Formation and dissociation kinetics of Eu(III) complexes with H5do3ap and similar dota-like ligands

Article abstract of DOI:10.1016/j.poly.2007.05.014

Complexation kinetics of the europium(III)-H₅do3ap complex (1,4,7,10-tetraazacyclododecane-1,4,7-triacetic-10-(methylphosphonic acid)) was studied at 25 °C and I = 0.1 M KCl and compared with the analogous H₄dota-like ligands. The mechanism of the formation reactions between the europium(III) ion and H₃do3a, H₄dota and H₄dota analogs having one methylphosphonic (H₅do3ap) or phosphinic acid pendant arms with a propionate side chain (H₅do3ap^PrA) was proposed on the basis of TRLIFS measurements. The experimental data of the dissociation kinetics of the europium(III) complexes with H₅do3ap and H₅do3ap^PrA ligands show that there is no change in reactivity of the complexes due to the side chain of the phosphinic acid bifunctional chelate. The TRLIFS study of the proton-assisted decomplexation reaction of the europium(III) complexes with H₃do3a, H₄dota, H₅do3ap and H₅do3ap^PrA demonstrates different behaviour influenced by a change in the number of water molecules during the reaction. The advantages and disadvantages of the TRLIFS methodology as a new experimental technique for simultaneous evaluation of kinetics and reaction mechanisms are discussed.

Full text of DOI:10.1016/j.poly.2007.05.014

Polyhedron 26 (2007) 4119–4130
www.elsevier.com/locate/poly
Formation and dissociation kinetics of Eu(III) complexes
with H5do3ap and similar dota-like ligands
a
a,b
a,
c
Petr Taborsky , Ivona Svobodova , Premysl Lubal *, Zbigniew Hnatejko ,
´
´
´
ˇ
c
d
Stefan Lis , Petr Hermann
a
c
Department of Analytical Chemistry, Faculty of Science, Masaryk University, Kotla´rˇska´ 2, 61137 Brno, Czech Republic
b
Institute of Analytical Chemistry, Academy of Sciences of the Czech Republic, Veverˇı´ 97, 61142 Brno, Czech Republic
Department of Rare Earths, Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60780 Poznan, Poland
Department of Inorganic Chemistry, Faculty of Science, Charles University, Hlavova 2030, 12840 Prague, Czech Republic
d
Received 15 January 2007; accepted 4 May 2007
Available online 24 May 2007
Abstract
Complexation kinetics of the europium(III)-H5do3ap complex (1,4,7,10-tetraazacyclododecane-1,4,7-triacetic-10-(methylphosphonic
acid)) was studied at 25 ꢀC and I = 0.1 M KCl and compared with the analogous H4dota-like ligands. The mechanism of the formation
reactions between the europium(III) ion and H3do3a, H4dota and H4dota analogs having one methylphosphonic (H5do3ap) or phosphi-
nic acid pendant arms with a propionate side chain (H5do3apPrA) was proposed on the basis of TRLIFS measurements. The experimen-
tal data of the dissociation kinetics of the europium(III) complexes with H5do3ap and H5do3apPrA ligands show that there is no change
in reactivity of the complexes due to the side chain of the phosphinic acid bifunctional chelate. The TRLIFS study of the proton-assisted
decomplexation reaction of the europium(III) complexes with H3do3a, H4dota, H5do3ap and H5do3apPrA demonstrates different behav-
iour influenced by a change in the number of water molecules during the reaction. The advantages and disadvantages of the TRLIFS
methodology as a new experimental technique for simultaneous evaluation of kinetics and reaction mechanisms are discussed.
ꢁ 2007 Elsevier Ltd. All rights reserved.
Keywords: Macrocyclic ligands; Cyclen derivatives; Phosphinate and phosphonate complexes; Europium(III) complexes; Thermodynamics and kinetics;
Molecular spectroscopy; Time-resolved laser-induced fluorescence spectroscopy (TRLIFS); Luminescence probes
1. Introduction
ism (e.g. monoclonal antibodies, small peptides, hormones,
sugars, etc.), and thus they may serve as luminescent labels
for immunoassays (Eu3+, Tb3+) [3–8]. Macrocyclic ligands
binding metal radioisotopes (90Y, 153Sm, 166Ho, 177Lu) are
utilized as carriers in nuclear medicine [9]. They are used as
the so-called bifunctional chelates (BFC) enabling conjuga-
tion with the biomolecules. The ligands employed as BFCs
are mostly based on acyclic H5dtpa or macrocyclic H4dota.
They should sequester lanthanide(III) ions with a high
thermodynamic stability, and the complexes formed should
exhibit a high kinetic inertness under physiological condi-
tions [1,9]. Especially, in case of luminescent probes, the
number of water molecules directly coordinated to the cen-
tral ion should be as low as possible due to the quenching
effect of proximal O–H oscillators [4–8,10]. These properties
Lanthanide(III) complexes of H4dota and its derivatives
are used for diagnostic and medical purposes, e.g. the
majority of contrast agents in magnetic resonance imaging
(MRI) are based on gadolinium(III) complexes of such
ligands [1,2]. Complexes of some lanthanide(III) ions (e.g.
Eu3+/Tb3+ emitting in the VIS and Yb3+/Nd3+ emitting
in the NIR regions, respectively) are employed as lumines-
cent probes [3–8]. They can be attached to a bioactive
molecule responsible for a desired distribution in an organ-
*
Corresponding author. Tel.: +420 549 49 5637; fax: +420 541 211 214/
549 492 494.
E-mail address: lubal@chemi.muni.cz (P. Lubal).
0277-5387/$ - see front matter ꢁ 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.poly.2007.05.014

4120
P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
are strongly influenced by the type of derivatization of the
ligand skeleton, as has been demonstrated on the H4dota
derivatives with phosphorus acid pendant arms [11]. These
macrocyclic ligands have some similarities to the acetic par-
ent compound due to the acid character of the groups, but
the other properties (bulkiness, basicity, hydrogen bond
formation ability) are different [11]. Generally, they form
more stable complexes with lanthanide(III) ions than do
the respective macrocyclic dota-like ligands [11,12].
The experimental methodology for the kinetic study of
the europium(III) complexation and decomplexation was
the same as for other lanthanide(III) complexes with
H5do3ap, and details are given elsewhere [12].
All spectrophotometric kinetic measurements were car-
ried out on a diode array spectrophotometer HP-8453 A
(Hewlett–Packard, USA) at the temperature of
25.0 0.1 ꢀC. The formation kinetics of the [Eu(H2O)
(do3ap)]2ꢀ complex was followed under pseudo-first order
The thermodynamic and kinetic properties of euro-
pium(III) complexes with macrocyclic ligands (see Scheme
1) were studied for H2do2a [13], H3do3a [14], H4dota [15–
19], H5do3ap [12] and H8dotp [20,21] with the application
of various experimental techniques; mostly pH glass-elec-
trode potentiometry [13,15,18–20], molecular absorption
spectroscopy in the UV/VIS region [14–21] and lumines-
cence spectroscopy [14,16,17,21]. Also, the thermodynamic
and kinetic studies of other lanthanides (mostly gadoli-
nium(III)) complexes were performed, e.g. Gd(III)-
H3do3a [22,23], Gd(III)-H4dota [24] and Gd(III)-H8dotp
[25]. In addition, the analogous system Y(III)-H4dota was
studied from theoretical [26,27] and experimental [28]
points of view. In this contribution, the kinetic properties
of europium(III) complexes of cyclen derivatives contain-
ing acetic and phosphonic/phosphinic acid pendant groups
were investigated (Scheme 1) by means of UV/VIS molec-
ular absorption spectroscopy. Time-resolved laser-induced
fluorescence spectroscopy (TRLIFS) was applied for deter-
mination of the hydration numbers of the europium(III)
ion during the course of complex formation and dissocia-
tion in order to elucidate the intimate reaction mechanism.
conditions (cEu = (0.8–4.0) · 10ꢀ3 mol lꢀ1
,
cdo3ap = 8 ·
10ꢀ5 mol lꢀ1, I = 0.1 mol lꢀ1 KCl) in the pH range 4.0–
5.5 and in the wavelength region 290–340 nm. Dissociation
kinetics of the europium(III) complexes were measured in
the proton concentration range 0.10–3.00 mol lꢀ1 and ionic
strength I = 3.00 mol lꢀ1 (Na,H)ClO4 (cEuL ꢁ 5 · 10ꢀ3
mol lꢀ1). The decomplexation of the europium(III) com-
plexes was followed by a decrease of its CT band [15,21].
Data from kinetic experiments were processed by non-lin-
ear regression using EXCEL, HP and/or PROK-II [31] software,
giving identical results. The measured values of absor-
bances were corrected for background analytical signals.
The luminescence lifetime measurements at room tem-
perature were carried out using a detection system consist-
ing of
a nitrogen laser and a tunable dye laser
(kexc = 394 nm), as described earlier [32,33]. The kinetics
of the formation reaction of the europium(III) complexes
were studied in 1-cm sample cells where the ligand excess
over europium(III) was ensured: cEu = 0.005 mol lꢀ1
,
cL = 0.01 mol lꢀ1, cMES = 0.3 mol lꢀ1 (pH 5.6). The forma-
tion kinetics experiments were initiated by the addition of
the Eu(III) stock solution to the cell containing the ligand
and a buffer. After mixing of all the reagents, the first decay
curve was usually measured between the 10th and the 15th
second (reaction dead time). The experiments were stopped
when the luminescence decay became constant. The kinet-
ics of the dissociation reaction of the europium(III) com-
plexes (cEuL ꢁ 0.01 mol lꢀ1) was followed in acidic media
(perchloric, hydrochloric acids) with acid concentrations
between 0.3 and 3.0 mol lꢀ1. The reaction was initiated
by the addition of the complex solution to the cell contain-
ing an acid. The first measurement was usually done
between the 30th and the 60th second after the reaction
was started (reaction dead time). Experiments were
stopped when the measured lifetime of the luminescent
decay was equal to the lifetime of the ‘‘free’’ Eu(III)
hydrated ion (ꢁ110 ls). All lifetime experiments were
repeated at least three times in order to get average values,
and they were corrected for the dead time in the kinetic
treatment. The experimental luminescence decay data were
fitted by one-term, two-term or three-term exponential
equations as follows:
2. Experimental
A stock solution of europium(III) perchlorate/chloride
(0.05 mol lꢀ1) was obtained by dissolving Eu2O3 (spectro-
scopically pure, prepared at the Department of Rare
Earths, Faculty of Chemistry, Adam Mickiewicz Univer-
´
sity, Poznan or from Alfa, Darmstadt, Germany) in a per-
chloric/hydrochloric acid solution (Analar grade, Fluka).
The H3do3a Æ H2SO4 was a kind gift of Bracco SpA (Italy).
The other ligands were prepared according to previously
described procedures: H4dota [29], H5do3ap [30] and
H5do3apPrA [28]. Stock solutions of the ligands were pre-
pared by dissolving a weighed amount in bidistilled water.
All other chemicals of the highest available purity were
used as received.
R1
R2
H
Ligand
R2
R1
R1
CO2H
H3do3a
H4dota
H5do3ap
N
N
N
N
t
1
t
2
t
s
3
Itot ¼ I1 ꢂ eꢀ þ I2 ꢂ eꢀ þ ðI3 ꢂ eꢀ
Þ
ð1Þ
s
s
CO2H CH2CO2H
CO2H CH2PO3H2
CO2H CH2P(O)(OH)(CH2)2CO2H H5do3apPrA
where Itot is measured intensity of fluorescence as a func-
tion of time (ls), In are the fluorescence intensities and sn
are the lifetimes of the luminescence decay of the individual
species. Monoexponential decay was observed only for the
R1
PO3H2 CH2PO3H2
H8dotp
Scheme 1.

P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
4121
formation (H3do3a, H5do3ap, H5do3apPrA) and dissocia-
tion kinetic studies (H3do3a) whilst a two-exponential de-
cay was found for the study of the dissociation of the
europium(III) complexes of the H4dota, H5do3ap and
H5do3apPrA. In agreement with the literature [19], tri-expo-
nential decay was observed for the formation of the euro-
pium(III) complex with H4dota. The luminescence decay
measurements were used for the estimation of the number
of water molecules as discussed earlier [10,33–35]. In this
work, the hydration numbers, q, of the complexes were
determined by means of the equation below [33,36]
torted capped square antiprismatic arrangement [42] which
is crystallographically isostructural with sodium salts of the
[Y(H2O)(dota)]ꢀ and [Gd(H2O)(dota)]ꢀ complexes [43].
The water molecule in the first coordination sphere of the
complex is also present in solution [33].
The presence of the phosphonic acid pendant arm in
H5do3ap leads to an increase in the stability of the
[Eu(H2O)(do3ap)]2ꢀ complex in comparison to those of
the europium(III) complexes of H3do3a and H4dota (Table
1) [12]. Attachment of other functional groups to the phos-
phorus atom, as in the bifunctional chelator (BFC)
H5do3apPrA, caused a slight decrease in the stability of its
europium(III) complex compared with that of H4dota
[28]. Since the europium(III) complexes of H5do3ap and
H5do3apPrA bind one water molecule in the first coordina-
tion sphere [33] all pendant arms have to be coordinated to
europium(III) ions, similarly to other lanthanide(III) com-
plexes of H5do3ap [30], its monoethyl ester [44] and its
aminobenzylphosphinic acid analogs [45] in solution.
qB ¼ 1:05 ꢂ sꢀ1 ꢀ 0:7
ð2Þ
which is a simplified modification of Horrock’s equation
[33,35,37,38], demonstrated in our previous work. Results
based on both equations are in a good agreement [33].
The calculated parameters for the luminescent decay as
functions of time were used for the calculation of rate
constants.
3. Results and discussion
3.2. Formation kinetics
3.1. Thermodynamic stability of europium(III) complexes of
the macrocyclic ligands
The formation of the europium(III) complex with
H5do3ap was studied by molecular absorption spectros-
copy and a monotonic increase of absorbance in the 270–
300 nm region was observed. The same phenomena was
described for the europium(III)-H4dota system [15].
Pseudo-first order reaction conditions were employed
(10–50 molar excess of europium(III) ion over ligand),
and the resulting data follow a rate law for complex forma-
tion given by Eq. (3) (the charges of the complexes are
omitted for the sake of clarity).
The europium(III) ion forms stable complexes [11–20] of
EuL stochiometry with the H4dota-like ligands (see Table
1). The solid-state structure of the sodium salt of the
[Eu(H2O)(dota)]ꢀ complex was determined by X-ray crys-
tallography [42]. The eight coordination sites of the euro-
pium(III) ion are occupied by four nitrogens atoms of the
cyclen ring and four oxygen donor atoms from each of
the four carboxylate arms of the ligand. The coordination
sphere is completed by a water molecule, leading to a dis-
d½EuLꢃ
Eu
¼
k
ꢂ ½Lꢃ
ð3Þ
f;obs
tot
dt
The model frequently used to describe the complexation
reaction assumes fast formation of a reaction intermediate
Table 1
Eu
characterized by the conditional stability constant K**
The summary of dissociation constants of the macrocyclic ligands and
their stability constants with the europium(III) ion (T = 298.2 K,
I = 0.1 mol lꢀ1
(Eq. (4))
)
½EuðHnLÞꢃ
Ligand
H3do3a H4dota H5do3apg H5do3apPrAh H8dotpi
EuKꢄnꢄ
¼
ð4Þ
½Eu3þꢃ ꢂ ½Lꢃtot
pK1
pK2
pK3
pK4
pK5
pK6
pK7
12.46a
11.9b
9.72b
4.60b
4.13b
2.36b
13.83
10.35
6.54
4.34
3.09
1.63
1.07
27.8
12.32
9.20
4.91
4.19
2.93
1.8
14.65
12.40
9.28
8.09
6.12
5.22
9.49a
4.26a
3.51a
1.97a
This reaction step is followed by a slow rate-determining
step, leading to the final product which is defined by rate
constant Eukf.
3þ
Eukf ꢂ EuKꢄnꢄ ꢂ ½Eu
ꢃ
Eu
tot
k
¼
ð5Þ
f;obs
3þ
logb(EuL) 20.7c
23.4d
26.2e
26.5f
25.3
29.5
1 þ EuKꢄnꢄ ꢂ ½Eu
ꢃ
tot
As a consequence of this fact, the conditional pseudo-
first order rate constant
(analytical) concentration of europium(III) (Eq. (5)). The
pseudo-first order rate constant
c(H5do3ap)) was observed to be practically independent
on total europium(III) concentration in the pH regions
4.0–5.5. The same effect was observed for the cerium(III)-
H5do3ap system (metal ion or ligand excess with respect
to the other reactant [12]). This means that the formation
Eu
a
k
f,obs
is dependent on the total
Ref. [39] TMACl.
Ref. [40] TMANO3/Cl.
Ref. [14] KCl.
Ref. [17] KCl.
Ref. [13] NaCl.
b
Eu
c
d
e
f
k
(for c(Eu3+) P 10
f,obs
Ref. [19] TMACl.
Ref. [12] TMACl.
Ref. [28] TMACl.
Ref. [41] TMACl.
g
h
i

4122
P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
Eu
of
(
the
reaction
intermediate
is
quantitative
Eukf.
The rate constant
k
= (2.7 0.2) · 106 Mꢀ1 sꢀ1 is
OH
EuK** · [Eu3+
]
tot ꢅ 1 in the denominator of Eq. (5)), and
given by the slope of the linear dependence, and
k0 = (0.9 0.5) · 10ꢀ3 sꢀ1 is its intercept (Fig. 1). The
water-assisted (proton-transfer) pathway characterized
by k0 was neglected in the description of the formation
reaction of europium(III) ion with some macrocyclic
ligands (Table 2). Both hydroxide- and solvent-assisted
Eu
the relationship can be simplified as
k
ꢆ
f,obs
Eu
The measured conditional equilibrium constant K** is
dependent on the pH of the solution [13,15], while other
protonated species of ligand are presented in solution
(Eq. (6), Kp,n are stepwise ligand protonation constants),
½EuðH3LÞꢃ
EuKꢄ3
EuKꢄ3ꢄ
¼
¼
ð6Þ
2
½Eu3þꢃ ꢂ ½H3Lꢃ ꢂ ð1 þ Kp;4 ꢂ ½Hþꢃ þ Kp;4 ꢂ Kp;5 ꢂ ½Hþꢃ Þ
H3LðHÞ
a
Eu
and therefore the equilibrium constant K* is defined by
reaction pathways were also observed for the formation
the following equation:
of the gadolinium(III) complex with H5do3ap [12]. The
Eu
rate constant
k
OH
for H5do3ap is slightly lower than
½EuðH3LÞꢃ
EuKꢄ3 ¼
ð7Þ
the respective rate constant for H4dota (see Table 2)
½Eu3þꢃ ꢂ ½H3Lꢃ
Eu
and comparable with the value
k
= (4.8 0.07)
OH
· 106 Mꢀ1 sꢀ1 (I = 1.0 M KCl, T = 298.2 K) for the
do3a-butriol derivate [13].
The equilibrium constant EuK3 is a pH-dependent
parameter, and it can be calculated from the absorbance
values extrapolated to zero time (At=0) [12,15]. The condi-
tional equilibrium constant EuK3** is corrected according to
**
The formation kinetics in the europium(III)-H5do3ap
system was also followed by means of TRFLIS under
similar experimental conditions as studied by molecular
absorption spectroscopy in the UV region (see Fig. 2). In
addition, to determine the kinetic parameters the technique
provides information about the nature of the reaction
intermediates. The luminescent decays recorded at different
reaction times were monoexponential (see Eq. (1)), and the
number of water molecules obtained from the lifetimes of
luminescent decay decreased during the reaction time.
The mechanism of europium(III) complex formation dis-
cussed above can be briefly written as (the charges of com-
plexes and protons bound to the ligand are omitted for the
sake of clarity)
Eu
*
Eq. (7) in order to calculate
K3 , and the value
log EuK3* = 3.01 0.03 was estimated. This value should
be constant for the intermediate species prevailing in solu-
tion under the given experimental conditions. However,
this requirement was not fulfilled for the [Eu(H2do3ap)]*
+
species. The value of EuK3 of the [Eu(H3do3ap)]* species
*
+
differs from that log EuK2 of the [Eu(H2dota)]* species
obtained by UV molecular absorption spectroscopy
(4.4 0.1) or potentiometry (4.32 0.05) [15]. However,
different values for the same [Eu(H2dota)]*+ intermediate
species (5.88 and 6.26) were obtained by means of TRLIFS
[16,17]. The hypothesis is confirmed by the fact that the
most abundant protonated species of the monophospho-
nate ligand in the pH region of the study is H3do3ap2ꢀ
[12]. In order to determine the composition of the most
probable reaction intermediate, knowledge about the kinet-
ics of the other lanthanide(III) systems with H5do3ap
(Ce3+ and Gd3+ [12] ) or other europium(III)-macrocyclic
ligand systems (H2do2a [13], H3do3a [14] and H4dota
[15,17–19]) should be taken into account. Thus, the
[Eu(H3do3ap)]*+ reaction intermediate should be consid-
ered as the most abundant species in the studied pH region.
The [Eu(H2do3ap)]* and the [Eu(Hdo3ap)]*ꢀ species are
minor ones and all the species are in a fast protonation
equilibrium (Scheme 2); the [Eu(Hdo3ap)]*ꢀ species, pres-
ent in only a trace concentration, is probably kinetically
the most reactive species.
*
Kꢄꢄ
¢
Eukf
EuðH2OÞ3þ þ L þðmꢀnÞH O
EuLðH2OÞꢄ ! EuLðH2OÞ
ðAÞ
n
m
p
2
The reaction intermediate is formed in a fast equilib-
rium, and its transformation to the final product pro-
ceeds via a slower rate-determining step characterized
by the first-order rate constant Eukf. If there is a ligand
excess with respect to the europium(III) ion, as in our
experiment, only the reaction intermediate and the final
product (see reaction (A)) are present in solution. Both
species differ in the number of coordinated water mole-
cules and their normalized concentrations can be fol-
lowed by TRFLIS with assumptions that the average
number of water molecules consists of contributions
from both species and that the number of water mole-
cules is independent of species concentration. Thus, the
average number of water molecules as function of time
is defined as
The rate-limiting step of the formation reaction is the
deprotonation of the nitrogen atoms in the intermediate
species, catalyzed by hydroxide ions and simultaneous
translocation of the metal ion inside the ligand cavity
(Eq. (8), Scheme 2, Fig. 1)
qt ¼ qtðEuLꢄÞ þ qtðEuLÞ
ð9Þ
The change in the number of water molecules is driven
by the first-order kinetics:
ꢀ
Eu
Eu
Eu
Eukf ¼
k
¼
k
ꢂ ½OH ꢃþ k0
ð8Þ
f;obs
OH

P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
4123
H2O
H2O
O-
H2O
-O
Eu3+
+NH
NH+
O
C
P
-O2C
-O2C
PO3H-
CO2-
OH
O
N
NH+
N
EuK
fast
*
-O
O
N
O-
H2O
N
HN+
C
C
H2O
H2O
H2O
O
[Eu(H3L)]+*
H3L2-
H2O
H2O
Eu3+
+
+H+
fast
H+
H2O
H2O
Eu3+
H2O
H2O
2
-O2C
-O2C
PO3
-
H2O
O-
H2O
H2O
N
+HN
HO
P
O
O
fast
C
C
-O
O
-O
N
N
N
O-
O-
C
C
P
NH+
N
Eu3+
O
N
+NH
CO2-
-O
O
N
O-
O
H2L3-
C
-O
O
NH+
N
O-
[Eu(HL)]-
C
O
H+
[Eu(H2L)]*
Eu
k
+H+
fast
OH
+H+
fast
logβ1Eu = 5.41
-O2C
-O2C
PO3
-
2
slow
N
N
N
H+
H2O
Eu3+
N
H2O
slow
Euk0
fast
-O
CO2-
O
O
HL4-
-O
O-
O
C
P
-O
N
N
O-
O-
P
C
C
Eu3+
O
N
N
N
N
H+
-O
O
N
N
O-
O
-O
O
O-
O
C
C
C
[Eu(L)]2-
[Eu(HL)]-*
Scheme 2. The proposed reaction mechanism for complexation of europium(III) with H5do3ap (sites of the protonations are tentative). The
thermodynamic dissociation constant of [Eu(H2O)(Hdo3ap)]ꢀ is taken from [12].
Eukf ꢂt
Eukfꢂt
Eukf ꢂt
ꢄ
ꢄ
qtðEuLꢄÞ ¼ qt¼0ðEuL Þ ꢂ eꢀ
ð10Þ
ð11Þ
qt ¼ qt¼0ðEuL Þ ꢂ eꢀ
þ qt¼1ðEuLÞ ꢂ ð1 ꢀ eꢀ
Þ
Eukf ꢂt
Eukf ꢂt
qtðEuLÞ ¼ qt¼1ðEuLÞ ꢂ ð1 ꢀ eꢀ
Þ
¼ eꢀ
ðqt¼0ðEuLꢄÞ ꢀ qt¼1ðEuLÞÞ þ qt¼1ðEuLÞ ð12Þ
The combination of Eq. (9) with Eqs. (10) and (11) leads
to relationship (12)
After rearrangement, the final relationship (13) is
obtained:
lnðqt ꢀ qt¼1ðEuLÞÞ ¼ lnðqt¼0ðEuLꢄÞ ꢀ qt¼1ðEuLÞÞ
ꢀ
Eukf ꢂ t
ð13Þ
The linearized relationship (13) or relationship (12) com-
bined with a non-linear least-square procedure, can be used
for determination of the rate constant Eukf and the number
of water molecules in the final product and in the reaction
intermediate at the beginning of the reaction, i.e. immedi-
ately after mixing of the reactants. The results of the
non-linear fit for the reactions of europium(III) with the
three macrocyclic ligands (H3do3a, H5do3ap and
H5do3apPrA) are given in Table 3. Also the number of
water molecules determined from equilibrium and the
kinetic measurements are in fair agreement (see Table 3,
[33]). A special case is the europium(III) complexation by
H4dota. It was shown that two reaction intermediates
([EuHn(dota)(H2O)5](nꢀ1)
(intermediate
1)
and
**
Fig. 1. Dependence of the observed pseudo-first order rate constants
[EuHn(dota)(H2O)3](nꢀ1) (intermediate 2)) and the final
product ([Eu(dota)(H2O)]ꢀ (3)) are formed at pH ꢆ 2.5–
*
Eu
k
on [OHꢀ] for the formation of the [Eu(H2O)(do3ap)]2ꢀ complex
f,obs
(UV–Vis measurements).

4124
P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
Table 2
Table 3
The overview of the rate constants for the formation/dissociation
reactions of europium(III) complexes of cyclen derivatives (T = 298.2 K)
The summary of the results obtained from the TRFLIS study of the
formation of Eu3+-complexes with H4dota-like ligands
Ligand
H4dota
Eu3+
Species
pH
s
Final
Reaction intermediatef
(H2O)e product
(ms)
Formation
Dissociatione,f
qe
qf
q
kf,obs (sꢀ1
)
kOH = 1.1 · 107 Mꢀ1 sꢀ1
logK2* = 4.4 (4.32)
kH1 = 1.4. · 10ꢀ5 Mꢀ1 sꢀ1
kH2 = 1.0 · 10ꢀ3 Mꢀ2 sꢀ1
kd,1 = 1 · 10ꢀ6 sꢀ1
kd,2 = 6.2 · 10ꢀ4 sꢀ1
K1 = 14 Mꢀ1
K2 = 0.12 Mꢀ1
Ref. [15]c
a
(Ref. [15])
Eu3+
[Eu(do3a)]
2.2a 0.1082
5.6b 0.375c
5.6b 0.371d
5.6b 0.6765
9.0
2.1 2.2 4.6c (9.56 0.87) · 10ꢀ3c
2.1
0.9
kOH = 7.2 · 106 Mꢀ1 sꢀ1
logK2* = 5.88 (6.22)
(Ref. [16])b
[Eu(dota)]ꢀ
see
see text
text
[Eu(do3ap)]2ꢀ
[Eu(do3apPrA)]2ꢀ 5.8b 0.674
5.6b 0.692
0.8 0.7 3.0c (4.69 0.30) · 10ꢀ3c
0.9 0.7 3.9c (5.71 0.47) · 10ꢀ3c
H8dotp
kH1 = 1.3 · 10ꢀ3 Mꢀ1 sꢀ1
kd,2 = 6.2 · 10ꢀ4 Mꢀ1 sꢀ1
HK5 = 2.0 Mꢀ1
a
No buffer used.
MES used as buffer.
c(Eu) = 0.005 mol lꢀ1, c(L) = 0.006 mol lꢀ1
c(Eu) = 0.005 mol lꢀ1, c(L) = 0.010 mol lꢀ1
Thermodynamic study [33].
b
c
.
.
Ref. [21]
d
e
f
H5do3apd
kOH = 2.7 · 106 Mꢀ1 sꢀ1
k0 = 0.9 · 10ꢀ3 sꢀ1
logK3* = 3.01
kH1 = 9.8 · 10ꢀ5 Mꢀ1 sꢀ1
kd,2 = 4.6 · 10ꢀ4 Mꢀ1 sꢀ1
HK3 = 0.21 Mꢀ1
This work; kinetic study.
H5do3apPrAd
kH1 = 1.03 · 10ꢀ4 Mꢀ1 sꢀ1
kd,2 = 5.3 · 10ꢀ4 Mꢀ1 sꢀ1
HK3 = 0.20 Mꢀ1
ring [24]. The measured luminescence decay traces mea-
sured here were deconvoluted with published lifetimes
(taken from [19]: s1 = 0.6427 ms, s2 = 0.2851 ms and
s3 = 0.2013 ms; see Eq. (1)), and the intensities calculated
for the intermediate species (after normalization) are pre-
sented in Fig. 3. As it can be seen, a decrease in solution
acidity (a pH rise from 2.5–3.0 in [19] to 5.5 here) acceler-
ates the rate of complex formation from days to minutes,
and the same effect was observed in the studies with the
pH range 2.5–4.6 [15,19].
The parameters are defined in the article or otherwise are given under
table.
a
I = 1.0 mol lꢀ1 NaCl.
b
I = 0.1 mol lꢀ1 KCl.
c
I = 3.0 mol lꢀ1 NaClO4.
d
This work: formation I = 0.1 mol lꢀ1 KCl, dissociation I = 3.0 mol lꢀ1
(H,Na)ClO4; determined by UV–Vis spectroscopy.
e
kd,obs = kH1 · [H+] + kH2 · [H+]2.
kd;2
ꢂ
HKnꢂ½Hþꢃ
(n = 3 for H5do3ap, n = 5 for H8dotp).
f
kd;obs
¼
1þHKnꢂ½Hþꢃ
On the basis of these observations, a reaction mechanism
for formation of the [Eu(H2O)(do3ap)]2ꢀ complex can be
postulated. In the first fast step, the reaction intermediate
[Eu(H2O)3(H3do3ap)]*+, having three water molecules in
the first coordination sphere, is formed. Analogously, the
[Ce(H3do3ap)]*+ species was also found in the ceriu-
m(III)-H5do3ap system in weakly acidic medium [12], and
this species is probably rather stable towards further depro-
tonation under those conditions. The same phenomena was
3.0 [19]. The intermediates are stable for several days and
were characterized by EXAFS and luminescence spectros-
copy; they differ in the number of coordinated water mol-
ecules (5 and 3) [19]. By analyzing NMR spectra
recorded immediately after mixing of europium(III) and
H4dota at pD ꢆ 4.3–4.6, it was shown that the intermedi-
ate(s) demonstrate the rigidity of the tetraaza macrocycle
Fig. 2. Time dependence of change in the number of bound water
molecules (q) during formation of the europium(III) complexes with given
macrocyclic ligands (cEu = 0.005 mol lꢀ1, cL = 0.006 mol lꢀ1, pH 5.6).
Fig. 3. Time dependence of abundance of the kinetic species during
formation of the [Eu(H2O)(dota)]ꢀ complex (cEu = 0.005 mol lꢀ1
cL = 0.006 mol lꢀ1, pH 5.6).
,

P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
4125
½EuðHnLÞꢃ
observed in the case of the europium(III)-H4dota system
HKn ¼
ð14Þ
n
½EuðLÞꢃ ꢂ ½Hþꢃ
[15,18] where the presence of the corresponding double-pro-
tonated species [Eu(H2dota)]*+ is crucial. The structure of
the reaction intermediates for both ligands (H5do3ap and
H4dota) is probably similar under the assumption that
two nitrogen atoms of the cyclen ring are protonated. In
the [Eu(H2O)3(H3do3ap)]*+ species, the third proton is
probably attached to the phosphonate moiety coordinated
to the lanthanide(III) ion. Recently, such double nitrogen
protonation was observed in the solid-state structure of
the [Er(H2O)2(H2do3apPh)]2Cl2 dimeric complex crystal-
lized from acid solutions (pH < 4.5; H4do3apPh is the phe-
nylphosphinic acid analog of H5do3ap) [46] as well as in
the gadolinium(III) complex of the diprotonated form of
dotam (dotam is the tetraamide of H4dota) in the solid state
where four water molecules are bound to the central metal
ion [47]. On the other hand, a different structure (proton-
ated on one nitrogen atom) was predicted for an intermedi-
ate in complexation in the yttrium(III)-H4dota system by
quantum chemical calculations [26]. Such a monoproto-
nated species [Eu(HL)]* is supposed to be a crucial interme-
diate for the transformation of the reaction intermediate(s)
to the final product having one water molecule. This sce-
nario, with participation of the monoprotonated species,
is very probable because of the increase in values of the rate
constant kf with increasing ionic strength for yttrium(III)
complexation by the same H4dota-like ligands [28]. This
supports the hypothesis that the reaction takes place
between reactants of the same charge (i.e. here [Eu(HL)]ꢀ
vs. OHꢀ for the phosphorus acid derivatives) [28].
then generally, the rate of dissociation of the europium(III)
complexes is defined as
n
X
d½EuLꢃ
Eu
ꢀ
¼
k
ꢂ ½EuLꢃ
¼
kd;i ꢂ ½EuðHiLÞꢃ ð15Þ
d;obs
tot
dt
i¼1
taking into account the mass-balance equation (Eq. (16))
n
X
½EuLꢃtot
¼
½EuðHiLÞꢃ
ð16Þ
i¼0
Combining Eqs. (14)–(16), the following relationship
(17) can be written as
2
þ
þ
H
H
H
kd;1 ꢂ K1 ꢂ ½H ꢃ þ kd;2 ꢂ K1 ꢂ K2 ꢂ ½H ꢃ
Eu
k
¼
d;obs
2
þ
þ
H
H
H
1 þ K1 ꢂ ½H ꢃ þ K1 ꢂ K2 ꢂ ½H ꢃ
ð17Þ
In weakly acidic medium ([H+] < 0.0001–0.001 mol lꢀ1),
the simplified Eq. (18) was described for the acid-assisted
dissociation of lanthanide(III) complexes with H3do3a or
H4dota [15,16,48]:
þ
Eu
H
k
¼ kd;1 ꢂ K1 ꢂ ½H ꢃ
ð18Þ
d;obs
An additional term k0, that characterizes the spontane-
ous dissociation of the complex, can be determined, but
with large errors [12,15,21].
For H5do3ap and the H5do3apPrA, one extra proton is
attached to the phosphonate group or the carboxyl group
of the phosphinate side chain, and therefore, in the acidity
region employed for complex dissociation, there is no
[Ln(H2O)(do3ap)]2ꢀ species present in the solution and
our systems are formally shifted by one proton (Scheme
3a) compared to the complexes with H3do3a or H4dota,
and the dependence of Eukd,obs on the proton concentration
can be reformulated as follows:
The proposed reaction mechanism can be also assumed
for complexation of europium(III) ion by the other macro-
cyclic ligands (H3do3a, H5do3apPrA) as was proved for the
yttrium(III) complex formation [28]. The reaction interme-
diates formed differ in the number of bound water mole-
cules and in the number of protons (see Scheme 2), but
their structure should be similar. In the case of H4dota,
the reaction mechanism proposed in the literature [19]
was verified in the present study.
2
þ
þ
H
H
H
kd;1 ꢂ K2 ꢂ ½H ꢃ þ kd;2 ꢂ K2 ꢂ K3 ꢂ ½H ꢃ
Eu
k
¼
d;obs
2
þ
þ
H
H
H
1 þ K2 ꢂ ½H ꢃ þ K2 ꢂ K3 ꢂ ½H ꢃ
ð19Þ
3.3. Dissociation kinetics
From Scheme 3a, one can suggest that kd,1 ꢇ kd,2. Fur-
thermore, 1 ꢇ HK2 · [H+] + HK2 · HK3 · [H+]2 (compare
data in Table 2) and therefore Eq. (22) can be simplified
in the following way:
Acid-assisted decomplexation was investigated in order
to determine the kinetic inertness of the europium(III)
complexes with the macrocyclic ligands under study since
the rate of complex dissociation is slow in slightly acidic
media [48]. The kinetic inertness of the europium(III) com-
plexes with H4dota-like ligands is attributed to the rigid
structure of the coordinated cyclen ring. The proton-
assisted dissociation kinetics is usually studied in the pres-
ence of strong mineral acids (c = 0.1–1.0 mol lꢀ1) since the
europium(III) complexes are thermodynamically unstable
under these experimental conditions. In the literature, the
mechanism for dissociation of the europium(III) complex
with the H4dota has been established [15,48]. Assuming
the [Eu(HnL)]* species as the active ones in the dissociation
process with respective protonation constants
þ
H
kd;2 ꢂ K3 ꢂ ½H ꢃ
Eu
k
ꢆ
ð20Þ
d;obs
þ
H
1 þ K3 ꢂ ½H ꢃ
For a low value of HK3 or low acidity of the solution
(1 ꢅ HK3 · [H+]), this equation can be rewritten as Eq. (21):
þ
k
ꢆ kd;2 ꢂ K3 ꢂ ½H ꢃ ¼ kH;1 ꢂ ½Hþꢃ
ð21Þ
Eu
H
d;obs
The kinetics of the proton-assisted decomplexation of
the europium(III) complexes with the phosphorus acid
ligands H5do3ap and H5do3apPrA were studied in the
region 0.50–3.00 mol lꢀ1 HClO4. The dependence of the
Eu
pseudo-first order rate constants
k
on the proton
d,obs

4126
P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
concentration for both complexes is presented in Fig. 4. As
it can be seen, the experimental points for both euro-
pium(III) complexes fall together. Eq. (20) was used to fit
the experimental points, and the following parameters were
estimated: kd,2 = (4.62 0.98) · 10ꢀ4 sꢀ1
0.046 Mꢀ1
kd,2 = (5.25 0.91) · 10ꢀ4 sꢀ1
,
HK3 = 0.212
kH1 = 0.977 · 10ꢀ5 Mꢀ1 sꢀ1 (H5do3ap);
HK3 = 0.196 0.035 Mꢀ1
,
,
,
kH1 = 1.027 · 10ꢀ4 Mꢀ1 sꢀ1 (H5do3apPrA). The estimated
parameters are almost identical, however they are uncer-
tain because of the simplifying assumptions made in deriv-
ing the relationship used for the fitting. Therefore, the
parameters kH1 were calculated in order to compare them
with the parameters of dissociation for other lantha-
nide(III) complexes with H5do3ap, see Refs. [12,28]:
kH1 = 1.22 · 10ꢀ3 Mꢀ1 sꢀ1 (Ce3+); kd,2 = 7.0 · 10ꢀ3 sꢀ1
HK3 = 0.2 Mꢀ1, kH1 = 1.09 · 10ꢀ3 Mꢀ1 sꢀ1 (Y3+), kd,2
5.8 · 10ꢀ2 sꢀ1 HK3 = 0.048 Mꢀ1 kH1 = 2.78 · 10ꢀ3
ꢀ1 sꢀ1 (Gd3+); and the similar kinetic inertness of the
,
=
Eu
Fig. 4. Dependence of the pseudo-first rate constants
k
d,obs
on the
solution acidity for the dissociation of europium(III) complexes with
phosphorus-containing macrocyclic ligands (cEuL = 0.015 mol lꢀ1
,
,
,
I = 3.00 mol lꢀ1 (Na/H)ClO4, UV–Vis measurements). The dashed
lines were calculated according to Eq. (22) using the parameters given in
Table 2.
M
[Y(H2O)(do3apPrA)]2ꢀ complex (kd,2 = 3.4 · 10ꢀ3 sꢀ1
,
HK3 = 1.3 Mꢀ1, kH1 = 4.4 · 10ꢀ3 Mꢀ1 sꢀ1 [28]). The results
are in agreement with the kinetic behaviour of both euro-
pium(III) complexes demonstrated above.
varies its hydration number between 8 and 9, lying just on
the borderline between lighter (hydration number 9) and
heavier (hydration number 8) lanthanide(III) ions [34].
An equilibrium was observed between the differently
hydrated europium(III) complex species with H2do2a and
H3do3a, and the squaric acid derivative of H3do3a, deviat-
ing by one water molecule in the first coordination sphere
of the complex [51–53]; the corresponding constants and
thermodynamic parameters describing the equilibrium
were determined. The formation of the species with higher
coordination and hydration numbers (more abundant at
The rate of the [Eu(H2O)(do3ap)]2ꢀ complex dissocia-
tion is about 10 times slower than that of the other lantha-
nide(III) complexes, and it seems that the europium(III)
complex is the most inert among the studied lantha-
nide(III) complexes of H5do3ap. A similar exceptional
behaviour was described for acid-assisted dissociation of
lanthanide(III) complexes of a triacetate derivative of the
pyridine-containing cyclen analog [49] or the H4edta ligand
[50]. It can be possibly explained by a different hydration of
the ‘‘free’’ ions. It is known that the europium(III) aqua ion
a) with H5do3ap
+ H+ HK2
fast
+ H+ HK3
fast
[Eu(Hdo3ap)]-
[Eu(H3do3ap)]+
[Eu(H2do3ap)]
slow
kd,2
kd,1
slow
+ H+
fast
[Eu(H3do3ap)]+*
[Eu(H2do3ap)]*
fast
+ x H+
Eu3+ + Hx+3do3apx-2
b) with H3do3a
+ H+ HK1
+ H+ HK2
fast
[Eu(H2do3a)]2+
kd,2
[Eu(Hdo3a)]
[Eu(do3a)]
fast
+
slow
slow
kd,1
+ H+
fast
[Eu(H2do3a)]2+
*
[Eu(Hdo3a)]+*
fast
H+
Eu3+ + Hx+2do3ax
+
x
-1
Scheme 3. The proposed reaction mechanism for the dissociation of the europium(III) complex: (a) with H5do3ap and (b) with H3do3a.

P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
4127
room temperature) is preferred at lower temperature in
comparison with the species with lower coordination and
hydration numbers [18,51–53], which would be probably
more kinetically inert species. It can be assumed that the
nine-coordinated complexes of lighter lanthanides(III) ions
would be less kinetically inert than the eight-coordinated
complexes of heavier lanthanides(III) ions. Another effect,
having an influence on the kinetic inertness, can be a differ-
ence in protonation constants of the complexes (e.g.
Eu(III) vs. Gd(III) complex in Table 2 and Ref. [12] or
Ref. [49]).
In order to elucidate the intimate reaction mechanism of
the complex dissociation, TRFLIS was again employed.
The decay traces of the europium(III) complexes with the
macrocyclic ligands were recorded at different time points
during the course of the dissociation reaction (see example
in Fig. 5). The europium(III) complexes can be divided into
two groups according to their behavior in the presence of
an acid.
For the first group, involving europium(III) complexes
of H4dota and H5do3ap, their luminescence decay traces
recorded at the beginning and the end of the dissociation
reaction can be deconvoluted monoexponentially (see Eq.
(1) and Fig. S1 in the supplementary material) and the
decay lifetimes s are related to the number of coordinated
water molecules in the complex and the free europium(III)-
aqua ion, respectively (see Table 3). Thus, the luminescent
decays recorded during the dissociation reaction have to be
deconvoluted with two exponentials giving lifetimes (see
Eq. (1)) corresponding to the starting monoaqua euro-
pium(III) complex and the final free nona-aqua euro-
pium(III) ion, while no other intermediate luminescence-
active europium(III) species were detected in these systems.
The decreasesing intensity of the luminescence signal of the
monoaqua europium(III) complex species determined by
luminescent decay deconvolutions (see Eq. (1)) for different
time points recorded during the dissociation reaction (see
Fig. S1) can be used for the determination of rate constants
(see Table 4). In the case of H4dota (Fig. S1A) and
H5do3ap (see Fig. S1B), the pseudo-first rate constants in
perchloric and hydrochloric acids calculated from the
TRFLIS experimental data are almost identical (see Table
4). The agreement between the results obtained from TRF-
LIS and UV spectroscopy is also satisfactory taking into
account the precision of the measurements, and the slight
difference between the values can be ascribed to the differ-
ent experimental techniques and conditions employed in
these studies. In addition, the dissociation of the euro-
pium(III) complexes of H4dota and H5do3ap is similar
(see Fig. 4), and the process is not dependent on the nature
of the anion (perchlorate vs. chloride) as was described for
the luminescence behavior of the europium(III)-aqua ion
[54–58]. Our results presented above confirm that the inner
coordination sphere of the europium(III) ion in the
[Eu(H2O)(dota)]ꢀ complex is not affected by protonation
in strongly acidic medium [15,18].
Fig. 5. Examples of TRFLS traces during decomplexation of the
[Eu(H2O)(do3ap)]2ꢀ
complex
recorded
at
different
times
([HClO4] = 3.00 mol lꢀ1, ccomplex = 0.01 mol lꢀ1).
Table 4
The summary of the results obtained for the dissociation of Eu3+ complexes with H4dota-like ligands (the ionic strength was not adjusted)
Species
Method
Acidity
Rate constantkd,obs (sꢀ1
)
Hydration number q
of the intermediate
[Eu(do3a)]
TRFLIS (q)
0.3 mol lꢀ1 HClO4
kd,1 = (8.20 0.47) · 10ꢀ4
kd,2 = (1.80 0.04) · 10ꢀ3
(6.12 0.20) · 10ꢀ3
5.6
2.8
2.1
3.1
TRFLIS (q)
TRFLIS (q)
1.0 mol lꢀ1 HClO4
3.0 mol lꢀ1 HClO4
(1.22 0.08) · 10ꢀ2
[Eu(dotp)]5ꢀa
Eu(dota)ꢀ]
TRFLIS (q)
3.0 mol lꢀ1 HClO4
(1.53 0.08) · 10ꢀ4a
(2.95 0.08) · 10ꢀ4
(3.14 0.17) · 10ꢀ4
(1.62 0.33) · 10ꢀ4b
0.4a
TRFLIS (intensity)
TRFLIS (intensity)
UV spectroscopy
3.0 mol lꢀ1 HClO4
3.0 mol lꢀ1 HCl
3.0 mol lꢀ1 HClO4
[Eu(do3ap)]2ꢀ
TRFLIS (intensity)
TRFLIS (intensity)
UV spectroscopy
3.0 mol lꢀ1 HClO4
3.0 mol lꢀ1 HCl
3.0 mol lꢀ1 HClO4
(2.16 0.61) · 10ꢀ4
(2.91 0.11) · 10ꢀ4
(1.80 0.55) · 10ꢀ4c
[Eu(do3apPrA)]2ꢀ
UV spectroscopy
3.0 mol lꢀ1 HClO4
(1.94 0.48) · 10ꢀ4c
a
Ref. [21]; for qt=1 = 4.1.
b
Recalculated from Ref. [15].
c
Recalculated from parameters in Table 2 and Fig. 4.

4128
P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
On the contrary, for the second group of europium(III)
Two steps were observed at lower acidity while only one
step was identified at higher acidities (Fig. 6b). The analysis
gives the values of the rate constants with estimates of the
number of water molecules in the reaction intermediates
(the precision of the measurement is 0.5) and the values
are given in Table 4. The number of water molecules in
the starting [Eu(H2O)2(do3a)] complex is equal to two, as
it was determined formerly (see Chapter Formation Kinet-
ics or Refs. [33,52]), while the reaction intermediate has
three water molecules in its coordination sphere. The value
of the first protonation constant of the [Eu(H2O)(dota)]ꢀ
complex was estimated to be logK ꢆ 1 [15,18] and this
value can also be taken as an approximation for the corre-
sponding constant of the [Eu(H2O)2(do3a)] complex. This
means that the [Eu(Hdo3a)(H2O)3]+ species should be con-
sidered as a reactive intermediate at the beginning of the
dissociation reaction. Taking into account the reaction
mechanism proposed for the dissociation of the
[Eu(H2O)(dota)]ꢀ complex [15], an identical reaction
mechanism can be adopted for the [Eu(H2O)2(do3a)] com-
plex (see Scheme 3b). The reaction step, represented by the
rate constant kd,1 can be detected only at lower acidities
while the pathway with the kd,2 rate constant is fully dom-
inating at higher acidities (see Eq. (19)) [15,18]. The same
reaction mechanism (see Scheme 3b) has been proposed
for the acid-catalysed dissociation of the [Eu(dotp)]5ꢀ com-
plex, when the final product for the given reaction time-
scale has four (for perchlorate) or five (for chloride)
coordinated water molecules (see Table 4, [21]); this means
that the phosphonic acid pendant arms can coordinate the
europium(III) ion even in strongly acidic media. The same
effect was observed for lanthanide(III) complexation by
diphosphonate ligands [59] and it can be an explanation
of the differences in the apparent kinetic inertness among
europium(III) complexes of H8dotp and the other
H4dota-like ligands (see Fig. 4, Tables 2 and 4).
complexes, of H3do3a (this work) and H8dotp [21], the
lumininiscence-decay traces are always deconvoluted
monoexponentially (see Eq. (1)). The lifetime decay s was
used for the determination of the average number of bound
water molecules in the europium(III) complex (see Eq. (2))
as a function of the time of the dissociation reaction
(Fig. 6a). The average number of water molecules (q) is a
weighted value defined analogously as in the section on
the formation kinetics
Eukd ꢂt
Eukd ꢂt
ꢄ
qt ¼ qt¼0ðEuL Þ ꢂ eꢀ
þ qt¼1ðEuÞ ꢂ ð1 ꢀ eꢀ
Þ
Eukd ꢂt
¼ eꢀ
ðqt¼0ðEuLꢄÞ ꢀ qt¼1ðEuÞÞ þ qt¼1ðEuÞ
ð22Þ
The final relationship (23) is obtained after
rearrangement:
lnðqt¼1ðEuÞ ꢀ qtÞ ¼ lnðqt¼1ðEuÞ ꢀ qt¼0ðEuLꢄÞÞ
ꢀ
Eukd ꢂ t
ð23Þ
For H3do3a, Eq. (23) was used for treatment of the
experimental data. The rate of dissociation was not depen-
dent on the nature of the anion (perchlorate vs. chloride).
It is interesting to note that the kinetic inertness seems to
be related to the spectroscopic properties. It was postulated
recently [60,61] that the luminescence band intensity ratio
(DJ = 2/DJ = 1) related to the 5D0–7F2 (619 nm) and
5D0–7F1 (594 nm) transitions of europium(III) in com-
plexes is a sensitive and useful parameter for evaluation
of changes in the ion coordination environment. The first
group of europium(III) complexes (H4dota, H5do3ap,
H5do3apPrA
)
shows
a
luminescence intensity ratio
(DJ = 2/DJ = 1) of about 0.65–0.75, while the ratio
(DJ = 2/DJ = 1) is equal to 1.60–1.70 for the second group
(H3do3a, H8dotp) [33]. It was shown for H4dota-like
ligands that this ratio is a relative measure of the thermo-
dynamic stability of ternary europium(III) complexes (hav-
ing the third ligand in the axial position) and the free
energy describing the formation of the complex is an
expression of the strength of the interaction between the
europium(III) ion and the donor atom of the axial ligand
[61]. This effect was correlated with structural information
obtained by NMR spectroscopy [61]. Here, it can be sug-
gested that this parameter can be used for a prediction of
Fig. 6. (a) Time course of change in the number of coordinated water
molecules (q) during dissociation of the [Eu(H2O)2(do3a)] complex
(cEuL = 0.01 mol lꢀ1); (b) the linearized transformation (Y = ln(9 ꢀ qML))
of the change in the number of coordinated water molecules for the
Eu(III)-H3do3a system measured at different solution acidities. The ionic
strength of the solutions was not kept constant; it is identical with the acid
concentration.

P. Ta´borsky´ et al. / Polyhedron 26 (2007) 4119–4130
4129
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4. Conclusions
Formation kinetics of the [Eu(H2O)(do3ap)]2ꢀ complex
was studied and the results show that the reactivity is simi-
lar to that observed in the europium(III)-H4dota system.
TRLIFS, as a new experimental tool for the study of such
chemical reactions, seems to be suitable for kinetic investi-
gations. It can be used for the detailed study of the reaction
mechanism of complex formation, also in cases when this
process is a multistep one. This methodology has some
limitations for the study of the reaction mechanism of com-
plex dissociation as this method gives reliable results in the
case where the number of coordinated water molecules
changes during the course of the reaction. Kinetic con-
stants obtained by UV–Vis spectroscopy and TRLIFS
are comparable. The bifunctional phosphinate ligand
H5do3apPrA shows similar chemical properties towards
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