Ind. Eng. Chem. Res. 2002, 41, 5079-5084
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Binding Properties of a Water-Soluble Chelating Polymer with Divalent Metal Ions Measured by Ultrafiltration. Poly(r-acethylaminoacrylic acid) Keiko Kawano,† Kinya Hamaguchi,‡ Seizo Masuda,‡ and Tahei Tomida*,‡ Department of Chemical Science and Technology and Graduate School of Engineering, The University of Tokushima, Tokushima 770-8506, Japan
Binding equilibria of a water-soluble chelating polymer, poly(R-acethylaminoacrylic acid), with divalent metal ions (Co(II), Ni(II), Cu(II), Zn(II), Pb(II)) were measured by a batch ultrafiltration method in the pH range 4-6. It was shown that the binding equilibrium curves were reasonably well represented by the complexation model accounting for the formation of three kinds of complexes (LM+, L2M, and L2M(HL)2) proposed previously. 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 variations of the average coordination number depending on solution pH and metal ion concentration were well explained on the basis of the relative concentration of each complex to total polymer. 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.1-14 Ultrafiltrations are also shown to be useful to determine the interaction of metal ions with water-soluble chelating polymers.15,16 Previous papers from this laboratory described a novel method using water-soluble chelating polymers and microporous membranes for recovering and/or concentrating metal ions from aqueous solutions.17-20 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. From this point, we previously studied the binding properties of water-soluble chelating polymers, poly(acrylic acid) (abbreviation: PAA), with several divalent metal ions by an ultrafiltration method, and determined the stability constants of PAA-metal complexes on the basis of a complexation model accounting for the formation of three kinds of complexes.21 It was shown that the model could express the binding equilibrium of PAA with metal ions in the wide ranges of pH and concentration of metal ions. In the present study, we measured the binding equilibria of poly(R-acethylaminoacrylic acid) (abbreviation: P4A) with several divalent metal ions by the ultrafiltration method, as described previously, and discussed the applicability of the model to P4A-divalent metal complexes. Different from PAA, P4A has three donors in each monomer unit which can form complexes of a five-membered ring or a seven-membered ring. It was concluded that the equilibrium curves were well * To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: (81)-88-656-7425. Fax: (81)-88-655-7025. † Graduate School of Engineering, The University of Tokushima. ‡ Department of Chemical Science and Technology, The University of Tokushima.
represented by the complexation model, and the successive stability constants were determined by matching the calculated binding curves to the experimental ones irrespective of the solution pH. The average coordination number was also discussed on the basis of the complexation model. Experimental Section Materials. The water-soluble chelating polymer, poly(R-acethylaminoacrylic acid), was prepared by polymerization of 2-acetamidoacrylic acid with 2,2′-azobisisobutyronitrile as the initiator in our laboratory. After dialysis using a dialysis membrane with a molecular weight cutoff (MWCO) of 14 000 in water over 24 h, the polymer was lyophilized. The weight average molecular weight of the polymer determined by gel permeation chromatography was 1 100 000. A fixed weight of the polymer was diluted to the required concentration (50-100 mM in monomer units) with water. For each experimental run, P4A aqueous solutions were adjusted to the fixed pH and concentrations. All 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 (metal: 1000 ppm in 0.1 M nitric acid. pH ∼ 1; Wako Pure Chemical Industries, Ltd. in Japan). Deionized and distilled water was used. Experimental Procedure. The dissociation constant of P4A was determined by a pH titration method. An aqueous solution of P4A (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 pH of the solution was adjusted to the
10.1021/ie0200050 CCC: $22.00 © 2002 American Chemical Society Published on Web 09/07/2002
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Figure 1. Henderson-Hasselbach plots of pH titration for poly(R-acethylaminoacrylic acid).
Figure 2. Binding equilibrium curves of Co(II) at different solution pH: dotted lines, calculated; symbols, experimental values.
fixed value by adding a small amount of an aqueous solution of sodium hydroxide or nitric acid at intervals of about 2 h until no further change in pH of the solution was observed. After stirring over 24 h, the final volume of the mixture was determined by weighing. The mixture was ultrafiltrated using a ultrafilter unit with a MWCO of 10 000 (Advantec Inc.). For each run, about 3 cm3 of 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. In general, the dissociation constant of a polymer acid is expressed by the following equation:22
Ka ) [H+]{[L-]/[HL]}β
(1)
Figure 3. Binding equilibrium curves of Ni(II) at different solution pH: dotted lines, calculated; symbols, experimental values.
We determined the dissociation constant of P4A by pH titration using the modified Henderson-Hasselbach equation:
(1 -R R)
pH ) pKa - β log
(2)
Figure 1 shows the experimental results of pH titration for P4A in the absence of any neutral salts other than NaNO3 produced by adding NaOH. The degree of neutralization, R, is the molar ratio of NaOH to P4A in the monomer unit. As seen from the figure, the curve is nearly straight in the pH range 3.8-7.2. 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, were determined to be 3 and 6.3 × 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 and the membrane; (2) permeation of the polymer and permeation of the polymer-metal complexes are 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) amounts of metal hydroxides are neglected. The amount of metal ions bound to the polymer of the monomer unit,
Figure 4. Binding equilibrium curves of Cu(II) at different solution pH: dotted lines, calculated; symbols, experimental values.
q, was determined from a change in concentration of the metal ions in the solutions on the basis of a mass balance. The binding equilibrium curves for Co(II), Ni(II), Cu(II), Zn(II), and Pb(II) are shown in Figures 2-6, respectively. As 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 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. 41, No. 20, 2002 5081 Table 1. Stability and Equilibrium Constants of P4A-Divalent Metal Complexes, and Correlation Coefficients between Calculated q Values and Experimental Ones metal ion
log b1
log b2
log k3
log B2
correlation coefficient
Co(II) Ni(II) Cu(II) Zn(II) Pb(II)
-2.9 -2.4 -1.7 -2.7 -1.3
-1.7 -2.2 -0.08 -2.1 -0.05
7.7 8.0 8.1 8.0 7.5
-4.6 -4.6 -1.8 -4.8 -1.3
0.938 0.963 0.885 0.942 0.958
L2M(HL)n denotes the complex formed without protonation, and the equilibrium constant, k3, is defined as follows: Figure 5. Binding equilibrium curves of Zn(II) at different solution pH: dotted lines, calculated; symbols, experimental values.
k3 )
[L2M(HL)n] [L2M][HL]n
(7)
Then, 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}
Figure 6. Binding equilibrium curves of Pb(II) at different solution pH: dotted lines, calculated; symbols, experimental values.
Analysis of Binding Equilibrium Based on a Complexation Model. Previously, we proposed the complexation model to represent the binding equilibrium of PAA with divalent metal ions.21 Similarly, the binding equilibrium of P4A with divalent metal ions was analyzed on the basis of the complexation model. On the basis of the modified Bjerrum model,22 the successive formation of polymer-metal complexes for divalent metal ions is expressed as follows:
HL + M2+ ) LM+ + H+; b1
(3)
HL + LM+ ) L2M + H+; b2
(4)
where the successive stability constants b1 and b2 are defined as follows:
b1 )
[LM+][H+] [HL][M2+]
and b2 )
[L2M][H+] [HL][LM+]
(5)
However, the experimental binding equilibrium curves of P4A with divalent metal ions were not well represented from eqs 3-5. Thus, in analogy with the case of PAA-divalent metal complexes,21 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 ) L2M(HL)n; k3
(6)
(8)
where [Mp] and [Pt] are the total concentration of metal ions bound to the polymer and the total concentration of the polymer, respectively (see Appendix). Determination of Binding Equilibrium and Stability Constants. It is considered that P4A binds with divalent metal ions to form complexes of seven-membered rings and/or five-membered rings. Considering the fact that the primary coordination number of the divalent metals used is four, it seems that P4A-divalent metal complexes have square planar or tetrahedral structures, as illustrated in Figure 7. In addition to those complexes, it is likely that the complexes of which two coordinations are satisfied by the two carboxyl anions, and the residual two coordinations are satisfied by another donors in the polymer. It is impossible at present to verify the structure of P4A-metal complexes. However, as described below, better agreement of the calculated binding equilibrium curves with the experimental ones was obtained in the case when n ) 2 for P4A-divalent metal ions, similar to the case for PAAdivalent metal ions.21 In Figures 2-6, calculated binding equilibrium curves 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 influenced the slope of curvature and the pH dependence of the binding curves. As seen from Figures 2-6, the calculated values agree well with the experimental ones for all kinds of metals examined. The correlation coefficients shown in Table 1 indicate a good reliability of the constants for the complexation model. The overall complexation constant, B2 ()b1b2), of Cu(II) is close to that of Pb(II), and they are much larger than those of the other metal ions (see Table 1). The overall complexation constants decrease in the order Pb(II), Cu(II) . Co(II), Ni(II), Zn(II). It is noted that the average coordination number of water soluble chelating polymer-metal complexes varies from zero to more than 2 depending on the solution
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Figure 7. Schematic structures of P4A (a) and P4A-divalent metal complexes of five-membered rings (b) and seven-membered rings (c).
Figure 8. Calculated relative concentrations and the average coordination numbers for P4A-Co(II) complexes at pH 5 (a) and pH 6 (b).
pH and the concentration ratio of the polymer to the metal ions.6,15,16 To understand the variation of the average coordination number depending on solution pH and/or concentration of metal ions, the relative concentrations of the three kinds of complexes to the total polymer were calculated from the model equation described above, using the parameters shown in Table 1 (see Appendix). Typical examples of the estimated concentrations of the complexes and the average coordination numbers for Co(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 Co(II) at pH 5 and Cu(II) at pH 4 are predominantly formed in all concentration ranges examined. The complexes LM+ and L2M, on the contrary, increase slightly with an increase in metal ion concentration. The average coordination number is consequently much higher than three. With respect to Co(II) at pH 6 and Cu(II) at pH 5, the concentration of L2M increases with an increase in metal ion concentration and becomes much higher than others in the higher concentration region of metal ions. With an increase in
Figure 9. Calculated relative concentrations and the average coordination numbers for P4A-Cu(II) complexes at pH 4 (a) and pH 5 (b).
metal ion concentration, LM+ increases, but L2M(HL)2 decreases gradually. The values of nav decrease with an increase in the concentration of metal ions and/or the solution pH. The complexation behaviors of Ni(II) and Zn(II) are similar to those of Co(II), and the behaviors of Pb(II) complexes are similar to those of Cu(II), but their illustrations are omitted. Conclusions The binding equilibria of poly(R-acethylaminoacrylic acid), P4A, with divalent metal ions (Co(II), Ni(II), Cu(II), Zn(II), 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 accounting for the formation of three kinds of complexes. The successive stability constants for P4A-metal complexes were determined by fitting the calculated curves to the experimental ones irrespective of the
Ind. Eng. Chem. Res., Vol. 41, No. 20, 2002 5083
solution pH. The orders of magnitude of the overall complexation constants of P4A complexes are comparable to those of PAA complexes. They decreased in the order Pb(II), Cu(II) . Ni(II), Co(II), Zn(II). 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. Appendix As described in the previous paper,21 the total amount of metal ions bound to the polymer and the total amount of the polymer are expressed as eqs A-1 and A-2, respectively.
[Mp] ) [LM] + [L2M] + [L2M(HL)n] ) b1[M]
[HL] +
[H ]
{ } { } [HL]
2
+ [H ] [HL] 2 [HL]n (A-1) b1b2k3[M] + [H ]
+ b1b2[M]
+
[Pt] ) [HL] + [L-] + [LM] + 2[L2M] + (2 + n)[L2M(HL)n]
{ ( )}
) 1+
Ka
1/β
+
[H ]
[HL] + b1[M]
2b1b2[M]
{ } [HL]
2
+
[H ]
(2 + n)b1b2k3[M]
[HL] [H+]
+
+
{ } [HL] [H+]
2
[HL]n (A-2)
Since the values of [Pt] and [H+] are known under experimental conditions, the value of [HL] can be determined for a given value of [M] provided that the values of b1, b2, and k3 are known. So, the relationship between q and [M] is obtained:
q ) [Mp]/[Pt]
(A-3)
Similarly, the average coordination number, nav, is represented as a function of each complex concentration or [M] as follows:
nav ) {[LM+] + 2[L2M] + 4[L2M(HL)2]}/{[LM+] + [L2M] + [L2M(HL)2]} (A-4) Acknowledgment The authors are grateful to K. Nii, K. Horie, and A. Shirota, students of The University of Tokushima, for their experimental support. This work was also supported by the Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (B)), which is greatly appreciated. Nomenclature b1 ) successive stability constant (-) b2 ) successive stability constant (-) B2 ) overall complexation constant ()b1b2) (-) 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) [ ] ) molar concentration of species in the bracket (M) R ) degree of neutralization (-) β ) constant (-)
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Received for review January 2, 2002 Revised manuscript received July 18, 2002 Accepted July 28, 2002 IE0200050
