+
+
Anal. Chem. 1996, 68, 394-401
General Method for the Determination of Stability Constants of Lanthanide Ion Chelates by Ligand-Ligand Competition: Laser-Excited Eu3+ Luminescence Excitation Spectroscopy Shu Ling Wu and William DeW. Horrocks, Jr.*
Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802
A highly sensitive, convenient, direct spectroscopic method for the measurement of stability constants of Eu3+ ion complexes of multidentate ligands is described. Eu3+ ion complexation is monitored by means of 7F0 f 5D0 excitation spectroscopy. The method involves the competition against one another, of two ligands, one (L′) of known and one (L) of unknown stability constant for its Eu3+ complex. With laser excitation at a particular wavelength (in the 578-581 nm range), the excitation intensity of EuL and/ or EuL′ is measured by either a time-resolved method, if the excited state lifetimes of EuL and EuL′ are sufficiently different, or in a non-time-resolved manner, if the emission intensities (λem ) 614 nm) of EuL and EuL′ are significantly different at the exciting wavelength. These data lead to the determination of relative conditional stability constants (Krel ) [EuL′][L]t/[EuL][L′]t) of the two ligands which, with knowledge of the protonation constants of the ligands, can be used to calculate the thermodynamic formation constant of the fully deprotonated ligand, L. Using ethylenediaminetetraacetic acid (edta) as the reference ligand, formation constants for the 1:1 complexes of Eu3+ with N-(2-hydroxyethyl)ethylenediaminetriacetic acid (hedta), diethylenetriaminepentaacetic acid (dtpa), and 1,4,7,10-tetraazacyclododecane-1,4,7triacetic acid (do3a) were determined, all in good to excellent agreement with their literature values. The method was also applied to the Eu3+-dtpa-dien [1,4,7tris(carboxymethyl)-9,17-dioxo-1,4,7,10,13,16-hexaazacyclooctadecane] system, where the species EuH(dtpadien)+, Eu(dtpa-dien), and Eu(OH)(dtpa-dien)j exist in different pH regions. The respective formation constants are log KEuL ) 17.2 ( 0.1, log KEuHL ) 14.2 ( 0.2, and, for the reaction EuL + OH- ) Eu(OH)L-, log KOH ) 5.7 ( 0.2 (pKa ) 8.3 ( 0.2). Advantages of the present method include high sensitivity (1-10 µM concentrations of Eu3+ and ligand), small sample volumes (1 mL or less), and the ability to detect directly and characterize the species present in solution under particular pH conditions using excitation spectroscopy and lifetime measurements. The determination of stability constants of lanthanide ion (Ln3+) chelates is fundamental to understanding their coordination chemistry. Knowledge of these constants has practical importance in the characterization of such chelates for applications in the areas
of magnetic resonance imaging (MRI) contrast agents,1-5 luminescent labels for immunoassay,6-13 nucleic acid hybridization,14-16 and cleavage reagents.17,18 Potentiometic titrations19 have been widely employed in the determination of the formation constants of Ln3+ ion complexes of protonic ligands; however, when the formation constants are extremely high and/or the kinetics of formation is slow,20-24 this method may be difficult to apply. Recently developed alternative methods include the use of a chromaphoric chelate (arsenazo III) as a competitive spectral indicator,25,26 proton relaxation measurements in cases where water proton relaxation rates are significantly different for the complex and the free Ln3+(aq) ion,27,28 and methods based on formation and dissociation kinetics measurements.29 All of these (1) Cacheris, W. P.; Quay, S. C.; Rocklage, S. M. Magn. Reson. Imaging 1990, 8, 467-481. (2) Carvalho, J. F.; Kim, S.-H.; Chang, C. A. Inorg. Chem. 1992, 31, 40654068. (3) Wedeking, P.; Kumar, K.; Tweedle, M. F. Magn. Reson. Imaging 1992, 10, 641-648. (4) Lauffer, R. B. Chem. Rev. 1987, 87, 901-927. (5) Kumar, K.; Tweedle, M. F. Pure Appl. Chem. 1993, 65, 515-520. (6) Diamandis, E. P.; Christopoulos, T. K. Anal. Chem. 1990, 62, 1149A-1157A. (7) Khosravi, M. J.; Diamandis, E. P. Clin. Chem. 1987, 33, 1994-1999. (8) Diamandis, E. P.; Morton, R. C.; Reichstein, E.; Khosravi, M. J. Anal. Chem. 1989, 61, 48-53. (9) Morton, R. C.; Diamandis, E. P. Anal. Chem. 1990, 62, 1841-1845. (10) Diamandis, E. Clin. Biochem. 1988, 21, 139-150. (11) Mathis, G., Clin. Chem. 1993, 39, 1953-1959. (12) Canji, A.; Bailey, M. P.; Rochs, B. F. Analyst 1989, 114, 1407-1411. (13) Ozinskas, A. J. In Topics in Fluorescence Spectroscopy; Lakowicz, J. R., Ed.; Plenum Press: New York, 1994; Vol. 4, pp 449-496. (14) Diamandis, E. P. Electrophoresis 1993, 14, 866-875. (15) Selvin, P. R.; Rana, T. M.; Hearst, J. E. J. Am. Chem. Soc. 1994, 116, 60296030. (16) Selvin, P. R.; Rana, T. M.; Hearst, J. E. J. Am. Chem. Soc. 1994, 116, 60296030. (17) Morrow, J. R.; Buttrey, L. A.; Shelton, V. M.; Berback, K. A. J. Am. Chem. Soc. 1992, 114, 1903-1905. (18) Kolasa, K. A.; Morrow, J. R.; Sharma, A. P. Inorg. Chem. 1993, 32, 39833984. (19) Martell, A. E.; Motekaitis, R. J. Determination and Use of Stability Constants, 2nd ed.; VCH: New York, 1992. (20) Locin, M. F.; Desreux, J. F.; Merciny, E. Inorg. Chem. 1986, 25, 26462648. (21) Broan, C. J.; Cox, J. P. L.; Craig, A. S.; Kataky, R.; Parker, D.; Harrison, A.; Randall, A. M.; Ferguson, G. J. J. Chem. Soc., Perkin Trans. 1991, 2, 8799. (22) Aime, S.; Anelli, P. L.; Botta, M.; Fedeli, F.; Grandi, M.; Paoli, P.; Uggeri, F. Inorg. Chem. 1992, 31, 2422-2428. (23) Clarke, E. T.; Martell, A. E. Inorg. Chim. Acta 1991, 190, 37-46. (24) Delgado, R.; Sun, Y.; Motekaitis, R. J.; Martell, A. E. Inorg. Chem. 1993, 32, 3320-3326. (25) Cacheris, W. P.; Nickle, S. K.; Sherry, A. D. Inorg. Chem. 1987, 26, 958960. (26) Kumar, K.; Chang, C. A.; Tweedle, M. F. Inorg. Chem. 1993, 32, 587-593.
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methods are necessarily indirect, and the validity of the results depends on the correctness of the assumptions made concerning the species present in solution and the attainment of equilibrium at the time of the measurement. Laser-excited Eu3+ luminescence spectroscopy is a powerful tool for monitoring the binding of this ion to ligands in solution.30,31 In its most useful form, the 7F0 f 5D0 transition of Eu3+ in the range 577-581 nm is excited by a tunable dye laser while the 5D f 7F emission is monitored at 614 nm. Since the absorptive 0 2 transition is between nondegenerate levels, each unique Eu3+ environment produces a single excitation band. Absent any accidental coincidences, each Eu3+ complex will produce a unique excitation spectrum, the intensity of which is proportional to the concentration of the complex in solution. Use of a pulsed laser as the excitation source allows the measurement of Eu3+ excited state lifetimes, τ, which are characteristic of each complex. This technique has been used to determine relative (to Eu3+) binding constants of many different metal ions by competition experiments between Eu3+ and another ion for a given ligand.32 Furthermore, we have recently developed33 a general method for measuring very large formation constants (>1020 M-1) by following the intensity of the 7F0 f 5D0 excitation band as a function of pH. The present work establishes a general method, useful over a large range of pH values, for determining stability constants for a given ligand relative to that of a reference ligand by means of ligand-ligand competition experiments. Differences in the excitation spectra (peak wavelengths) and/or the excited state lifetimes between the unknown and reference complexes are exploited to accomplish these measurements. Our method complements pH-potentiometric measurements, which are necessary in any case to establish the protonation constants of the ligands required in the anaylsis involved in determining thermodynamic stability constants. EXPERIMENTAL SECTION Materials. 1,4,7,10-Tetraazacyclododecane-1,4,7-triacetic acid (do3a) was a gift from Nycomed Salutar, Inc. (Sunnyvale, CA). 1,4,7-Tris(carboxymethyl)-9,17-dioxo-1,4,7,10,13,16-hexaazacyclooctadecane (dtpa-dien) was a gift from S. J. Franklin and K. N. Raymond of the University of California, Berkeley. Ethylenediaminetetraacetic acid (edta, 99%), piperazine hexahydrate, and 2-(N-morpholino)ethanesulfonic acid (Mes) were purchased from Sigma Chemical Co. Hydrated EuCl3, 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (Hepes), N-(2-hydroxyethyl)ethylenediaminetriacetic acid (hedta, 99%), and diethylenetriaminepentaacetic acid (dtpa, 97%) were purchased from Aldrich Chemical Co. Homo-1,4-piperazinediethanesulfonic acid (Homopipes) was purchased from Research Organic Inc. The water used was deionized and doubly distilled, and all remaining reagents were the purest commercially available. The EuCl3 stock solution (10 mM) used was standardized against edta by using an arsenazo indicator. The concentrations of ligand stock solutions (∼4 mM) were determined via titrations with standardized Eu3+ at pH 6 on (27) Cortes, S.; Brucher, E.; Geraldes, C. F. G. C.; Sherry, A. D. Inorg. Chem. 1990, 29, 5-9. (28) Brucher, E.; Cortes, S.; Chavez, F.; Sherry, A. D. Inorg. Chem. 1991, 30, 2092-2097. (29) Wang, X.; Tianzhu, J.; Comblin, V.; Lopez-Mut, A.; Merciny, E.; Desreux, J. F. Inorg. Chem. 1992, 31, 1095-1099. (30) Horrocks, W. D., Jr.; Sudnick, D. R. Acc. Chem. Res. 1981, 14, 384-392. (31) Horrocks, W. D., Jr. Methods Enzymol. 1993, 226, 495-538. (32) Albin, M.; Farber, G. K.; Horrocks, W. D., Jr. Inorg. Chem. 1984, 23, 16481651. (33) Wu, S. L.; Horrocks, W. D., Jr. Inorg. Chem., submitted.
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Table 1. Protonation Constants of edta, hedta, dtpa, do3a, and dtpa-dien ligand edtaa hedtab dtpac do3ad dtpa-diene
log K1H
log K2H
log K3H
log K4H
log K5H
log K6H
10.19 9.81 10.45 11.59 (10.51) 10.02
6.13 5.37 8.53 9.24 (9.08) 8.87
2.69 2.6 4.28 4.43 (4.36) 4.10
2.00
1.5
0
2.65 3.48 (3.48) 2.62
1.82 1.80
a Smith, R. M.; Martell, A. E. Critical Stability Constants; Plenum Press: New York, 1974; Vol. 1, p 204. b Ibid., p 199. c Ibid., p 281. d Reference 36, at µ ) 0.1 ((Me N)Cl) and 25.0 ( 0.1 °C; the numbers 4 in parentheses are at µ ) 0.1 (NaCl) and 25.0 ( 0.1 °C. e Reference 39, at µ ) 0.1 (KCl) and 25.0 ( 0.1 °C.
equilibrated samples using laser-excited Eu3+ luminescence to monitor complexation. Methods. Eu3+ excitation spectra, excited state lifetimes, and excitation intensities were measured using a Continuum YG-581C pulsed (10 Hz) Nd-YAG laser-pumped tunable TDL-50 dye laser described previously.34 The 7F0 f 5D0 transition of the Eu3+ ion (578-581 nm) is excited by using a mixture of Rhodamine 590 (Excition Co.) and 610 (Kodak Chemical Co.). The 5D0 f 7F emission band at 614 nm is monitored in each case. Two 2 alternative methods of signal intensity measurement are available: time resolved or non-time-resolved, both of which are carried out at a fixed excitation wavelength. In the time-resolved measurements, the luminescence decays are accumulated over a period of time (usually 5 min) and averaged. The resulting averaged decay is analyzed for the amplitudes, I, of the component exponentials (intensities at time t ) 0). These amplitudes are corrected for fluctuations in the laser power over the course of a series of measurements. In the non-time-resolved method of data collection, the total photon emission from t ) 4 µs following each laser flash is measured and summed over a period of 10 s (100 laser pulses). These accumulated sums, corrected for fluctuation in laser power, are again summed over a period of 5 min. The intensity of a blank measurement on buffer alone under the same conditions is then subtracted. Since the complexation reactions of Eu3+ with do3a and dtpadien are slow, solutions of these ligands were allowed to equilibrate in buffer at the appropriate pH. These samples (2 mL) were kept in plastic tubes, first at 70 °C for 2 days, followed by an additional 4 days at 25 °C. To ensure that equilibrium has been reached, the order of mixing (either EuL + L′ or EuL′ + L, where L represents the ligand whose stability constant is being determined and L′ is the reference ligand) was varied, with the requirement that the resulting intensities be identical and that there was no further change in signal intensity as a function of time. All spectroscopic experiments were performed at 25 ( 0.1 °C on solutions with ionic strength adjusted to 0.10 with KCl. The buffers used were 0.02 M KOOCH (pH < 4), 0.02 M Homopipes (pH 4-5), 0.02 M Mes (pH 5-7), 0.02 M Hepes (pH 7-9), and 0.02 M piperazine (pH 9-10). The value19 of Kw ) [H+][OH-] was taken as 10-13.78. The protonation constants for the chelating ligands used in the computations were previously determined and are listed in Table 1. (34) Frey, S. T. Ph.D. Thesis, The Pennsylvania State University, University Park, PA, 1994.
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Computational Methods. For the multidentate ligands of interest here, which individually form only 1:1 complexes with Eu3+, the competition between the ligand, L, for which the formation constant of EuL is unknown, and a reference ligand, L′, of known formation constant can be written,
Time-Resolved Measurements. In this method, a reference ligand, L′, is chosen such that the lifetime, τ2, of the EuL′ complex is sufficiently different from the lifetime, τ1, of the EuL species that the luminescence decay can be resolved into two-component exponentials according to eq 10. Since τ1 and τ2 can be measured
EuL + L′ S EuL′ + L
It(t) ) I1 exp(-τ1-1t) + I2 exp(-τ2-1t)
(1)
The equilibrium constant for eq 1 can be expressed as follows:
Krel )
[EuL′][L]t [EuL][L′]t
)
K′RL′ KRL
(2)
where K and K′ are the thermodynamic equilibrium constants corresponding to eqs 3 and 4, respectively: 3+
Eu Eu
3+
+ L S EuL, K
(3)
+ L′ S EuL′, K′
(4)
which are related to the conditional stability constants,
Kcond ) [EuL]/[Eu3+][L]t
on the isolated systems, those values are held fixed in the analysis, and using the nonlinear regression analysis program Peak Fit (Jandel), the decay curves for the equilibrated, mixed system are analyzed for the quantities I1 and I2, which yield the concentrations of the individual complexes present via eq 9. According to relationships 11-14,
I2 ) k2[EuL′]
(11)
[Eu3+]i ) [EuL] + [EuL′]
(12)
[L]t ) [L]i - [EuL]
(13)
[L′]t ) [L′]i - [EuL′]
(14)
(5) the equilibrium expression of eq 2 is reduced to a function of I2, k2, and the initial concentrations:
where [L]t represents the sum of the equilibrium concentrations of the nonprotonated and all of the protonated forms of ligand L.
[L]t ) [Ln-] + [HL(n-1)-] + [H2L(n-2)-] + ...
(10)
(6)
The thermodynamics and conditional formation constants are related by eq 7,
Kcond ) KRL
(7)
RL ) (1 + K1H[H+] + K1HK2H[H+]2 + ...)-1
(8)
K′RL′/KRL ) (I2/k2){[L]i - [Eu3+]i + (I2/k2)}/ ({[Eu3+]i(-I2/k2)}{[L′]i - (I2/k2)}) (15) Similarly, eq 2 can also be expressed as a function of I1 and k1 and the initial concentrations:
K′RL′/KRL ) {[Eu3+]i - (I1/k1)}{[L]i - (I1/k1)}/ ((I1/k1){[L′]i - [Eu3+]i + (I1/k1)}) (16)
where
K1H, K2H, etc. represent the stepwise protonation constants of the fully deprotonated ligand, L. Analogous expressions apply for the reference ligand, L′. The present experiments were carried out at pH values greater than 3. The initial concentrations of Eu3+ present in the samples, [Eu3+]i, were in the 2-5 µM range, and both initial ligand concentrations [L] and [L′] are equal to or greater than [Eu3+]i. Since each ligand used forms a strong 1:1 complex with Eu3+, and the total concentration of ligands in solution is at least twice the Eu3+ ion concentration, the concentration of free Eu3+(aq) ion at equilibrium is negligible. For excitation at a given wavelength, the total intensity, It, represents the sum of contributions from the two complexes present according to eq 9, where k1 and k2 are proportionality
It ) I1 + I2 ) k1[EuL] + k2[EuL′]
(9)
constants which may be determined, respectively, by measurements on systems containing only EuL or EuL′.
where the subscript i indicates the initial concentration of the species indicated. Non-Time-Resolved Measurements. In this mode, an excitation wavelength is sought where the proportionality constants k1 and k2 (eq 9) are markedly different. Since excitation spectra of this type are generally quite narrow, this is usually readily accomplished. Thus, eqs 9, 12, 13, and 14 simplify eq 2 to a function of It, k1, and k2, and the initial concentrations as given in eq 17.
K′RL′/KRL ) {(It - k1[Eu3+]i)([L′]i(k2 - k1) + It - k2[Eu3+]i)}/{(k2[Eu3+]i - It)([L]i(k2 - k1) It + k1[Eu3+]i)} (17) The non-time-resolved method will, of course, fail if k1 ) k2 or if these quantities are close in magnitude. RESULTS Characterization of the Complexes via Eu3+ Luminescence. The 7F0 f 5D0 excitation spectra of Eu3+ complexes of the ligands edta, hedta, dtpa, do3a, and dtpa-dien (see Chart 1), recorded under the same experimental conditions (pH 7.10, 2 µM), are shown in Figure 1. The uniqueness of each spectrum is
+
Figure 1. Regression analysis fits to the 7F0 f 5D0 excitation spectra of five Eu3+ complexes: Eu(edta)- (s), Eu(hedta) (- -), Eu(dtpa)2(- ‚ ‚ -), Eu(do3a) (- ‚ -), and Eu(dtpa-dien) (‚‚‚), all recorded under identical conditions with [EuL] ) 2 µM.
Chart 1
apparent. The 5D0 excited state lifetimes of these complexes were also measured under the same conditions: Eu(edta)- (315 µs), Eu(hedta) (265 µs), Eu(dtpa)2- (627 µs), Eu(do3a) (291 µs) and Eu(dtpa-dien) (591 µs). The stoichiometries of the Eu3+ complexes were determined by titrating 4 µM solutions of each ligand with Eu3+ while monitoring complex formation at the excitation maximum of each complex. It is clear from Figure 2 that a precise 1:1 complex is formed in each of the systems. The measured lifetimes remain constant throughout the course of the titrations. It was noted, however, that if an extreme excess of Eu3+ is added (>1 mM Eu3+), then the intensity and lifetime are affected. This is probably due to contributions from the free Eu3+(aq) ion and to interaction of Eu3+ with the complex to form weakly associated species. These conditions do not occur in the present stability constant determinations. Also explored was the effect of adding an excess of a given ligand over the Eu3+ ion concentration. Addition of up to 50 mM of edta or dtpa in the presence of 4 µM Eu3+ revealed no change in excitation spectra or lifetimes, indicating that EuLx (x > 1) complexes do not form under these conditions. Thus, under the conditions of our experiments, only 1:1 complexes will be present, in addition to excess free ligand. Edta was chosen as the competing ligand in the present work since the stability constant of its Eu3+ complex is well established
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Figure 2. Intensities for 7F0 f 5D0 excitation spectra of Eu3+ complexes obtained using the time-resolved method of (1) hedta (λex ) 579.55 nm), (2) dtpa-dien (λex ) 579.88 nm), (3) do3a (λex ) 579.70 nm), (4) edta (λex ) 579.60 nm), and (5) dtpa (λex ) 579.89) as a function of total Eu3+ ion concentration added to 4 µM ligand solutions.
Figure 3. 7F0 f 5D0 excitation spectrum of a solution 2 µM in Eu3+, 2 µM in dtpa and 100 µM in edta at pH 5.18, 25 °C. The experimental spectrum is shown resolved into its components: Eu(edta)- (‚‚‚) and Eu(dtpa)2- (- ‚ -).
and is of the appropriate magnitude. The 7F0 f 5D0 excitation spectrum and the luminescence decay curve for each mixed ligand competitive system were recorded. Typical results, in this case for the 2:2:100 (µM) Eu3+/dtpa/edta system, are shown in Figures 3 and 4, respectively. The spectrum is a linear combination of the spectra of Eu(edta)- and of Eu(dtpa)2-; it is shown resolved into its components in Figure 3. The luminescence decay curve (Figure 4) is fit to two exponential functions (eq 10), holding the previously determined τ-values [Eu(edta)-, 315 µs; Eu(dtpa)2-, 627 µs] constant in the analysis in order to obtain accurate values for the amplitudes I1 and I2. Similar results were obtained for the remaining mixed ligand competition systems. Conditional Stability Constants and the Precision of the Method. The normal equilibrium expression for the thermodynamic stability constant of a metal chelate is given by eq 18, where
K ) [ML]/[M][L]
(18)
M represents the free, unhydrolyzed aqua metal ion and L
+
+
Table 2. Conditions and Results of Mixed Ligand Competition Determinations of log KEuL at 25 °C, µ ) 0.1, Where edtaa is the Reference Ligand
complex Eu(hedta) Eu(dtpa)2Eu(do3a)
log K
excitation wavelength (nm)
pH
580.06 579.57 579.89 579.74
7.38b 7.10c 5.18d 7.10e
time-resolved non-time-resolved lit. method method value 15.36 ( 0.20 15.59 ( 0.10 22.40 ( 0.06
15.45f 15.50 ( 0.10 20.69 ( 0.01
22.39f 21.0g
a The log K of Eu(edta)- is 17.29 (see Table 1, footnote a). b R edta ) 1.46 × 10-3; Rhedta ) 3.67 × 10-3. c Redta ) 7.37 × 10-4; Rhedta ) 1.91 -3 d -7 -9 e × 10 . Redta ) 9.83 × 10 ; Rdtpa ) 2.13 × 10 . Redta ) 7.37 × 10-4; Rdo3a ) 2.32 × 10-3. f See Table 1, footnotes b and c. g Reference 26 for Gd(do3a).
Figure 4. Excited-state luminescence decay for the system containing 2 µM Eu3+, 2 µM dtpa, and 100 µM edta at pH 5.18, 25 °C. The decay was resolved into two-component single-exponential functions. The shorter component (τ ) 315 µs) corresponds to Eu(edta)-, while the longer component (τ ) 627 µs) corresponds to Eu(dtpa)2-.
more basic ligands, giving the less basic ligand an advantage in the competition for the metal ion. A successful determination of an equilibrium constant by mixed ligand competition methods requires that there be an approximately equal distribution of the metal ion between the two ligands in solution i.e., the ratio [EuL′]/ [EuL] is near unity. The present methods directly monitor the complexation of the two ligands. One is able to influence the distribution of the metal ion between the two ligands either by adjusting the pH to where the Kcond values of the two ligands are close (Figure 5) or by adjusting the ratio of the two ligands (eqs 1 and 2). To achieve a statistical analysis of the present luminescence measurements, the titration data of Figure 2, obtained using the time-resolved method, were fitted to the theoretical expression for the intensity, I, at the excitation maximum as a function of solution conditions, using the literature values of Kcond. It is easily shown that I is given by -1 2 I ) (k′′/2){c1 + c2 + K-1 cond - [(c1 + c2 + Kcond) -
4c1c2]1/2} (20) Figure 5. pH dependence of conditional stability constants for Eu(edta)- (‚‚‚), Eu(hedta) (- ‚ -), Eu(dtpa)2- (- ‚ ‚ -), and Eu(do3a) (s).
represents the uncomplexed, totally deprotonated form of the ligand. However, the thermodynamic stability constant does not directly reflect the degree of metal ion chelation at a given pH. Each ligand has a different response to proton competition for the metal ion binding which depends upon its intrinsic basicity. The affinity of a ligand for metal ion at a given pH is described by the conditional stability constant (Kcond) (eqs 5 and 19),
Kcond ) [ML]/{[M]([L] + [HL] + [H2L] + ...)}
(19a)
or
Kcond ) KRL
(19b)
where RL ) (1 + K1H[H+] + K1HK2H[H+]2 + ...)-1 and K is the thermodynamic stability constant. Figure 5 shows plots of the variation of the calculated conditional stability constants for four Eu3+ chelates as a function of pH. At low pH, the hydrogen ions compete for the coordination moieties more effectively for the
where k′′ is the proportionality constant between I and the concentration of the complex, c1 is the initial total concentration of Eu3+, and c2 is the initial total concentration of ligand. The curves of Figure 2 represent nonlinear regression fits of the data points to eq 20 using the program Peakfit. For each of the ligand systems, the following coefficients of determination, r2, and precisions, respectively, as defined in footnote 35 were generated: hedta, 0.991, 3.4%; dtpa-dien, 0.980, 5.1%; do3a, 0.996, 2.2%; edta, 0.998, 1.8%; dtpa, 0.992, 3.0%. These statistics compare favorably with those obtainable by other analytical techniques. Stability Constants of Eu(hedta), Eu(dtpa)2-, and Eu(do3a). The accuracy of the present method is verified by determining the thermodynamic stability constants of several ligands and comparing them with literature values. Edta is used as the reference ligand in each case. The results obtained from measurements on samples containing Eu3+/hedta/edta 5:5:5 (µM) are given in Table 2, along with literature values. The values of log K for Eu(hedta) determined by the time-resolved method at (35) r2 ) 1 - [∑ni)1(yi - Yi)]/[∑ni)1(yi - jy)], where Yi is the y value of the ith data point and yi is the y value of the curve fit at the ith data point. Precision ) n (yi - Yi)2/ν]1/2, where ν ) (number of data (SCF/Y h ) × 100. SCF ) [∑i)1 points) - (number of parameters).
+
+
Figure 6. Intensity of luminescence emission of Eu(dtpa)2- at λex ) 579.89 nm versus the initial concentration of edta in a system initially containing 2 µM Eu3+ and 2 µM dtpa. The solid curve represents the nonlinear regression fit of the data to eq 21, as described in the text. The fitting yields log K of Eu(dtpa)2- ) 22.40 ( 0.06.
two different pH values and by the non-time-resolved method are in good agreement with one another and with the literature values. The thermodynamic stability constant of Eu(dtpa)2- is about 5 log units higher than that of Eu(edta)-, and the conditional stability constant of Eu(dtpa)2- remains higher than that of Eu(edta)- at all pH values greater than 2 (Figure 5). In such cases, it is useful to increase the concentration of the more weakly binding ligand in order that it may compete effectively for the Eu3+ ion. Figure 6 shows a plot of the variation of the luminescence intensity of Eu(dtpa)2-, IEu(dtpa)2-, as a function of edta concentration in solutions initially 2 µM in both Eu3+ and dtpa. The solution was buffered at pH 5.18. The complexation was monitored by the time-resolved method with excitation at 579.89 nm. A regression analysis fit of eq 21 (derived from eq 16), where
IEu(dtpa)2- ) {B - (B2 - 4[Eu3+]i[dtpa]i(1 - Krel))1/2}k1/ (2 - 2Krel) (21)
B ) [Eu3+]i + [dtpa]i + Krel([edta]i - [Eu3+]i), gives the log K of 22.40 ( 0.06, in excellent agreement with the literature value of 22.39. Do3a (Chart 1) is a recently synthesized macrocyclic ligand which forms complexes with Ln3+ ions of high stability at a slow rate.26,36,37 The lifetime of the 5D0 state of Eu(do3a) (291 µs) is close to that of Eu(edta)- (315 µs), making the time-resolution method less appropriate for stability constant measurements. However, when excitation is accomplished at 579.74 nm, the peak maximum of the Eu(do3a) excitation spectrum, where the excitation intensity of Eu(edta)- is significantly different (Figure 1), It is readily resolved into its IEu(edta)- and IEu(do3a) components by the non-time-resolved method. Measurements made on two sets of samples with the concentration ratios Eu3+/do3a/edta 2:2:2 (µM) (36) Kumar, K.; Tweedle, M. F. Inorg. Chem. 1993, 32, 4193-4199. (37) Kumar, K.; Jin, T.; Wang, X.; Desreux, J. F.; Tweedle, M. F. Inorg. Chem. 1994, 33, 3823-3829.
and 2:2:4 (µM) at pH 7.10 yield a log KEu(do3a) value38 of 20.69 ( 0.01, in good agreement with the 21.0 value recently reported by Kumar et al.26 for Gd(do3a). Determination of Stability Constants for the Eu3+-dtpadien System. The present methods provide a means for determining values of the conditional stability constants for Eu3+ complex formation over a wide pH range if the selected reference ligand forms a single, stable, unprotonated, unhydrolyzed 1:1 complex with the Eu3+ ion in the same range. This will be particularly useful for studies of ligands which form Eu3+ complexes whose state of protonation or hydrolysis changes with pH. Dtpa-dien is a new dtpa-based macrocyclic ligand, containing a nitrogen heteroatom within the bis-amide linkage (Chart 1). The lanthanide complexes of dtpa-dien have been shown to be protonated at the central nitrogen atom of the linking moiety.39 We have studied the formation kinetics of Eu(Hdtpa-dien)+ and determined its stability constant in the low-pH region by a pHluminescence titration.40 The protonated complex is expected to deprotonate as the pH is raised. In previous work,40 the 7F0 f 5D excitation spectrum and the lifetime of 5D state of this 0 0 complex were found to remain constant over a wide pH range (pH 2.5-pH 8.2). These results suggest that the dissociation of the proton from the uncoordinated central aza moiety does not cause a detectable change in the coordination environment at the Eu3+ ion. However, for electrostatic reasons, the departure of one proton from Eu(Hdtpa-dien)+ is expected to bring about a significant change in the conditional stability constant. Competition experiments were carried out with this ligand using edta as reference ligand in the pH range 3.03-9.67. The ratio Eu3+/dtpa-dien/edta used in this experiment was 5:5:5 (µM). Luminescence decays for excitation at 579.86 nm were recorded by the time-resolved method and fit to eq 10 to get IEu(edta)- and IEu(dtpa-dien). The conditional stability constant at each pH value was calculated, and the results are plotted in Figure 7. The variation of the conditional stability constant of Eu(edta)- over the same pH range (dotted line) is shown for comparison (Figure 7). No single stoichoimetric composition for the Eu3+-dtpa-dien complex can account for these data over the entire pH range. At pH values less than 4, the complex exists primarily in its protonated form, Eu(Hdtpa-dien)+; in the pH 4-8 range, a mixture of Eu(Hdtpa-dien)+ and Eu(dpta-dien) exits; while above pH 8, hydrolysis to Eu(OH)(dtpa-dien)- occurs. The complex behavior of the plot of Kcond for Eu(dtpa-dien) vs pH, when compared with that for Eu(edta), is reflective of the fact that the former complex exists in several different forms over the pH range. Spectra recorded on 5:5:5 (µM) Eu3+/dtpa-dien/ edta solutions at pH 7.01 and 9.67 reveal how the competition shifts in favor of the dtpa-dien complex (λmax ) 579.92 nm) at the higher pH (Figure 8). There is also a slight shift in the position of the band maximum from 579.86 to 579.92 nm (Figure 9), and (38) Owing to weak complexation by the Na+ ions, ligand protonation constants measured in 0.1 M NaCl (KnH′) are observed to be systematically smaller than those measured in 0.1 M (Me4N)Cl (KnH), where the noncoordinating Me4N+ cation is present (Table 1). Using the present measurements of Kcond in 0.1 M KCl, one obtains log K′Eu(do3a) ) 19.38 ( 0.01, if the KnH′ set of protonation constants is used. It has been shown (S. L. Wu, unpublished calculations) that a stability constant corrected for competition by alkali metal ions in the ionic strength medium is given by KEu(do3a) ) K′Eu(do3a) (K1HK2HK3HK4H)/K1H′K2H′K3H′K4H′), which yields the value quoted in the text. (39) Franklin, S. J.; Raymond, K. N. Inorg. Chem. 1994, 33, 5794-5804. (40) Wu, S. L.; Franklin, S. J.; Raymond, K. N.; Horrocks, W. D., Jr. Inorg. Chem., in press.
+
+
Figure 7. Plot of the log of the conditional stability constant (log Kcond) of Eu3+-dtpa-dien versus pH. The data were fit to eq 25 in the text (r ) 0.984) (solid line). For comparison, the pH dependence of conditional stability constant of Eu(edta)- is also plotted (- -).
Figure 9. 7F0 f 5D0 excitation spectra of a solution intially containing 5 µM Eu3+ and 5 µM dtpa-dien at pH 7.01 (O) and 9.67 (4).
Kcond )
[EuL]t [Eu3+][L]t
(26)
sum of the concentrations of all forms of the complex including protonated and hydrolyzed species, and [L]t is the sum of all uncomplexed forms of the ligand including protonated and fully deprotonated forms. Fitting the Kcond values to eq 25 yields log KEuHL ) 14.2 ( 0.3, log KEuL ) 17.2 ( 0.1, and log KOH ) 5.7 ( 0.2 (pKa ) 8.3 ( 0.2). Among them, the stability constant of Eu(Hdtpa-dien)+, log KEuHL (14.2), is good agreement with our previous determination of this quantity (14.0) by a pH-luminescence titration.40
Figure 8. 7F0 f 5D0 excitation spectra of a solution intially containing 5 µM Eu3+, 5 µM edta, and 5 µM dtpa-dien at pH 7.01 (O) and 9.67 (4).
the lifetime increases from 591 (pH 7.01) to 621 µs (pH 9.67). Deprotonation of Eu(Hdtpa-dien)+ cannot account for the above observations, which, however, are consistent with the formation of a hydrolyzed species, Eu(OH)(dtpa-dien)-, at the highest pH values. The various equilibria established over the pH range studied are represented by eqs 22-24,
Eu3+ + Hdtpa-dien2- S Eu(Hdtpa-dien)+, KEuHL
(22)
Eu3+ + dtpa-dien3- S Eu(dtpa-dien), KEuL
(23)
Eu(dtpa-dien) + OH- S Eu(OH)(dtpa-dien)-, KOH
(24)
from which an expression for the overall conditional stability constant, Kcond, is derived:
Kcond ) KEuHLRL + {(KEuLRL(1 + KOH[OH-])}
(25)
where L ) dtpa-dien and Kcond is given by eq 26. [EuL]t is the
DISCUSSION The present methods offer several distinct advantages in the determination of extremely high (>1015 M-1) stability constants in systems involving multidentate ligands. First, the method is direct: the concentration of the Eu3+ complex is directly measured via 7F0 f 5D0 laser excitation spectroscopy. The technique is extremely sensitive, with measurements routinely carried out on small volumes (1 mL or less) of micromolar concentrations of Eu3+ and ligand. The excitation spectroscopic method is speciesspecific and able to detect and quantitate different Eu3+-containing species when more than one is present in solution. For instance, the present method requires that the reference complex exist as a single 1:1 species over the pH range studied. Monitoring its excitation spectrum and its excited state lifetime as a function of pH and the presence of excess ligand readily establishes whether this condition is fulfilled, as it is in the present study, which uses Eu(edta)- in this capacity. Different Eu3+ complexes are easily distinguished using excitation spectroscopy (Figure 1), and even if there were too great an overlap in the spectra (between the subject and reference complexes), any differences in excited state lifetime can be exploited to allow the stability constant determination to be carried out using the time-resolved method. In this regard, it is useful to have available a number of different reference ligands which differ in the magnitudes of their Eu3+ complex formation constants and in their lifetimes. Table 3 lists four such ligands, two with lifetimes near 600 µs and two with τ-values near 300 µs. Their log K values are in the 15-23 range. For the measurement of extremely high stability constants by potentiometric titrations, it has sometimes been necessary to
+
+
Table 3. Wavelength of Excitation Maxima, Excited State Lifetimes, and Formation Constants for Potential Reference Ligands reference ligand, L′
excitation maximum (nm)
lifetime of EuL′ (µs)
log K of EuL′
dtpa dtpa-oamc hedta edta
579.9 579.9 579.5 579.6, 580.1
627a 605c 265a 315a
22.40a 17.48c 15.45b 17.29b
a This work. b See footnotes to Table 2. c Reference 42; dtpa-oma, 1,4,7-tris(carboxymethyl)-9,10-dioxo-13,16-dioxa-1,4,7,10,19-pentaazacyclohemicosane.
resort to the use of a competing reference ligand.41 The requirement here is that there be an equitable distribution of the metal ion between the two ligands and that the ligands themselves have very different protonation constants. Furthermore, the competing ligands must be present in about equal concentrations. In the Eu3+ luminescence technique, there is no such limitation. For instance, using dtpa as a reference ligand (log K of Eu(dtpa)2- ) 22.40) and a solution of composition Eu3+/L/dtpa 1:1:10 000 (µM), it should be possible to measure stability constants as high as 1027 M-1. Having one ligand in large excess is not a problem, since the concentration of the Eu3+ complex is directly measured rather than the competition between the metal ion and protons, as in potentiometry. Another strategy which can be used with the present methods, which are carried out at a constant pH, is to adjust the value of this quantity such that the conditional stability constants of the reference and subject ligand complexes are more nearly equal. Since it has been established that a higher ligand basicity usually correlates with a larger formation constant for metal ion complexes, downward adjustment of the pH will generally cause the conditional stability constants to differ by less than the thermodynamic constants (Figure 5), permitting a reliable competition experiment at the lower pH. Potentiometric titrations by their nature involve changing the pH, and this strategy is not available using them. A further advantage of the present technique is that it is well adapted to batch methods, where a series of samples is allowed to equilibrate over a period of time before measurements are made. This is necessary in cases where the kinetics of formation is slow, as is often found for macrocyclic ligand systems. Batch methods are, of course, possible using potentiometry; however, problems with atmospheric carbon dioxide and instrumental stability are more critical in this case. The present method of determining stability constants, while applicable over a broad range of pH values, measures conditional (41) Harris, W. R.; Martell, A. E. Inorg. Chem. 1976, 15, 713-720. (42) Frey, S. T.; Chang, C. A.; Carvalho, J. F.; Varadarajan, A.; Schultze, L. M.; Pounds, K. L.; Horrocks, W. D., Jr. Inorg. Chem. 1994, 33, 2882-2889. (43) Cronce, D. T.; Horrocks, W. D., Jr. Biochemistry 1992, 31, 7963-7969. (44) Burroughs, S. E.; Eisenman, G.; Horrocks, W. D., Jr. Biophys. Chem. 1992, 42, 249-256.
stability constants at particular, known pH values. This is important if, as is the case in the Eu3+-dtpa-dien system, different species of complex (protonated, hydrolyzed, etc.) exist at different pH values. Measurement of formation constants by potentiometry necessarily involves pH as a variable, and the analysis of the results requires the assumption that the composition of the metal complex is independent of pH. Use of the herein-described spectroscopic methods to probe the composition of the system at different pH values and to measure the equilibrium concentrations of the species present under particular conditions thus offers a significant advance in our ability to understand complicated systems. A practical drawback of the present method is that it requires the use of a complex and expensive laser apparatus. While the present methods are unique to Eu3+, it should be pointed out that stability constants for other metal ions may be readily determined by metal ion competition experiments, with a Eu3+ complex acting as a reference and Eu3+ spectroscopy providing the means of monitoring the solution composition. This technique is described elsewhere, with applications to simple chelating agents,32 macrocyclic ligands,42 and calcium-binding proteins.43,44 It provides a means of determining the formation constant for any metal ion once that of Eu3+ has been established by the present method or by the pH-luminescence titration method.33 It should be noted that the determination of the thermodynamic stability constants of protonic ligands necessarily requires knowledge of the appropriate protonation constants, which can be gotten only by potentiometry. In the present method, such potentiometry need only be done on the ligands in the absence of the metal ion. For many practical applications, on the other hand, it is generally necessary only to evaluate conditional stability constants. How much dissociation can be expected for a particular complex under physiological conditions of pH and Ca2+ and Mg2+ ion concentration? This type of question can be answered using the present methods without any knowledge of protonation constants. Thus, the present methods possess several advantages in sensitivity, versatility, and selectivity over other available techniques. While Eu3+ excitation spectroscopy provides an ideal means of monitoring complex formation, the proposed methods may be adaptable to other spectroscopies, such as metal- or ligandbased absorption or fluorescence. Only the latter, of course, has the potential for time resolution. ACKNOWLEDGMENT We gratefully acknowledge the financial support provided by the National Science Foundation (Grant CHE-9123801). We thank Ms. S. J. Franklin and Professor K. N. Raymond for the gift of dtpa-dien. Received for review May 23, 1995. Accepted October 24, 1995.X AC9504981 X
Abstract published in Advance ACS Abstracts, December 1, 1995.
