Kp V Kp S
(7)
Assuming the pores to be cylindrical with a radius r, the ratio of the internal solution volume to the internal surface area of the membrane, V/S, can be estimated to be r/2. For comparison, K′ads values for Celgard and Accurel membranes were computed by substituting the values of KD (Table 1) and Kp ()10) in eq 7 and were found to be 3.4 × 10-3 and 4.4 × 10-3 m, respectively. K′ads(Celgard)/K′ads(Accurel) is 0.77, which is fairly close to the value of 1 expected for membranes that are chemically identical. The difference may be due to the fact that pores are not cylindrical and/or the surface concentration of adsorption sites on the pore wall, Γsites, for Celgard and Accurel are different due to different polymer morphology. (25) Agraz, R.; van Leeuwen, H. P.; Buffle, J., unpublished results. (26) Danesi, P. R.; Chiarizia, R. CRC Rev. Anal. Chem. 1980, 10, 1.
Equation 4 can then be rewritten by substituting D h mKD from eq 8:
[
]
δ l 1 Cso ) ) + P J Daq DmKp
Figure 8. Schematic representation of the adsorption process occurring in the pore of the membrane. [M]aq, metal concentration in the source aqueous phase. [ML]x, concentration of metal-carrier complex adsorbed on the pore wall (x ) ads) and dissolved in the organic solution of the membrane (x ) org). Kp and Kads are the thermodynamic partition and adsorption coefficients. Dm is the true diffusion constant of the metal complex in the solvent obtained by the Stokes equation. KD and D h m are the measured distribution coefficient and effective metal-complex diffusion coefficient in the membrane, respectively.
The validity of this adsorption process can also be checked as follows: the effective diffusion coefficient, D h m, is a weighted average of the molecular diffusion coefficients of the various complexes in the membrane phase (eq A3 of the Appendix) in particular those of the dissolved (Dm) and adsorbed (Dads m ) complex. When Dads ∼ 0, it can be shown (Appendix) that m
D h m ) Dm(Kp/KD)
(8)
Dm can be estimated from the Stokes equation (eq 6), using the 22DD radius (r ) 3.71 Å) evaluated from crystallographic data27 by assuming a planar structure and using solvent mixture viscosity, η ) 1.122 cP, estimated by averaging the values reported in the literature for the two pure solvents.28,29 Dm was found to be 5.2 × 10-6 cm2 s-1, which is in good agreement with the value Dm ) 6.2 × 10-6 cm2 s-1 obtained using eq 8. Since KD . Kp, K′ads ) (KD/Kp)(V/S) (eq 7), and the temperature dependence of D h m can be expressed as (eq 8)
d(ln D h m) d(1/T)
)
d(ln Dm) d(1/T)
-
d(ln K′ads) d(1/T)
(9)
d(ln Dm)/d(1/T) was estimated to be -17 kJ mol-1 using the solvent viscosity values reported in the literature. An experimental value of -21 kJ mol-1 was found for d(ln D h m)/d(1/T) (Figure 6). Thus, from eq 9 the enthalpy for the adsorption process in our system is estimated to be ∼4 kJ mol-1, which is of the same order of magnitude as that reported for similar compounds.30 Hence, the validity of the adsorption process on the pore walls of the membrane described in Figure 8 is confirmed by these computations. (27) Herceg, M.; Weiss, R. Bull. Soc. Chim. Fr. 1972, 2, 549. (28) Phenylhexane viscosity, η ) 1.655 cP (T ) 293 K) from: Beilsteins, Zweiter Teil, 1964, Syst. Nr. 470. (29) Toluene viscosity, η ) 0.590 cP (T ) 292.47 K) from: International Critical Tables of Numerical Data, Physical Chemistry and technology; Washburn, E. W., Ed.; McGraw-Hill Book Co. Inc.: New York, 1930. (30) Shinoda, K.; Nakagawa, T.; Tamamushi, B. I.; Isemura, T. In Colloidal surfactants: some physicochemical properties; Loebl, E. M., Ed.; Academic Press: New York, 1963.
(10)
Comparison of eqs 4 and 10 shows that the flux is not modified by the adsorption process on the membrane. In fact, adsorption increases the flux by increasing Kp to KD, but simultaneously it has an exactly opposite effect by decreasing Dm to D h m. CONCLUSION The results of the present study on a copper(II) transport mechanism through a 22DD/LA/toluene/phenylhexane-supported liquid membrane at a pH close to natural water have first shown that countercation gradient is due to the sodium ion and not to the proton. This is important for practical application of SLM for in situ trace metal speciation studies as it does not perturb the tested medium. Second, the rate-limiting step is the diffusion of the metal-carrier complex in the membrane and metal in the aqueous stagnant layer. A simple diffusion model for diffusionlimited transport was used to verify this mechanism.1 Experimental transport data revealed that (i) the decomplexation at the membrane/source interface is fast, (ii) flux across the membrane is at a steady state, and (iii) the diffusion gradient in the membrane is linear. Third, the results of the effect, on the flux, of variations of stirring rate, membrane thickness, and temperature all support a diffusion-controlled mechanism coupled with an adsorption process in the membrane. Diffusion in the aqueous Nernst layer is rate limiting for a membrane thickness of 130 µm. A metal-carrier complex diffusion coefficient (D h m) of 5.2 × 10-8 cm2 s-1 was found from the lag time experiments. An interesting finding of this study is that a decrease of pore size does not seem to significantly affect the flux. Further work needs to be done to get a clearer insight into the structure of the complex formed in the membrane and the reaction at the interface to be able to design improved SLM. This work is underway. ACKNOWLEDGMENT The authors thank H. P. van Leeuwen for stimulating discussions. We thank Hoechst for kindly supplying us the Celgard membranes and AKZO for the Accurel membranes. The Plexiglas diffusion cell used for transport experiments was designed by C. Bernard and F. Bujard. APPENDIX Relation between K′ads, KD, and Kp. The adsorption constant of the complex on the pore wall of the membrane can be defined as
K′ads ) KadsΓsites ) ΓMLads/[ML]org
(A1)
where K′ads and Kads are the apparent and thermodynamic adsorption constants, respectively, Γsites is the surface concentration Analytical Chemistry, Vol. 71, No. 4, February 15, 1999
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of adsorption sites on the pore wall, ΓMLads is the surface concentration of adsorbed metal-carrier complex and [ML]org is the metal-carrier complex concentration in the solvent, respectively. The mass balance in the membrane is defined as
[ML]t,m ) [ML]org + ΓMLads(S/V)
KD - Kp V Kp S
(31) Heyrovsky, J.; Kuta, J. Principle of polarography; Academic Press: New York, 1968.
Analytical Chemistry, Vol. 71, No. 4, February 15, 1999
(A3)
where Dads m is the diffusion coefficient of the metal complex adsorbed onto the adsorption sites and [ML]org/[ML]t,m and ΓMLads(S/V)/[ML]t,m represent the weighting factors, i.e., the fraction of [ML]t,m dissolved in the organic solvent and that bound to the membrane, respectively. Assuming MLads does not move on the polymer, Dads m ) 0. By combining eqs A1, A2, 7, and A3, one obtains
(7)
Relation between D h m and Dm. The effective diffusion coefficient, D h m, is a weighted average of the molecular diffusion
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ΓMLadsS [ML]org 1 + Dads D h m ) Dm m [ML]t,m [ML]t,m V
(A2)
where S is the internal surface area of the membrane, V the volume of solution in the membrane, and [ML]t,m the total metal concentration in the membrane solution. Thus, by combining eqs 2, A1, and A2, one obtains
K′ads )
coefficient of the various complexes in the membrane phase,31 i.e.,
D h m ) Dm(Kp/KD)
(8)
Received for review May 5, 1998. Accepted November 20, 1998. AC9804947
