15014
J. Phys. Chem. B 2008, 112, 15014–15020
NMR Study of the Reversible Trapping of SF6 by Cucurbit[6]uril in Aqueous Solution Luca Fusaro,†,‡ Emanuela Locci,† Adolfo Lai,† and Michel Luhmer*,‡ Dipartimento di Scienze Chimiche, UniVersita` di Cagliari, Cittadella UniVersitaria di Monserrato, S.S. 554 BiVio per Sestu, 09042 Monserrato (CA), Italy, and Laboratoire de RMN haute re´solution CP 160/08, UniVersite´ Libre de Bruxelles, 50 AV. F.-D. RooseVelt, 1050 Brussels, Belgium ReceiVed: July 28, 2008; ReVised Manuscript ReceiVed: September 10, 2008
The complexation of sulfur hexafluoride (SF6), a highly potent greenhouse gas, by cucurbit[6]uril (CB) was studied at various temperatures in Na2SO4 aqueous solutions by 19F and 1H NMR. CB shows a remarkable affinity for SF6, suggesting that it is a suitable molecular container for the design of materials tailored for SF6 trapping. At 298 K, the equilibrium constant characterizing the inclusion of SF6 by CB is 3.1 × 104 M-1 and the residence time of SF6 within the CB cavity is estimated to be of the order of a few seconds. The enthalpic and entropic contributions to the free energy of encapsulation were determined and are discussed. This work also reports on the interest of SF6 in the framework of the spin-spy methodology. The advantages and drawbacks of solution-state 19F NMR of SF6 with respect to 129Xe NMR are discussed. SF6 comes forward as a versatile and informative spin-spy molecule for probing systems in solution because its detection limit by 19F NMR reaches the micromolar range with standard equipment and because quantitative integral measurements, relaxation time measurements, and demanding experiments, such as translational diffusion coefficient measurements, are easily carried out in addition to chemical shift measurements. Solution-state 19F NMR of SF6 emerges as a promising alternative to 129Xe NMR for probing cavities and for other applications relying on the encapsulation of an NMR active gaseous probe. Introduction Molecular recognition of gases is an emerging area of chemistry that has multiple applications such as gas sensing, gas storage, gas purification, gas conversion, and biosensors.1 Synthetic receptors comprise notably a variety of metalloporphyrins, which mimic natural systems, and molecular containers capable of gas encapsulation. Gas encapsulation within organic cavities was demonstrated for a variety of systems in solution and/or in the solid state. R-Cyclodextrin, cryptophane-A, cucurbit[6]uril, homologues or analogs of these cavitands, and various other molecular containers were shown to trap a large variety of gases.1 Multiple works report on the trapping of xenon gas as studied by 129Xe NMR.2-8 An innovative application of the ability of cryptophane-A to encapsulate xenon is the development of 129Xe NMR biosensors by Pines and co-workers.9,10 Such biosensors consist of a specific recognition pattern chemically attached to a molecular container capable of gas trapping. The binding to the target, typically a protein, is detected by the observation of a new NMR signal for the encapsulated gas. Cucurbit[6]uril (CB) is a macrocyclic methylene-bridged glycoluril hexamer (Figure 1).11 It is a cavitand with a hollow core of approximately 5.8 Å diameter.12 The cavity is accessible from the exterior through two carbonyl-fringed portals of 3.9 Å diameter that may produce significant steric barriers to guest inclusion and release. The portals are cation-binding regions, while the cavity is a hydrophobic binding region. CB is essentially insoluble in pure water and in common organic solvents, but it is soluble in the range of 10-2 M in strongly acidic aqueous solutions and also in neutral saline aqueous * Corresponding author. Phone: +32 2 650 6637. Fax: +32 2 650 6642. E-mail:
[email protected]. † Universita ` di Cagliari. ‡ Universite ´ Libre de Bruxelles.
Figure 1. Structure of cucurbit[6]uril (CB).
solutions. CB shows exceptional affinity toward aliphatic and aromatic ammonium ions. Association constants of the order of 108 M-1 were reported for the formation of 1:1 complexes with n-alkyl diammonium ions.13,14 CB also forms 1:1 inclusion complexes with neutral molecules, but the corresponding association constants are much smaller; they are typically of the order of 102-103 M-1.11 Very few studies report on the trapping of gases by CB.15 Crystalline CB, synthesized using concentrated HCl instead of H2SO4, was recently shown to exhibit remarkable sorption properties toward acetylene.16 X-ray analysis revealed acetylene molecules in 1D supramolecular channels but not in the molecular cavity of CB. The trapping of xenon was investigated in solution by 129Xe and 1H NMR; in 0.2 M Na2SO4 aqueous solution, the inclusion constant of xenon by CB was found to be of the order of 2 × 102 M-1 at 298 K.7,8 Recently, the trapping of xenon by a CB derivative was studied by isothermal titration calorimetry and by hyperpolarized 129Xe NMR.17 In 0.2 M Na2SO4 aqueous solution,
10.1021/jp806685z CCC: $40.75 2008 American Chemical Society Published on Web 10/29/2008
Reversible Trapping of SF6 by Cucurbit[6]uril the binding constant for the complexation of xenon was determined to be 180 M-1 at 295 K. In pure water, the inclusion constant is of the order of 103 M-1 and the complexation of xenon is driven to a similar extent by both enthalpy and entropy. It was suggested that this CB derivative may serve as an effective molecular “carrier” for 129Xe NMR-based biosensors. The chemical shift of monatomic 129Xe (I ) 1/2) is very sensitive to intermolecular interactions, and therefore, 129Xe is used as a spy reporting on the structural and dynamic properties of its local environment.18-24 However, signal broadening due to chemical exchange, long 129Xe longitudinal relaxation times (typically of the order of 101-102 s in solution), and the rather low NMR receptivity of 129Xe (5.7 × 10-3 with respect to 1H) are responsible for long measurement times and poor signalto-noise ratios, prevent quantitative interpretation of the signal integrals, and drastically restrict the range of feasible NMR experiments. Obviously, these are serious drawbacks that may limit the scope of applicability of thermally polarized 129Xe NMR. Using hyperpolarized 129Xe, signal-to-noise ratios may be increased by 4-5 orders of magnitude, offering new possibilities, notably for the characterization of biological systems.9,22-30 Xenon biosensors also rely on the use of hyperpolarized 129Xe that allows one to readily detect analyte concentrations of the order of 10 µM.30 Hyperpolarized 129Xe NMR requires optical-pumping equipment for 129Xe polarization. In addition, the transient nature of the 129Xe hyperpolarization imposes additional experimental constraints (in order to bring fresh hyperpolarized gas into the sample, for instance) and may restrict the range of feasible NMR experiments. Sulfur hexafluoride (SF6) is a nontoxic, colorless, odorless, and chemically inert gas with high dielectric strength and high thermal stability that is used primarily in electrical applications and metal casting processes. SF6 is hydrophobic; its solubility in water (2.2 × 10-4 M at 298 K and 1 atm)31 is 1 order of magnitude lower than the corresponding value for xenon (4.4 × 10-3 M).32 The SF6 molecule has an octahedral geometry and is somewhat larger than a xenon atom (diameters of 5.3 and 4.2 Å, respectively).33 The chemical shift of 19F ranges over hundreds of ppm. Recently, 19F gas-to-solution shifts of SF6 were determined by Jackowski et al. and compared to the corresponding values for 129Xe.34 Both nuclei experience deshielding on gas dissolution. A very good correlation was found between the 129Xe and 19F data, and it was concluded that the same mechanism operates for both nuclei. Accordingly, 19F gas-to-solution shifts of SF are primarily due to both 6 dispersive and repulsive van der Waals interactions with solvent molecules. The observed range of solvent effects is about 8 ppm on the 19F chemical shift of SF6 and 250 ppm on the 129Xe chemical shift. Reported values of the 19F longitudinal relaxation time of gaseous SF6 range between a few milliseconds and hundreds of milliseconds;35,36 it is orders of magnitude shorter that the 129Xe longitudinal relaxation time. In both the gas and the pure liquid phases, the 19F longitudinal relaxation of SF6 is dominated by the spin-rotation mechanism.37,33 19F NMR of gaseous SF6 has deserved much attention38-40 and remains a subject of investigations, notably because applications for lung imaging are being developed.36,41 D. O. Kuethe has pioneered the technique of void space imaging using highly fluorinated inert gases in lieu of noble gases; short 19F longitudinal relaxation time, high 19F NMR receptivity, and the presence of multiple equivalent 19F nuclei were highlighted as major advantages.42,43 19F NMR spectroscopy studies of SF6 in condensed phases are rather rare. A few works deal with 19F NMR of SF6 in the pure liquid phase,37 in simple solvents,44,34
J. Phys. Chem. B, Vol. 112, No. 47, 2008 15015 and for probing zeolites,45-47 Vycor glass,48 polymers,49,50 liquid crystals,51,52 and clathrate hydrates.53-57 To the best of our knowledge, solution-state 19F NMR studies on the encapsulation of SF6 within organic cavities have never been reported apart from our works in communications at congresses.58,59 The goal of the present study is 2-fold. On the one hand, SF6 is identified as a highly potent greenhouse gas that contributes to climate change and was designated in 1997 as one of the gases to be regulated.60 Emissions of SF6 are by far smaller than CO2 emissions, but SF6 is extremely long-lived in the atmosphere. Therefore, the present study is aimed at contributing to the selection of a molecular container suitable for the design of materials tailored for SF6 trapping. On the other hand, 19F possesses a high NMR receptivity, 0.83 with respect to 1H, 2 orders of magnitude larger than 129Xe. SF6 possesses six chemically equivalent 19F nuclei and the longitudinal relaxation time is much shorter than that for 129Xe. Consequently, for thermal equilibrium polarizations and identical line widths, the detection limit of SF6 by 19F NMR is expected to be at least 3 orders of magnitude lower than the detection limit of natural abundance xenon by 129Xe NMR. Therefore, the present study is also aimed at contributing to the investigation of the advantages and drawbacks of solution-state 19F NMR of SF6 as an alternative to 129Xe NMR, notably for probing cavities and for other applications relying on the encapsulation of an NMR active gaseous probe. Experimental Methods SF6 gas (99,97%) was purchased from Air Liquide. D2O (99.98%) and Na2SO4 were purchased from Sigma-Aldrich. CB was synthesized according to procedures described elsewhere.61 CB solutions of known concentration were prepared using 0.2 M Na2SO4-D2O as solvent. The samples, approximately 0.6 mL of CB solution in 5 mm J. Young valve tubes (Wilmad 528-JY-7), were degassed by three cycles of evacuation and sonication in an ultrasound bath. Up to approximately 1.2 atm of SF6 gas were loaded at room temperature using a vacuum line equipped with a mercury manometer. The tube was then shaken, inserted into the magnet, and left to reach equilibrium at the desired temperature for at least 30 min. 1H and 19F NMR spectra were recorded at 9.40 T on a Varian VNMRSystem 400 spectrometer (399.917 MHz for 1H and 376.318 MHz for 19F, respectively) equipped with temperature regulation and an Automated Triple Broadband probe simultaneously tuned to 1H and 19F. 1H NMR spectra were recorded using a 12.2 µs pulse (90°), 3.0 s acquisition time, 2.0 s relaxation delay, a spectral width of 16 ppm centered at 5.0 ppm, and 128 scans for the more diluted samples (1.0 × 10-4 M in CB). The signal of HDO was used for 1H chemical shift referencing (4.80 ppm at 298 K). 19F NMR spectra were recorded using a 13.0 µs pulse (90°), 2.0 s acquisition time, 3.5 s relaxation delay, and, typically, 128 scans and a spectral width of 30 ppm. A sample of SF6 dissolved in the solvent (1 atm) was used as a secondary 19F chemical shift reference. At 298 K, the signal of 32SF6 in the solvent was measured to be +59.362 ppm with respect to pure liquid CFCl3 (external reference in a coaxial capillary tube). Variable temperature chemical shift measurements were performed unlocked, on a single day, at constant Z0 field; the number of scans was reduced to 16. 19F spin-lattice relaxation times were measured using the inversion-recovery pulse sequence, 17 recovery delays ranging between 0.1 and 5 s, a 5.5 s repetition time, and 4 scans. For both 1H and 19F NMR measurements, the processing included exponential multiplication of the free induction decay
15016 J. Phys. Chem. B, Vol. 112, No. 47, 2008
Figure 2. 19F NMR spectra of SF6 (1 atm, 298 K) dissolved in (a) the solvent (0.2 M Na2SO4 in D2O), (b) a 1.0 × 10-4 M CB solution, and (c) a 1.0 × 10-2 M CB solution. In spectrum a, the chemical shift of the signal of 32SF6 in the solvent (32SF6 solv) is set to 0 ppm; it was measured to be +59.362 ppm with respect to pure liquid CFCl3. The full line width at half-height of the signal of 32SF6 solv is 1.5 Hz including broadening due to exponential multiplication of the free induction decay (lb ) 0.3 Hz). The vertical scale of the dotted spectrum is increased 10-fold times; the concentration of 34SF6 solv is about 10 µM. In spectrum b, the subscripts “in” and “out” are used to distinguish SF6 included in the CB cavity and SF6 free in solution, respectively. The symbol × indicates the signal of 34SF6 out. The full line widths at half-height are 1.3 Hz for the signal of 32SF6 out and 1.8 Hz for the signal of 32SF6 in (lb ) 0.3 Hz). In spectrum c, the symbol / indicates the signal of 34SF6 in and the vertical scale of the dotted spectrum is reduced 30-fold times. The full line widths at half-height are 8.5 Hz for the signal of 32SF6 out and 1.6 Hz for the signal of 32SF6 in (lb ) 0.3 Hz). Each of these spectra was recorded at 9.4 T using 128 transients in about 12 min measurement time.
with a line broadening factor of 0.3 Hz and two levels of zerofilling prior to Fourier transform. T1 data were determined using integrated intensities and a three-parameter nonlinear fit; reported confidence intervals correspond to twice the fitting errors. Results and Discussion 19F NMR spectra of SF dissolved in CB solutions and in 6 the solvent (0.2 M Na2SO4 in D2O) are shown in Figure 2 (298 K, about 1 atm of SF6). In the solvent, two singlets with relative integrated intensities in the ratio 100:4.4 are readily observed (Figure 2a): the intense signal corresponds to 32SF6 (95.06% natural abundance, chemical shift set to 0.000 ppm), while the weak singlet arises from the species 34SF6 (4.18%, -0.052 ppm with respect to 32SF6).62 Considering that the solubility of SF6 in the solvent is similar to the solubility in pure water (2.2 × 10-4 M at 298 K and 1 atm),31 the concentration of 34SF6 that is observed in the spectrum of Figure 2a is estimated to be about 10 µM. Consequently, it can be stated that the detection limit of SF6 by 19F NMR at 9.4 T using a 5 mm probe lies in the micromolar range for measurement times of a few minutes. In the presence of 1.0 × 10-4 M of CB, an additional singlet is observed at -0.070 ppm (Figure 2b). As the amount of CB in solution is increased, the intensity of this signal also increases and a weaker singlet can be observed at -0.122 ppm (i.e., 0.052 ppm highfield from the signal at -0.070 ppm; Figure 2c). The ratio between the total integrated area of the 19F signals observed in the presence of 1.0 × 10-2 M of CB and in the solvent is about 38:1. These observations (i) highlight the encapsulation of dissolved SF6 by CB, (ii) indicate that the residence time of SF6 in the CB cavity is long, since the kinetics of exchange between SF6 free in solution (SF6 out) and SF6 included in the CB cavity (SF6 in) is slow on the 19F NMR spectral time-scale despite the small difference in resonance frequency (0.070 ppm ) 28 Hz at 9.4 T), and (iii) suggest that the inclusion constant is large.
Fusaro et al.
Figure 3. 1H NMR spectra of a 1.0 × 10-2 M solution of CB in 0.2 M Na2SO4-D2O at 298 K: (a) degassed solution and (b) under 1 atm of SF6. In part b, the signals of the CB-SF6 complex are indicated by filled circles (b) and those of CB that does not contain a SF6 molecule by empty circles (O).
The inclusion of xenon into the cavity of CB induces a 129Xe shielding of about 68 ppm with respect to the chemical shift in the solvent (0.2 M Na2SO4 in D2O; 298 K).8 Gas-to-solution shift measurements suggest that the magnitude of medium effects on the 19F chemical shift of SF6 is approximately 30 times weaker than on the 129Xe chemical shift.34 Accordingly, a 19F shielding of the order of 2 ppm might have been expected upon inclusion of SF6 in CB. The observed shielding is only 0.070 ppm at 298 K (0.2 M Na2SO4 in D2O). As a matter of fact, the correlation between medium effects on the chemical shift of monatomic 129Xe and on the 19F chemical shift of SF6, as evidenced by Jackowski et al.34 via gas-to-solution shift measurements in simple solvents, is not applicable to the shielding associated with the encapsulation by CB in aqueous solution. If medium effects on the chemical shift of both nuclei are originating from van der Waals interactions, as concluded by Jackowski et al.,34 the discrepancy between the predicted and measured 19F inclusion shift might arise from the balance between the contribution of dispersive and repulsive interactions. Indeed, a SF6 molecule is somewhat larger than a xenon atom and in a confined space, such as the cavity of CB, repulsive van der Waals interactions might be responsible for an enhanced deshielding contribution to the 19F chemical shift of SF6. However, it must be pointed out that water does not belong to the series of solvents investigated by Jackowski et al.34 and that models describing solvent shifts due to van der Waals interactions fail to account for the 129Xe chemical shift in water.63 The failure of the gas-to-solution shift correlation to predict inclusion shifts might thus be restricted to aqueous solutions. 19F longitudinal relaxation time (T ) measurements were 1 carried out at 9.4 T and 298 K for SF6 dissolved to saturation (1 atm) in the solvent and in a 1.0 × 10-4 M solution of CB. The longitudinal relaxation time measured for SF6 out, T1 out ) (0.99 ( 0.02) s, is not significantly different from the value measured in the solvent.64 However, the value determined for SF6 in, T1 in ) (0.46 ( 0.02) s, is significantly smaller. At 298 K, the kinetics of exchange is thus slow on the 19F longitudinal relaxation time scale also. The 1H NMR spectrum of a degassed 1.0 × 10-2 M CB solution and the corresponding spectrum in the presence of SF6 (298 K, about 1 atm) are shown in Figure 3. Additional narrow signals are observed in the presence of SF6, indicating infinitely slow exchange kinetics on the corresponding 1H NMR spectral time scale (298 K, 9.4 T). The encapsulation of SF6 induces a highfield shift of about 0.04 ppm (15 Hz) for both Hb and Hc, but the chemical shift of Ha is not affected. This contrasts with the encapsulation of xenon by CB for which infinitely fast
Reversible Trapping of SF6 by Cucurbit[6]uril
J. Phys. Chem. B, Vol. 112, No. 47, 2008 15017
exchange conditions were observed on the 1H spectral time scale (298 K, 8.5 T) and for which the chemical shift of all of the CB signals were affected (extrapolated induced highfield shift at 298 K: 0.08, 0.04, and 0.02 ppm for Ha, Hb, and Hc, respectively).8 Considering the size of the SF6 molecule and the diameter of the CB cavity, a 1:1 stoechiometry of encapsulation can be assumed. The equilibrium can be written as ki
SF6 out + CB0 y\z SF6 in
(1)
ke
where ki and ke are the kinetic constants associated with the inclusion and escape of SF6, respectively, and where CB0 stands for CB that does not contain a SF6 molecule.65 The corresponding equilibrium constant, Keq, is defined by eq 2, where [SF6 in] is equal to the molar concentration of the inclusion complex, since a 1:1 stoechiometry is assumed. The residence time of SF6 within the cavity of CB, τin, and the residence time of SF6 free in solution, τout, are defined by eq 3, where ∆ν1/2 in, ∆ν1/2 out, and ∆ν1/2 S are the line widths measured for SF6 in, SF6 out, and SF6 in the solvent, respectively (see the Supporting Information).
[SF6 in] ki ) [SF6 out][CB0] ke
(2)
1 1 ≈ ke π(∆ν1/2 in - ∆ν1/2 S)
(3a)
1 1 ≈ ki[CB0] π(∆ν1/2 out - ∆ν1/2 S)
(3b)
Keq )
τin )
τout )
Keq was calculated from eq 4, which is obtained by multiplying both sides of eq 2 by [CB], i.e., by the total molar concentration of CB in solution. The mole fraction of CB that does not contain a SF6 molecule, x0, was determined from the 1H NMR spectrum using the integral of the Hc singlet signals. The mole ratio of included and free SF6 was obtained from integration of the 19F NMR signals of 32SF6.
Keq[CB] )
[CB0] 1 [SF6 in] with x0 ) x0 [SF6 out] [CB]
(4)
From spectra recorded at 298 K and [CB] ) 1.0 × 10-4 M, Keq is determined to be 3.1 × 104 M-1 with a relative error on the order of 5% (see the Supporting Information). It is 2 orders of magnitude larger than the xenon inclusion constant measured at 298 K in the same solvent (about 2 × 102 M-1).7,8 Actually, to the best of our knowledge, it is the largest value ever found for the inclusion of a neutral guest into the CB cavity. In diluted solutions of CB, ∆ν1/2 out is not significantly different from ∆ν1/2 S, but it increases with the CB concentration (see Figure 2). This broadening is the consequence of the shortening of τout as the equilibrium concentration of CB available for encapsulation, [CB0], increases (see eq 3b). ∆ν1/2 in is independent of the CB concentration, and it is not significantly different from ∆ν1/2 S, indicating that τin is long (see eq 3a); it is at least longer than T1 in, since the exchange is slow on the 19F longitudinal relaxation time scale. Line
widths are independent of the SF6 pressure (not shown),66 indicating that, in contrast with the inclusion of xenon,8 the degenerate exchange mechanism is not operating and τin can be estimated using eq 5 (see the Supporting Information). From the spectra recorded at 298 K and [CB] ) 1.0 × 10-2 M (Figure 2c, ∆ν1/2 out ) 8.5 Hz, and Figure 3b, x0 ) 0.23), using Keq ) 3.1 × 104 M-1 and ∆ν1/2 S ) 1.5 Hz, τin is found to be about 3 s. It is 3 orders of magnitude longer than the residence time of xenon within the cavity of CB. Indeed, 129Xe line widths of hundreds of Hz were observed for the signal of Xein and this corresponds to a residence time in the millisecond range.8
τin ) Keq[CB]
x0 π(∆ν1/2 out - ∆ν1/2 S)
(5)
The NMR characterization of the inclusion of SF6 by CB is by far less demanding than the NMR characterization of the xenon inclusion, because slow exchange conditions prevail in the 1H spectrum, but also because the extremely low detection limit of SF6 by 19F NMR, the absence of severe signal broadening, and the 19F longitudinal relaxation time of SF6 permit precise and exact integral measurements. This gives the opportunity to investigate the encapsulation of SF6 at various temperatures. NMR spectra were recorded for three samples of a 1.0 × 10-4 M solution of CB in 0.2 M Na2SO4-D2O at different SF6 loadings (0.5, 1.0, and 1.2 atm at 298 K), for one sample of a 1.0 × 10-2 M solution of CB at a single SF6 loading (about 1 atm at 298 K), as well as for one sample of SF6 dissolved in the solvent (about 1 atm at 298 K). In the whole investigated temperature range, 278-358 K, the exchange between SF6 out and SF6 in is slow on both the 19F and 1H spectral time scales, as well as on the 19F longitudinal relaxation time scale.67 Weak signal broadening was observed upon temperature increase, but ∆ν1/2 in did not exceed about 5 Hz including broadening due to instrumental and sample imperfections (see the Supporting Information). For SF6 free in the solvent, as well as for SF6 encapsulated in the cavity of CB, the 19F longitudinal relaxation rate increases with temperature, indicating that the spin-rotation mechanism prevails in both environments and, consequently, that SF6 undergoes facile rotational motion within the cavity (see Supporting Information Figure S1). At 318 K, the signals of 32SF6 out and 32SF6 in are superimposed but they are distinct again at higher temperatures and were assigned by DOSY (diffusion ordered spectroscopy; see the Supporting Information). The 19F chemical shift of SF6 out (δout) increases with temperature, and the variation is linear within the investigated temperature range (see Figure 4). This contrasts with the 129Xe chemical shift of free xenon dissolved in nonaqueous media, which typically decreases with temperature,6,68 as well as with the 129Xe chemical shift in water that slightly increases up to about 318 K and decreases at higher temperatures.22 Opposite temperature dependences are observed in the pure gas phase also.38 The screening constant of an isolated 129Xe atom is temperature independent, as a consequence of the absence of vibrational and rotational degrees of freedom, while the 19F screening constant of an isolated SF6 molecule varies with temperature and this intrinsic dependence corresponds to a downfield shift for increasing temperatures.38 However, for both xenon and SF6 in the gas phase, pair interactions are responsible for highfield shifts with increasing temperatures. On the whole,
15018 J. Phys. Chem. B, Vol. 112, No. 47, 2008
Figure 4. Temperature variation of the 19F chemical shift of 32SF6 measured in a 1.0 × 10-4 M solution of CB (δin and δout, about 1 atm of SF6, 0.2 M Na2SO4-D2O) and temperature variation of the 19F chemical shift of gaseous 32SF6 extrapolated to zero pressure (δ°gas, from ref 38). The value measured at 298 K for 32SF6 out was set to zero, and for 32SF6 gas, the interpolated value at 298 K was set to the value measured at 298 K for 32SF6 in.
Fusaro et al. similar to the temperature dependence of the screening constant of an isolated SF6 molecule (see Figure 4). The temperature dependence of δout is weaker, and by analogy to the situation in the gas phase, this is likely to be the consequence of the temperature dependence of the contribution due to intermolecular interactions. As indicated by the decrease of Keq with increasing temperatures, the overall SF6 encapsulation process is exothermic (see inset of Figure 5). The semilogarithmic representation of Keq as a function of the inverse temperature (1000/T), which is equivalent to a van’t Hoff plot, clearly exhibits curvature over its 80° temperature range (Figure 5). Nonlinear van’t Hoff plots are commonly obtained for wide temperature ranges, and this is typically interpreted as arising from the fact that the enthalpy (∆H°) and entropy (∆S°) changes of the process are not temperature-invariant.72 The relevant equations are
(
Keq ) exp -
∆G° RT
)
∆G° ) ∆H° - T∆S°
(6b)
∆H° ) ∆H◦ref + (T - Tref)∆C◦p
(6c)
∆S° ) ∆S◦ref + ∆C◦p ln
Figure 5. Semilogarithmic representation of the equilibrium constant characterizing the inclusion of SF6 by CB (Keq) in 0.2 M Na2SO4-D2O solutions as a function of the inverse temperature. The inset shows the decrease of Keq with temperature. [CB] ) 1.0 × 10-4 M; (0) 1.2, (]) 1.0, and (b) 0.5 atm of SF6 at 298 K. The confidence intervals correspond to a relative error of 5%. The plain and dotted lines are the best fit curves following eq 6 with ∆C°p ) -0.5 and ∆C°p ) 0 kJ mol-1 K-1, respectively (see the Supporting Information).
the chemical shift of gaseous 129Xe decreases with temperature while the 19F chemical shift of gaseous SF6 increases with temperature. The 19F chemical shift of SF6 in (δin) also increases with temperature (downfield shift), and its variation is slightly nonlinear (see Figure 4). This is analogous to the 129Xe chemical shift temperature dependence observed for xenon in confined spaces, such as the cavity of cryptophane-A or in zeolite NaA at high xenon loading.6,69-71 For 129Xe, such a temperature dependence is the signature of the contribution of repulsive van der Waals interactions to the screening constant. This cannot be stated for the 19F chemical shift of SF6, since the intrinsic temperature dependence of the screening constant corresponds to a downfield shift for increasing temperatures. Actually, for SF6 in the CB cavity, this intrinsic temperature dependence is dominating. Indeed, the temperature dependence of δin is highly
(6a)
T Tref
(6d)
where ∆Cp° is the heat capacity change, which is assumed to be temperature-independent, Tref is an arbitrarily selected reference temperature (chosen as 298 K), and where the subscript ref indicates that the thermodynamic property is calculated at Tref. ∆H°ref, ∆S°ref, and ∆C°p were the three varied parameters in the best fit analysis of the experimental Keq data: ∆Href ° ) -(13 ( 1) kJ mol-1, ∆Sref ° ) +(43 ( 3) J mol-1 K-1, and ∆Cp° ) -(0.49 ( 0.06) kJ mol-1 K-1; the corresponding Keq value at 298 K is (3.16 ( 0.07) 104 L mol-1 (see the Supporting Information for error estimations). ∆Cp° associated with the encapsulation of SF6 by CB in 0.2 M Na2SO4-D2O solutions is found to be negative and is of the same order of magnitude as the values reported in the literature for the complexation of a variety of guests by cyclophane hosts in aqueous media.72 Actually, negative ∆Cp° values of a few hundreds of J mol-1 K-1 are typical of the binding of small organic molecules in water,72,73 while positive ∆Cp° values of this order of magnitude are typical of the dissolution of a nonpolar solute in water.74 At 298 K, the negative ∆G°, -(25.67 ( 0.05) kJ mol-1, arises from favorable enthalpic and entropic contributions that are equal in magnitude (see Figure 6). At lower temperatures, the entropic contribution is dominant and the encapsulation of SF6 is almost entirely entropically driven at 278 K. Conversely, the enthalpic contribution prevails above 298 K and the process is totally enthalpically driven for temperatures higher than about 325 K. Such a reversal of the balance between the enthalpic and entropic contributions is the direct consequence of the large negative ∆Cp°. This and the large positive ∆S° at room temperature are consistent with the classical view of hydrophobic association.74 In the framework of the “iceberg” model,75 the favorable ∆S° at room temperature is interpreted as originating from the release of “ordered” water molecules from the first solvation shell of nonpolar solutes to the bulk. This certainly applies to SF6 but also concerns the hydration of the
Reversible Trapping of SF6 by Cucurbit[6]uril
Figure 6. Temperature variation of the enthalpic (∆H°) and entropic (-T∆S°) contributions to the free energy (∆G°) of encapsulation of SF6 by CB in 0.2 M Na2SO4-D2O. For ∆G°, estimated confidence intervals are smaller than the size of the symbols (see the Supporting Information).
hydrophobic CB cavity.65 The entropic cost of bringing SF6 and CB together as one supramolecular assembly is expected to be overcompensated by the concomitant release of more than one water molecule. In addition, the entropic cost of encapsulation is limited by the fact that the CB cavity is a preorganized binding site and because SF6 is a quasi-spherical molecule that maintains facile rotational motion within the cavity. ∆H° is negative over the whole investigated temperature range (see Figure 6). It becomes more favorable as the temperature increases, while ∆S° becomes less favorable. This is consistent with the predictions of an iceberg-like model for the hydration of nonpolar solutes according to which first-shell hydrogen bonds in cold liquid water have lower enthalpy and lower entropy than bulk hydrogen bonds while, in warm water, the first-shell hydrogen bonds are more broken, having higher enthalpy and higher entropy than in the bulk.74 However, the overall enthalpy change of a host-guest association process depends on solvent-solvent, host-solvent, guest-solvent, and host-guest interactions in an intricate way. In addition to hydrogen bonds between water molecules, omnipresent van der Waals interactions certainly play a role, notably between CB and encapsulated SF6. Indeed, both in water and in nonpolar solvents, host-guest association processes involving neutral species are usually characterized by negative ∆H° values that are generally explained as originating from host-guest dispersive van der Waals interactions.76 The SF6 molecule possesses an electric hexadecapole moment and favorable electrostatic interactions between the fluorine atoms, which carry a negative charge density, and the carbon atoms of the carbonyl functions might also come into play. In these regards, the good size matching between SF6 and the CB cavity must be pointed out. Indeed, the ratio between the volume of a SF6 molecule (78 Å3, as calculated using a diameter of 5.3 Å) and the volume of the CB cavity (164 Å3),33 i.e., the packing coefficient, is 0.4877 and it has been shown that the best binding via encapsulation is reached when the packing coefficient is in the range 0.55 ( 0.09.78 Conclusions Cucurbit[6]uril (CB) shows a remarkable affinity for SF6. In 0.2 M Na2SO4 aqueous solution, the inclusion constant is 3.1
J. Phys. Chem. B, Vol. 112, No. 47, 2008 15019 × 104 M-1 at 298 K. To the best of our knowledge, it is the largest value ever found for the inclusion of a neutral guest into the CB cavity. At 298 K, the encapsulation process is driven by enthalpic and entropic contributions that are equal in magnitude. Hydrophobicity plays an important role in the complex formation. However, good size matching between SF6 and the CB cavity is an essential characteristic that translates into favorable host-guest interactions while the rigidity of the CB structure and the symmetry of SF6 are expected to limit the entropic cost for encapsulation. SF6 is identified as a highly potent greenhouse gas that contributes to climate change, and it is extremely long-lived in the atmosphere. CB is easily synthesized from inexpensive starting materials and facile direct perhydroxylation permits further cucurbituril chemistry.79 CB is thus a suitable molecular container for the design of materials tailored for SF6 trapping. The 19F chemical shift of SF6 is by far less sensitive to the local environment than the 129Xe chemical shift. However, highprecision chemical shift measurements are easily achieved in solution and chemical shift variations of the order of 10-2 ppm can be exploited. In contrast with the NMR of thermally polarized 129Xe, which primarily deals with chemical shift measurements, solution-state 19F NMR of SF6 allows quantitative integral measurements, relaxation time measurements, and demanding experiments such as translational diffusion coefficient measurements. The present study suggests that solutionstate 19F NMR of SF6 is a promising approach for probing systems in solution and highlights the potential of SF6 for applications relying on the encapsulation of an NMR active gas. Acknowledgment. The authors acknowledge Dr. Gilles Bruylants (Universite´ Libre de Bruxelles) for helpful discussions. The authors thank the Executive Program for Belgium-Italy Scientific Cooperation (project 2007-2008 05618-S) and the “Communaute´ franc¸aise de Belgique” (ARC 2002-2007 n°286) for financial support. M.L. thanks the “Fonds de la Recherche Scientifique” (FNRS-FRS), the “Bureau des relations internationales et de la coope´ration” (BRIC) of the Universite´ Libre de Bruxelles. and the “Regione Autonoma della Sardegna” for financing missions in Cagliari. Supporting Information Available: (1) Estimation of the residence time of SF6 in the CB cavity. (2) Graph of the 19F longitudinal relaxation rate (R1) of SF6 dissolved in the solvent (0.2 M Na2SO4 in D2O) and in CB solutions as a function of temperature. (3) Variable temperature 19F chemical shift measurements and DOSY spectra. (4) Analysis of the temperature dependence of the equilibrium constant characterizing the inclusion of SF6 by CB. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Rudkevich, D. M. Angew. Chem., Int. Ed. 2004, 43, 558–571. (2) Cram, D. J.; Tanner, M. E.; Knobler, C. B. J. Am. Chem. Soc. 1991, 113, 7717–7727. (3) Branda, N.; Grotzfeld, R. M.; Valdes, C.; Rebek, J., Jr. J. Am. Chem. Soc. 1995, 117, 85–88. (4) Robbins, T. A.; Knobler, C. B.; Bellew, D. R.; Cram, D. J. J. Am. Chem. Soc. 1994, 116, 111–122. (5) Bartik, K.; Luhmer, M.; Heyes, S. J.; Ottinger, R.; Reisse, J. J. Magn. Reson., Ser. B 1995, 109, 164–168. (6) Bartik, K.; Luhmer, M.; Dutasta, J.-P.; Collet, A.; Reisse, J. J. Am. Chem. Soc. 1998, 120, 784–791. (7) El Haouaj, M.; Ko, Y. H.; Luhmer, M.; Kim, K.; Bartik, K. J. Chem. Soc., Perkin Trans. 2 2001, 11, 2104–2107. (8) El Haouaj, M.; Luhmer, M.; Young, H. K.; Kim, K.; Bartik, K. J. Chem. Soc., Perkin Trans. 2 2001, 5, 804–807.
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