Solvent isotope effects on the complexation and exchange kinetics of Tl(I), K+ and Na+ with 18-crown-6 by competitive NMR spectroscopy: Competition between homo- and heterobimolecular cations exchange

Article abstract of DOI:10.1016/j.poly.2011.02.007

The thermodynamic properties of complexation and exchange kinetics of thallium by 18-crown-6 have been studied by thallium NMR spectroscopy. Effects of solvent isotope, counterion (ClO₄^- and NO ₃^-) and presence of competitive cations, such as Na ⁺ and K⁺, on the exchange characteristics of the system have been considered. The obvious relationships between the effects of D ₂O-H₂O solvent isotope on the thermodynamic properties and activation parameters of complexation have been investigated. In the absence of competitor cations, the mechanism of thallium exchange is unimolecular decomplexation and in the presence of competitor cations, homobimolecular cation exchange is the predominant mechanism at low concentrations of the ligand. At higher concentrations of the ligand, the measured rate constants show that the complexation/decomplexation process obeys a heterobimolecular cation interchange mechanism. The rate constants ratios (k_D2O/k_H2O < 1) for unimolecular mechanisms also show an inverse solvent isotope effect.

Full text of DOI:10.1016/j.poly.2011.02.007

Polyhedron 30 (2011) 1267–1273
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Polyhedron
journal homepage: www.elsevier.com/locate/poly
Solvent isotope effects on the complexation and exchange kinetics of Tl(I), K+ and
Na+ with 18-crown-6 by competitive NMR spectroscopy: Competition between
homo- and heterobimolecular cations exchange
⇑
Naader Alizadeh , Hedayat Haddadi
Department of Chemistry, Faculty of Basic Science, Tarbiat Modares University, P.O. Box 14115-175, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history:
The thermodynamic properties of complexation and exchange kinetics of thallium by 18-crꢀown-6 have
ꢀ
Received 28 December 2010
Accepted 4 February 2011
Available online 18 February 2011
been studied by thallium NMR spectroscopy. Effects of solvent isotope, counterion (ClO4 and NO3
)
and presence of competitive cations, such as Na+ and K+, on the exchange characteristics of the system
have been considered. The obvious relationships between the effects of D2O–H2O solvent isotope on
the thermodynamic properties and activation parameters of complexation have been investigated. In
the absence of competitor cations, the mechanism of thallium exchange is unimolecular decomplexation
and in the presence of competitor cations, homobimolecular cation exchange is the predominant mech-
anism at low concentrations of the ligand. At higher concentrations of the ligand, the measured rate con-
Keywords:
Solvent isotope effects
Thallium NMR
Exchange kinetics
Complexation
stants show that the complexation/decomplexation process obeys
a heterobimolecular cation
interchange mechanism. The rate constants ratios (kD2O/kH2O < 1) for unimolecular mechanisms also
show an inverse solvent isotope effect.
Counterion effect
Heterobimolecular exchange
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
the selectivity and stability of metal ion complexes with macrocy-
clic ligands are of special importance for their use as suitable
The solvent effects on thermodynamic and kinetic properties of
the complexation of macrocyclic ligands have been widely studied
in relation to both the structures of the ligands and the solvation of
the solutes. Usually, in going from one solvent to another, the
changes of molecular shapes and local liquid structures are so sub-
stantial that thermodynamic, kinetic or other characteristics of the
solutes have to be considered virtually on an individual basis for
comparing each solvating medium. Some of the difficulties are
avoided if the thermodynamic and kinetic properties of the solute
or/and solution are treated in H2O and D2O, and solvent isotope
effects in such properties then give useful information on both
the structure-related differences between ordinary and heavy
water and the interactions between the solute and H/D isotopically
distinguishable solvents [1–9].
Considerable efforts have been dedicated to investigating mac-
rocyclic ligands and their interactions with a wide variety of cat-
ions, anions and neutral guests [10–20]. Structural, spectral,
electrochemical, thermodynamic and kinetic properties of macro-
cyclic complexations have been investigated, and detailed thermo-
dynamic and kinetic data for different macrocyclic complexes
evaluated by different physico-chemical methods in various sol-
vent media have been reported [21–23]. During their formations,
neutral carriers for selective transport across liquid membranes
[24–26] and also for constructing membrane-selective sensors for
different metal ions [27–32].
Information concerning the complexation kinetics of macrocy-
clic ligands with alkali metal ions is rather sparse, despite the
importance of such data for the elucidation of the mechanism of
complexation reactions. There are several reports related to the
kinetics and mechanisms of cation complexation and decomplex-
ation using crown ethers [16,21,33,34]. The kinetics of the cation
exchange between the solvent and the ligand has a strong influ-
ence on the overall transport of cations across bulk liquid
membranes.
Thallium has long been proposed as a suitable probe for alkali
metal cations, especially potassium, in biological systems due to
its chemical similarity to group 1 metals, like atomic radius
(1.33 Å for K+ versus 1.40 Å for Tl(I)), dehydration energy (80
kcal/mol versus 82 kcal/mol) and bond lengths (2.4–2.7 Å) [35–
37]. Thallium (201) has become a standard for myocardial perfu-
sion imaging. Thallium is a potassium analog and its uptake in
the myocardium is partly dependent on active transport mediated
by the sodium–potassium ATP-ase pump, whereas the remainder
enters the myocyte passively.
In recent years, we have used proton and metal NMR techniques
to study the thermodynamic [12–14,17,20] and kinetic
[16,21,33,34] properties of metal ion complexation with some
⇑
Corresponding author. Fax: +98 21 82883455.
E-mail address: alizaden@modares.ac.ir (N. Alizadeh).
0277-5387/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.poly.2011.02.007

1268
N. Alizadeh, H. Haddadi / Polyhedron 30 (2011) 1267–1273
macrocyclic ligands in non-aqueous and mixed solvents. In this
study, we were interested in investigating the thermodynamic
and exchange kinetic properties of complexation of Tl(I), K+ and
Na+ ions with 18-crown-6 (L) in H2O and D2O. The effects of the
counterion on the complexation/decomplexation were also
studied.
3. Result and discussion
3.1. Solvent isotope effect on the thermodynamics of complexation
Fig. 1 shows the resulting thallium chemical shifts-mole ratio
data at different temperatures for a series of solutions containing
equal concentrations of thallium, but varying concentrations of L
in D2O. The thallium chemical shifts were measured as a function
of the mole ratio, L/Tl(I) (total mole of L to total mole of thallium)
in H2O and D2O solutions. In all cases, only one population-
averaged resonance was observed, which indicates that the
exchange rate of the cation between the bulk solution and the
complexed site is fast on the NMR timescale. A typical thallium
NMR spectrum is shown in the insert of Fig. 1. The observed trans-
verse relaxation rate (1/T2) is affected by chemical exchange in
addition to inhomogeneity contributions. When the stability of
the magnet is appropriate and the field is homogeneous, the ob-
served transverse relaxation rate can be calculated from the width
of the signal peak at half-height (W1/2obs) according to the relation-
ship given by Pople et al. [39]. Transverse relaxation rates (1/T2)
were determined by measuring line widths at half peak height
(W1/2obs). On the basis of the chemical shift behavior, one would
expect a similar curve for W1/2obs as a function of the L/Tl(I) ratio.
A typical plot of W1/2obs against mole ratio is given in the insertion
of Fig. 1 at 308 K. Addition of L to the Tl(I) solution resulted in an
increase in the relaxation rates for thallium. It displays a maximum
for equal populations of free and complexed metal ions. This obser-
vation is in agreement with a moderately rapid-exchange model
for a two-site exchange system with the equal populations of the
solvated and complexed species in a 1:l complex [40].
2. Experimental
2.1. Chemicals
The ligand 18-crown-6 (L) was purchased from Aldrich. The
used nitrate and perchlorate salts of all cations were of the highest
purity available from Fluka, and they employed without any fur-
ther purification except for vacuum drying over P2O5. Thallium(I)
perchlorate was prepared by treating 1 g of thallium(I) nitrate with
4 mL of 3 mol Lꢀ1 perchloric acid, evaporating to dryness and then
recrystallizing three times from water and drying at 120 °C [38].
The D2O was obtained from Aldrich (99.9 at.% D).
Caution! Although we have not encountered any problems, it
should be noted that the perchlorate salts of metal complexes with
organic ligands are potentially explosive and they should be han-
dled only in small quantities with appropriate precautions.
2.2. Thallium NMR spectroscopy
All thallium NMR experiments were performed at 11.7 T
(285 MHz 203Tl) using a Bruker DRX-500 pulsed Fourier transform
NMR spectrometer. Operating conditions for thallium measure-
ments involved a flip angle of 30°, spectral frequency of 285.677
MHz, delay time of 1.0 s, acquisition time of 0.039 s and line broad-
ening of 1.0 Hz. All 203Tl spectra were internally referenced to a
capillary tube containing 0.24 mol Lꢀ1 TlNO3 in D2O. The complex-
ation behavior of the ligand towards metal cations was studied by
adding the ligand into the NMR tube containing the thallium salt
(0.02 mol Lꢀ1) dissolved in the H2O and D2O. Stepwise additions
of the ligand were made and chemical shifts were recorded.
The complexation of the Tl(I) cation by L in solvent is given by
Eq. (1):
k1
TlðIÞ þ L $ TlLþ
ð1Þ
ð2Þ
k
ꢀ1
KTl ¼ ½TlLþꢁ=½TlðIÞꢁ½Lꢁ
180
160
140
120
100
80
60
40
20
0
5.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
-5.0
-15.0
-25.0
-35.0
-45.0
-55.0
-65.0
-75.0
-85.0
-95.0
L/Tl(I)
T(K)
338
328
318
308
293
0.0
1.0
2.0
3.0
4.0
5.0
6.0
mole ratio (L/Tl(I))
Fig. 1. Thallium chemical shifts (ppm) as a function of the L/Tl(I) mole ratio at different temperatures; insertion of W1/2obs (Hz) and thallium NMR spectra for the TlClOꢀ
L
4
system against mole ratio at 308 K in D2O solutions (CTl = 0.02 mol Lꢀ1).

N. Alizadeh, H. Haddadi / Polyhedron 30 (2011) 1267–1273
kA
1269
TlðIÞ $ Tl ꢀ Lþ
where KTl is the formation constant of the Tl(I)–L system. The thal-
kB
ð5Þ
lium chemical shifts were monitored as a function of the L/Tl(I)
mole ratio in H2O and D2O solutions (Eq. (1)). The formation con-
stants of the 1:1 Tl(I)–L complexes were calculated from the varia-
tion of the thallium chemical shift with the L/Tl(I) mole ratio. It has
been shown that in solutions containing fixed concentrations of me-
tal ion, Tl(I), and varying amounts of L, the observed chemical shift
of the probe ion Tl(I) is given by the following equation:
ðAÞ
ðBÞ
In Eq. (5), kA and kB are the pseudo-first-order exchange rate
constants for the forward and reverse reactions, respectively. A
represents the solvated thallium, and B represents the complexed
thallium. The value of kA in Eq. (5) may be obtained if the value
of the formation constant (KTl) is independently determined in
the same solvent system along with kB, since KTl = kA/kB. In H2O
and D2O, Tl(I)–L was in the fast-exchange limit of the thallium
NMR timescale for all of the accessible temperature ranges, and
no kinetic data could be derived with complete line shape analysis.
The exchange contribution to the full widths at half resonance
amplitude observed (W1/2obs) is directly related to the relaxation
dobs ¼ PTldTl þ Pcomplexdcomplex
ð3Þ
The observed thallium chemical shift is obtained from Eq. (3),
where PTl and Pcomplex are the mole fractions of the free and com-
plexed Tl(I) ions, respectively. By substitution from Eq. (2) and
the mass balance equation CTl = [Tl(I)] + [Tl(I)–L], Eq. (3) can be
written as:
time,
s
= (kA + kB)ꢀ1, and to the difference between the chemical
shifts of the two sites, mA and mB (expressed in hertz), Eq. (6) [42].
nh
dobs
¼
ðKTlCTl ꢀ KTlCL ꢀ 1Þ þ ðK2 C2 þ K2 C2 ꢀ 2K2 CLCTl
Tl
L
Tl Tl
Tl
i
o
2
pW1=2obs ¼ PA
p
W1=2A þ PB
p
W1=2B þ 4
p
2PAPBðmA
ꢀ
mBÞ ðkA þ kBÞꢀ1
1=2
þ 2KTlCTl þ 2KTlCL þ 1Þ
ꢂ ðdTl ꢀ dcomplexÞ=2KTlCTl þ dcomplex
ð4Þ
ð6Þ
where PA and PB are the populations of sites A and B, W1/2A and
W1/2B are their full widths at half resonance amplitude expressed
in hertz for sites A and B in the absence of chemical exchange,
which were measured at L/Tl(I) = 0 (PA = 1) and L/Tl(I) >> 1 mole
ratios (PB ꢃ 1), respectively (insert of Fig. 1). The mole fractions of
the free (PA) and complexed Tl(I) ion (PB) were calculated by using
the formation constant and initial total concentrations.
Two basic mechanisms have been proposed to account for the
observed NMR results in the presence of cation exchange, as de-
picted in Eq. (5). The first part refers to the unimolecular dissocia-
tion or dissociative exchange pathway and it is conveniently
represented by Eq. (1). Notice that this equation is identical to
where CL and CTl are total concentrations of the L and Tl(I) ions,
respectively, and dTl and dcomplex are the chemical shifts of the free
and complexed Tl(I) ion, respectively. The non-linear least-squares
curve fitting program KINFIT [41] was used to evaluate the KTl and
dcomplex values by fitting dobs versus CL data. Table 1 lists the solvent
isotope effect on the values of KTl, and the free energies of complex-
ation (DG°) of the thallium ion with L. The values of DS° and DH°
(presented in Table 1) were evaluated from a linear Van’t Hoff plot,
thereby in essence treating these two thermodynamic parameters
as constants over the experimental temperature range employed
(293–338 K). A relatively stable complex is formed in D2O with dif-
ferent strength and structural order of the intermolecular hydro-
gen bonds. The importance of this factor is supported by finding
that the backward thermodynamics activation parameters of com-
plexation differ in H2O and D2O. These differences have been as-
cribed to deuterium isotope effects on solvent reorganization
processes accompanying the chemical exchange event. These,
however, induce compensative enthalpy and entropy changes that
result in small changes in the free energy of binding. The results of
Table 1 indicate that the complexation/decomplexation process is
entropically more favored in D2O with respect to H2O.
Eq. (5), except that the rate constant k has been used instead
ꢀ1
of the rate kB, and kl [L] instead of kA. The second part is a bimolec-
ular cation-interchange mechanism (homobimolecular), which is
also known as the associative exchange mechanism involving a
second cation (⁄Tl(I)), as shown in Eq. (7).
kb
ꢄTlðIÞ þ Tl ꢀ Lþ $ ꢄTl ꢀ Lþ þ TlðIÞ
ð7Þ
The general expression for the relaxation time
s
= (kA + kB)ꢀ1 of
the metal in terms of the first and the second mechanisms
[16,23,34] is:
3.2. Solvent isotope effect on the exchange kinetics
1=
s
¼ kꢀ1CTl=½TlðIÞꢁ þ 2kbCTl
ð8Þ
The exchange kinetics of the complexation of Tl(I) with L were
studied in H2O and D2O solutions by thallium NMR at different
temperatures. In the case of the two-site exchange process, thal-
lium is exchanged between the two sites of free (A) and complexed
(B), Eq. (5).
where CTl and [Tl(I)] are the total concentration of the cation and
the concentration of the uncomplexed cation, respectively. Accord-
ing to Eq. (8), at a given temperature, the contributions of these two
mechanisms to the metal interchange process are determined by a
plot of 1/
sCTl versus 1/[Tl(I)]. The first mechanism predicts the
dependency of
s
on the relative population of the free cation,
Table 1
ꢀ
Solvent isotope effect on the thermodynamic and exchange kinetics of the complexation/decomplexation of the thallium ion with 18C6 (in all cases ClO4 is the counterion).
Solvent
H2O
T (K)
KTl (L molꢀ1
)
k1 (L molꢀ1 sꢀ1
)
kꢀ1 (sꢀ1
)
Thermodynamic parametersa
Backward activation parametersb
293
308
318
328
338
149.6 2.2
95.5 1.3
70.9 0.4
59.5 0.6
45.0 0.5
1.25 ꢂ 109
1.48 ꢂ 109
1.82 ꢂ 109
2.12 ꢂ 109
5.09 ꢂ 109
6.84 ꢂ 108
1.30 ꢂ 109
1.61 ꢂ 109
2.51 ꢂ 109
2.89 ꢂ 109
8.34 ꢂ 106
1.55 ꢂ 107
2.56 ꢂ 107
3.6 ꢂ 107
Ea (kJ molꢀ1): 43.70
D
D
D
H° = ꢀ21.66 (kJ molꢀ1
)
D
D
D
H– (kJ molꢀ1): 41.08
S– (J molꢀ1 Kꢀ1): 26.8
S° = ꢀ32.4 (J molꢀ1 Kꢀ1
)
G°300 = ꢀ11.94 (kJ molꢀ1
)
G–
(kJ molꢀ1): 33.05
300
11.32 ꢂ 107
D2O
293
308
318
328
338
157.6 4.0
93.5 1.3
82.8 1.1
62.8 0.6
49.1 0.6
4.34 ꢂ 106
1.39 ꢂ 107
1.94 ꢂ 107
4.00 ꢂ 107
5.88 ꢂ 107
Ea (kJ molꢀ1): 47.46
D
D
D
H° = ꢀ21.03 (kJ molꢀ1
)
D
D
D
H– (kJ molꢀ1): 44.84
S– (J molꢀ1 Kꢀ1): 35.9
S° = ꢀ29.7 (J molꢀ1 Kꢀ1
)
G°300 = ꢀ12.12 (kJ molꢀ1
)
G–
(kJ molꢀ1): 34.1
300
a
Thermodynamic parameters were calculated by using ꢀRTln K =
D
G° =
D
H° ꢀ TDS°.
b
Unimolecular decomplexation (dissociative mechanism).

1270
N. Alizadeh, H. Haddadi / Polyhedron 30 (2011) 1267–1273
same salts of the two cations, and chemical shifts of the probe ion
1.E+10
8.E+09
6.E+09
4.E+09
2.E+09
0.E+00
(a)
were determined with varying amounts of the ligand. In all cases,
only one resonance line for Tl(I)–M–L was observed, irrespective of
the L/Tl(I) mole ratio, which indicates a fast exchange between the
solvated and the complexed cation sites on the chemical shift
timescale.
The variations of thallium chemical shift with the L/Tl(I) mole
ratio were used to calculate the formation constants of Tl(I), K+
and Na+ complexes with L in the presence of different anions in
H2O and D2O solutions. The competitive complex formation equi-
libria, in which only the 1:1 complexes between L and both Tl(I)
and M+ ions are formed, and shown in Eqs. (1) and (10).
KM
þ þ L $ MLþ
ð10Þ
ð11Þ
0
50
100 150 200 250 300 350 400
M
1/[Tl]
KM ¼ ½MLþꢁ=½Mþꢁ½Lꢁ
7.E+09
6.E+09
5.E+09
4.E+09
3.E+09
2.E+09
1.E+09
0.E+00
(b)
The observed chemical shift of the probe ion Tl(I) in the pres-
ence of the competitor cation M+ is given by the expression.
dobs ¼ ðdTl þ dcomplex½L0ꢁK0 Þ=ð1 þ ½L0ꢁK0 Þ
ð12Þ
Tl
Tl
where [L0] and K0Tl are the apparent concentration of ligand and
apparent formation constant of Tl(I) in the presence of the compet-
itor cation, respectively. Meanwhile, the conservation of mass im-
plies that
½L0ꢁ ¼ ½Lꢁ þ ½MLþꢁ ¼ ½Lꢁð1 þ ½MLþꢁ=½LꢁÞ ¼ ½Lꢁð1 þ ½MþꢁKM
Þ
ð13Þ
K0TI ¼ KTI=ð1 þ ½MþꢁKM
Þ
ð14Þ
0
50
100
150
200
250
300
1/[Tl]
where [L] and [ML+] are the concentrations of the free and com-
plexed ligand, K0Tl, KTl and KM are competitive and non-competitive
formation constants for Tl(I) and M+, respectively. The values of KTl
and K0Tl were evaluated by fitting the observed chemical shift–mole
ratio data into Eq. (4), in the absence and presence of the competitor
cation, respectively. Under the experimental conditions [M+] >>
[Tl(I)] (since [M+] ꢃ [M+]tot), KM is obtained from Eq. (14). A sample
of the thallium chemical shift–mole ratio data and computer fit are
shown in Fig. 3, and the calculated KTl and KM values are given in
Table 2. A fair agreement between the observed and calculated
chemical shifts, which is shown in Fig. 3, further supports the for-
mation of a complex with a 1:1 stoichiometry between Tl(I) and
M+ with L.
Fig. 2. Plots of 1/
different temperatures; 338 (ꢂ), 328 (s), 318 (
s
CTl vs. 1/[Tl(I)] for the TlClOꢀ4 L system in (a) H2O, (b) D2O at
), 308 (h), 293 (Ç).
D
whereas the second mechanism predicts the dependency of
inverse total concentration of the cation. Thus, when the exchange
process proceeds via a dissociative pathway, the 1/ CTl versus
1/[Tl(I)] plot results in a straight line that passes through the origin,
whereas the plot results in a line parallel to the 1/[Tl(I)] axis in the
case of the predominance of a bimolecular mechanism.
Such plots for the Tl(I)–L system at various temperatures for
H2O and D2O are shown in Fig. 2. As is quite obvious from Fig. 2
that in this system a dissociative mechanism is predominant over
the entire temperature range and for the solvent isotope effect
investigated (correlation coefficients were between 0.90 and
s on the
s
The results of the equilibrium constant measurements indicate
that the binding constants of Tl(I) and K+ are more sensitive to the
anion effect than Na+ in both heavy and light water. While the
binding constant of Tl(I) is certainly different from those of K+
and Na+, it appears to be less sensitive to the solvent effect with
0.99). The corresponding k values for the dissociative exchange
mechanisms can be then evaluated from the slopes of the plots
of 1/sCTl versus 1/[Tl(I)], and the resulting exchange rate constants
ꢀ1
are included in Table 1. When the dissociative mechanism is dom-
inant, a plot of lnkꢀ1 versus inverse temperature gives an Arrhenius
plot. The activation energies for the release of the metal from its
Tl–L+ ion complex were determined from the slopes of such plots,
-10.0
-30.0
-50.0
-70.0
-90.0
and the activation parameters (
D
H–,
D
S– and
D
G–) were calcu-
lated by using Eyring’s equation (Eq. (9)) [43].
lnðkꢀ1=TÞ ¼ lnðkBoltz=hÞ þ
D
S–=R ꢀ
D
H–=RT
ð9Þ
In this equation, kBoltz is Boltzmann’s constant, T is the absolute
temperature, h is Plank’s constant, and R is the gas constant. The
enthalpy and entropy of activation are obtained from the slope
and intercept of the Eyring plot, respectively (Eq. (9)). The results
of these calculations are reported in Table 1.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
mole ratio (L/Tl(I))
3.3. Solvent isotope effect and anion effect on the competitive
complexation and exchange kinetics
Fig. 3. Thallium chemical shifts in the absence (e) and presence (s) of 0.1 mol Lꢀ1
KNO3 as a function of the L/Tl(I) mole ratio in D2O at 293 K (CTl = 0.02 mol Lꢀ1); (e)
and (s) experimental points; (—) computer fit; (ꢂ) experimental and calculated
points are the same within the resolution of the plot.
In the presence of a competitor cation (M+ = K+ and Na+), a ser-
ies of solutions were prepared containing a constant amount of the

N. Alizadeh, H. Haddadi / Polyhedron 30 (2011) 1267–1273
1271
Table 2
Stability constants and calculated rate constants for the metal exchange of 18C6 complexes with Tl(I), K+ and Na+ ions at 293 K (data in bracket are the ratios of D2O to H2O, kD2O
kH2O).
/
K (L molꢀ1
)
(L molꢀ1 sꢀ1
)
a
b
b
System
Solvent
H2O
KTl
KM
Kexch.
2kb
kTl
kM
Tl(I)–K–ClO4
Tl(I)–K–NO3
Tl(I)–Na–ClO4
Tl(I)–Na–NO3
149.6 2.2
111.9 2.3
149.6 2.2
111.9 2.3
613.3 61.6
522.9 36.4
6.8 0.3
0.244 (1.30)
0.214 (1.25)
22 (1.21)
1.32 ꢂ 108 (0.83)
1.54 ꢂ 108 (0.74)
3.22 ꢂ 108 (0.61)
2.59 ꢂ 108 (1.40)
3.07 ꢂ 108 (1.07)
2.68 ꢂ 108 (1.4)
7.55 ꢂ 108 (0.77)
6.07 ꢂ 108 (1.13)
1.26 ꢂ 109 (0.83)
1.25 ꢂ 109 (1.12)
3.43 ꢂ 107 (0.64)
3.69 ꢂ 107 (0.92)
6.7 0.3
16.46 (1.22)
Tl(I)–K–ClO4
Tl(I)–K–NO3
Tl(I)–Na–ClO4
Tl(I)–Na–NO3
D2O
157.6 4.0
96.3 3.5
157.6 4.0
96.3 3.5
498.4 29.4
360.4 27.8
5.9 0.3
0.316
0.267
26.71
20.06
1.10 ꢂ 108
1.14 ꢂ 108
1.95 ꢂ 108
3.63 ꢂ 108
3.29 ꢂ 108
3.74 ꢂ 108
5.85 ꢂ 108
6.84 ꢂ 108
1.04 ꢂ 109
1.40 ꢂ 109
2.19 ꢂ 107
3.41 ꢂ 107
4.8 0.2
a
Homobimolecular exchange mechanism.
Heterobimolecular exchange mechanism.
b
heterobimolecular metal interchange rate constant, kTl, can be ob-
tained from exchange equilibrium constant Kex and kM in the same
solvent and anion system.
both nitrate and perchlorate as counterions (Table 2). The ex-
change equilibrium constant (Kex in Table 2) of Tl(I)–K–L in the
case of perchlorate as a counterion is found to be more sensitive
to the solvent isotope effect than any other system.
Fig. 4 shows the variation of the calculated 1/s
CTl[M+] value as a
function of 1/[Tl(I)]. The type of bimolecular exchange was depen-
The thallium NMR spectrum in the presence of a competitor
cation at L/T(I) = 0 mole ratio is a sharp line (figure not shown).
An increase in the concentration of the ligand resulted in an
increasing linewidth. These observations in solution can be reason-
ably explained by a hetero-exchange process, which is shown in
Eq. (15).
dent on the relative ratio [M+] to [Tl(I)]. At higher values of [M+]/
[Tl(I)] (in the case of Fig. 4, [M+]/[Tl(I)] > 4), 1/ CTl[M+] is propor-
s
tional to 1/[Tl(I)]. For 1/[Tl(I)] > 57, perfect agreement with a single
mechanism is obtained, namely heterobimolecular exchange (Eq.
(15)). When 1/[Tl(I)] < 54, the observed rate constant becomes
independent of 1/[Tl(I)]. The leveling of the rate constant shows
that a residual homobimolecular mechanism becomes operative
at low values of 1/[Tl(I)]. Once the mechanisms were known, the
exchange rate constants were listed in Table 2. The effect of the
solvent isotope and counterion type on the exchange rate con-
stants (kb, kTl and kM) and Kex for Tl(I), K+ and Na+ were determined
and compared (Table 2). We visualized the transition state for the
heterobimolecular cation exchange as being close to a Tl(I)–L–M+
complex with a quasi-planar structure, in which two groups of
kTI
TlðIÞ þ MLþ $ Tl ꢀ Lþ þ Mþ
ð15Þ
kM
Kex ¼ kTl=kM ¼ KTL=KM ¼ ½Tl ꢀ Lþꢁ½Mþꢁ=½TlðIÞꢁ½MLþꢁ
ð16Þ
where kTl and kM are the heterobimolecular metal interchange rate
constants. Thus, in this case, the use of a competitor two-site equa-
tion is also valid to evaluate the corresponding relaxation time val-
ues. Meanwhile, for a fast-exchange process, Eq. (6) was used to
determine the corresponding relaxation times. It can be readily
shown that for the represented reaction path in Eq. (15), three lim-
iting mechanistic hypotheses exist for the exchange of thallium be-
tween the free and complexed sites in the presence of a competitor
cation M+: (1) dissociative pathway, (2) homobimolecular exchange
and (3) heterobimolecular exchange mechanism. In the first case,
2.E+11
(a)
1.E+11
8.E+10
4.E+10
0.E+00
the relaxation time
1=
¼ kꢀ1CTl=½TlðIÞꢁ
The second case is a homobimolecular metal interchange (Eq.
(7)):
1=
¼ 2kbCTl
s in term of Eqs. (1) and (10) is
s
ð17Þ
s
ð18Þ
48
50
52
54
56
58
60
Without presenting the detailed derivation of the equations, suffice
it to say that the relaxation time for the third case, which is defined
as a heterobimolecular exchange reaction (Eq. (15)), is given by Eq.
(19) (details are given in the Appendix):
1/[Tl]
8.E+09
(b)
1=
s
¼ kM½MþꢁCTl=½TlðIÞꢁ
ð19Þ
6.E+09
4.E+09
2.E+09
0.E+00
where kM and [M+] are the heterobimolecular metal interchange
rate constant and free concentration of the competitor cation,
respectively. In the presence of an excess concentration of the com-
petitor cation ([M+] >> [Tl(I)]), the exchange process does not obey
the dissociative mechanism. Therefore, the bimolecular metal ex-
change (homo and hetero) is the predominate mechanism. It is
fairly easy to determine the relative contributions of the two com-
47
52
57
62
67
peting bimolecular mechanisms by simply plotting 1/s
CTl[M+] ver-
1/[Tl]
sus 1/[Tl(I)]. From the slope and intercept, it is easy to obtain the
values of the exchange rate constants, kM and kb and thus to deter-
mine the relative importance of their respective contributions. The
Fig. 4. Plots of 1/s
CTl [K+] vs. 1/[Tl(I)] for the TlClOꢀ4 L system in the presence of
0.1 mol Lꢀ1 KClO4 in H2O (a) and D2O (b) at 293.

1272
N. Alizadeh, H. Haddadi / Polyhedron 30 (2011) 1267–1273
where
on sites A (free) and B (complexed), respectively. The relaxation
time ( ) is expressed as:
sA and sB represent the mean residence times of the thallium
three oxygens face the opposite sides of the molecular plane, and
each group complexes with one cation.
s
The exchange reaction also shows an inverse solvent isotope ef-
fect (kD2O/kH2O < 1) for the homobimolecular mechanism (kb) in the
case of perchlorate as the counterion, Table 2. D2O is more struc-
tured (i.e., it forms stronger hydrogen bonds than H2O), which re-
sults in a higher density, viscosity and boiling point, and lower
solubility of inorganic salts. A decrease in the zero-point vibra-
tional energy of water molecules caused by their deuteration
brings about the formation of deuterium bonds in an aqueous
medium that are stronger but more susceptible to destruction un-
der the influence of a complexation and decomplexation process,
compared with the similar protium bonds. These results indicated
the deuterium bonding is stronger than the hydrogen bonding. The
larger the force constant of the vibrations, in which isotope inter-
acted bonds are involved, the larger the observed isotope effect.
Because usually the stronger the bond involved in the vibration,
the larger the force constant, it can be expected that the decrease
of the isotope effect reflects the weakening of the bond involved
in the isotope interaction [7]. However, solvent isotope affects on
the exchange rate constants values depend on the counterion type.
1=
s
¼ 1=sA þ 1=sB ¼ kTl½MLþꢁ þ kM½Mþꢁ
¼ kM½MþꢁðkTl½MLþꢁ=kM½Mþꢁ þ 1Þ
ða7Þ
On substitution of Eq. (4) into (7), the following final equation
can be obtained:
1=
s
¼ kM½MþꢁCTl=½TlðIÞꢁ
ða8Þ
where CTl and [Tl(I)] represent the total and free concentrations of
thallium, respectively.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.poly.2011.02.007.
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ða1Þ
ða2Þ
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TlðIÞ þ MLþ $ Tl ꢀ Lþ þ Mþ
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where [M+] and [ML+] are the concentration of free and complexed
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change rate constants, KTl and KM are the non-competitive forma-
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equilibrium constant. It can be readily shown that for the reaction
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1=sA ¼ ꢀd½TlðIÞꢁ=½TlðIÞꢁdt ¼ kTl½MLþꢁ
ða5Þ
ða6Þ
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