J. Phys. Chem. 1994, 98, 1288-1292
1288
Novel Method for Determinations of the Successive Formation Constants for Complexation of Transition Metal Ions with Polymer Ligands Keiko Seki, Mitsuru Isobe, Kazutaka Yanagita, Toshiyuki Abe, and Yoshimi Kurimura' Department of Chemistry, Ibaraki University, Mito. Ibaraki 31 0, Japan Tetsuya Kimijima Nippon Sanso Co., Tsukuba Laboratory, Ohkubo, Tsukuba. Ibaraki 305, Japan Received: October 28, 1993@
The successive formation constants for the complexation of copper(I1) with poly(N4nylimidazole) (PVIm) have been determined by means of spectral deconvolution. Based on these results, definitions of the successive formation constants for the complexation of transition metal ions with multidentate polymer ligands are proposed. These a r e K1 = [CuL*]/[Cu][L*], K2 = [CuL*2]/[CuL*], K3 = [CuL*3]/[CuL*2], and K4 = [CuL*4]/ [CuL*3](L*is ligand residue on the polymer, charge omitted). The definitions of K2,4, and K4 are quite unlike the generally used definition, and the difference is ascribed to the nature of a polymer chain, which makes a microheterogeneous region in the solution. The results indicate that the concentration ratio [CuL*]: [CuL*2]: is constant when [L*] is varied. Present results seem to strongly suggest that the commonly [CuL*3]:[CuL*4] used definitions of the successive formation constants for the complexation of transition metal ions with multidentate polymer ligands would be replaced by those proposed here, and re-examinations of the complexation of transition metal ions with multidentate polymer ligands may be necessary.
Introduction A variety of complexations of copper(I1) ions with polymer ligands such as polypeptides,l-1° poly(acry1ic acid),"J2 polypoly(N4nylim(methacrylic acid),'3 poly(N-~inylpyridine),l~-~~ idazole),16 and have been investigated. Kotliar and MorawetzI3 and Morawetz and Sammak22pointed out that the usual treatment of association equilibria of a cation with n ligand groups X characterized by formation constants of the form Kf = (MX,)/(M)(X),is not applicable for thepolymerscarrying large numbers of ligand. Thus, if copper(I1) ions are added to a dilute solution of polymer ligands such as poly(acry1ic acid) and poly(methacrylic acid), only the association with the first carboxylate should depend on the overall carboxylate concentration in the solution. Once the copper ion is bounded to a polyion, any further binding will depend only on the number and spatial distribution of ligand groups in the one-chain m01ecule.l~ However, the quantitative treatment of the successive formation constants based on the above consideration has not yet been investigated.
Experimental Section Poly(N-vinylimidazole) (PVIm) was prepared by free radical polymerization of N-vinylimidazole in water-methanol (50% v/v) with AIBN as initiator. The average molecular weight, M,, of PVIm was about 9.6 X lo4. N-Ethylimidazole (EtIm) was distilled under reduced pressure just before use. Imidazole (Im) was recrystallized from benzene. Aqueous solutions of copper(11) were prepared by dissolving G.R. reagnet grade Cu(N03)2 in redistilled water. Solutions of Cu(1I)-EtIm, Cu(I1)-Im, and Cu(I1)-PVIm were carefully prepared to avoid the formation of Cu(I1) hydroxide. After dropwise addition of the copper(I1) nitrate solution into an aqueous solution of the ligand, the pH of the solutions was adjusted to the desired value with dilute solutions of nitric acid andlor sodium hydroxide. For the Cu(I1)-EtIm and Cu(1I)-Im systems, the solutions containing no appreciable amounts of the Cu(I1) hydroxide species could be prepared even ~
~~
e
~
Abstract published in Advance ACS Abstracts, January 1, 1994.
0022-365419412098- 1288$04.50/0
at relatively high pH (-5.5) in the presence of a large excess of the ligand since large excess of the ligand were present in the solution. However, preparation of Cu(I1)-PVIm solutions containing no appreciable amounts of Cu(1I) hydroxy species was difficult at pH higher than about 4.5 under the conditions employed. Hydrogen ion concentrations were determined with a Horiba M- 13 pH meter. Measurements were repeated at 3-min intervals, and care was taken to maintain the precision of the measurementsat f0.005 pH. Aciddissociation constantsof PVIm and EtIm were determined by means of potentiometric titration. Absorption spectra were recorded on a Shimadzu Model 265 spectrophotometer. The precision of the absorbances was within fO.OO1 Abs units. Spectral deconvolutions werecarriedout using a personal computer employing a Gauss-Newton program.23All the determinations of the formation constants were carried out at 0.1 M NaNO3 and 25 "C.
Results and Discussion The acid dissociation constant of imidazole (Im) has been reported to be pKa = 7.12 at I (ionic strength) = 0.1 M and 25 0C.24 In the present study, the pKa value of N-ethylimidazole (EtIm) was determined to be 7.28 f 0.01 at I = 0.1 M and 25 "C by means of potentiometric titration. For the polymer ligand, the values of pKa and n, which is a measure of the effect of neighboring groups on dissociation of proton, were also determined by means of potentiometric titration using a modified Henderson-Hasselbach equation:*S p H = pKa - n log((1 - (Y)/(Y)
(1) where a is the degree of neutralization. From the intercept and the slope of the straight line of pH versus log{(1 -CY)/.) plot, pK, and n, respectively, can be obtained. In the present study, the values of pK, and n were calculated to be 5.07 f 0.05 and 1.94 f 0.05 (0.1 M NaNO3), respectively. Prior to determination of the successive formation constants for the Cu(I1)-PVIm complexes, those of Cu(I1)-EtIm and Cu(11)-Im were determined by means of spectral deconvolution. 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 1289
Complexation of Transition Metals and Polymers
B
CuL4 .- ..-...-.
C
CULZ
CULB
D
CUL .._._.....c u ~
3\
22
20
18
16
14
12 22
20
18
16
14
1
Wavenumber / 1OB cm-' Figure 1. Absorption spectra of the solutions containing 4.00 X M Cu(I1) at different concentrations of EtIm with their resolved bands at pH 3.64. A: Original absorption spectra. B: Resolved bands for CuL4 and CuL3. C: Resolved band for CuL2. D: Resolved bands for CuL and Cu. Rough dotted lines in Figure A represent the absorption spectra calculated by summation of the component spectra which were obtained using the obtained values of e,, Y, and (HI/&, for the components and the estimated formation constants. [EtIm]~/1@'M: (1) 2.00, (2) 4.00, (3) 6.00,(4) 10.0, ( 5 ) 15.0.
The spectral parameters such as absorption maximum (vmax), molar absorptivity (emax), and half-width (Hip) of the absorption band of Cu2+were determined from the absorption spectra of the solution of Cu(N03)2 (pH 2.0). The values of emaxand vmax for Cu(Im)d2+have been reported to be 53 M-I cm-I and 1.68 X lo4 cm-I, respectively.26 The molar absorptivity and the maximum wavenumber for Cu(EtIm)d2+ were determined from the absorption spectra of Cu-EtImsolutions in the higher concentration range of the ligands ([L] = 0.4-1.0 M) at pH 4.5. The values of €4 and A,,, were estimated, respectively, from the intercepts of the straight lines obtained by extrapolating l/(absorbance) vs 1/ [ L ] ~ a n d1/hmaxVS1/[LIT plots to 1/[LIT-+(). The absorption bands due to Cu2+,Cu(EtIm)d2+, and Cu(Im)d2+were found to fit a single Gaussian distribution. The spectral parameters used for the spectral resolutions were emax = 11.0 M-I cm-l (Vmax = 1.26 X lo4 cm-I) for Cu2+,emax = 56.2 M-I cm-I (vmax = 1.68 X lo4 cm-I) for Cu(EtIm)d2+, and emax = 53.0 M-' cm-I (vmax = 1.68 X 104 cm-I) for C U ( I ~ ) . ? + . ~ ~ Absorption spectra of the Cu(I1)-EtIm solutions a t pH 3.64 are shown in Figure 1A by the solid lines. Curves 1-5 in Figure 1A represent the absorption spectra of the solutions containing M Cu(I1) a t different concentrations of EtIm. These 4.00 X le3 absorption spectra in Figure 1A (solid lines) can be resolved into five spectral bands due to the chemical species of Cu, CuL, CuL2, CuL3, and CuL4. The component spectral bands obtained by the spectral deconvolution are shown in Figure 1B for CuL3 and CuL4, Figure 1C for CuL2, and Figure 1D for Cu and CuL. These figures show that, at pH 3.64, well-recognized bands due to Cu, CuL, CuL2, and CuL3 are observed whereas a small band for CuL4 is seen. The absorption spectra of the solutions
containing 1.0 X le3 M Cu(I1) and different concentrations of EtIm a t pH 5.25 are represented in Figure 2. At pH 5.25, three distinct bands due to CuL2, CuL3, and CuL4 are observed and very small bands due to Cu and CuL are seen as shown in Figure 2B-D. The values of v r v 4 (VO and v 4 are known) and AwA4, where v,andA,are thewavenumber and theabsorbanceat themaximum wavenumber of the corresponding CuL,, at several concentrations of lignad were determined from the well-analyzed bands, i.e., those for Cu, CuL, CuL2, and CuL3 in Figure 1 and those for CuL2, CuL3, and CuL4 in Figure 2. At a given pH, the following equation is applicable:
[CUI, = A,/% + 4 / t , + A2/e2 + A3/% + A d e l
(2)
where [cu]T is the total concentration of the Cu(I1) and e, is the molar absorptivity for CuL,. To calculate the exact values of €1, 62, and e3 by means of a computer-fitting routine, approximate values of these were initially estimated by assuming that the molar absorptivities of CuL, increase linearly with increasing n from 0 to 4. The known values of €0 and e4; the approximate values of e l , €2, and e3; and the observed values of A r A 4 were substituted into the right-hand side of eq 2. Then, five simultaneous equations were obtained corresponding to five different concentrations of the ligand for each solutions at pH 3.64 and 5.25. The values of e l , €2, and e3 were then adjusted as the errors of [cu]T of the five equations were minimized by iterative computer calculations. The values of e l , e2, and e3 (M-1 cm-I) were calculated to be 22.3, 33.6, and 44.0, respectively.
1290 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994
Seki et al.
D
CuL2
22
20
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12 22
20
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Wavenumber / 1O3 cm-’ Figure 2. Absorption spectra of the solutions containing 1.O X le3 M Cu(I1) at different concentrationsof EtIm with their resolved bands at pH 5.25. A: Original absorptionspectra. B: Resolved bands for CuL4 and CuLs. C: Resolved band for CuLz. D: Resolved bands for CuL and Cu. [EtIm]/ le2 M: (1) 3.00,(2)6.00,(3) 15.0,(4)40.0,(5) 100.
Using the values of &A4 and those of e r e 4 , the concentrations of CuL, at a given ligand concentration and pH were calculated. Thus, the formation constantsdefined by K,, = [CuL,]/ [CUL,I][L] could be determined since the total concentration of the uncoordinated EtIm is essentially equal to that of the ligand under the conditions employed. The concentration of the nonprotonated ligand, [L], is given by eq 3
(3) where [LIT is total concentration of the ligand and K , is the acid dissociation constant of EtIm. The values of the successive formation constants for the Cu(11)-EtIm system were determined by means of the spectral resolution. From the data obtained a t pH 5.25, log K3 = 2.97 f 0.05 and log K4 = 2.62 f 0.1 were determined. At this pH, exact values of log K , and log K2 could not be determined because the values of A0 and A I were very small. On the other hand, at pH 3.64, the exact value of log K4 could not be determined because the value of A4 was very small. From the data obtained at pH 3.63, log K1 = 4.1 1 f 0.05, log K2 = 3.66 f 0.06, and log K3 = 3.07 0.05 were obtained. The log K3 value lised in Table 1 is the average of two values obtained a t pH 5.25 and 3.64. The successive formation constants for the complexation of Cuz+ with Im were also determined using a method similar to that used for the Cu(I1)-EtIm system. The results are summarized in Table 1 along with those of Cu(I1)-EtIm. Unfortunately, reported values of the successive formation constants for Cu(I1)-EtIm could not be found in the literature. However, good agreement between the successive formation constants for
*
TABLE 1: Successive Formation Constants for Complexation of Cu(II) witb Imidazoles Determined by Means of Spectral Resolution at 0.1 M NaNO3 and 25 O c a ligand log K 1 log Kz loa K3 loa KA ~
Im EtIm
4.25i0.07 3.75f0.07 2.90i0.05 (4.33) (3.54) (2.82) 4.1 1 f 0.05 3.66 i 0.06 3.02 i 0.05
_ _ _ _ _ ~
2.05h0.11 (2.03) 2.62 f 0.10
Data in parentheseswere obtained by means of potentiometrictitration (ref 25). Cu( 11)-Im complexes obtained here and those obtained by means of potentiometric titrationz7 seems to indicate that the method of the deconvolution of the absorption spectra for determination of the successive formation constants is valid in Cu(I1)-imidazole system. The component spectra for the given [cu(II)]T, [LIT, and pH could be obtained using the known values of en, v,,, and (Hip),,for the components and the successive formation constants obtained in the present study. An example of the summation of the component spectra for Cu(I1)-EtIm is shown in Figure 1A by the rough dotted lines. It is clear that the absorption of spectra of Cu(I1)-EtIm obtained by summation of the component spectra give a good fit of the observed spectra. It was also ascertained that in the Cu(I1)-Im systema good fit exists between the observed absorption spectra and those obtained by summation of the component spectra. On the basis of the success of the determinations of the successive formation constants for the Cu( 11)-imidazoles system by means of spectral deconvolution, we attempted to repeat the analysis for the polymer system in order to determine the successive formation constants for the complexation of Cu(I1) with PVIm. For the polymer system, well-defined resolved spectral bands due
Complexation of Transition Metals and Polymers
The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 1291
6
A
t
I
P(
'0 r
\
Q)
0 C Q
2 $ n
CUL
D
............ c u
a
1
lot 5
Wavenumber / 1O3 cm-'
Wavenumber / 1O3 cm-'
Figure 3. Absorption spectra of the solutions containing 1.00 X lC3M Cu(I1) at different concentrations of PVIm at pH 3.10 with their resolved spectral bands. A: Original absorption spectra of the solution. B: Resolved bands for CuL*4 and CuL*3. C: Resolved band for CuL*2. D: Resolved bands for CuL* and cu. [L*]T/1C3 M: (1) 1.00, (2) 3.00, (3) 6.00, (4) 10.0, ( 5 ) 20.0.
imidazole residues given by [L*]" = [L*]T - [CuL*] - 2[CUL*,]
log
[L*I
Figure 4. Plots of the Cu(I1) species as a function of the logarithmic concentration of nonprotonated imidazole residue, log [L*], in Cu(I1)PVIm solutions containing 1.00 X l t 3 M Cu(I1) and different concentrations of PVIm at pH 3.10: (1) Cu, (2) CuL*, (3) CuL*2, (4)
- 3[CUL*J -
4ICUL*,I ( 5 ) The relationship between the concentrations of dissolved Cu(11) species and the logarithmic concentration of the nonprotonated ligand residue, log [L*], was obtained in a similar manner for the Cu(I1)-EtIm system, and the result is shown in Figure 4. Some remarkable characteristics of the polymer ligand are seen in Figure 4. For example, the concentrations of all the CuL, complex species tend to increase continuously with increasing [L*] in the lower concentration region of L*. Furthermore, the ratio [CUL*]:[CUL*~]:[C~L*~]:[CUL*~] is essentially constant over the concentration region of L*. The results shown in Figure 4 indicate that, for the polymer system, the successive formation constant of the first step ligation, (Kl),, can be represented in the same form as that of the low molecular weight analogue. However, it is noteworthy that the definitions of the 2nd, 3rd, and 4th step ligations are truly distinct from the usual definitions. Consequently, the successive formation constants, (KJp, for the polymer system are represented by eqs 6-9:
CUL*S, ( 5 ) CUL"4.
to all the Cu(Im*), (Im* = imidazole residue on PVIm, n = 1-4) species were obtained at the lower concentration region of imidazole residues a t p H 3.10 (Figure 3). The concentration of the nonprotonated ligand residue (L*]) is calculated by the following equation:
[L*] = [L*]"(l
+ 10'pK.-PH'/")-'
(4) where [L*Iu is the total concentration of the uncoordinated
(K4Ip =
[C~L*,I/[C~L*,I
(9)
For PVIm, the polymer chain in the solution occupies a definite volume, V,, which depends on the physico-chemical environment
1292 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994
been determined by means of potentiometric titration]' to be 8 4 = 10" M4 (0.1 M ionic strength) at 2 5 OC.']
TABLE 2: Successive Formation Constants for Cu(I1)-PVIm Complexes at 0.1 M NaNOk pH 3.10, and 25 O C" (K1)pIM-I 330 f 8 0
W2)P
W3)P
W4)P
1.22 f 0.05
1.69 f 0.07
3.37 f 0.05
(KZ)pr(K3)p, and
(K4)p are
B4 = [cuL*,2']/[cu][L*]4
dimensionless values.
1
11
Seki et al.
(10)
Present results suggest that the definition of 84for the polymer system is quite different from that used before. The overall formation constant for the polymer complex defined by the new definition, (/34)p is
(B4Ip= [C~L*4l/[C~I~L*l
(11)
The value of (/34)p for the complexation of Cu(I1) with PVIm is 2.6 X lo3 M-1 at pH 3.10 and 0.1 M NaN03. It appears that the re-examination of the complexation of transition metal ions with multidentate polymer ligands would be necessary in the light of new definitions of the successive formation constants as demonstrated in the present study.
Acknowledgment. We are grateful to Professors E. Tsuchida, H. Nishide, and G . Challa for helpful discussion, Professor T. Oriyama for measuring N M R spectra, K.Takato and E. Suzuki for making a program for the spectral deconvolutions, and M. Yagi for his assistance. I
-6
-4
-2
0
log [LI Figure 5. Distributions of Cu(I1) species at different concentrations of
PVIm calculated from the estimated successive formation constants a t [Cu(II)] = 1.00 X le3M and pH 3.10: (1) Cu, (2) CuL*, (3) CuL.2, (4) CUL*3, (5) CuL*4. of the polymer chain such as the concentration of salt, the charges on the polymer backbone, and the pH of the solution. In the first step of the complexation, however, the reaction proceeds similar to that of nonpolymer since this reaction would take place between the imidazole residues on voluntary polymer backbone and the Cu2+ in the bulk solution. This leads to the same definition as that found for the low molecular weight case. The estimated values of the successive formation constants for the complexation of Cu(1I) with PVIm are shown in Table 2 . For the polymer ligand, the values of ( K Z ) (K3)p, ~ , and ( K 4 , increase in the order (K2)pC (K3)p
