On-line Supplementary Material for Journal of Solution Chemistry
Studies of Size-Based Selectivity in Aqueous Ternary Complexes of
Americium(III) or Lanthanide(III) Cations
Christina J. Leggett · Mark P. Jensen
C.J. Leggett · M.P. Jensen ()
Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL, USA
e-mail: mjensen@anl.gov
C.J. Leggett
Department of Nuclear Engineering, University of California, Berkeley, CA, USA
S1 Analysis of Tb Spectrofluorimetric Data
Two approaches were used to analyze the spectrofluorimetric titrations of Tb(CDTA)– with Ox2–.
In the first method, the change in the luminescence lifetime of the Tb species in solution was
used. The average number of inner sphere water molecules of a Eu3+ or Tb3+ complex, 𝑁Hobs
, is
2O
related to the luminescence decay constants by
Nobs
H2 O = (kH2 O –
kD2 O )ALn
(S1)
where 𝑘H2 O and 𝑘D2 O are the luminescence decay constants of the complexes in H2O and D2O,
respectively, in ms–1 and ALn is an empirically determined constant. The values of 𝑘D2O (0.30)
and ATb (4.2) have been previously reported by Horrocks and Sudnick, who also report the
absolute uncertainty in 𝑁Hobs
determined by this method to be 0.5 water molecules [1].
2O
Consequently, we used the number of inner sphere water molecules bound to Tb(CDTA)– and
Tb(CDTA)(Ox)3– as a function of added oxalate concentration to calculate the equilibrium
constant.
When Tb(CDTA)– and Tb(CDTA)(Ox)3– are the only significant Tb(III) containing
species in solution, the average number of water molecules can be calculated using the equation
Nobs
H2 O = NTb(CDTA)
NTb(CDTA)(Ox)
[Tb(CDTA)– ]
[Tb(CDTA)(Ox)3- ]
CTb
tot
CTb
tot
+
(S2)
where NTb(CDTA) and NTb(CDTA)(Ox) are the numbers of waters coordinated to Tb(CDTA)– and
Tb
Tb(CDTA)(Ox)3–, respectively, and Ctot
is the total concentration of terbium in a given solution.
Using equation S1 and the measured 𝑘H2 O , 0.79 ms–1, the number of residual water molecules
bound to the binary Tb(CDTA)– complex, NTb(CDTA), was readily determined to be 2.07, as
expected for octacoordinate terbium complexed by hexadentate CDTA. Introducing the
equilibrium constant expression for K111 (Eq. 1) and realizing that [Tb(CDTA)–] +
Tb
[Tb(CDTA)(Ox)3–] = CTot
, NTbCDTAOx and K111 can be obtained from Eq. S2. The solver function
in Excel was used to minimize the sum of the squared residuals between the observed and
calculated number of water molecules by varying NTbCDTAOx and K111. For each titration, eighteen
data points corresponding to successive additions of 0.075 mol·L–1 oxalate were collected and
used for fitting, giving NTbCDTAOx = 0.51  0.01 and log10 K111 = 2.78  0.02.
In the second method, the intensity of emitted fluorescence at 544 nm was used to
calculate the equilibrium constant according to the equation
–
Icalc
n = ε1 [Tb(CDTA) ] +
ε2 [Tb(CDTA)(Ox)3– ]
(S3)
where Incalc is the measured fluorescence intensity and the constants 1 and 2 are the operational
molar fluorescence intensities of Tb(CDTA)– and Tb(CDTA)(Ox)3–, which are valid for a
particular instrumental configuration. The value of 1, (2.48  0.03) × 103 L·mol–1·cm–1, was
determined from intensity measurements of known concentrations of Tb(CDTA)–. The terms 2
and K111 were then obtained by fitting to the experimental titration data in a manner similar to the
luminescence lifetime measurements described above, giving values of 2 = (4.24  0.08) × 103
L·mol–1·cm–1 and log10 K111 = 2.75  0.02.
The uncertainties in the fitted parameters for both methods were estimated using the
jackknife error method. [2]
S2 Determination of the Enthalpies of Protonation of CDTA
The enthalpies corresponding to the first three protonations of the CDTA4– ligand were measured
at 1 mol·L–1 ionic strength using isothermal titration calorimetry. In a typical experiment, 0.9
mL of 0.001 mol·L–1 CDTA/1 mol·L–1 NaNO3 at pcH = 9.9 was titrated with 0.1 mL of 0.031
mol·L–1 HNO3/1 mol·L–1 NaNO3 in 2 μL increments. Using the known pKa values [3], the pcH
and changes in the amounts of H(CDTA)3–, H2(CDTA)2–, and H3(CDTA)– were readily
calculated for each addition of acid. The total heat evolved from the beginning of the titration
was calculated using the equation
∑(∆Hi ∆ni ) = –Qcalc
(S4)
i
where ΔHi is the enthalpy of protonation for HiCDTA(i–4) in kJ·mol–1, Δni is the change in the
number of moles of HiCDTA(i–4) from the beginning of the titration, and Qcalc is the cumulative
heat after each addition, after correction for the heat of dilution and the heat of water formation
by the reaction H+ + OH–
®
¬
H2O. The Solver application in the program Excel was used to
minimize the sum of the squared residuals between the calculated and measured cumulative
heats by varying ΔHi. Four replicate titrations were used to determine the enthalpies. Figure S1
compares the calculated and measured heats from a representative titration.
Table S1 Thermodynamic data for protonation reactions of ligands used in this work
Ligand
Protonation reaction(s)
log10 K a
H(prot), kJ·mol–1 b
®
¬
9.98  0.08
–33  0.4 c
8.29  0.04
–18  0.4 c
H+ + DTPA5–
®
¬
H+ + HDTPA4–
H5DTPA
HDTPA4–
H+ + H2DTPA3–
®
¬
H3DTPA2–
4.15  0.03
–6.3  0.4 c
H+ + H3DTPA2–
®
¬
H4DTPA–
2.6  0.1
–1.3  0.8 c
2.1  0.2
+2.1  0.8 c
HOx–
3.57  0.04
+3.2  0.3
H2Ox
1.07  0.07
+1.3
HMal–
5.08  0.06
+2.0  0.04
H2Mal
2.58  0.02
–1.5  0.04
HIDA–
9.26  0.06
–35.6  0.0
H2IDA
2.60  0.03
–4.2  0.8
H3IDA+
1.85  0.06
–4.2  0.0
9.22
–25.6  0.3 d
H2CDTA2–
5.84
–12.4  0.4 d
H3CDTA–
3.21  0.04
–8.6  2.4 d
2.42  0.01
n/a
1.6  0.1
n/a
6.194  0.008 e
–4.35  0.07 e
®
¬
H+ + H4DTPA–
H2Mal
H+ + CDTA4–
®
¬
®
¬
®
¬
®
¬
HCDTA3–
®
¬
H+ + HCDTA3–
®
¬
H+ + H2CDTA2–
H+ + H3CDTA–
H+ + H4CDTA
HMES
¬
®
H+ + HIDA–
H+ + H2IDA
H4CDTA
®
¬
H+ + HMal–
H+ + IDA2–
H2IDA
®
¬
H+ + HOx–
H+ + Mal2–
H+ + MES
H5DTPA
®
¬
H+ + Ox2–
H2Ox
H2DTPA3–
®
¬
®
¬
®
¬
H4CDTA
H5CDTA+
HMES
OH–
H+ + OH–
®
¬
H2O
13.78
–56.94
All stability constants are valid for 1 mol·L–1 ionic strength at 25 °C. Unless otherwise noted, data are taken from
[3]
b
Unless otherwise noted, all enthalpy values are valid for 1 mol·L–1 ionic strength at 25 °C and were obtained from
[3]
c
Enthalpy values valid for ionic strength = 0.1 mol·L–1 at 25 °C
d
Enthalpy values measured in present work.
e
Values taken from [4]
a
Table S2 Tabulation of calorimetric titration data for titration of Ln(CDTA)– with Ox2–
–
Ln(CDTA)
[Ln(CDTA)–] /
Runs
[Ox] /
a
–1 b
mol·L
–1 b
pcHfinal
Qmeas / cal
Qdil / cal
Qprot / cal
Qcorr / cal
mol·L
Nd(CDTA)–
4
0.0100
0.0733
6.003
0.188 ± 0.004
–0.017 ± 0.018
0.003 ± 0.001
0.202 ± 0.018
Sm(CDTA)–
3
0.0100
0.0733
6.034
0.178 ± 0.001
–0.017 ± 0.018
0.001 ± 0.001
0.194 ± 0.018
Tb(CDTA)–
4
0.0100
0.0753
6.003
0.294 ± 0.008
–0.017 ± 0.018
0.002 ± 0.002
0.312 ± 0.020
Ho(CDTA)–
4
0.0101
0.0733
5.991
0.262 ± 0.008
–0.017 ± 0.018
0.001 ± 0.001
0.278 ± 0.020
Er(CDTA)–
4
0.0100
0.0733
5.991
0.312 ± 0.008
–0.017 ± 0.018
0.001 ± 0.001
0.328 ± 0.020
a
b
Number of replicate titrations
Initial analytical concentrations of titrant and titrand solutions used in titrations
Table S3 Tabulation of calorimetric titration data for titration of Ln(CDTA)– with Mal2–
–
Ln(CDTA)
[Ln(CDTA)–] /
Runs
[Mal] /
a
–1 b
mol·L
–1 b
pcHfinal
Qmeas / cal
Qdil / cal
Qprot / cal
Qcorr / cal
mol·L
Nd(CDTA)–
5
0.0402
0.502
5.965
0.035 ± 0.004
–0.107 ± 0.008
0.062 ± 0.001
0.080 ± 0.009
Sm(CDTA)–
3
0.0401
0.502
5.958
–0.125 ± 0.016 –0.107 ± 0.008
0.062 ± 0.001
–0.080 ± 0.018
Ho(CDTA)–
3
0.00395
1.022
5.995
–0.569 ± 0.006 –0.472 ± 0.018
0.029 ± 0.001
–0.126 ± 0.019
Er(CDTA)–
4
0.0394
1.022
5.990
–0.475 ± 0.009 –0.472 ± 0.018
0.029 ± 0.001
–0.032 ± 0.020
a
b
Number of replicate titrations
Initial analytical concentrations of titrant and titrand solutions used in titrations
Table S4 Tabulation of calorimetric titration data for titration of Ln(CDTA)– with IDA2–
–
Ln(CDTA)
[Ln(CDTA)–] /
Runs
[IDA] /
a
–1 b
mol·L
–1 b
pcHfinal
Qmeas / cal
Qdil / cal
Qprot / cal
Qcorr / cal
mol·L
Nd(CDTA)–
3
0.0103
1.499
6.716
–1.137 ± 0.020 –0.949 ± 0.010 –0.464 ± 0.002
0.276 ± 0.022
Sm(CDTA)–
4
0.0216
1.499
6.392
–0.886 ± 0.012 –0.949 ± 0.010 –1.010 ± 0.010
1.073 ± 0.016
Ho(CDTA)–
3
0.0101
1.499
6.742
–0.794 ± 0.003 –0.949 ± 0.010 –0.391 ± 0.002
0.546 ± 0.011
Er(CDTA)–
3
0.00999
1.499
6.802
–0.756 ± 0.003 –0.949 ± 0.010 –0.300 ± 0.002
0.493 ± 0.011
a
b
Number of replicate titrations
Initial analytical concentrations of titrant and titrand solutions used in titrations
Figure S1 Representative titration of 0.9 mL of 0.001 mol·L–1 CDTA/1 mol·L–1 NaNO3 (initial
pcH = 9.9) with 0.1 mL of 0.031 mol·L–1 HNO3/1 mol·L–1 NaNO3. The blue diamonds represent
the cumulative heat after each 0.002 mL addition of titrant. The solid line shows the fit of the
calculated heats obtained by varying ΔHi to minimize the sum of the squared residuals
Figure S2 Normalized Sm(CDTA)– + Ox2– spectra. Left plot, titration of 10 mL of 0.01 mol·L–1 Sm(CDTA)– with 0.075 mol·L–1
oxalate; right plot, molar absorptivities at selected wavelengths as a function of the total oxalate concentration. Wavelengths shown
are indicated as follows: , 403.75 nm; , 404.1 nm; , 404.45 nm
Figure S3 Normalized Sm(CDTA)– + Mal2– spectra. Left plot, titration of 10 mL of 0.01 mol·L–1 Sm(CDTA)– with 0.50 mol·L–1
malonate; right plot, molar absorptivities at selected wavelengths as a function of the total malonate concentration. Spectra are not
corrected for absorption of the free Mal2– ligand. Wavelengths shown are indicated as follows: , 403.75 nm; , 404.25 nm; , 405
nm
Figure S4 Normalized Sm(CDTA)– + IDA2– spectra. Left plot, titration of 10 mL of 0.022 mol·L–1 Sm(CDTA)– with 1.50 mol·L–1
IDA; right plot, molar absorptivities at selected wavelengths as a function of the total IDA concentration. Wavelengths shown are
indicated as follows: , 404.9 nm; , 405.2 nm; , 405.5 nm
Figure S5 Normalized Ho(CDTA)– + Ox2– spectra. Left plot, titration of 10 mL of 0.01 mol·L–1 Ho(CDTA)– with 0.073 mol·L–1
oxalate; right plot, molar absorptivities at selected wavelengths as a function of the total oxalate concentration. Wavelengths shown
are indicated as follows: , 451.5 nm; , 453.5 nm; , 454.5 nm; *, 538 nm
Figure S6 Normalized Ho(CDTA)– + Mal2– spectra. Left plot, titration of 10 mL of 0.01 mol·L–1 Ho(CDTA)– with 1.02 mol·L–1
malonate; right plot, molar absorptivities at selected wavelengths as a function of the total malonate concentration. Wavelengths
shown are indicated as follows:
, 451.5 nm;
, 453.5 nm;
, 454.5 nm
Figure S7 Normalized Ho(CDTA)– + IDA2– spectra. Left plot, titration of 25 mL of 0.01 mol·L–1 Ho(CDTA)– with 1.50 mol·L–1
IDA; right plot, molar absorptivities at selected wavelengths as a function of the total IDA concentration. Wavelengths shown are
indicated as follows: , 453.5 nm; , 454.5 nm; *, 539.75 nm
Figure S8 Normalized Er(CDTA)– + Ox2– spectra. Left plot, titration of 10 mL of 0.01 mol·L–1 Er(CDTA)– with 0.073 mol·L–1
oxalate; right plot, molar absorptivities at selected wavelengths as a function of the total oxalate concentration. Wavelengths shown
are indicated as follows:
, 379.25 nm;
, 518.75 nm;
, 521 nm;
, 525.25 nm
Figure S9 Normalized Er(CDTA)– + Mal2– spectra. Left plot, titration of 10 mL of 0.01 mol·L–1 Er(CDTA)– with 0.50 mol·L–1
malonate; right plot, molar absorptivities at selected wavelengths as a function of the total malonate concentration. Wavelengths
shown are indicated as follows: *, 487 nm;
, 518 nm;
, 520.75 nm;
, 525 nm
Figure S10 Normalized Er(CDTA)– + IDA2– spectra. Left plot, Titration of 10 mL of 0.01 mol·L–1 Er(CDTA)– with 1.50 mol·L–1
IDA; right plot, molar absorptivities at selected wavelengths as a function of the total IDA concentration. Wavelengths shown are
indicated as follows:
, 379.2 nm;
, 520 nm;
, 522.4 nm;
, 525.6 nm
Figure S11 Spectra of M(DTPA) and M(DTPA) + L2 solutions. Top plot, Nd(III) complexes;
bottom plot, Er(III) complexes
References
1. Horrocks Jr., W.D., Sudnick, D.R.: Lanthanide ion luminescence probes of the structure of
biological macromolecules. Acc. Chem. Res. 14, 384–392 (1981)
2. Caceci, M. S.: Estimating error limits in parametric curve fitting. Anal. Chem. 61, 2324–2327
(1989)
3. Smith, R., Martell, A., Motekaitis, R.: NIST Critically Selected Stability Constants of Metal
Complexes Database Vol. 8. NIST, Gaithersburg, MD (2004)
4. Leggett, C. J., Liu, G., Jensen, M. P.: Do aqueous ternary complexes influence the
TALSPEAK Process? Solvent Extr. Ion Exch. 28, 313–334 (2010)