Dynamic NMR study of the kinetics of complexation of Tl+ ion with Calix[4]crown-6

Article abstract of DOI:10.1021/jp101662f

The complexation and exchange kinetics and mechanism for the dissociation and conformational change of thallium ion complex of calix[4]crown-6 were studied in CD₃CN/CDCl₃ (4:1 v/v) solution by dynamic ¹H NMR. The results show the formation of a 1:1 complex with cone conformation. From variable temperature dynamic NMR analysis in the range 223-293 K, two coalescence temperatures at 228 and 243 K were ascertained. The activation parameters for the dissociation process, E_a (kJ/mol), δS^? (J/mol.K), and δH^? (kJ/mol) are 11.0, -133.2, and 10.1 for the bimolecular regime and 21.5, -112.8, and 20.6 for the unimolecular regime, respectively. In addition, the dynamic ¹H NMR spectroscopy shows that the exchange of Tl⁺ between the two crown sides of the complexed ligand proceeds through an intramolecular tunneling. An Arrhenius convex curve was observed for intramolecular exchange. This phenomenon is explained in terms of two conformer state formations differentiated by hydrogen bond association.

Full text of DOI:10.1021/jp101662f

7462
J. Phys. Chem. A 2010, 114, 7462–7469
Dynamic NMR Study of the Kinetics of Complexation of Tl+ Ion with Calix[4]crown-6
Hedayat Haddadi,† Naader Alizadeh,*,† Mojtaba Shamsipur,‡ and Zouhair Asfari§
Department of Chemistry, Faculty of Basic Science, Tarbiat Modares UniVersity, P.O. Box14115-175, Tehran,
Iran, Departments of Chemistry, Razi UniVersity, Kermanshah, Iran, and Laboratoire de Chimie Analytique et
Minerale, UMR 778, ULP/CNRS/IN2P3(LC4), ECPM, 25 Rue Becquerel, F-67087, Strasbourg Cedex, France
ReceiVed: February 24, 2010; ReVised Manuscript ReceiVed: May 31, 2010
The complexation and exchange kinetics and mechanism for the dissociation and conformational change of
1
thallium ion complex of calix[4]crown-6 were studied in CD3CN/CDCl3 (4:1 v/v) solution by dynamic H
NMR. The results show the formation of a 1:1 complex with cone conformation. From variable temperature
dynamic NMR analysis in the range 223-293 K, two coalescence temperatures at 228 and 243 K were
ascertained. The activation parameters for the dissociation process, Ea (kJ/mol), ∆S‡ (J/mol.K), and ∆H‡
(kJ/mol) are 11.0, -133.2, and 10.1 for the bimolecular regime and 21.5, -112.8, and 20.6 for the unimolecular
regime, respectively. In addition, the dynamic 1H NMR spectroscopy shows that the exchange of Tl+ between
the two crown sides of the complexed ligand proceeds through an intramolecular tunneling. An Arrhenius
convex curve was observed for intramolecular exchange. This phenomenon is explained in terms of two
conformer state formations differentiated by hydrogen bond association.
Introduction
SCHEME 1: The Structure of Calix[4] crown-6
Calixarenes are flexible macrocyclic compounds that are the
focus of considerable interest as useful building blocks for the
construction of relatively rigid lipophilic cation receptors and
carriers with desired properties.1,2 Among the interesting proper-
ties of calixarenes and their derivatives, perhaps the prominent
one is their binding ability with metal ions.3 The efficiency and
selectivity in metal ion binding by calixarene ionophores
depends not only on the ring size of the calix but also on the
nature of the binding groups attached, nature of the cation,
degree of deprotonation and, especially for calix-[4]arene
derivatives, on the conformation of the macrocycle (cone, partial
cone, 1,3-alternate, and 1,2-alternate).1,4-7
It is well-known that natural ionophores such as valinomycin
and monensin mediate alkali cation transport through biological
membranes.8-10 Meanwhile, thallium(I) has long been proposed
as a suitable probe for alkali metal cations, especially potassium
ion, in biological systems due to its chemical similarity.11 By a
materials approach, there is an increasing interest on the
chemistry as well as a number of potential applications of
calixarene derivatives.12 Formation of thallium complexes with
different stoichiometry was reported earlier for calixarene
derivatives.13-18
we wish to report the results of proton NMR studies of the
complexation of thallium(I) ion with calix[4]crown-6 (L, scheme
1), a fast exchange system, in a 4:1 (v/v) mixture of deuterated
acetonitrile and chloroform. The activation parameters of the
exchange kinetics were evaluated by using the simple Eyring
and Arrhenius equations in the presence of excess ligand.
However, the Arrhenius plot revealed a nonlinear convex shape
for the Tl+-L system at metal ion/ligand molar ratios g1. The
1
results of dynamic H NMR spectroscopy at low temperatures
showed that this phenomenon is in fact an intramolecular event
impeded by the steric effects of hydrogen bonding.
Experimental Section
1H NMR Spectroscopy and Conductometry. Variable
temperature 1H NMR studies were carried out on a Bruker DRX-
500 pulsed Fourier transform NMR spectrometer at 500 MHz,
from 293 to 223 K, using 5-mm o.d. NMR tubes. The
temperature of the probe was adjusted with a temperature-control
unit, using liquid nitrogen at low temperatures and a heating
element at high temperatures. To reach the equilibrium tem-
perature, each sample tube was left in the probe for at least 10
min before measurements. At all temperatures used, the accuracy
of the temperature measurement was (0.1 °C. The TMS signal
in CD3CN/CDCl3 (4:1 v/v) was used as an internal reference
for the 1H chemical shifts. The 1H NMR spectra were recorded
with a 90° pulse width of 15.0 µs. The acquisition time and the
delay between two pulses were 1.6 and 6.0 s, respectively. The
concentration of ligand in all experiments was used 0.002 M.
To the best of our knowledge, there is no literature on the
kinetics and mechanism of the formation and dissociation of
thallium ion complexes with calix[4]arenes in solution. A deeper
understanding of the factors affected and of the mechanisms
responsible for the host-guest complexation in solution neces-
sitates the studies on the thermodynamics and kinetics of the
corresponding complexation and dissociation processes. Al-
though many thermodynamic studies on the complexation
processes of calixarenes have appeared in the past few years,
kinetic and mechanistic studies are still scarce.19 In this paper,
* To whom correspondence should be addressed. Fax +98-21-82883455.
E-mail: alizaden@modares.ac.ir.
† Tarbiat Modares University.
‡ Razi University.
§ ULP/CNRS/IN2P3(LC4).
10.1021/jp101662f  2010 American Chemical Society
Published on Web 06/24/2010

Kinetics of Complexation of Tl+ with Calix[4]crown-6
J. Phys. Chem. A, Vol. 114, No. 28, 2010 7463
Conductance measurement was carried out with a Metrohm 712
conductivity meter. A dip-type cell, made of platinum black,
was used. During the conductance measurement, the cell were
thermostatted using a circulating water bathes (Frigomix B.
Braun UM-S) for adjusting the temperature with accuracy of
(0.1 °C.
Chemicals and Solutions. Deuterated acetonitrile and chlo-
roform were purchased from Armar Chemicals and were used
throughout. Thallium perchlorate was synthesized according to
the method of Coetzee et al. by reaction of thallium nitrate and
perchloric acid.20 The thallium salt was recrystallized three times
from water and drying at 120 °C and store in vacuum desiccator
over P2O5. All other materials were purchased from Merck. The
mixed solvents were dried over molecular sieve material before
1
use (the water signal is not observed in H NMR spectra of
solvent). Calix[4]crown-6 (L) was prepared and purified as
described in our previous publication.21 The temperature-
1
dependent H NMR spectra were subjected to complete line
shape analyses using modified Bloch equations to obtain the
temperature variation of the lifetimes.22
Safety Note. Thallium compounds are highly toxic. Accord-
ingly, appropriate personal protective equipment should be worn
when handling thallium solutions to prevent accidental exposure.
Thallium compounds are readily absorbed through various routes
of exposure. The water-soluble salts are rapidly and completely
absorbed from the respiratory tract, gastrointestinal (GI) tract,
or skin (no information was found regarding the absorption of
thallium salts via inhalation).23,24 Although we have not
encountered any problems, it is noted that perchlorate salts of
metal complexes with organic ligands are potentially explosive
and should be handled only in small quantities with appropriate
precautions.
Figure 1. Proton chemical shift of the hydroxyl groups of L as a
function of [Tl+]/[L] mole ratio in deuterated acetonitrile/chloroform
(4:1) at 296 K (A). Molar conductance vs [L]/[Tl+] mole ratio in
acetonitrile/chloroform at 296 K (B).
Results and Discussion
Stability Constant Determination. In order to evaluate the
formation constant of the Tl+-L complex in a binary mixture
of deuterated acetonitrile:chloroform (4:1 v/v), the proton NMR
spectra of the ligand in the presence of different concentrations
of Tl+ ion were recorded at 296 K. The resulting chemical shift
of the hydroxyl groups of L vs [Tl+]/[L] mole ratio (R) plot is
shown in Figure 1A. As seen, only one average response signal
was observed, indicating that the exchange rate of the cation
between the bulk solution and the complexed site is fast on the
NMR time scale at room temperature. Figure 1A clearly shows
that an increase in the Tl+ ion concentration gradually shifts
the proton resonance of L hydroxyl groups upfield until a R
value of about 1 is reached; further addition of the cation does
not change the resonance frequencies considerably. This be-
havior is indicative of the formation of a stable 1:1 complex.
The formation constant of the resulting complex was evaluated
by the computer fitting of the mole ratio data to a previously
derived equation, which relates the observed chemical shift to
the formation constant (Appendix A).25 The resulting log Kf
value was found to be g5.0.
Figure 2. Proton NMR spectra of L in the presence (A) and absence
(B) of Tl+ ion.
absence (B) of 1:1 Tl+ ion in deuterated acetonitrile/chloroform
(4:1 v/v) at 296 K. The NMR spectral characteristics of the
uncomplexed L, with L being in the cone conformation (Figure
2B), are summarized as follows: δ 7.69 (s, 2, ArOH), 7.10 (d,
4, ArH), 6.92 (d, 4, ArH), 6.75 (t, 2, ArH), 6.65 (t, 2, ArH),
4.38 (br d, 4, ArCH2Ar), 3.7-4.1 (m, 16, OCH2), 3.57 (s, 4,
OCH2), 3.39 (br d, 4, ArCH2Ar).
The chemical shifts of the hydroxyl groups could be affected
by a number of factors, such as polarity of a solvent, presence
of traces of water, acids or bases, participating of groups in
hydrogen bonding, temperature, and presence of a cation.
However, it is known that calix[4]arenes with two hydroxyl
groups at lower rim of calix[4]arene platform (like in ligand L)
are stabilized in cone conformation due to hydrogen bonding
between the hydroxyl groups.1
The stoichiometry and formation of the resulting Tl+-L
complex was also determined by conductometric titration of 10
mL of 5.0 × 10-5 mol/L of Tl+ solution with L in acetonitrile:
chloroform (4:1 v/v). The best-fit to the conductometric data
confirmed the stoichiometry and formation of Tl+-L complex
1
determined by the H NMR method (the details of the deriva-
tions are given in Appendix B). The resulting molar conductance
versus the [L] /[Tl+] mole ratio plot is shown in Figure 1B.
Spectral Changes During Complexation. Figure 2 shows
1
the H NMR spectra of ligand L, in the presence (A) and

7464 J. Phys. Chem. A, Vol. 114, No. 28, 2010
Haddadi et al.
the broadness and overlapping of the signals. Consequently, for
the exchange of thallium ion, we may assume the following
two-site exchange system:
Tl+ + L T Tl+-L
(1)
Equation 1 is meant for a general situation of the dissociation
process and does not imply any specific mechanism for the
exchange system. The activation parameters Ea, ∆H‡, and ∆S ‡
for the dissociation of the complex were evaluated from the
Arrhenius and Eyring eqs 2 and 3, at Tl+/L molar ratios <1.0.
Figure 3. Typical proton NMR spectra of the -OH protons of Tl+-L
complex at various temperatures for a mixture of [L] ) 0.002 M and
[Tl+] ) 0.001 M in deuterated acetonitrile/chloroform (4:1).
k ) A exp[-(Ea/RT)]
(2)
(3)
k/T ) (kb/h) exp[(-∆H‡/RT) + (∆S‡/R)]
As observed in Figure 2, the symmetry of the NMR signals
corresponds to the possibly restricted geometry of Tl+-L
complex in solution. The largest shift of -0.41 ppm, from 7.69
to 7.28 ppm, was observed for the OH-bearing phenyl signal
of L upon complexation with Tl+ ion, reflecting the strong
interaction of Tl+ ion with the hydroxyl groups of L. The singlet
at 7.28 ppm at a molar ratio of 1 is assigned to the phenolic
protons of Tl+-L complex. Four multiplet signals with equal
integrals at around 3.7-4.1 ppm can be attributed to the -CH2-
groups of the crown loop, and also a singlet at 3.57 ppm can
be assigned to the two equivalent neighboring -CH2- groups
of the crown loop (spectrum B). The benzylic protons signals
showed the AB systems (at 3.39 and 4.38 ppm) indicating the
cone conformation of this diphenol. However, the benzylic
coupling for the diphenol (NMR in CD3CN/CDCl3 (4:1 v/v), J
) 13 Hz) and chemical shift difference between two benzylic
protons (∆δ ) 1.01 ppm) clearly indicate its presence in the
cone conformation (spectrum B).26,27 The remaining portion of
the spectrum showed four sharp aromatic signals, two doublets
(7.10 and 6.92 ppm), and two triplets (6.75 and 6.65 ppm).
Dynamic 1H NMR Studies. The kinetics of the complexation
of Tl+ ion at 1ower temperature range of 223-293 K was
investigated in the deuterated acetonitrile/chloroform (4:1 v/v)
Thus, it may be taken into account the possibility of the two
following dissociation mechanisms for the Tl+- L complex:33
ku
9
Mechanism (I) Tl+-L 7
8 Tl+ + L
(4)
kb
Mechanism (II) Tl+-L + L* 798 Tl+-L* + L (5)
The first one is referred to as a unimolecular dissociation
mechanism, and the second is a bimolecular ligand exchange,
also known as an associative exchange mechanism. The general
expression for the mean lifetime (τ) of the ligand in terms of
mechanisms (I) and (II) is:
1/τ ) 2kb[L]t + ku[L]t/[L]f
(6)
where [L]t and [L]f are the total concentration of the ligand
and the concentration of uncomplexed ligand, respectively.
Therefore, we can determine the relative contribution of the two
dissociation mechanisms by the study of concentration depen-
dence of the life times of the Tl+-L complex. Mechanism (I)
predicts the linear dependence of 1/τ upon the relative population
of the free ligand, whereas mechanism (II) predicts the linear
dependence of 1/τ upon the total concentration of the ligand.
Thus, when the exchange process proceeds via a dissociative
pathway, the 1/τ[ L]t versus 1/[L]f plot results in a straight line
that passes through the origin, whereas in the case of the
predominance of a bimolecular mechanism the plot results in a
1
binary solvent system. The H NMR spectrum of L in R ) 0
exhibits very well separated signals for the crown and benzylic
protons at temperature ranges of 223-293 K, indicating that
the cone conformation is stabilized by the presence of circular
arrays of intramolecular hydrogen bonds. Such a stabilation of
a given conformation by hydrogen-bonding because of rigidify-
ing of the host molecule and consequent reduction of exchange
rates, has already been reported in the literature.28-32 Figure 3
depicts the representative proton NMR spectra of Tl+-L system
of a metal/ligand molar ratio of 0.5 at different temperatures.
The observation of a pair of broad peaks corresponding to a
metal/ligand molar ratio of 0.5 at low temperatures is also in
support of the above discussion (Figure 3). It should be noted
that the spectra at a metal/ligand molar ratio of 1.0 became a
simple pattern again, where the spectrum is assigned to the cone
conformation of the resulting complex. At higher metal/ligand
molar ratios than 1.0 (i.e., up to 3.0), no further spectral change
was observed. As it can be seen from Figure 3 (metal/ligand
molar ratio of 0.5), the decrease in temperature from 293 to
223 K induces some changes in the ArOH signal and causes
the single average signal, resulting from fast OH resonance, to
separate into two signals, for free and complexed ligands, under
a slow exchange protocol. The same changes were also observed
for aromatic signals. Additional changes in the aliphatic region
of the proton NMR spectra were difficult to interpret, due to
line parallel to the 1/[L]f axis. The corresponding kb and k
u
values for the two exchange mechanisms can then be evaluated
from the intercept and slope of the plots of 1/τ[L] t versus 1/[L]f,
respectively.
To evaluate the mean lifetime (τ) at different mole ratios and
temperatures, a nonlinear least-squares program was used to fit
100-200 points of the spectral data of the phenolic protons of
L to the exchange equations (modified Bloch equations).22,33
The line widths of the free and complexed ligands were
measured by fitting a Lorentzian function to their spectra of
the phenolic protons of L. The modified Bloch equations can
be obtained for an uncoupled two-site exchange of the free (L)
and complexed ligand (Tl+-L), the details are given in
Appendix C.

Kinetics of Complexation of Tl+ with Calix[4]crown-6
J. Phys. Chem. A, Vol. 114, No. 28, 2010 7465
Figure 4. Concentration dependence of the peak width of -OH protons
of calix[4]crown-6 at 296 K.
Figure 6. Concentration dependence ([L]f: 0.0015, 0.001, and 0.0005
M) of the relaxation times (τ) of the thallium complex at low
temperatures of 228 K (2) and 223 K (•).
Figure 5. Typical representation of experimental and calculated proton
NMR spectra of -OH protons L at R ) 0.5 and 223 K: (•) calculated
and observed signal are equal, (2) observed signal, (Θ) calculated
signal.
Figure 7. Arrhenius plots of Tl+-L complex for R < 1: (9)
bimolecular ligand exchange; (2) unimolecular ligand exchange.
Study of the Interaction of Tl+ Ion with L at Metal/Ligand
Mole Ratios R < 1. The signals at 7.70 and 7.28 ppm are
ascribed to the free and complexed species of L, respectively
(Figure 2). Figure 4 shows the concentration dependence of the
peak width of OH protons of calix[4]crown-6 at 296 K. As can
be seen, the chemical shift and the line width of the complexed
signal is affected by an increase in the concentration of Tl+.
This exchange pattern permits an easy test of the exchange
mechanism.34 These results allow discrimination between the
two possible mechanisms for the decomplexation of the Tl+-L
complex. As is evident from Figure 4, the plot of line width as
a function of the R ) [Tl+]/[L] ratio passes through a maximum
at R ) 0.3, and the curve is not symmetrical with respect to
this maximum, under conditions of a quantitative complex
formation. It should be noted that, in the case of an associative
interchange mechanism, the variations in line width should be
symmetrical with respect to a maximum at R ) 0.5.
Figure 5 shows the experimental and calculated proton NMR
spectra of L at R ) 0.5 and 223 K. The two observed signals
are due to hydroxyl protons of the free (lower field) and
complexed species L (higher field), under slow exchange
conditions. The life times (τ) of the thallium complex were
obtained using the complete line shape analysis for two-site
exchange of L between the free and complexed sites.33,35 Figure
6 shows the concentration dependence of the relaxation times
τ of the thallium complex at low temperatures of 228 and 223
K. As is evident from Figure 6, over the molar ratio range of R
) 0.25-0.50 (1/[L]f ) 666-1000), the life times of the Tl+-L
complex are almost constant while in the range of R ) 0.5-0.75
(1/[L]f ) 1000-2000), the life times (τ) increased by increasing
concentration of the thallium complex. The results indicate that,
for R values e0.5, a bimolecular mechanism is dominated in
the dissociation of the Tl+-L complex, whereas for a range of
0.5 e R e 0.75 an unimolecular pathway is the dominant
mechanism at low temperatures. The corresponding kb and ku
values for the two exchange mechanisms can then be evaluated
according to eq 6. The corresponding Arrhenius plots are shown
in Figure 7, and the resulting relaxation times, rate constants,
‡
and activation parameters (Ea, ∆H‡, and ∆S ) for the unimo-
lecular and bimolecular exchange mechanisms are summarized
in Table 1.
Study of the Interaction of Thallium and L at Mole Ratios
R g 1. Figure 8 shows the proton NMR spectra, in the region
3.3-3.5 ppm, of Tl+-L complex at different temperatures in
the presence of excess Tl+ ion. As seen, by a decrease in sample
temperature, the single signal of OCH2 of crown loop broadens
and splits into two lines of equal integrals. It can be inferred
that there are two exchangeable sites for methylene protons over
the entire temperature range studied. The exchange is apparently
quite swift even at 223 K. This observation can be interpreted
in two different ways: (i) Tl+ is bound to one of the two sides
of crown loop, and the two binding sites are actually inequivalent
(see Scheme 2), but they appear equivalent due to rapid ligand
exchange. (ii) Tl+ occupies the central position in the crown
loop cavity, so that the complex is symmetric and all OCH2
groups and benzene rings become equivalent to those of free
ligand. If explanation (ii) is correct, a symmetrical signal pattern
should appear at lower temperatures. As can be seen, the
coalescence of signals for OCH2 groups, especially the singlet
of two neighboring OCH2, were observed at 228 K. Thus, the
explanation (ii) is not correct because of incompatibility of this
hypothesis with the observed unsymmetrical signals.
In addition, the explanation (i) can occur in two different
ways: (a) hopping of Tl+ ion between the two binding sites via
an intermolecular metal exchange process or (b) intramolecular
alternations of Tl+ ion between the two binding sites through a
δ hole of crown. To discriminate between these two possibilities,
we examined the influence of the metal concentration on the
relaxation times of the exchange process at different tempera-
tures (Figure 9 and Table 2). If route (a) is dominant, 1/τ should
be increased linearly with free Tl+ concentration (eq 7), with a
slop of 2kbM, and if route (b) is dominant a straight line with an
intercept of 2kt, or concentration-independent of life times should

7466 J. Phys. Chem. A, Vol. 114, No. 28, 2010
Haddadi et al.
TABLE 1: Life Times, Calculated Rate Constants, and Activation Parameters for Unimolecular and Bimolecular Exchange
Mechanism in R < 1 from the Half Width of the -OH Protons of L ([L] ) 0.002 M)
τ (ms)
exchange rate constants
activation parameters
a
b
T (K) R ) 0.25 R ) 0.50 R ) 0.75 kb (M-1s-1
)
ku (s-1
)
A (Hz)
Ea(kJ/mol) ∆H‡ (kJ/m ol) ∆S‡ (J/molK) ∆G‡258(kJ/mol)
223
228
243
258
273
293
12.9
10.5
2.1
0.9
0.5
12.4
10.2
3.9
6.0
0.08
0.06
7.71
6.47
0.3
24.2
72.0
63.5
3.95 × 104
20.7
4.83 × 104
1.82 × 105
2.14 × 105
23.6 3.82 × 104 a
11.0a
21.5b
10.1a
20.6b
-133.2a
-112.8b
33.3a
49.7b
1081.3
5131.7 4.61 × 105 b
0.1
8363.6
a Bimolecular regime. b Unimolecular regime.
intramolecularly to another side of the crown loop. So the
elimination of two exchange sites caused by intramolecular event
does not affect significantly in calculation of relaxation times
of intermolecular kinetics for R < 1.
1/τ ) 2kbM[Tl]f
1/τ ) 2kt
(7)
(8)
The Occurrence of Convex Arrhenius Curve and Its
Interpretation. To obtain information about the activation
parameters of the exchang reaction, the Arrhenius plot of ln(k)
vs 1/T was constructed and is shown in Figure 10. The observed
slope of the Arrhenius plot at higher temperatures is smaller
than that at lower temperatures. A literature survey reveals the
presence of a few reports on the convex temperature behavior
of rate constants in chemical and biological systems.37-42 Kohen
et al. have interpreted this phenomenon by means of theoretical
and experimental observations.37 A convex Arrhenius curve
means that by increasing temperature, the activation energy
decreases. This phenomenon can be explained by Tolman’s
interpretation of the activation energy, which may be written
as.43-45
Figure 8. Proton NMR spectra of Tl+-L complex at R ) 1.46 in the
region 3.3-3.5 ppm at different temperatures.
SCHEME 2: Flip-Flop-Type Motion of Thallium Ion
through the Crown Hole of Calyx[4]crown-6
c
j
Ea ) E - E
(9)
c
j
where E represents an average over all reacting systems, and E
is an average over all systems, whether or not they react.
Tolman’s eq 9 states that the negative of the local slope of an
Arrhenius plot will be equal to the average energy of molecules
that react minus the average energy of all possible reactants. A
result (eqs 8).33 As is seen from Figure 9, the results show the
concentration-independence of life times, emphasizing on the
occurrence of an intramolecular exchange of Tl+ through the δ
hole of crown or a flip-flop-type motion.36 These results implied
that the metal cation bound to the calix[4]crown-6 tends to
dissociate intermolecularly into the solvent rather than to move
c
convex Arrhenius plot means that E decreases or that it increases
less rapidly than as temperature increases. This model suggests
new microscopic interpretations. It is assumed that the exchange
in complex adopts two different states 1 and 2 at equilibrium,
where state 2 is less reactive than state 1. In the less-reactive
state 2, which dominates at lower temperatures, the rate constant
of metal exchange is given by k2t, whereas in the more reactive
state dominating at higher temperatures, it is given by k1t. At
lower temperatures, the observed rate constant is smaller than
the expected one. In addition, the observed pre-exponential
factor is unusually large.
It is only at higher temperatures that the measurement of
Arrhenius curve is true, which results in a normal pre-
exponential factor. Limbach et al. explained this phenomenon
in terms of the hydrogen-bond association of the reactants.41,42
There are also several reports available on the effect of
hydrogen-bonding on stabilization of calixarenes in a especial
conformation and also reduction of exchange rates because of
Figure 9. Influence of the metal concentration on the relaxation times
for R g 1 at different temperatures.

Kinetics of Complexation of Tl+ with Calix[4]crown-6
J. Phys. Chem. A, Vol. 114, No. 28, 2010 7467
TABLE 2: Life Times, Calculated Rate Constants, and Activation Parameters for Intramolecular Exchange Mechanism in R g
1 from the Half Width of the -OH Protons of L ([L] ) 0.002 M)
τ(ms)
activation parameters
T (K) R ) 1.0 R ) 1.3 R ) 1.5 R ) 1.7 kt (s-1
)
A (Hz)
Ea(kJ/mol) ∆H‡ (kJ/m ol) ∆S‡ (J/molK) ∆G‡300(kJ/mol)
223
228
243
258
273
293
265
81.4
24.2
9.6
5.6
4.8
150
90.3
21.7
9.7
5.2
4.8
214
94.7
22.2
9.7
5.1
4.7
216
97.0
22.8
9.6
5.4
4.5
2.8
5.5
22.0
51.9
93.6
1.49 × 1033a
41.3a
4.8b
139.4a
2.4b
325.8a
237.1a
61.5b
7.21 × 102 b
-197.0b
106.1
a Low temperature regime. b High temperature regime.
Figure 10. Arrhenius plot of Tl+-L complex for R g 1.
Figure 12. Trend of chemical shift of hydroxyl groups in calix[4]crown-
6 vs mole ratio at different temperatures.
SCHEME 3: Proposed Conformer States of 1 and 2
change from upfield at 293 K (curve 6) to downfield at 223 K
(curve 1), so that at a middle temperature of 258 K (curve 4), the
resulting mole ratio plot shows the lowest change in chemical shift
(i.e., about 0.02 ppm) in the series, from R ) 0 to R ) 1.35. The
observation at 258 K can be explained in two possible ways: (a)
negligible interaction between thallium ion and L, and (b) tem-
perature dependence of internal conversion of conformers. The
hypothesis (a) is too hard to be accepted because of obvious
significant interaction of the components. The hypothesis (b)
assumes two conformer states of 1 and 2 as mentioned already.
State 1 denotes the dominant conformer at high temperatures and
state 2 to the less-reactive one at low temperatures (Scheme 3).
At low temperatures, the complex is in a rigid hydrogen-bonded
state, and at high temperatures, dissociation of the hydrogen bonds
of the complex occurs, and the temperature dependence of the
observed rate constants may also affected by the Gibbs free energy
of the hydrogen-bond association. These two conformers experience
different anisotropic and/or electron density by addition of thallium
ion, and then two negative and positive trends are observed for
this complexation. Hence, we thought the concentration indepen-
dency of chemical shift at 258 K is because of the balance of
electron density of states 1 and 2. The activation parameters for
the two temperature regimes were evaluated by drawing tangents
at the upper and lower temperature regimes of the Arrhenius plot
(Figure 10), and the results are summarized in Table 2. The
observation of smaller activation parameters for the high temper-
Figure 11. Temperature dependency of hydroxyl and OCH2 signals
of free L at different temperatures.
rigidifying of the host molecule.28-32 Figure 11 shows the
temperature dependency of hydroxyl and OCH2 signals of ligand
L. As can be seen, one of the OCH2 signals is shifted as of OH
signal shifts. This may be attributed to hydrogen-bonding effect.
Figure 12 shows the trend of chemical shift of the hydroxyl
groups of the free (R ) 0) and complexed L versus the metal/
ligand mole ratio at different temperatures. Obviously, at the highest
temperature of 293 K (curve 6), the signal shows an upfield shift
with molar ratio, while at the lowest temperature of 223 K (curve
1) a downfield shift is observed with increasing R. In other words,
the direction of chemical shift with metal/ligand mole ratio will

7468 J. Phys. Chem. A, Vol. 114, No. 28, 2010
Haddadi et al.
Appendix B: Evaluation of Formation Constant by
Conductometry.
The molar conductances, Λobs, in (S cm2 mol-1) can be
ature regime is in agreement with the destruction of hydrogen bonds
and consequent compensation of the tunneling energy barrier. In
addition, the unusually high activation parameters for the low
temperature regime can be contributed to the formation of a rigid
hydrogen bonded state.
calculated by using the following equation:
Λobs ) 1000k/CTl
(5)
Conclusion
The variable temperature proton NMR studies, in the range
of 223-293 K, on the calix[4]crown-6-Tl+ system in a binary
deuterated acetonitrile/chloroform (4:1v/v) mixture showed two
coalescence temperatures at 243 and 228 K, corresponding to
unimolecular and/or bimolecular and conformational transitions,
respectively. The dynamic proton NMR spectroscopy at lower
temperatures showed that the metal ion alternates intramolecu-
larly between the two sides of the crown loop. A convex
Arrhenius curve was observed, which indicate the tunneling of
thallium ion through the hole of crown loop in the ligand
because of two possible conformers of the complex.
where k is the conductance of the test solution in S cm-1. The
formation constants, Kf, in terms of the molar conductance can
be expressed as:
Kf ) [Tl-L+]/[Tl+][L] ) (ΛTl - Λobs)/
(Λobs - Λcomplex)[L] (6)
[L] ) CL - {CTl - (ΛTl - Λobs)/(Λobs - Λcomplex)}
(7)
Appendices
1
Here, ΛTl is the molar conductance of the metal ion before
addition of ligand, Λcomplex is the molar conductance of the
complexed ion, and Λobs is the molar conductance of the solution
during titration. The formation constants, Kf, and the molar
conductance of the complex, Λcomplex, were evaluated by
computer fitting of eqs 6 and 7 to the molar conductance
[L]/[Tl+] mole ratio data using a nonlinear least-squares
program.
Appendix A: Evaluation of formation constant by H
NMR Spectroscopy.
The complexation of Tl+ cation by L in solvent is given by the
eq 1.
k1
Tl+ + LTTl-L+
(1)
(2)
k-1
Appendix C: Two-Site Exchange Equations.
Kf ) [Tl-L+]/[Tl+][L]
The general case of exchange between the two sites A (free
ligand) and B (complexed ligand) with different relaxation times
is described by the following modified Bloch equation.22
where Kf is the formatin constant of Tl+-L system. The use of
Debey-Huckel limiting law of 1:1 electrolytes leads to the
conclusion that f(Tl+) and f(Tl-L+), so that the activity
coefficients in eq 2 cancel out. The proton chemical shifts were
monitored as a function of [Tl+]/[L] mole ratio in solution (eq
1). The formation constants of 1:1 Tl+-L complexe were
calculated from the variation of the proton chemical shift with
[Tl+]/[L] mole ratio. It has been shown that in solution
containing fixed concentration of L, and varying amount of Tl+
ion, the observed chemical shift of the proton is given by
following equations:
G ) u + iV
(2)
(3)
V ) -γH1Mo(SU + TV)/(S2 + T2)
u ) -γH1Mo(UT + SV)/(S2 + T2)
(4)
where G is the complex moment of magnetization, and V and u
are the pure absorption and pure dispersion line shapes,
respectively. The γ, H1, and Mo are the gyromagnetic ratio, field
strength, and macroscopic magnetization, and
δobs ) PLδL + Pcomplexδcomplex
(3)
where PL and Pcomplex are the mole fractions of the free and
complexed ligand, respectively. By substitution from eq 2 and
the mass balance equation CL ) [L] + [Tl-L+], eq 3 can be
written as:
S ) PA/T2A + PB/T2B + τ/T2AT2B - τ(ωA-ω)(ωB-ω)
(5)
U ) 1 - τ(PB/T2A + PA/T2B)
(6)
T ) (PAωA + PBωB - ω) + τ[(ωA-ω)/T2B
+
δobs ) {[KfCTl - KfCL - 1) + (K2f CT2l + Kf2CL2 -
(ωB-ω)/T2A] (7)
1
2K2f CLCTl + 2KfCTl + 2KfCL + 1) ] ×
/
2
V ) τ(PBωA + PAωB - ω)
(8)
(δL - δcomplex)/2KfCTl} + δcomplex (4)
where PA and PB are the relative population at sites A and B,
respectively; ωA and ωB are the resonance frequencies at the
two sites in the absence of exchange; and T2A and T2B are the
respective relaxation times at each site in the absence of
exchange. The τ is the mean lifetime of the exchange processes
defined by
where CL and CTl are total concentrations of the L and Tl+ ion,
respectively, and δL and δcomplex are the respective chemical
shifts of the free and complexed ligand. The nonlinear least-
squares curve fitting program was used to evaluate Kf and δcomplex
values by fitting the δobs versus CTl data.25

Kinetics of Complexation of Tl+ with Calix[4]crown-6
J. Phys. Chem. A, Vol. 114, No. 28, 2010 7469
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τ ) τAτB/(τA + τB)
(9)
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where τA and τB represent the mean residence times of the on
sites A (free ligand) and B (complexed), respectively.
The shape function, adapted for our case of Fourier-transform
spectroscopy, may be written as follows:
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Acknowledgment. This work has been supported by grants
from the Tarbiat Modares University Research Council, which
is hereby gratefully acknowledged.
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