J. Phys. Chem. B 2009, 113, 14247–14256
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Kinetics, Thermodynamics, and Modeling of Complex Formation between Calix[4]biscrowns and Cesium Alexandre Korovitch,† Jean-Baptiste Mulon,† Vincent Souchon,‡ Claude Lion,† Bernard Valeur,‡ Isabelle Leray,‡ Nguyeˆt-Thanh Ha-Duong,† and Jean-Michel El Hage Chahine*,† Interfaces, Traitements, Organisation et Dynamique des Syste`mes, UniVersite´ Paris-Diderot, CNRS UMR 7086, Baˆtiment LaVoisier, 15 rue Jean-Antoine de Baı¨f, 75205 Paris Cedex 13, France; Laboratoire Photophysique et Photochimie SupraMole´culaires et Macromole´culaires, De´partement de Chimie, Ecole Normale Supe´rieure de Cachan, 61 aVenue du Pre´sident Wilson, 94235 Cachan Cedex, France; and Laboratoire de Chimie Ge´ne´rale, ConserVatoire National des Arts et Me´tiers, 292 rue Saint Martin, 75141 Paris Cedex, France ReceiVed: June 4, 2009; ReVised Manuscript ReceiVed: August 11, 2009
Complex formations between calix[4]arene-bis(crown-6-ether) calix-COU2 (A1) and the tetrasulfonated species calix-COUSULF (A2) with Cs+ are investigated in water and ethanol, and in 9:1 (M1) and 1:9 (M2) H2O/ EtOH v:v mixtures, by chemical relaxation and molecular modeling. In ethanol and M2, two Cs+ are included in A1 in two kinetic steps, whereas complex formation in M1 becomes controlled by a slow first-order kinetic process, which is accompanied by very fast Cs+ inclusions, second-order rate constant: k′1 ) (3.4 ( 0.8) × 107 M-1 s-1. In water and M1, A2 forms 1:1 and 1:2 cesium complexes in a single kinetic step, whereas in M2, two Cs+ are included in two kinetic steps. The rate and thermodynamic constants involved are reported. They show that the second-order rate constants increase with the ethanol-to-water ratio, e.g., A2, secondorder rate constant for the first Cs+ in water: k1A2water ) (9.7 ( 0.3) × 104 M-1 s-1 and in M2: k1A2M2 ) (6.3 ( 0.4) × 109 M-1 s-1. The affinities of both A1 and A2 for Cs+ also increase with the ethanol-to-water ratio, e.g., first inclusion of A1 in M1: K1A1M1 ) (5 ( 1.3) × 103 and in ethanol: K1A1EtOH ) (7 ( 3) × 106. The deviation from the expected mechanism of complex formation with alkali is attributed to the comparatively more difficult access of Cs+ to the inclusion cavity of the capped calixarene. An analysis of calix-COU2 and calix-COUSULF and their Cs+ complexes with only one rim capped by the crown ether confirms the thermodynamic and kinetic results, by showing that the inclusion cavity of calix-COUSULF is more adapted to Cs+ than that of calix-COU2. This added to the presence of the shielding effect of the negative sulfonates can explain that the affinity of calix-COUSULF for Cs+ is higher than that of calix-COU2. These results can be of interest in the search of an efficient Cs+ decontaminant. Introduction
SCHEME 1: Calix-COU2 and Calix-COUSULF
Although alkali metal complexes are subject to intense investigations, their mechanisms of formation are not fully understood.1-9 Among these metals, cesium possesses a unique chemical behavior. Indeed, its large atomic radius coupled with a low charge-to-surface ratio leads to poor solvation with low hydration energy. This results in a cation which has a smaller hydration radius than the other alkali elements.10 Some ligands, such as crown ethers, form complexes with Cs+ extremely rapidly.6,7,11 A more representative family of these Cs+ ligands is that of calix crown ethers,5,8,12-20 such as the 1,3-alternate calix[4]arene-crown-6 ethers which can exhibit affinities as high as 105 for Cs+ in water and up to 107 in other solvents such as ethanol or acetonitrile.12,14-17 This led to the recent synthesis of series of cesium-selective fluoro-ionophores.5,12,13,18-20 Two of these fluorescent molecular sensors consisted of a calix[4]arenebis(crown-6-ether) and of the same tetrasulfonated molecule to both of which two dioxycoumarins were grafted (Scheme 1, A1-calix-COU2 and A2-calix-COUSULF).19,20 These molecules * To whom correspondence should be addressed. E-mail: chahine@ univ-paris-diderot.fr. Tel: 33157277238. Fax: 33157277263. † Universite´ Paris-Diderot. ‡ Ecole Normale Supe´rieure de Cachan and Conservatoire National des Arts et Me´tiers.
exhibited high affinities and selectivities for Cs+. Moreover, the two coumarin fluorophores allowed the detection of complex formation with Cs+ by fluorescence emission. The affinities of A1 and A2 for Cs+ were reported in ethanol and in water, respectively. Both calixarenes form stable complexes with one or two Cs+ according to a sequential mechanism I (eqs 1 and 2).19,20
10.1021/jp9052506 CCC: $40.75 2009 American Chemical Society Published on Web 10/05/2009
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Mechanism 1. k1
A + Cs+ h ACs+ k1
(1)
k2
ACs+ + Cs+ h ACs2+ 2 k2
(2)
with + + K11 ) [ACs+]/[A][Cs+], K21 ) [ACs2+ 2 ]/[ACs ][Cs ]
Complex formation of Cs+ with a crown ether is considered tobeanextremelyfastprocess,whichispracticallydiffusion-controlled.3,6,7 However, with some sterically hindered and capped calix[6-8]arenes, it can be very slow.8 Most of the other investigations concerning these Cs+ complexations were performed by 1H, 13C and/or 133Cs NMR. They always indicated fast kinetic processes occurring in the subsecond time range.2 These are also assumed to be host-guest processes in which Cs+ is included in the calixarene cavity. Thus, although widely studied, the nature and mechanism of these host-guest reactions is not yet well-known.21 Furthermore, in 1986, the Chernobyl accident led to the accumulation of the radioactive 137Cs in the soils and vegetations of a large area in Europe. The half-life of this isotope (30 years) can explain its high negative impact on health, mainly with the recrudescence of cancers and other related diseases.22 This highlights further the importance of understanding the mechanisms of complex formation with Cs+. Indeed, beside its fundamental interest, this comprehension can also lead to a better approach for the design and synthesis of new Cs+ decontamination agents. The aim of this study is to investigate the mechanisms of Cs+ inclusion in the calix-COU2 and calix-COUSULF. This was achieved by use of chemical relaxation methods and techniques,23-25 which allowed us to report an original mechanism for complex formation between Cs+ and the two calixarenes in water, ethanol, and alcohol-water mixtures. This mechanism takes into account the role of crown ether capping and implies that the inclusion of Cs+ requires when, necessary, a prior adjustment of the calixaren cavity before complex formation. The role of the solvent is also discussed. A theoretical approach using the B3LYP/6-31G and the B3LYP/LANL2DZ methods,26 brought further support to our proposals. Experimental Methods Calix-COU2 and calix-COUSULF were synthesized according to published procedures.19,20 All the other products were of the purest possible grade (Sigma, Merck, Acros or Aldrich). Ethanol was Merck spectroscopy grade, and water was demineralized and doubly distilled. Spectrophotometric Measurements. Absorption measurements were performed at 25 ( 0.5 °C on a Cary 500 spectrophotometer equipped with a thermostated cell carrier. Fluorimetric measurements were performed at 25 ( 0.5 °C on an Amino-Bowman series 2 luminescence spectrometer equipped with a thermostated cell carrier. Kinetics. T-jump experiments were performed on a modified Joule effect Messanlagen and Studien absorption and fluorescence emission T-jump spectrophotometer. The apparatus was equipped with a 200 W Xe/Hg light source, a Jarrel Ash
monochromator, and a thermostated cell holder maintained at 20 ( 1 °C. The T-jump was performed by discharging an 0.05 µF condenser charged at 14 kV, which gives a approximate temperature jump of about 5 ( 1 °C.7,27 The electrolyte was NH4Cl (0.4 M). In M1, the T-jump occurred in about 10 µs. Stopped-flow experiments were performed by mixing solutions of each of the two calixarenes with solutions of CsCl (water and ethanol/water) or CsOAc (ethanol) on a Hi-Tech Scientific SF61DX2 stopped-flow spectrophotometer equipped with a Xe/Hg light source and a thermostated bath at 25 ( 1 °C. In both type of experiments, all signals were accumulated at least 10 times. The excitation wavelength was set at 365 nm, which is one of the emission peaks of the Xe/Hg light source. Detection was set at λem g 400 nm. Quantum Chemical Calculations. Calculations were performed with the Gaussian software (Gaussian 03, RevisionC.02)26 at the MESO calculation center of the ENS Cachan (NecTX7 with 32 processors Itanium 2). All calculations were performed using the B3LYP/6-31G and the B3LYP/LANL2DZ method. Data Analysis. The data were analyzed by linear and nonlinear least-squares regressions, and all uncertainties were twice the standard deviations. Affinity constants were determined spectrophotometrically by use of the SPECFIT32 Global Analysis programme.28 All the observed kinetic processes were pure single or multiexponentials. All experimental conditions were set so as to allow the use of the methods and techniques of chemical relaxation.24,25,29 Stock Solutions. The ethanol-to-water ratio is given in volume. In purely aqueous media, the solutions of A2 and those of CsCl were prepared in a 50 mM MES (4-morpholineethanesulfonic acid) buffer, the pH of which was adjusted to 7.0 by microinjections of NaOH or HCl. The solubilities of A1 in water and of A2 in ethanol are very poor. Therefore, A1 was first dissolved in pure ethanol (2 × 10-4 M) and then diluted (10-5-10-8 M in the final media). As for A2, it was first dissolved in pure water (2 × 10-4 M) and then diluted (10-5-10-8 M in the final media). Results A1 (calix-COU2) is insoluble in water, whereas A2 (calixCOUSULF) is insoluble in organic media.19,20 This explains why the affinity of the first for Cs+ was reported in ethanol, while that of the second was reported in water.19,20 Kinetic and thermodynamic runs were performed with A1 and A2 in absolute ethanol and in purely aqueous buffer, respectively. On the other hand, since one of our aims is to compare the behavior of the two calixarenes in aqueous and alcoholic media, we also performed kinetic experiments in media very close to water or to alcohol. Thus, A1 and A2 were dissolved in mixtures: H2O/ EtOH 9:1 v:v (medium 1, M1) and H2O/EtOH 1:9 v:v (medium 2, M2). Thermodynamics of Complex Formation between A1, A2, and Cs+. The absorption and emission spectra A1 and A2, as well as those of their cesium complexes were reported in ethanol for A1 and in aqueous buffers for A2.19,20 In M1 (H2O/EtOH 9:1), adding Cs+ to A1 (calix-COU2) leads to a 4 nm hypsochromic shift (from 419 to 415 nm) and to a decrease in the fluorescence emission down to a first plateau at an analytical concentration of Cs+ (c1 ≈ 4.5 × 10-3 M), which is followed by an increase of fluorescence emission up to a second plateau at c1 g 2 × 10-2 M and a 4 nm blue shift (Figure
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Figure 2. Variation of the fluorescence emission with time for λ g 400 nm at λex ) 365 nm after stopped-flow mixing of a solution of A1 (c2 ) 5 × 10-9 M) with a solution of Cs+ (c1 ) 5 × 10-4 M) in ethanol at 25.0 ( 0.5 °C.
Figure 1. Evolution of the emission spectra of calixarenes upon addition of Cs+ at 25.0 ( 0.5 °C: (A) A1 (2.0 × 10-5 M) in M1 (H2O/ EtOH 9:1), λex ) 340 nm; (B) A1 (1.72 × 10-5 M) in M2 (H2O/EtOH 1:9), λex ) 340 nm; (C) A2 (1.72 × 10-6 M) in M2 (H2O/EtOH 1:9), λex ) 365 nm.
1A). A SPECFIT analysis indicates sequential 2 Cs+ complex formation obeying mechanism I (eqs 1 and 2), with log K11A1M1 ) 3.7 ( 0.1 and log K21A1M1 ) 2.0 ( 0.2. K11A1M1 and K21A1M1 are the affinity constants defined for eqs 1 and 2 for A1 in M1. These experiments were performed with the smallest excitation slits and in the shortest lapse of time ( 10-3 M, by a second process which appears as an exponential increase in the fluorescence intensity occurring in the 10-50 s range (Figure 4). The reciprocal relaxation times associated with these two processes seem to be independent of the Cs+ and A1 concentrations. However, their respective amplitudes depend on both c1 and c2, and are in agreement with the variation in the absorption spectra of A1 subsequent to Cs+ addition (Figure 1A). The fact that the reciprocal relaxation times associated with these processes seem to be independent of c1 and c2 suggests that they describe first order kinetic processes, such as conformation changes or tautomerisms.23,24 These processes should, therefore, rate-control complex formation between Cs+ and A1.23 The inclusion of the first Cs+ can be expressed by eqs 7 and 8: k′3
A1 h A1′(slow) ′ k-3
Figure 3. (A) Plot of τ1-1 against c1 for A1 (c2 ) 5 × 10-9 M) in ethanol at 25.0 ( 0.5 °C. Intercept, 6 ( 2 s-1; slope, (4.8 ( 0.2) × 107 M-1 s-1; r ) 0.99653. (B) Plot of τ2-1 against c1 for A1 (c2 ) 5 × 10-9 M) in ethanol at 25.0 ( 0.5 °C. Intercept, 0.13 ( 0.03 s-1; slope, (7.0 ( 0.7) × 102 M-1 s-1; r ) 0.991 86.
(7)
Figure 4. Variation of the fluorescence emission with time for λ g 400 nm at λex ) 365 nm after stopped-flow mixing of a solution of A1 (c2 ) 1 × 10-6 M) with a solution of Cs+ (c1 ) 5 × 10-3 M) in M1 at 25.0 ( 0.5 °C.
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k′1
A1′ + Cs+ h A1Cs+(fast)
(8)
′ k-1
The reciprocal relaxation time equation associated with eq 7, if rate-limiting, is expressed as eq 9:24
τ4-1 ) k'3 + k'-3(1 + [Cs+]K3A1M1)
(9)
with
K3A1M1 ) [A1Cs+]/[A1′][Cs+] ) K1A1M1[A1′]/[A1] In eqs 7 and 8, the thermodynamic product is assumed to be A1Cs+. In this case we can write [A1′] , [A1], [A1Cs+]. This implies that K3A1M1 < K1A1M1. Under our experimental conditions, 1 × 10-6 M e c1 e 2 × 10-6 M and 2 × 10-5 M e c2 ≈ [Cs+] e 5 × 10-4 M, [Cs+]K1A1M1 and, subsequently, [Cs+]K3A1M1 , 1. Therefore, eq 9 can be expressed as eq 10:
τ4-1 ≈ k′3 + k′-3
Figure 5. Variation of the fluorescence emission with time for λ g 400 nm at λex ) 365 nm after a fast (∼10 µs) T-jump, from 20 to about 25 ( 2 °C, performed on a solution of A1 (c2 ) 1 × 10-5 M) in the presence of Cs+ (c1 ) 3 × 10-4 M) and 0.4 M NH4Cl in M1.
(10)
This implies that τ4-1 should be independent of the concentrations of the species present in the medium, which is the case here. The same reasoning can be applied to the second Cs+ inclusion in A1Cs+ (eqs 11 and 12).
A1Cs+ h A1′Cs+(slow)
(11)
A1′Cs+ + Cs+ h A1(Cs+)2(fast)
(12)
Here also the experimental reciprocal relaxation times associated with rate-limiting eq 11 should be independent of c1 and c2. Therefore, the kinetic processes of Figure 4 are ascribed to ratelimiting processes which are a prerequisite to the inclusion of 1 and 2 Cs+ in the complexation cavity of A1 in media close to aqueous, such as M1 (H2O/EtOH 9:1). When a fast T-jump, from 15 to about 25 °C, is performed on solutions of A1 (containing 0.4 M NH4Cl) in the presence of [Cs+], at final equilibrium, a very fast (50 µs to 1 ms) weak but perfectly detectable exponential increase in the fluorescence emission is observed (Figure 5). This process is not detected in the absence of Cs+ and depends on c1. Rate-limiting eq 7 controls A1Cs+ formation when A1 is mixed with Cs+. This insinuates that, when kinetic species A1′ is slowly formed, it reacts very rapidly with Cs+ to yield A1Cs+. Both eqs 7 and 8 are reversible. Therefore, when an extrinsic perturbation, such as a fast T-jump, is performed on an equilibrated solution containing A1, A1′, A1Cs+, and Cs+, in order to attain the new equilibrium conditions at the final temperature, the rearrangement with time of the concentrations of the species present in the medium will first occur according to fast reaction 8 and afterward to slow reaction 7.24,25,27 This was, also, reported for other multistep mechanisms.24,25,27 In this case, the reciprocal relaxation time equation associated with eq 8 is expressed as eq 13:24,25,27
τ5-1 ) k′1([A1′] + [Cs+]) + k′-1
(13)
Figure 6. Plot of τ5-1 against c1 for A1 (c2 ) 1 × 10-5 M) in M1 in the presence of 0.4 M NH4Cl at 25 ( 2 °C. Intercept, (-5 ( 10) × 103 s-1; slope, (3.4 ( 0.8) × 107 M-1 s-1; r ) 0.9806.
The affinity constants (K11 ) 5 × 103 and K21 ) 100) of A1 for Cs+ in M1 imply that under our experimental conditions (c2 ) 1 × 10-5 M and 2 × 10-3 M > c1 > 10-4 M), the thermodynamic products are A1Cs+ and A1, whereas species A1′ is a kinetic intermediate, which should be very slightly present. Therefore, eq 13 can be expressed as eq 14:
τ5-1 ) k′1c1 + k′-1
(14)
A linear least-squares regression of the experimental τ5-1 against c1 is obtained (Figure 6). The fast process of Figure 5 is, therefore, associated with eq 8. k′1 ) (3.4 ( 0.8) × 107 M-1 s-1 is determined from the slope of the best line, while the uncertainty on the intercept is much too high to allow the determination of k′-1. These results bring further evidence in favor of a two-step complex formation between A1 and Cs+: a slow monomolecular process leading to the calix-COU2 intermediate species (eq 7), in which Cs+ is very rapidly included (eq 8). Kinetics of Complex Formation between A2 and Cs+. In an aqueous medium, complex formation between A2 (calixCOUSULF) and cesium leads to an increase in the fluorescence
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Figure 7. Variation of the fluorescence emission with time for λ g 400 nm at λex ) 365 nm after stopped-flow mixing of a solution of A2 (c2 ) 5 × 10-6 M) with a solution of Cs+ (c1 ) 2.5 × 10-4 M) in aqueous buffer (µ ) 5 × 10-2) at pH 7.01 and 25.0 ( 0.5 °C.
Figure 9. Variation of the fluorescence emission with time for λ g 400 nm at λex ) 365 nm after stopped-flow mixing of a solution of A2 with a solution of Cs+ in M2 for (A) c2 ) 2.5 × 10-8 M, c1 ) 3 × 10-8 M, (B) c2 ) 1 × 10-7 M, c1 ) 1 × 10-6 M. Figure 8. Plot of τ1-1 against c1 for A2 (c2 ) 5 × 10-6 M) in aqueous buffer (µ ) 5 × 10-2) at pH 7.01 and 25.0 ( 0.5 °C. Intercept, 11.2 ( 0.6 s-1; slope, (9.7 ( 0.3) × 104 M-1 s-1; r ) 0.998 46.
intensity (λex ) 330 nm for λem > 420 nm).20 When a neutral aqueous buffered solution of A2 is mixed with a similarly neutral solution of Cs+, only a single kinetic process is observed (Figure 7). It is an exponential increase in fluorescence with time, which occurs in the 50-250 ms range and whose rate depends on c1 and c2. The same stopped-flow mixing experiments of A2 with Cs+ were performed in M1 (H2O/EtOH 9:1). A kinetic process similar to that of Figure 7 was observed. In water, a very good linear least-squares regression of the experimental reciprocal relaxation time against eq 4 is obtained (Figure 8). From the intercept and the slope, k1A2water ) (9.7 ( 0.3) × 104 M-1 s-1, k-1A2water ) 11.2 ( 0.6 s-1, and the K11A2water ) (9 ( 1) × 103 are determined. The same applies to complex formation in M1 (not shown) which allowed the determination of k1A2M1 ) (9.5 ( 0.2) × 105 M-1 s-1, k-1A2M1 )11 ( 3 s-1 K11A2M1 ) (9 ( 3) × 104. The same experiments were performed by decreasing the H2O/EtOH ratio to 1:9 (M2). When a solution of A2 in M2 is mixed with Cs+ solution, at least two kinetic processes are observed (Figure 9, A and B). The first (Figure 9A) is an exponential increase in the fluorescence occurring in the 5 to 20 ms range. The second is observed at higher Cs+ concentrations. It occurs as another exponential increase in the fluores-
cence intensity in the 20-100 ms range (Figure 9B). Both processes depend on c1 and c2. If we assume that these two processes are those described in mechanism I, we can write reciprocal relaxation eq 4 for the first complex formation (eq 1, with A ) A2 in M2). A very good linear least-squares regression of the reciprocal relaxation times associated with the first kinetic process (Figure 9A) against eq 4 is obtained (Figure 10A). From the slope and intercept of the best line, k1A2M2 ) (6.3 ( 0.4) × 109 M-1 s-1, k-1A2M2 ) 240 ( 20 s-1, and K11A2M2 ) (2.6 ( 0.4) × 107. Another very good linear least-squares regression of the experimental reciprocal relaxation times associated with the second process (Figure 9B) against eq 6 is obtained (Figure 10B). From the slope and intercept of the best lines, k2A2M2 ) (1.3 ( 0.1) × 108 M-1 s-1, k-2A2M1 ) 15 ( 4 s-1, and K21A2M2 ) (9 ( 3) × 106. Modeling. To investigate the possible metal ion binding sites in the ligands, Density Functional Theory (DFT) calculations were performed with the Becke-3-Lee-Yang-Parr (B3LYP) exchange functional by the means of the Gaussian 03 package.26,30,31 The 6-31G basis set was used for the ligands, whereas the LANL2DZ basis was used for Cs+. No convergence was obtained with A2 and A1 (Scheme 1). Therefore, molecular geometry optimization was performed on
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J. Phys. Chem. B, Vol. 113, No. 43, 2009 14253 SCHEME 3: Optimized Structures of the Calix-MOD and Calix-MODSULF Cs+ Complexes
TABLE 1: Interatomic Distances in the Optimized Structures of the Cesium Complexes of Calix-MOD and Calix-MODSULF distance (Å) bond Cs+-O1 Cs+-O2 Cs+-O3 Cs+-O4 Cs+-O5 Cs+-O6 Cs+-OS1 Cs+-OS2 Figure 10. (A) Plot of τ1-1 against c1 for A2 (c2 ) 2.5 × 10-8 M) in M2 at 25.0 ( 0.5 °C. Intercept, 240 ( 20 s-1; slope, (6.3 ( 0.4) × 109 M-1 s-1; r ) 0.9909. (B) Plot of τ2-1 against c1 for A2 (c2 ) 1 × 10-7 M) in M2 at 25.0 ( 0.5 °C. Intercept, 15 ( 4 s-1; slope, (1.3 ( 0.1) × 108 M-1 s-1; r ) 0.995 92.
SCHEME 2: Optimized Structures of Calix-MOD and Calix-MODSULF
the ligands and Cs+ complexes of two simplified structures containing only one chromophore on one rim in the gas phase (Scheme 2). The attachment of a sulfonate group in the para position of the benzene ring induces important modifications in the overall structure of the calixarene ligand (Scheme 2). Indeed, in CalixMOD, the benzene rings are nearly parallel with a dihedral angle
Calix-MOD Cs complex 3.35 3.19 5.00 3.41 3.08 3.19
+
Calix-MODSULF Cs+ complex 3.36 3.12 3.16 3.31 3.11 3.49 3.21 5.51
of approximately 15°, whereas with Calix-MODSULF, this angle is about 60°. Furthermore, in Calix-MODSULF, the estimated distance between the two sulfur atoms (S1 and S2) is 10.8 Å and the average distances between the oxygens of the two sulfonate group (OS1 and OS2) and those of the coumarin (O1 and O2) is 4.26 Å (Scheme 2). With Calix-MOD, complex formation with Cs+ leads to significant changes in the geometry of the calixarene basket (Scheme 3). Indeed, a restructuring of the crown ether chains along with a conformational change of the benzene rings is manifested by a variation in the dihedral angle, between the opposite rings, which goes from 15° in the ligand to 35° in the complex (Schemes 2 and 3). Moreover, the average distance between Cs+ and the oxygen atoms (O1-O6) ranges from 3.08 to 3.41 Å (Table 1). This value is in good agreement with those reported for the crystallographic structures of similar compounds.15 In the case of the Calix-MODSULF Cs+ complex, the average distance between Cs+ and an oxygen atom is 3.49 Å (Scheme 3). This value is close to that observed for Cs+⊂Calix-MOD (Table 1). However, the optimized structure of Scheme 3 indicates that the average distance between Cs+ and the oxygen atoms of the sulfonate group (OS1 and OS2) is only 3.21 Å (Table 1). Moreover, there is a significant decrease in the distance between the two sulfonate groups upon complex formation (Tables 1 and 2). Discussion In Table 3, we summarize the kinetic and thermodynamic data determined here. Besides A1 in M1, the kinetic runs were performed by the stopped-flow mixing technique which allows
Korovitch et al.
(3.6 ( 0.2) × 102 (1.3 ( 0.1) × 108 (7.0 ( 0.7) × 102 a
EtOH (100%)
M2 (H2O/EtOH 1:9)
Is related to the kinetic determination of the K values. b Is related to their spectrophotometric determination. c This value is that of k′1 (eq 8).
3.79 ( 0.05 2.0 ( 0.2 2.8 ( 0.2 bleaching 3.8 ( 0.1 3.2 ( 0.2 6.9 ( 0.2 3.7 ( 0.4 11.2 ( 0.6 11 ( 3 13 ( 6 240 ( 20 6(2 M1 (H2O/EtOH 9:1)
s )
(9.7 ( 0.3) × 104 (3.4 ( 0.8) × 107c (9.5 ( 0.2) × 105 (4.2 ( 0.3) × 106 (6.3 ( 0.4) × 109 (4.8 ( 0.2) × 107 4.03 ( 0.02 3.7 ( 0.1 4.7 ( 0.1 5.5 ( 0.2 bleaching 6.7 ( 0.1 3.95 ( 0.05 4.9 ( 0.2 5.5 ( 0.5 7.4 ( 0.1 6.9 ( 0.3 A1 calix-COU2 A2 calix-COUSULF A1 calix-COU2 A2 calix-COUSULF A1 calix-COU2 A2 calix-COUSULF A1 calix-COU2 A2 calix-COUSULF H2O (100%)
k2 (M-1 s-1) log K21b k-1 (s )
log K21
a
k1 (M
with Cs+----A, a solvent-separated form; CsA+, a contact form; (CsA)+, the final complex. Apart from the second-order rate constant determined for the first cesium uptake by A2 in M2 (6.3 × 109 M-1 s-1), all the second-order rate constants (k1) associated with eq 1 are several orders of magnitude lower than those expected (Table 3). Does this suggest that complex formation between A and Cs+ does not obey the Eigen-Winkler mechanism II? Or does it imply that one of the monomolecular steps involved in mechanism II (e.g., eqs 16 or 17) is slowed down to become rate-limiting, as with A1 in M1? Equations 7 and 8 depict a mechanism in which Cs+ inclusion is preceded by a slow monomolecular kinetic process yielding the calixarene intermediate A1′ (eqs 7, 11). A monomolecular process usually describes conformation changes or solvation processes, which are usually extremely fast.33 However, some conformation changes involved in rotations of bulky derivatives, in rigid structures, in complex formations with some macrocycles, large siderophores or siderophore-like molecules or reactions involving proteins, peptides, DNA, RNA and others, can be slow to very slow.23,34-37 Calixarenes are assumed quite flexible.38 Nonetheless, when their cavities are capped, such as in the case of mesitylene calix[6]arene, the inclusion of Cs+ occurs in the tens of seconds to the minutes range.8,39 The explanation of this sluggishness was, among other factors, related to the fact that capping rigidifies the overall structure of these calixarenes.8,39 On the other hand, complex formations withCs+ aretoacertainextentconsideredasdiffusion-controlled.3,6,7 With H+, it was shown that an acid-base reaction on a sterically hindered center leads to a nondiffusion-controlled proton transfer with a decrease in the second-order rate constant by about 3-4 orders of magnitude.40 Although the size of Cs+ is very large when compared to that of H+, these orders of decrease in the
log K11
CsA+ h (CsA)+(controlled by ligand rearrangement) (17)
log K11
Cs+----A h CsA+(controlled by cation desolvation) (16)
calixarene
(15)
TABLE 3: Kinetic and Thermodynamic Data Related to Complex Formation between Cs+ and Calixarenes A1 and A2
Cs+ + A h Cs+---A
second kinetic process
to investigate kinetic processes occurring in the 10-3-10 s range.32 The use of such a mixing technique was quite unexpected in our case, because complex formation between a macrocycle (such as a crown ether) and an alkali cation (such as Cs+) is usually an extremely fast process, known to occur in the microsecond to submicrosecond range.6,7,9 This explains the fact that most of the kinetic experiments related to these topics were performed by ultrasonic absorption, or temperature or electric field jumps.6,7 These processes supposedly obey the Eigen and Winkler mechanism that involves cation desolvation and macrocyclic ligand rearrangement. Both steps can be ratelimiting (mechanism II).9 Mechanism II.
solvent
10.13 3.55 3.28
-1
10.80 4.26 4.27
-1
d(S1-S2) d(OS1-O1) d(OS2-O2)
-1
Cs+⊂Calix-MODSULF
b
Calix-MODSULF
first kinetic process
distance/Å
k-2 (s-1)
TABLE 2: Interatomic Distances in Calix-MODSULF and the Cesium Complex of Calix-MODSULF
0.21 ( 0.02 15 ( 4 0.13 ( 0.03 -
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a
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rate constants are similar to those reported here for the Cs+ complex formation with A1 in M1′ (eq 8, k′1 ) 3.4 × 107 M-1 s-1). This can imply a difficulty of access to the inclusion cavity induced by the crown ether capping. Indeed, capping both rims of calixarenes increases the rigidity and, hence, the accessibility of Cs+ to the inclusion cavity.8,39 These criteria (rigid structure, steric effect, slow conformation changes) can, perhaps, clarify the differences in the magnitudes between the rate constants (Table 3) as compared to those reported for cesium complexation with crown ethers or other ligands.6,7,25 We shall, therefore, speculate and assume that the slow processes of eqs 7 and 11 depict changes in the conformation of species A1, before Cs+ inclusion. Furthermore, modeling reveals that the sulfonate moieties in Calix-MODSULF appear to adapt the conformation of the inclusion cavity to Cs+, which is not the case in CalixMOD. Indeed with Cs+ included in the cavities of Calix-MOD and Calix-MODSULF, the geometry optimizations indicate a serious modification in the structure of Calix-MOD and a lesser one in that of Calix-MODSULF (Table 2, Schemes 2 and 3). Although these results were obtained in the gas phase and concern only partial models for A1 and A2, they can cautiously be used to support our purpose, as already reported with other calix crown ether in methanol.5 Hence, with A1 (calix-COU2), the size of the cavity does not seem to be adapted to Cs+. In contrast, the complexation cavity of A2 is better adapted to Cs+. This can explain the fact that in the ethanol/water mixtures, complex formation between A2 (calix-COUSULF) and Cs+ is much faster than that with A1 (calix-COU2). Indeed, the secondorder rate constant, related to these processes, is more than 3 orders of magnitude higher for A2 than for A1. In alcoholic media, the k1 (6.3 × 109 M-1 s-1) value is of the same order of magnitude as those expected for other crown ether ligands.6,25 On the other hand, eqs 7, 8, 11, and 12 depict a mechanism for Cs+ inclusion that involves a monomolecular process prior to complexation with Cs+. In reciprocal relaxation time eq 9, with A1 in M1, the mathematical expression (1 + [Cs+]K3A1M1) ≈ 1. If we presume that this mechanism of inclusion can apply to both A1 and A2, in other media, [Cs+]K3 . 1 when (K1)-1 and (K3)-1 , [Cs+]. In this case eq 9 would be expressed as eq 18:
τ4-1 ) k′3 + k′-3[Cs+]K3
(18)
If k1 is an apparent rate constant (k1 ) k′-3K3), eq 18 becomes similar to eq 3, which we used to propose mechanism I. This may imply that mechanism I does not fully depict complex formation between A and Cs+, which can also explain some of the rather low values of k1 reported in Table 3. The second-order rate constant k1 (mechanism I, eq 1, Table 3) for complex formation between A1, A2, and Cs+ increases with the ethanol/water ratio. Hence, we can assume that Cs+ solvation is involved in the process. This can be the case of A2 (calix-COUSULF), where k1 varies from 9.5 × 105 in M1 to 6.3 × 109 M-1 s-1 in M2 (Table 3). In both A1 and A2, the affinities for Cs+ also increase with the EtOH/H2O ratio (Table 3). This underlines as well the role of the solvent and of Cs+ solvation in complex formation. Furthermore, the number of the kinetic steps observed depends on the nature of the solvent. With A2, a single kinetic step is observed in aqueous and M1, whereas two are observed in the more alcoholic M2 and ethanol (Table 3). This was also reported for alkali metal complexation by 18C6 crown ether in dimethylformamide and ethanol, and was ascribed to the solvating ability toward the cation.9
In A1 and A2, two Cs+ are included (mechanisms I and II).19,20 In a purely aqueous medium and in M1 (H2O/EtOH 9:1), two cesium cations can be present in the cavity of A2. These two complexations occur with small discrepancies in the K values (Table 3),20 which can be related to the statistical occupations of the sites. Indeed, in aqueous media and in M1, only a single kinetic process is observed (Figure 7), whereas a SPECFIT analysis leads in both cases to a double Cs+ inclusion. Furthermore, in aqueous media, the kinetically determined K′11 value for one Cs+ is equal to the average K reported for two Cs+. A2 (calix-COUSULF) is a symmetrical molecule whose inclusion cavity should offer equal opportunities for each Cs+. Nevertheless, in the alcoholic medium M2, two kinetic processes are observed during complex formation between A2 and Cs+ (Figures 9A and 9B). The fastest is ascribed to a first Cs+ inclusion and the slowest to a second one (mechanism I). This occurs despite the symmetry of the cavity of A2. Does this imply that there are two complexation sites? The answer to this question may be that the inclusion of the first Cs+ induces conformational changes, which inhibit that of the second. Bleaching did not allow a spectrophotometric determination the K values for these two inclusions. Indeed, the spectrophotometric determination of the K values is much too long as compared to a kinetic run which lasts less than a second, during which bleaching is negligible. With A1 (calix-COU2), the case is quite different. Although, the complexation cavity is also symmetrical, the important differences in the K values between the first and second Cs+ inclusions can no longer be justified by the statistical occupation of the sites. Therefore, in alcoholic media the first cesium inclusion to a certain extent inhibits a second one, which confirms the already reported anticooperative behavior.19 This effect can be explained by the electrostatic repulsion between the two cations. In A2 this electrostatic repulsion does not exist, because of the shielding effect of the sulfonate groups.19,20 Moreover, the cavity of calix[4]arene is considered hydrophobic.41 Thus the negative sulfonate groups seem to play an important role in complex formation with Cs+ by facilitating the approach of the cation. Indeed, the position of Cs+ is well centered in the inclusion cavity of the sulfonated species, as recently confirmed by an 13C NMR analysis with the Cs+ complex of calix[4]arene sulfonate.41 Furthermore, the presence of the sulfonates in A2 increases the K values in each of the solvents used. This also confirms the involvement of the sulfonate in complexation, as predicted by the modeling of Calix-MOD and Calix-MODSULF (Table 2, Schemes 2 and 3). Conclusion In this article, we propose a mechanism for Cs+ inclusion in capped calixarenes. With calix-COU2, we show that this inclusion is preceded by a slow monomolecular process and involves second-order formation rate constant which can be of several orders of magnitude lower that those reported for crown ethers. This is related, among others, to the necessity of the rigid calixarene cavity, to adapt its size and conformation to allow the inclusion of the large Cs+ alkali cation. With calixCOUSULF, when the calixarene cavity is more adapted to the inclusion of Cs+, the change in its size and conformation becomes less critical. Thus, the inclusion process is not preceded by the monomolecular process and the rate of complex formation with Cs+ tends toward those reported for other ligands. These results can be of interest in the search for new efficient cesium ligands and decontaminants.
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