Ind. Eng. Chem. Res. 2001, 40, 3557-3562
3557
Binding Properties of a Water-Soluble Chelating Polymer with Divalent Metal Ions Measured by Ultrafiltration. Poly(acrylic acid) Tahei Tomida,* Kinnya Hamaguchi, Shunsuke Tunashima, Masahiro Katoh, and Seizo Masuda Department of Chemical Science and Technology, The University of Tokushima, Tokushima 770-8506, Japan
Binding equilibria of a water-soluble chelating polymer, poly(acrylic acid), with divalent metal ions [Co(II), Ni(II), Cu(II), Zn(II), and Pb(II)] were measured by a batch ultrafiltration method in the pH range of 4-6. It was shown that the binding equilibrium curves were reasonably well represented by a complexation model accounting for the formation of three kinds of complexes [LM+, L2M, and L2M(HL)2]. The equilibrium and successive stability constants were determined by fitting the binding curves calculated from the model to the experimental ones at every solution pH. The average coordination number was discussed on the basis of the complexation model proposed. Introduction Many processes using water-soluble chelating polymers combined with membranes have been extensively studied to remove, recover, concentrate, or separate metal ions from aqueous solutions. Ultrafiltrations coupling with the polymer-metal complexation are shown to be useful and economical methods for treatment of metal ions in aqueous solutions.1-12 We previously reported a new method using water-soluble chelating polymers and membranes for recovering and/or concentrating metal ions from aqueous solutions.13-15 In this case, a higher mass-transfer rate of metal ions through the membrane can be achieved because there is no aqueous-organic interface that causes unfavorable mass-transfer resistance.16,17 In these processes using water-soluble chelating polymers and membranes, the efficiency and selectivity for recovering and/or separating metal ions should depend significantly on the binding properties of the chelating polymers with different metal ions. Binding properties of water-soluble chelating polymers, and the stability constants of the polymer-metal complexes have been extensively studied by many methods such as pH titration, potentiometric titration, UV absorbance, etc.18,19 Ultrafiltration and diafiltration methods are also useful methods to determine the binding equilibrium constants of the water-soluble chelating polymers with metal ions and the average coordination numbers without disturbing the medium.6,20-24 However, the published results are not enough to express the binding equilibrium of watersoluble chelating polymers with metal ions in the wide ranges of pH and concentration of metal ions. The main aim of this work is to find theoretical relationships to express the binding equilibrium of water-soluble chelating polymers with metal ions. In the present study, poly(acrylic acid) (PAA) is used as the water-soluble chelating polymer because many comparable data on binding properties of PAA have been * To whom correspondence should be addressed. E-mail:
[email protected]. jp. Tel: (81)-88-656-7425. Fax: (81)-88-655-7025.
published in the literature. The binding equilibria of PAA with several divalent metal ions [Co(II), Ni(II), Cu(II), Zn(II), and Pb(II)] were measured by a batch ultrafiltration method, and the binding curves were analyzed based on a complexation model accounting for the formation of three kinds of complexes. It was shown that the equilibrium curves were well represented by the proposed complexation model, and the successive stability constants were determined by matching the calculated binding curves to the experimental ones irrespective of the solution pH. Experimental Section Materials. The water-soluble chelating polymer used was commercially available PAA, with a molecular weight of 240 000 (25 wt % in water, Aldrich Chemical Co.). First a fixed weight of the polymer was diluted to the required concentration (50-100 mM in monomer unit) with water. For each experimental run, PAA aqueous solutions were adjusted to the fixed pH and concentrations. All of the chemicals used were analytical or special grades. Metal ion solutions were prepared by diluting standard aqueous solutions of metal nitrates for atomic absorption analysis. Deionized and distilled water was used. Experimental Procedure. The dissociation constant of PAA was determined by the pH titration method. An aqueous solution of PAA (5 cm3, 25 mM monomer unit) was titrated with a standard sodium hydroxide solution (25 mM) at room temperature (ca. 25 °C). The pH of the solution was measured with a pH meter (Yanako PH-8). The binding equilibria of the water-soluble chelating polymer and metal ions at a fixed pH were measured by a batch ultrafiltration at room temperature (ca. 25 °C). Aqueous solutions of the polymer (5 mM, 5 cm3) and the metal ion solution (5 cm3) prepared to the required pH and concentrations (0.2-5 mM) were mixed, and the change in the pH of solution was adjusted to the fixed value by adding a small amount of aqueous solution of sodium hydroxide or nitric acid at intervals of about 2 h until no further change in pH
10.1021/ie0009839 CCC: $20.00 © 2001 American Chemical Society Published on Web 07/10/2001
3558
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
Figure 1. Henderson-Hasselbach plots of pH titration for PAA.
Figure 2. Binding equilibrium curves of Co(II) at different solution pH values: dotted lines, calculated; symbols, experimental values.
of the solution was observed. After stirring for over 24 h, the final volume of the mixture was determined by weighing. The mixture was ultrafiltrated using an ultrafilter unit with a molecular weight cutoff (MWCO) of 10 000 (Advantec Inc.). For each run, about 3 cm3 of the filtrate was taken, and the concentration of the metal ions was measured with an inductively coupled plasma spectrometer (ICPS-5000, Shimadzu Seisakusho). The pH of the filtrate was measured with the pH meter. Results and Discussion Dissociation of the Polymer. It is reported that the dissociation of the polymer acid is expressed by the following equation:18
Ka ) [H+]{[L-]/[HL]}β
(1)
For pH titration, the relation between the pH and the degree of neutralization, R, can be expressed by the modified Henderson-Hasselbach equation:
(1 -R R)
pH ) pKa - β log
Figure 3. Binding equilibrium curves of Ni(II) at different solution pH values: dotted lines, calculated; symbols, experimental values.
(2)
Figure 1 shows the experimental results of the pH titration for PAA in the absence of any neutral salts. The values of R were the molar ratio of NaOH to PAA in a monomer unit. As can be seen from the figure, the curve is closely straight in the pH range of 4.5-7.2. From the slope and the intercept at log[(1 - R)/R] ) 0 of the straight line, the value of β and the dissociation constants, Ka, for PAA used were determined to be 2 and 3.16 × 10-7 M ()mol‚dm-3), respectively. Binding Equilibrium. To evaluate the binding equilibrium, the following assumptions were made by taking experimental conditions into account: (1) there is no interaction between free metal ions with the membrane; (2) permeation of the polymer and polymermetal complexes is completely rejected, and the complex concentrations are in equilibrium with the concentration of free metal ions which are going to permeate through the membrane; and (3) the amount of metal hydroxides is neglected. The amount of metal ions bound to the polymer of the monomer unit, q, was determined from a change in the concentration of the metal ions in the solutions on the basis of a mass balance.
Figure 4. Binding equilibrium curves of Cu(II) at different solution pH values:. dotted lines, calculated; symbols, experimental values.
The binding equilibrium curves for Co(II), Ni(II), Cu(II), Zn(II), and Pb(II) are shown in Figures 2-6, respectively. As can be seen from the figures, the binding equilibrium curves were affected significantly by the solution pH, and the values of q increased with an increase in the pH. The binding curves for Cu(II) and Pb(II) at pH 6 were not shown because precipitations were observed.
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3559
Figure 7. Schematic structure assumed for PAA-divalent metal complexes of L2M(HL)2.
L2M(HL)n denotes the complex formed without protonation, and equilibrium constant, k3, is defined as follows: Figure 5. Binding equilibrium curves of Zn(II) at different solution pH values: dotted lines, calculated; symbols, experimental values.
k3 )
[L2M][HL]n
(7)
[L2M][HL]n
Then, the total concentration of metal ions bound to the polymer, [Mp], and the total concentration of the polymer, [Pt], were expressed by eqs 8 and 9, respectively.
[Mp] ) [LM] + L2M + [L2M][HL]n ) b1[M] b1b2[M]
Figure 6. Binding equilibrium curves of Pb(II) at different solution pH values: dotted lines, calculated; symbols, experimental values.
Analysis of Binding Equilibrium Based on a Complexation Model. The binding equilibrium of the polymer with metal ions was analyzed on the basis of a complexation model. On the basis of the modified Bjerrum model,18 the successive formation of polymermetal complexes for divalent metal ions is expressed as follows:
HL + M2+ a LM+ + H+; b1
(3)
HL + LM+ a L2M + H+; b2
(4)
where successive stability constant, b1 and b2, are defined as follows:
b1 )
[LM+][H+] [HL][M2+]
and b2 )
[L2M][H+] [HL][LM+]
(5)
It is suggested that two or more ligands of the chelating polymer coordinate to a single metal ion, forming complexes such as the PAA-Cu(II) complex.6,21 From these facts, we assumed that more than one ligand of the polymer interacted with a single divalent metal ion without protonation in addition to the complexes of LM+ and L2M described above.
L2M + nHL a L2M(HL)n; k3
(6)
{ } [HL] +
[H ]
2
+ b1b2k3[M]
{ } [HL]
[HL] [H+]
2
+
[H ]
+
[HL]n (8)
[Pt] ) [HL] + [L-] + [LM] + 2[L2M] + (2 + n) Ka 1/β [HL] [HL] + b1[M] + + [L2M(HL)n] ) 1 + + [H ] [H ] [HL] 2 [HL] 2 + (2 + n)b1b2k3[M] [HL]n 2b1b2[M] + + [H ] [H ] (9)
{ ( )} { }
{ }
Under experimental conditions, [Pt] and [H+] are known. Consequently, the amount of metal ions bound to a monomer unit of the polymer, q, can be calculated as a function of the concentration of the free metal ions, [M], provided the values of b1, b2, k3, and n are given:
q ) [Mp]/[Pt] ) f{[M];b1,b2,k3,n}
(10)
Determination of Binding Equilibrium and Stability Constants. Considering the fact that the primary coordination number of the divalent metals used is 4, it is likely that PAA-divalent metal complexes have square planar or tetrahedral structure as illustrated in Figure 7. This means that the two coordinations of the metal ion are satisfied by the two carboxyl anions, and the residual two coordinations are satisfied by the oxygen of two carboxyl groups in the polymer. It is impossible at present to verify the structure of the PAA-metal complexes. However, as described below, better agreement of the calculated binding equilibrium with the experimental ones was obtained in the case when n ) 2 for PAA-divalent metal ions. In Figures 2-6, calculated binding equilibria were compared with experimental ones. The calculated curves were obtained by using the values of b1, b2, and k3 shown in Table 1, which were determined by fitting the calculated binding curves to the experimental ones at every solution pH. We were able to evaluate the values of b1, b2, and k3 independently because they differently
3560
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
Table 1. Stability and Equilibrium Constants of PAA-Divalent Metal Complexes metal salt
log b1
log b2
log k3
log B2
Co(NO3)2 Ni(NO3)2 Cu(NO3)2 Zn(NO3)2 Pb(NO3)2
-2.5 -2.3 -0.7 -2.5 -1.1
-1.8 -1.9 -0.2 -1.0 -0.2
6.5 6.3 7.0 5.0 0
-4.3 -4.2 -0.9 -3.5 -1.3
Table 2. Overall Complexation Constants from the Literature metal salt Cu(ClO4)2 CuCl2 CuSO4 CuCl2 Cu(II) Cu(II) in 2 M NaNO3 Ni(ClO4)2 NiCl2 ZnSO4
pH
nav
log B2
(II) > Zn(II) > Ni(II), Co(II). The complexation properties of PAA-Cu(II) have been extensively studied. For comparison of the stability constants obtained in this work, some results published in the literature are summarized in Table 2. Some of them were estimated from the dissociation constants and equilibrium constants reported in the literature. It should be noted that the values of B2 obtained in this work are comparable to the results in the literature. It is reported that the average coordination number of PAA-metal complexes varies from zero to more than 2 depending on the solution pH and the concentration ratio of PAA to the metal ions.6,8,23 To understand the variation of the average coordination number with changes in the conditions, the relative concentrations of the three kinds of complexes to the total polymer concentration were calculated from the model equation described above, using the parameters shown in Table 1. Typical examples of the estimated concentrations of the complexes for Ni(II) and Cu(II) are shown in Figures 8 and 9, respectively. It should be noted that the complexes of L2M(HL)2 for both Ni(II) at pH 5 and Cu(II) at pH 4 are formed much more than others in a lower concentration of metal ions, but they decrease gradually with an increase in the metal ion concentration. The complexes LM+ and L2M, on the contrary, increase with an increase in the metal ion concentration. With respect to Ni(II) at pH 6 and Cu(II) at pH 5, the complex L2M is predominantly formed in all concentration ranges of metal ions examined. With an increase in the metal ion concentration, LM+ increases significantly but L2M(HL)2 decreases gradually. Similar behaviors are observed for the other metal ions examined.
Figure 8. Calculated relative concentrations and the average coordination numbers for PAA-Ni(II) complexes at pH 5 (a) and pH 6 (b).
The average coordination numbers were estimated from the relative concentrations of the complexes of LM+, L2M, and L2M(HL)2:
nav ) {[LM+] + 2[L2M] + 4[L2M(HL)2]}/{[LM+] + [L2M] + [L2M(HL)2]} (11) The average coordination numbers for Ni(II) and Cu(II) are shown in Figures 8 and 9, respectively. The values of nav tend to decrease with an increase in the concentration of metal ions and/or the solution pH. These results show how the average coordination number varies depending on the metal ion concentration and the solution pH. Conclusions The binding equilibria of PAA with divalent metal ions [Co(II), Ni(II), Cu(II), Zn(II), and Pb(II)] were determined in the pH range of 4-6 by a batch ultrafiltration method. It was shown that the binding equilibrium curves for all kinds of divalent metal ions examined were well represented by the complexation model proposed. The successive stability constants for PAA-metal complexes were determined by fitting the calculated curves to the experimental ones irrespective of the solution pH. The orders of magnitude of the overall complexation constants are comparable to those reported in the literature. They decreased in the order Cu(II) > Pb(II) > Zn(II) > Ni(II), Co(II).
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3561 [ ] ) molar concentration of the species in the brackets (M) R ) degree of neutralization β ) constant
Literature Cited
Figure 9. Calculated relative concentrations and the average coordination numbers for PAA-Cu(II) complexes at pH 4 (a) and pH 5 (b).
The relative concentrations of the complexes of LM+, L2M, and L2M(HL)2 and the average coordination number were estimated from the model equation using the equilibrium and stability constants obtained. Acknowledgment The authors are grateful to K. Horie, A. Shirota, and T. Katayama, students of The University of Tokushima, for their experimental support. This work was also supported by the Sumitomo Foundation in Japan, which is greatly appreciated. Nomenclature b1 ) successive stability constant b2 ) successive stability constant B2 ) overall complexation constant ()b1 × b2) c ) metal molar concentration (M) HL ) chelating polymer Ka ) dissociation constant (M) k3 ) equilibrium constant defined by eq 7 (M-n) L- ) free ligand M ) metal ion [Mp] ) total concentration of metal ions bound to polymer (M) n ) number of polymer ligands coordinating to a single metal ion without protonation nav ) average coordination number [Pt] ) total concentration of polymer (M) q ) amount of metal ions bound to polymer (mol‚mol of polymer-1)
(1) Aulas, F.; Tyburce, B.; Rumeau, M.; Renaud, M. Concentration of Metal Ion Solutions by Ultrafiltration: Effects of the Complexation on the Performances of Process. Entropie 1980, 91, 48-51. (2) Nguyen, Q. T.; Aptel, P.; Neel, J. Application of Ultrafiltration to the Concentration and Separation of Solutes of Low Molecular Weight. J. Membr. Sci. 1980, 6, 71-82. (3) Strathmann, H. Selective Removal of Heavy Metal Ions from Aqueous Solutions by Diafiltration of Macromolecular Complexes. Sep. Sci. Technol. 1980, 15 (4), 1135-1152 (4) Geckeler, K.; Lange, G.; Eberthardt, H.; Bayer, E. Preparation and Application of Water-Soluble Polymer-Metal Complexes. Pure Appl. Chem. 1980, 52, 1883-1905. (5) Ouiminga, S. A.; Brandebourger, M.; Chaufer, B.; Deratani, A.; Sebille, B. Preparation of Water-Solble Chelating Aminated Starch Derivatives and Their Use for the Concentration of Metal Ions by Ultrafiltration. React. Polym. 1987, 5, 111-122. (6) Masse, P.; Choe, T. B.; Verdier, A. Separation of Cu(II)-Ni(II) by a Complexation-Ultrafiltration Method. Ann. Chim. (Rome) 1987, 77, 925-944. (7) Volchek, K.; Krentsel, E.; Zhilin, Yu.; Shtereva, G.; Dytnersky, Yu. Polymer Binding/Ultrafiltration as a Method for Concentration and Separation of Metals. J. Membr. Sci. 1993, 79, 253272. (8) Juang, R. S.; Liang, J. F. Removal of Copper and Zinc from Aqueous Sulfate Solution with Polyacrylic Acid by a Batch Complexation-Ultrafiltration Process. J. Membr. Sci. 1993, 82, 175-183. (9) Ahmadi, S.; Batchelor, B.; Koseoglu, S. S. The Diafiltration Method for the Study of the Binding of Macromolecules to Heavy Metals. J. Membr. Sci. 1994, 89, 257-265. (10) Rivas, B. L.; Moreno-Villoslada, I. Poly(sodium 4-styrenesulfonate)-Metal Ion Interactions. J. Appl. Polym. Sci. 1998, 70, 219-225. (11) Rivas, B. L.; Moreno-Villoslada, I. Binding of Cd2+ and Na+ Ions by Poly(sodium 4-styrenesulfonate) Analyzed by Ultrafiltration and Its Relation with the Concentration Theory. J. Phys. Chem. B 1998, 102, 6994-6999. (12) Rivas, B. L.; Moreno-Villoslada, I. Synthesis and Behavior of Two Copolymers of Poly(acrylamide-co-(N-(hydroxymethyl) acrylamide)) in Ultrafiltration Experiments. Polym. Bull. 2000, 44 (2), 159-165. (13) Tomida, T.; Ikawa, K.; Masuda, S. Recovery of Metal Ions from Dilute Solutions Using a Water-Soluble Chelating Polymer and Dialysis Membranes. J. Chem. Eng. Jpn. 1993, 26 (5), 575577. (14) Tomida, T.; Inoue, T.; Tsutiya, K.; Masuda, S. Concentration and/or Removal of Metal Ions Using a Water-Soluble Chelating Polymer and Microporous Hollow Fiber Membrane. Ind. Eng. Chem. Res. 1994, 33 (4), 904-906. (15) Tomida, T.; Inoue, T.; Fujita, K.; Masuda, S. Concentration of Copper(II) Ion in Water Using a Water-Soluble Chelating Polymer and a Microporous Hollow Fiber. Chem. Lett. 1994, 787788. (16) Tomida, T.; Katoh, M.; Inoue, T.; Minamino, T.; Masuda, S. Transient Analysis of Mass-Transfer Rate in Recovering Metal Ions Using a Microporous Hollow Fiber Membrane and a WaterSoluble Chelating Polymer. Sep. Sci. Technol. 1998, 33 (15), 22812293. (17) Marty, J.; Persin, M.; Sarrazin, J. Dialysis of Ni(II) through an Ultrafiltration Membrane Enhanced by Polymer Complexation. J. Membr. Sci. 2000, 167, 291-297. (18) Gregor, H. P.; Luttinger, L. B.; Loebl, E. M. MetalPolyelectrolyte Complexes. I. The Polyacrylic Acid-Copper Complex. J. Phys. Chem. 1955, 59, 34-39. (19) Yamashita, F.; Komatsu, T.; Nakagawa, T. Study of Metal-Polycarboxylate Complexes Employing Ion-selective Electrodes. II. Stability Constants of Copper(II) Complexes with Poly(acrylic acid) and Poly(methacrylic acid). Bull. Chem. Soc. Jpn. 1979, 52 (1), 30-33.
3562
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
(20) McLaren, J. D.; Watts, J. D.; Gilbert, A. Interactions of Nickel and Copper with Polyacrylic acid. J. Polym. Sci., Part C 1967, 16, 1903. (21) Yamaoka, K.; Masujima, T. Spectroscopic and Equilibrium Dialysis Studies of the Poly(acrylic acid)-Cu(II) complex in the pH range 3.5-7. Bull. Chem. Soc. Jpn. 1979, 52 (6), 18191827. (22) Rumeau, M.; Persin, F.; Sciers, V.; Persin, M.; Sarrazin, J. Separation by Coupling Ultrafiltration and Complexation of Metallic Species with Industrial Water Soluble Polymers. Application for Removal or Concentration of Metallic Cations. J. Membr. Sci. 1992, 73, 313-322.
(23) Juang, R. S.; Liang, J. F. Equilibrium Studies for the Interaction of Aqueous Metal Ions and Polyacrylic Acid by a Batch Ultrafiltration Method. J. Membr. Sci. 1993, 82, 163-174. (24) Juang, R. S.; Chen, M. N. Measurement of Binding Constants of Poly(ethylenimine) with Metal Ions and Metal Chelates in Aqueous Media by Ultrafiltration. Ind. Eng. Chem. Res. 1996, 35, 1935-1943.
Received for review November 20, 2000 Revised manuscript received March 10, 2001 Accepted May 21, 2001 IE0009839
