Simulation of Internal Concentration Profiles in a Multimetallic Ion

Nov 6, 2008 - Metal concentration profiles inside the particles at different reaction times were measured using an energy dispersive X-ray (SEM-EDX) ...
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Ind. Eng. Chem. Res. 2008, 47, 9297–9303

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Simulation of Internal Concentration Profiles in a Multimetallic Ion Exchange Process Nikolay Tikhonov,† Federico Mijangos,* Andreei Dautov,† and Monika Ortueta Department of Chemical Engineering, Faculty of Science and Technology, UniVersity of the Basque Country, PO Box 644, 48080 Bilbao, Spain

The kinetics of heavy metal uptakescopper and cobalt against sodiumsby chelating resins was analyzed experimentally by measuring the internal concentration profiles inside a single bead. Metal concentration profiles inside the particles at different reaction times were measured using an energy dispersive X-ray (SEMEDX) coupled to a scanning electron microscope. This technique provided a line scan along diametrical positions, yielding the metal concentration profiles needed in order to build mathematical models for the simultaneous uptake of copper and cobalt. This process is described by means of a mathematical model which uses the Nernst-Planck equation for diffusion and takes into account relevant physical and chemical effects. The diffusion model proposed here takes into account the mobility of ions through the macroporous ion exchanger and the corresponding electric field generated by the diffusion of ions with dissimilar diffusivities. The estimated diffusion coefficients are discussed in terms of the mobility of a single metal and the contribution of its co-ion. The dynamic behavior of a system composed of two intraparticular phases is correctly described by this diffusion model, including the nonmonotonous tendencies which are not associated with the different values of the diffusion coefficient. Introduction Ion exchange processes accompanied by a chemical reaction in multispecies systems comprise a common phenomenon in many cases with practical and theoretical interest. However, there are few studies dealing with fundamental kinetic aspects of this matter. There are even fewer studies regarding its theoretical issues, modeling, and kinetics predictions.1-3 Research papers on ion exchange kinetics in which structural modifications and intraparticular interactions happen are relatively scarce.4-6 In this context, the study by Helfferich and Hwang7 is remarkable, in that they succeed in developing a general model for multicomponent ion exchange that applies to systems with a simultaneous chemical reaction. To study the structure of the chelates formed, we reviewed the bibliography on compounds formed between copper and cobalt with the iminodiacetic group. The different spatial structures for compounds were taken from The Cambridge Structural Data Base, where each structure is registered by an alphanumerical code. All the possible chelates for copper and cobalt were checked, noting that the metal coordination number was 6 for copper and cobalt in the chelate obtained from a TGA data examination of samples fully saturated with each metal. Thus, the structures proposed for copper and cobalt chelates are those shown in Figure 1.8,9 Multimetallic solutions are commonly found in various fields of application. Chelating resins are frequently considered and applied to metal recovery or separation or even to water purification before disposal. These resins are very selective for heavy metals because the functional groups are able to catch metallic cations, forming a highly stable chemical structure called a chelate. It is thus possible to find “free” cations and “bound” cations in the internal structure of these ion exchangers. * To whom correspondence should be addressed. E-mail: [email protected]. Phone: +34 946012620. Fax: +34946013500. † Physics Department of Moscow State University, Mathematics Subdivision, Vorobiovy Gory, 119899 Moscow, Russia.

It is accepted that cations diffuse through the pores filled with the external solution and are blocked by the solid phase, with cation mobility being almost negligible in the last state. Simultaneous loading of several metals onto a chelating ion exchanger from an aqueous solution gives rise to “non-normal” kinetics behavior in which weaker-bound species show a maximum value of solid phase concentration. As a rule, different concentration layers surrounding an unreacted core are observed when analyzing a semireacted ion exchanger bead. One sharp boundary between predominant areas appears for each pair of species.10,11 These layers and boundaries are appreciated as reaction fronts, and they can be observed, under certain circumstances, as different colored zones associated with each chelate. The progress of the reaction can thus be evaluated by the motion of these reaction fronts.12 The process can be properly described mathematically via the unreacted core model (UCM, also called the shell progressive model) developed using the pseudo-steady-state approach, when only one heavy metal and the counterion initially loaded into the resin are considered. Dealing with only two exchanging species, Kalinitchev13 presents a very comprehensive study of the appearance of sharp boundaries and the prediction of concentration profiles inside the bead and also discusses the role of the co-ions. After numerically solving the theoretical kinetics model, he concludes that the shape of concentration distribution depends on selectivity, diffusivity, and bulk solution concentration values. Here, we present an approach that describes the loading of heavy metals onto a chelating (sodium form) commercial iminodiacetic-type resin. Metals are loaded from a bimetallic equimolar solution of cobalt and copper sulfate. In this system cobalt, which is the metal with least affinity for the functional group, can reach concentrations for intermediate reaction times in the solid phase as high as 15 times the final equilibrium value.14 It is demonstrated here that this behavior is in accordance with measured concentration profiles and can be predicted from basic considerations. The system of nonlinear diffusion equations is used to give a mathematical description

10.1021/ie800648v CCC: $40.75  2008 American Chemical Society Published on Web 11/07/2008

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Figure 1. Tridimensional configuration of (a) copper and (b) cobalt chelates. Table 1. Main Characteristics of the Commercial Resin Lewatit TP208 functional group

-N-(CH2COOH)2

matrix physical structure particle size (mm) average diameter (mm) metal capacity (Cu mol/kg dry resin) density (g/mL, Na form) volume change Na+-H+ (%) water content (%, Na form) composition (w/w, %) carbon hydrogen oxygen nitrogen

polystyrene-divinylbenzene macroporous beads 0.3-1.2 0.57 2.84 1.17 -30 55 66.3 6.6 22.4 5.15

of the process, including the equation in partial derivatives for ion diffusion. We consider the presence of the co-ion in the intraparticle liquid phase which is not excluded from the exchanger by the Donnan effect because it penetrates the resin as a neutral molecule due to its association with the counterions. The estimated diffusion coefficients are discussed in terms of the single metal and the corresponding co-ion contribution. The simulation of metal uptake kinetics from a solution for Lewatit TP 207 has been investigated previously.14 In this study the model used is more complicated because it takes into account the electrical field (E). The distinction is affected by the difference in physical properties between the ion exchangers. In the case of Lewatit TP 207 the diffusion coefficients of the components in the inner solution of an exchanger grain are similar and the difference between them during the simulation can be ignored. If all Di are equal, then the field E is zero, and it is not considered in the model. In the case of Lewatit TP 208 it is impossible to ignore the difference between the diffusion coefficients because they are markedly different, so the electrical field has to be taken into account in the model. Material and Methods Ion Exchanger. The experimental work was carried out using a commercial iminodiacetic-type chelating resin (Lewatit TP 208) in the sodium form. This resin was selected for its high selectivity for non-ferrous heavy metals. Its main characteristics are reported in Table 1.15

Before the start of the experiment the resin was carefully preconditioned by putting it through several regeneration cycles and finally balancing it with an alkaline solution of sodium hydroxide at pH 12.4. This secured the reproducibility of the experiments.5,6 Experimental Methods. Metals were supplied as sulfate, and salinity was set with sodium sulfate (analytical grade). The experiments were carried out at room temperature in a stirred batch reactor. Stirring needed to be quite high to prevent external diffusion from being the controlling step. On the other hand, stirring had to be limited to reduce the likelihood of broken beads appearing during the experiment. The metal was loaded onto the resin from mono- and bimetallic solutions. Metal solutions (200 mL) were introduced into the batch reactor, pH was adjusted, and 50 resin beads ranging from 680 to 700 µm in diameter were placed in the reactor. After the reaction started, one particle was taken out of the reactor at a preset time. This ion exchanger bead was analyzed using two techniques: optical and scattered electron microscopy.12 The rest of the beads were used for the chemical analysis of the loaded metal. The beads were kept in sulfuric acid solution (1 M, 100 mL) for 1 week to ensure that the metal was totally eluted from the resin. This solution was diluted with ultrapure water, and the metal concentration was measured by atomic absorption spectrometry. Microscopy. An important point in this technique is to stop the reaction to keep metal species from moving during observations. That is, internal concentration profiles must be “frozen”. To this end, washing the cut bead with slightly alkalized water is sufficient and yields reproducible results. Preparing the sample for electron microscopy is an important step for correct observation and characterization, particularly so if the materials are susceptible to changes in composition or microstructure. In the case of ion exchange resins, the drying method must not be aggressive because of the possibility of matrix structure alteration. To observe by microscopy the opaque beads that we were using and measure their dimensions, each bead was first cut in half under a magnifying glass using a scalpel. This enabled us to observe the internal reaction fronts or different colored layers that can be clearly seen in Figure 2. The cut bead was attached to the specimen stub with carbon glue and then coated with a layer of carbon or gold, depending on whether the samples were

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Figure 2. Microphotographs of a semireacted bead using optical (top left) and SEM microscopy: Backscattered electrons (bottom left, 140×) and structural photographs by secondary electrons of the layers: blue external layer of copper (top right, 10 000×) and the beige core of sodium (bottom right, 10 000×).

going to be analyzed by microscopy alone or also by microanalysis.11 A CEA 035 diode sputter-coating device was used for this purpose. This equipment was used in a high-vacuum evaporative technique for carbon coating at a distance of 35 mm. The microanalysis and examinations were carried out in a JEOL 6400 microscope coupled with an energy and wavelengthdispersive X-ray spectrophotometer, EDX Link EXL and WDX JEOL. With electron microscope analysis (SEM-EDX technique) it was also possible to draw a complete internal concentration profile to corroborate the data collected analytically and optically. Results and Discussion As can be seen in Figure 2, using a solution of two loading metals, here called a bimetallic copper/cobalt system, two clear zones can be distinguished besides the central core, i.e., as many zones as there were metals in the solution. In order to confirm the metal involved in each layer, an X-ray analysis was performed. The internal microstructural morphology of this semireacted bead is also shown in Figure 2, along with a microphotograph of different zones of the bead so as to show how the internal microstructure of the particle changes with the loaded cation. Reaction fronts were observed by collecting images using secondary and backscattered electron images. To check for the main elements in each zone, wavelength-dispersive X-ray spectrophotometry was used. Detailed microphotographs in Figure 2 show the microstructure of the copper layer (top right) and the central core of sodium (bottom right). The microstructures (microbead appearance and macropore size) of the copper and cobalt layers are indistinguishable by SEM, but the

Figure 3. Copper and cobalt internal concentration profiles for a semireacted bead for a reaction time of 30 min (pH ) 4.0, T ) 293 K, C0 ) 0.1 M, D0 ) 699.2 µm).

microbeads seem swollen within the sodium zone, so macroporous structure here is negligible. An X-ray line scan is useful for quantitative analysis and to discriminate kinetics models based on intraparticular evidence. Using this microanalytical technique, the internal concentration profiles were measured. The appearance of the internal profiles of a semireacted particle in a bimetallic system can be observed in Figure 3. Using a batchwise procedure, the kinetics of metal loading during the simultaneous retention of copper and cobalt were measured. The results are shown in Figure 4. The kinetics of simultaneous loading onto this iminodiacetic-type resin is

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Figure 4. Kinetics of metal load during the simultaneous retention of copper (O) and cobalt (4) on the resin particles (pH ) 3.0, T ) 293 K, L/S ) 5100 mL/g dry resin, and C0 ) 0.1 M for each metal). Results from modeling are plotted by the solid lines.

Some assumptions are needed in order to formulate the mathematical model. The ion exchange bead is considered to be perfectly spherical and surrounded by a constant concentration of the external solution. The beads are made up of two phases: a solid porous matrix where ion exchange takes place and the pores filled by the surrounding solution (Figure 2). The components diffuse through the intraparticular solution, and the surface or solid phase diffusion is assumed to be negligible. A difference in the diffusion coefficients must be taken into consideration for the simulation of the experimental data. It is known16,17 that in the case of distinct diffusion coefficients a local electric field is produced in an ion exchange process. The ion mobility, Ji, is described by using the Nernst-Planck equation which takes into account the electric field and is determined by

(

Ji ) Di

)

ji ∂C - ziCiE ∂r

(1)

where E is the strength of the electric field multiplied by a factor of fundamental physical constants and temperature.16 There is considered to be a local equilibrium inside the resin bead between the solution and the solid phase. Taking into account this equilibrium and the boundary conditions, it is possible to calculate the value of the diffusion coefficients for each metal and the sulfate. Considering eq 2 as the ion exchange process inside the resin bead: 1 1 1 1 R Cu + Mez+ S R zMe + Cu2+ 2 2 z z 2 Figure 5. Experimental (dashed line) and estimated (solid line) data on the internal moving boundary for copper.

characterized by the appearance of a maximum of metal load for cobalt, the cation with less affinity for the functional group. Theoretical Approach and Mathematical Model In order to describe the experimental behavior of the ion exchange system shown in Figure 4, a kinetics diffusion model was developed. The ion exchange kinetics is mainly characterized by the fact that cobaltsthe ion with least affinity for the functional groupsis first accumulated and then leaves the bead. As a result, the dependence on the quantity of cobalt loaded over time, MCo(t), is nonmonotonous. It passes a maximum. This can be noticed because this nonmonotonous tendency is not associated with the different values of diffusion coefficients.12,14 In the present paper we consider the two-phase structure of the exchanger so that in the solid phase metals are accumulated and in the liquid phase ions are transported. The process is the same as the ion exchange process in a column, where the components are transferred by solution flow, but in this case instead of solution flow the transfer is affected only by diffusion. This nonmonotonous tendency of the concentrations inside the bead also appears on analyzing ion exchange dynamics in columns, and it is also reported elsewhere,15 so a two-phase model is needed to simulate this behavior. Using a one-phase homogeneous model to simulate the ion exchange kinetics of a single bead gives rise to a monotonous increasing tendency, which is not in accordance with the experimental results reported above. The first step of the simulation model setup was to understand how complicated the mathematical model needed to be in order adequately to describe the experimental data and to determine the values of main parameters Di and Ki most accurately.

(2)

where R2Cu means the functional group loaded with copper ions, Mez+ designates metal ions in the outside solution, and R zMe is the chelate formed. If activity coefficients are neglected, in accordance with the mass action law KNa

( ) ( )

CNa CCo ) KCo qNa qCo

1/2

CCu qCu

)

1/2

(3)

The continuity equation can be derived under the Nernst-Planck law and can then be stated for spherical geometry as

(

jI 1 ∂ 2 ∂C ∂ j (εCI + qI) ) Di 2 - EziCI r ∂t ∂r r ∂r

)

0 < r < R (4)

j i is the total concentration of the species i within the where C pores, considering both free cations and nondissociated sulfate, as described by eq 5. j I ) CI + CI SO C 4 j SO ) CSO + C 4 4

(5)

∑C I

I SO4

(6)

Moreover, it is necessary to consider eq 7, which is the mass balance for the functional group that guarantees the maintaining electroneutrality within ion exchanger microspheres. Proton concentration bound to the functional group has been ignored in eq 7, following Mijangos and Diaz.18 qNa + 2(qCo + qCu) ) Q

(7)

where the Q is the acid-base ion exchange capacity. The condition of electroneutrality of the solution inside the pore can be expressed by the following equation:

Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9301

CNa + 2(CCo + CCu) ) 2CSO4

(8)

Consequently, it is necessary to state a correlation between the free ions and nondissociated species. The dissociation constants for homogeneous solution (βi) can be used for this purpose, assuming that their values are adequate for the pore solution. Sodium sulfate is assumed to be fully dissociated, βNa ) 0. βI )

CI SO4

(9)

CI CSO4

Finally, the following initial and boundary conditions are considered here (eqs 10 and 11). It is assumed that cations and neutral molecules of CuSO4 and CoSO4 penetrate from the external to the inner pore solution without discontinuity, so that there is no change in concentrations at the bead boundary. 1 init CNa ) CSO4 ) C Na , 2

t ) 0:

j I ) C Ibound ; C

r ) R:

CCo ) CCu ) 0 (10)

bound j SO ) C SO C 4 4

(11)

Figure 6. Effect of sodium equilibrium constant on cobalt internal concentration profiles. Experimental (dashed line) and estimated (solid line). (a) Low stability, KNa ) 0.03, and (b) higher stability, KNa ) 0.21.

The liquid phase is electrically neutral. As a result of this we can use eq 12. j SO ) 2CSO + 2{CCuSO + CCoSO } 2C 4 4 4 4 ) CNa + 2(CCo + CCu) + 2{CCuSO4 + CCoSO4} 3

)

∑ z Cj

I I

(12)

I)1

The value of the right-hand side of this equation does not change at the boundary, so the sulfate concentration inside the particle will not change. A computer program was created to simulate the metal diffusion process inside the resin beads. The set of equations (2)-(11) was solved by the finite differences method using the implicit scheme of first-order accuracy. The factorization method was applied, and the roots of algebraic equations were determined by the Newtonian method.17,19 The results of the numerical simulation of the process at different boundary conditions and at different values of diffusion coefficients are shown and discussed here. After the experiments described prior to the simulation, the porosity ε and the average radius of the bead R were measured. Different solutions were usedsCCuSO4 ) 0.1 M, CCoSO4 ) 0.1 M, and CNaSO4 ) 0.01 Msto proceed with the ion exchange process inside the beads. The internal profiles of copper and cobalt concentration inside a grain and their values MCu(t) and MCo(t) at any time were estimated, as can be seen in Figures 4-6. The internal concentration profile of the sulfate (SO42-) was also studied, as can be seen in Figure 7. As the commercial resin used in this work (Lewatit TP-208) is very similar to the one used in previous studies20 (Lewatit TP-207), the values used for the diffusion coefficients, Di, and for the equilibrium coefficients, K, were the same for the beginning of the simulation. Verification of the Model The experimental results shown in Figure 4 are compared with those obtained by simulation using the parameters from Table 2.

Figure 7. Sulfate concentration profiles for different reaction times (5, 15, and 30 min). Solid line shows the estimated internal concentration of sulfate.

The variation in the total quantity of metals loaded onto a bead, MCu and MCo, over time is shown in Figure 4, where the simulated results are indicated by continuous lines. Figure 5 shows the concentration profiles YCu(r,t) for different reaction timess5, 15, 35, and 90 minswith continuous lines used to show the data calculated by the simulation program and dashed lines for experimental data. Figure 7a also shows the concentration profiles YCo(r,t) for different reaction times of 5, 15, and 35 min. In this case the

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the physical properties between the two ion exchangers studied. For example, the value of the ion exchange equilibrium constant for Lewatit TP 208 is KCo ) 0.54 and for Lewatit TP 207 it is KCo ) 0.135. Also, the calculated diffusion coefficient for cobalt, DCo, is 1.6 10-10 m2/s for the Lewatit TP 208 and 1.0 × 10-10 m2/s for Lewatit TP 207.

Table 2. Model Parameters Used with the Simulation Program ε R β

Cu Co Na SO4 Co Cu Na Co

D

K Q Cbound

Na Cu Co SO4

0.6 7.5 × 10-4 m 204 L/mol 316 L/mol 2 × 10-10 m2/s 2 × 10-10 m2/s 1.6 × 10-10 m2/s 1.0 × 10-10 m2/s 0.21 0.54 4.76 mol/L 0.01 mol/L 0.1 mol/L 0.1 mol/L 0.205 mol/L

Conclusions

profile corresponding to 90 min is not drawn because it is approximately equal to the equilibrium value. Finally, the sulfate concentration profiles for different reaction bound times inside a particle, X(r,t) ) CSO4/CSO for 5, 15, and 30 4 min, are represented in Figure 7. As can be seen in Figures 5-7, all the simulated data follow the experimental ones very closely, even for the sulfate concentration (co-ion penetration) inside the particle. All the parameters of the model (except KNa) are firmly determined by all the characteristics of the concentration distribution obtained from the experimental data. But the validity of the model could be improved by considering more accurate values of form variations and position of the concentration profiles for different values of time. The determination of the stability coefficient and the coincidence of the simulation results with all the experimental results show the match and accuracy of the model. In stage one of the process (Figure 4), copper and cobalt diffuse into the center of the bead and sodium is rejected, if eq 13 describes the chemical affinity of the functional group.

( )

KNa

CNa qNa

1/2

< KCo < KCu ) 1

(13)

The cobalt/sodium and copper/cobalt ion exchange takes place at the same time at different radial positions of the bead, forming strongly pronounced internal fronts of concentration. As time passes the size of the sodium core decreases, the cobalt layer is enlarged, and the copper layer grows toward the center of the bead following the cobalt layer, with its concentration at the boundary conditions being higher than the equilibrium value. As the cobalt layer reaches the center of the bead the second stage (Figure 4) of the process begins as described above, characterized by a decrease in the average cobalt concentration inside the bead caused by the rejection of cobalt by copper. This process continues until equilibrium is reached. Dealing with the shape of the experimental curves, the value DCu/DCo influences the ratio of metal uptake rate; i.e., when calculations are running and DCo is increasing meanwhile DCu is kept constant, the height of the curve MCo(t) increases. The value KNa determines the width of the zone where the Na/Co exchange takes place. In other words, it determines the slope of the internal profile of cobalt. For purposes of comparison, the experimental and calculated internal profiles for two different values of KNa are shown in Figure 6. Also for purposes of comparison, it must be pointed out that if we use previous research data9 for the Lewatit TP 207, which is assumed to be nearly the same ion exchanger, the calculated values for all the coefficients for Lewatit TP 208 are found to be different. This means that there is a noticeable difference in

The nonmonotonous tendency observed for cobalt-copper retention is not associated with the different values of diffusion coefficients but with the affinity for the functional group anchored to the matrix. We have considered a two-phase internal structure system where metals are accumulated in the solid phase and in the liquid phase ions are transported. The whole set of experimental data is described with high accuracy by the mathematical model that takes into account the two-phase structure of the exchanger, the diffusion components, the ion exchange, and the complex formations in the solution. The first aim was to determine the complexity and the functional structure of the model that best corresponds to the process investigated and, finally, to determine all the parameters of the model. Because of the good fit of calculated data to experimental data throughout the entire set of experimental conditions tested, this simulation makes it possible to predict the kinetics behavior of metal retention by the ion exchanger Lewatit TP 208. The value of the equilibrium constant for sodium determines the width and the slope of the internal profile of the zone where the cobalt is predominant. The co-ion, that is to say sulfate anion, penetrates into the polymeric matrix bound to metallic species. The simulation of sulfate concentration profiles for different reaction times accurately fit experimental data, which also validates the proposed model. Nomenclature C(r,t) ) metal concentration as free cation in intraparticle liquid phase (mol/m3) C ) total concentration of the species within pores (mol/m3) D ) effective diffusion coefficient in pore (m2/s) E ) local value of electric-field strength inside a bead (E ) Fφ/ RT, m-1) F ) Faraday constant (C V K-1 mol-1) K ) ion exchange equilibrium constant (kg/m3) M(t) ) total metal concentration in solid phase (mol/kg dry resin); M(t) ) (3/R3)∫0Rr2q(r,t) dr Me ) metal cation Q ) acid-base ion exchange capacity (mol/kg Na-form dry resin) q ) local metal concentration in solid phase (mol/kg Na-form dry resin) R ) functional group of the ion exchanger R ) bead radius (m) r ) radial position (m) t ) time (s) bound X(r,t) ) normalized concentration of anions; X(r,t) ) CSO4/C SO 4 Y(r,t) ) normalized metal load in the solid phase; Y(r,t) ) q(r,t)/ Mequil z ) valence Greek Symbols β ) dissociation coefficient (mol/L)-1 ε ) internal porosity φ ) electric field (V m-1)

Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9303 Subscripts and Superscripts bound ) bead boundary equil ) equilibrium I ) metal species i ) species init ) initial

Literature Cited (1) Franzeb, M.; Ho¨ll, W. H.; Eberle, S. H. Liquid-phase Mass Transfer in Multicomponent Ion Exchange. 2. Systems with irreversible chemical reactions in the film. Ind. Eng. Chem. Res. 1995, 34, 2670. (2) Jia, Yi; Foutch, G. L. True Multicomponent Mixed Bed Ion-exchange Modeling. React. Funct. Polym. 2004, 60, 121. (3) Rodriguez, J. F.; de Lucas, A.; Leal, J. R.; Valverde, J. L. Determination of Intraparticle Diffusivities of Na+/K+ in Water and Water/ Alcohol Mixed Solvents on a Strong Acid Cation Exchanger. Ind. Eng. Chem. Res. 2002, 41, 3019. (4) Pritzker, M. Modified Shrinking Core Model for Uptake of Water Soluble Species onto Sorbent Particles. AdV. EnViron. Res. 2004, 8, 439. (5) Mijangos, F.; Dı´az, M. Kinetic of Copper Ion Exchange onto Iminodiacetic Resin. Can. J. Chem. Eng. 1994, 72, 1028. (6) Mijangos, F. Analysis and Modelling of the Metal Recovery from Hydrometallurgical Wastewaters by Ion Exchange; Ph. D. Dissertation, University of the Basque Country, Bilbao, Spain, 1989. (7) Hwang, Y. L.; Helfferich, F. Generalized Model for Multispecies Ion-exchange Kinetics Including Fast Reversible Reactions. React. Polym. 1987, 5, 237. (8) Ruiz-Perez, C.; Rodriguez, M. L.; Rodriguez-Romero, F. V.; Medero,s, A.; Gili, P.; Martin-Zarza, P. Tetraaqua-µ4-(phenylenediaminetetracetato-O1:O2:O3,O4,N:O5,O6,N1) dicopper (II) dihydrate. Acta Crystallogr. Sect. C-Cryst. Struct. Commun. 1990, 46, 1405. (9) Gonzalez, C. A.; Hernandez-Padilla, M.; Dominguez, S.; Mederos, A.; Brito, F.; Arrieta, J. M. Polymer Species in Aqueous Solutions of Paraphenylenediamine-N,N,N′,N′-tetraacetic acid (p-PhDTA) with Cobalt(II),

Nickel(II), Copper(II), Zinc(II) and Cadmium(II). X-ray Crystal Structure of Na4[Co2(p-PhDTA) 2] · 8H2O. Polyhedron 1997, 16, 2925. (10) Janauer, G. E.; Gibbons, R. E.; Bernier, W. E. A Systematic Approach to Reactive Ion Exchange. SolVent Extr. Ion Exch. 1985, 9, 53. (11) Mijangos, F.; Bilbao, L. Application of Microanalytical Techniques to Ion Exchange Processes of Heavy Metals Involving Chelating Resins. In RSC Special publication 196: Progress in Ion Exchange; Dyer, A.; Hudson, M. J.; Williams, P. A., Eds.; Royal Society of Chemistry: Cambridge, 1997, p 341. (12) Mijangos, F.; Ortueta, M.; Bilbao, L. Microkinetic Analysis of Heavy Metal Ion Exchange onto Chelating Resins. In RSC Special publication 239: AdVances in Ion Exchange for Industry and Research; Williams, P. A.; Dyer, A., Eds.; Royal Society of Chemistry: Cambridge, 1999, p75. (13) Kalinitchev, A. I. Diffusional Model for Intraparticle Ion Exchange Kinetics in Nonlinear Selective Systems. SolVent Extr. Ion Exch. 1998, 16, 345. (14) Mijangos, F.; Tikhonov, N.; Ortueta, M.; Dautov, A. Modelling Ion Exchange Kinetics in Bimetallic Systems. Ind. Eng. Chem. Res. 2002, 41, 1357. (15) Bayer A. G. Lewatit: Selective resin for treatment of brine. Technical information, OC/I 20543e, Leverkusen. DE 1984. (16) Helfferich, F. Ion Exchange; McGraw Hill: New York, 1962. (17) Tikhonov, N. A.; Poezd, A. D.; Khamizov, R. K. Modelling the Dynamics of Multicomponent Ion Exchange with Dissimilar Diffusivities of Components. React. Funct. Polym. 1995, 28, 21. (18) Mijangos, F.; Dı´az, M. Metal-Proton Equilibrium Relations in a Chelating Iminodiacetic Resin. Ind. Eng. Chem. Res. 1992, 31, 2524. (19) Samarskii, A. A. The Theory of Difference Schemes; Nauka: Moscow, 1989. (20) Mijangos, F.; Dı´az, M. Kinetic Analysis of a Bimetallic Ion Exchange System by Microscopic Measurement of the Moving Boundaries. J. Colloid Interface Sci. 1994, 164, 215.

ReceiVed for reView May 23, 2007 ReVised manuscript receiVed September 19, 2008 Accepted September 24, 2008 IE800648V