A Practical Integrated Approach to Supramolecular Chemistry III

In the Laboratory

A Practical Integrated Approach to Supramolecular Chemistry III. Thermodynamics of Inclusion Phenomena W Jesús Hernández-Benito, M. Pilar García-Santos, Emma O’Brien,1 Emilio Calle, and Julio Casado* Departamento de Química Física, Universidad de Salamanca, Facultad de Química, Plaza de la Merced, s/n, E-37008 Salamanca, Spain; *[email protected] There is more than one way to represent (and therefore recognize) a molecule. One could simply draw lines between atomic symbols. Or try to sketch the three-dimensional shape of the molecule. Or represent, somehow, the bulk of its atoms, a so-called space-filling model. Or estimate the electric field emanating from it. Or one (well, another molecule, that is) could ‘stroke’ the molecule. There are so many ways for us, or molecules, to ‘see’ or ‘feel’ one another. Roald Hoffmann

In the last two decades interest in the complex formation between cyclodextrins and their guest molecules (1) has grown. These reactions are important in drug-delivery technology and in the separation and food industries (2, 3). Increased insight about the mechanisms of molecular encapsulation has led to the appearance of many inclusion compounds on the market (4–10). In the pharmaceutical

A

field, for example, the complex β-cyclodextrin–piroxicam2 and the complex β-cyclodextrin–prostaglandin have been commercialized as Cycladol or Brexin and Prostarmon, respectively. Many tons of β-cyclodextrin are used in the production of low-cholesterol butter, where the β-cyclodextrin is used to remove cholesterol from milk fat. Cosmetic preparation is another area that utilizes a lot of cyclodextrin, mainly in volatility suppression of perfumes, room fresheners, fabric softeners, and detergents by controlling the release of fragrances from inclusion compounds. Despite the current importance of these complexes, which have resulted in the appearance of specialized journals such as Cyclodextrin News or Journal of Inclusion Phenomena and Macrocyclic Chemistry (see, for example, 11), they receive little attention in texts on physical chemistry (12–15). An experiment for studying inclusion complexes by fluorescence was proposed in 1993 (16, 17). Within the framework of a project designed to develop new practical work in physical chemistry (18, 19), in an earlier article (20) we proposed an experiment for detecting the inclusion of the azo-dye mordant yellow 7 (MY7)3 in α-cyclodextrin and measuring the equilibrium constant of the formation of the corresponding inclusion complex. In a second article (21), an experiment designed to study the kinetics of the inclusion complex of the guest molecule in α-cyclodextrin was described. In this article we propose a practical work aimed at familiarizing students with the thermodynamics of the inclusion phenomena. The Driving Force behind Inclusion Phenomena For chemical reactions, the direction of spontaneous change at constant temperature and pressure is towards lower values of the Gibbs energy, G. This means that for a reaction A B the Gibbs energy of reaction, ∆ rG, can be used as a criterion of spontaneity: if ∆ rG < 0, then the reaction A → B is spontaneous; if ∆ r G > 0, then the reaction B → A is spontaneous. Because of the relationship between the Gibbs energy of reaction and the equilibrium constant K, ᎑∆ rG ⬚ = RT ln K, and given that ∆ rG ⬚ = ∆ rH ⬚ − T∆ rS ⬚, enthalpy and entropy are the thermodynamic “driving forces” behind any chemical reaction. The arrangement of the functional groups of cyclodextrins in the three-dimensional structure is such that the inside is lipophilic while the outside is hydrophilic (Figure 1). This allows cyclodextrins to harbor nonpolar organic molecules and their hydrophilic exterior affords them water solubility. Accordingly, the greater the nonpolarity of the guest molecules, the greater the stability of the complexes formed. In 1982 Szejtli (22) rationalized the change in enthalpy through a mechanism of expulsion of the high-enthalpy water molecules entrapped in the nonpolar cyclodextrin cavity as a result of the spontaneous arrival of the guest molecules.

B

Figure 1. Structure of α-cyclodextrin.

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Vol. 81 No. 4 April 2004

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Szejtli believed that van der Waals and hydrogen bond interactions alone are too weak to account for the stability of the inclusion complexes, and showed the influence of steric factors. The thermodynamic quantities obtained for inclusion complexation are a consequence of the weighted contributions of these interactions. Although several attempts have been made to separate the contributions of the hydrophobic effect and the hydrogen-bonding interaction from the other terms that contribute to the overall thermodynamic complexation quantities, currently there is controversy about the influence of the different forces involved. Calorimetry is the only direct method for determining the reaction enthalpy. However, it is not the most widely used technique for studying the complexation thermodynamics of cyclodextrins (2). When using spectroscopic methods (as used here), the equilibrium constants determined at several temperatures, T, are analyzed by the van’ t Hoff equation,

ln K eq = −

∆G° ∆H° ∆S° = − + RT RT R

(1)

to give the thermodynamic quantities ∆H⬚, ∆S ⬚, and ∆G ⬚ for the complexation reaction. The experimental rate constants, k, measured at several temperatures are analyzed by the Eyring equation,

ln

k ∆H ‡ ∆S ‡ k = − + + ln B h T R RT

(2)

S + C

In this experiment we propose a spectrometric stoppedflow study of the inclusion of the azo-dye Biebrich scarlet4

k2 kⴚ2 K2, slow

CS

(BS) in α-cyclodextrin. BS was chosen as the inclusion species for two reasons: (i) its visible spectrum is altered to a considerable extent when it binds α-cyclodextrin, and (ii) the hydroxynaphthalene group of this molecule is too large to penetrate the cavity of α-cyclodextrin.5 As a consequence, the guest molecule can only enter the cavity by the opposite side (phenyl ring of the sulfonate group), simplifying the interpretation of the results (23). The kinetic parameters involved in the formation of the inclusion complexes were determined as described in ref 21. We followed the formation of the inclusion complex until equilibrium was reached. On the basis of our previous results (21), we used a mechanistic model in which the guest molecule is assumed to be buried in the cavity of the α-cyclodextrin through a two-step mechanism: the dye (substrate, S) reacts with the α-cyclodextrin, C, in a rapid equilibrium o form the intermediate (CS)*, which then gradually forms he final complex CS (Scheme I). When working in conditions such that [C]0 >> [S]0 the following equation is readily btained:

kobs =

K 1 k 2 [ C ]0

+ k −2

1 + K1 [C ]0

(3)

Thus, if the values of kobs at different reagent concentrations, are known, the K1, k2, and k᎑2 values can be obtained by fitting the kobs and [C]0 values to eq 3 by a nonlinear regression method (one alternative is to handle eq 3 in linear form; see ref 21).

0.5

Table 1. Kinetic Results for the Inclusion of Biebrich Scarlet in α-Cyclodextrin kobs /s᎑1

0.1

0.272 ± 0.004

0.2

0.317 ± 0.004

0.5

0.371 ± 0.004

1

0.403 ± 0.002

2

0.418 ± 0.008

5

0.423 ± 0.004

10

0.428 ± 0.008

ⴚ1

0.4

k obs / s

[C]0/mM

kⴚ1 K1, fast

(CS)*

Scheme I. Two-step mechanism for the inclusion process.

to obtain the activation quantities ∆H ‡, ∆S ‡, and ∆G ‡, which are identified by the symbol ‡ and represent the difference in quantity between the activated complex and the reactants (in eq 2 kB and h are the Boltzmann and Planck constants, respectively). Experiment

k1

0.3

0.2

0.1

NOTE: Solvent, phosphate buffer; pH = 11.0; T = 286 K; [BS]0 = 3.75 × 10᎑5 M.

0.0 0

2

4

6

8

10

[C]0 / mM Figure 2. Variation in kobs with [C]0 according to eq 3.

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In the Laboratory

Hardware and Chemical List

Hazards

We used a modular stopped-flow apparatus equipped with a Hewlett-Packard 6267BDD power supply, a 100-W tungsten lamp (commercial quartz–iodine projector lamp), and a Jobin Yvon H20UV monochromator (λ = 614 nm) with a fiber light guide. α-Cyclodextrin was obtained from Fluka; Biebrich scarlet (dye content ∼50%), mordant orange 10, and mordant yellow 10 were from Aldrich.

Cyclodextrins are chemically stable and all toxicity tests have shown that administered orally they are harmless. According to reports of the FAO, enzymatically modified starch (this includes cyclodextrins) is also toxicologically harmless (24). No toxicity has been reported for BS.

ln K 1

9

8

7

y = 11902x − 32.674 R 2 = 0.9927

6 3.30

3.35

3.40

1 T

3.45

3.50

(10ⴚ3 Kⴚ1)

Figure 3. Temperature dependence of K1, equilibrium constant of the first, fast, step of the inclusion phenomenon.

Table 2. Thermodynamic and Kinetic Constants for the Inclusion of Biebrich Scarlet in α-Cyclodextrin T/K

10᎑3 K1a/M᎑1

k2/s᎑1

k᎑2/s᎑1

286

7.1 ± 1.0

0.28 ± 0.02

0.16 ± 0.02

288

6.0 ± 3.0

0.30 ± 0.06

0.22 ± 0.07

290

4.6 ± 1.3

0.29 ± 0.03

0.29 ± 0.03

293

2.8 ± 1.5

0.62 ± 0.09

0.30 ± 0.11

298

1.4 ± 0.4

0.54 ± 0.03

0.54 ± 0.04

a

The equilibrium constant is formulated in terms of concentrations, in contrast to common usage in thermodynamics.

Table 3. Thermodynamic and Activation Parameters for the Inclusion Reaction of Biebrich Scarlet with α-Cyclodextrin at 298 K

Parameter ∆rH⬚/(kJ mol᎑1) ∆H2‡/(kJ mol᎑1) ᎑1

‡

∆H᎑2 /(kJ mol ) ᎑1

᎑1

∆rS⬚/(J K mol )

Fast Step ᎑99.0

Slow Step ᎑18.3

---

45.6

--᎑0.27

S + C

KF KD

CS

of the complexes formed with alternative guest molecules. The results are included for the following molecules: Biebrich scarlet (BS), mordant orange 10 (MO10),6 and mordant yellow 10 (MY10).7 With the methodology described in (20) the KD values given in Table 4 were obtained. Conclusions The experiment described here should allow the students: 1. To calculate the thermodynamic parameters corresponding to inclusion reactions.

3. To gain some insight into the driving forces behind inclusion reactions.

---

᎑95.9 ᎑35.8

∆rG⬚/(kJ mol᎑1)

--᎑18.5

∆G2‡/(kJ mol᎑1)

---

74.2

∆G᎑2‡/(kJ mol᎑1)

---

74.6

᎑0.4

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Mordant Yellow 7 in α-Cyclodextrin In previous articles (20, 21), the inclusion reaction of mordant yellow 7 in α-cyclodextrin was described. Since this azo dye is no longer included within current catalogs of chemicals, some colleagues asked us for the results published on the equilibrium constants of the formation (KF) or dissociation (KD = 1兾KF)

2. To calculate the activation parameters corresponding to the reactions involved in the inclusion mechanism.

∆rS᎑2‡/(J K᎑1 mol᎑1)


Typical results for the variation in kobs with the initial concentration of α-cyclodextrin [C]0 are shown in Table 1 and Figure 2. The kinetic and equilibrium constants obtained at different temperatures (286–298 K) are shown in Table 2. The fitting of the K1 values with the van’ t Hoff equation is shown in Figure 3. With this equation, the thermodynamic parameters for the first, fast step were determined and these are summarized in Table 3. The thermodynamic and activation parameters for the second, slow step were determined with eq 2, using k2 and k᎑2 values (Table 2). The results are also shown in Table 3. It may be observed that: (i) the Gibbs energy of reaction, ∆rG2⬚, for the slow process is smaller than the corresponding Gibbs free energy term, ∆rG1⬚, for the fast process; and (ii) the second, slow step is mainly controlled by the activation enthalpy both in the forward, ∆H2‡, and the backward, ∆H᎑2‡, processes.

63.9 ᎑60.1

∆S2‡/(J K᎑1 mol᎑1)

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Results and Discussion

4. To investigate the kinetics of the inclusion of different guest molecules in α-cyclodextrin as a host molecule.


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In the Laboratory

Acknowledgments This work was supported by the Junta de Castilla y León (Project US14兾02) and the Spanish Ministerio de Ciencia y Tecnología (Project BQ2001-1934). JH-B thanks the Spanish Ministerio de Educación, Cultura y Deporte for a Ph.D. grant. EOB wishes to thank the European Socrates兾Erasmus Program for financial assistance. Thanks are also given to the valuable comments made by the reviewers and the editorial suggestions. W

Supplemental Material

4. The chemical name of Biebrich scarlet is 2-[(2-hydroxy-1naphthalenyl)azo]-5-[(4-sulfophenyl)azo] benzenesulfonic acid, disodium salt. The structure is shown in Table 4. 5. The azo-dye mordant yellow 7 is not used (20, 21), having been removed from chemical catalogs. 6. The chemical name for mordant orange 10 is 2-hydroxy3-methyl-5-[[4-[(4-sulfophenyl)azo]phenyl]azo]benzoic acid, disodium salt. 7. The chemical name for mordant yellow 10 is 2-hydroxy5-[(4-sulfophenyl)azo]benzoic acid, disodium salt.

Literature Cited

Instructions for the students and notes for the instructor are available in this issue of JCE Online. Notes 1. On leave from School of Chemical Sciences, Dublin City University, Ireland. 2. This complex is a component of a nonsteroidal anti-inflammatory medication possessing analgesic and antipyretic properties. 3. The chemical name for mordant yellow 7 is 2-hydroxy-3methyl-5-[(4-sulfophenyl)azo] benzoic acid, disodium salt.

1. Cyclodextrins, Special Thematic Issue. Chem. Rev. 1998, 98, 1741–2076. 2. Szejtli, J. Chem. Rev. 1998, 98, 1743. 3. Crini, G.; Morcellet, M.; Morin, N. L’Actualité Chimique 2001, 11, 18. 4. Bender, M. L.; Komiyama, M. Cyclodextrin Chemistry; Springer Verlag: Berlin, 1978. 5. Saenger, W. Angew. Chem., Int. Ed. Engl. 1980, 19, 344. 6. Szejtli, J. Cyclodextrin Technology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988. 7. Frömming, K. H.; Szejtli, J. Cyclodextrins in Pharmacy; Kluwer

Table 4. Typical Data on the Dissociation of Azo Guests with α-Cyclodextrin Compound

λ/nm

KD /(10᎑4 M)

614 545

4.0 ± 0.2 4.0 ± 0.1

590

4.6 ± 0.4

489 423

3.5 ± 0.2 3.3 ± 0.3

Biebrich scarlet [4196-99-0] SO3Na NaO3S

N N

N N HO

Mordant orange 10 [6406-37-7]

NaO3S

COONa

N N

N N

OH CH3

Mordant yellow 10 [6054-99-5] COONa NaO3S

N N

OH

NOTE: Values obtained from the Benesi–Hildebrand plot (20). Solvent, phosphate buffer, pH = 13.0; T = 298 K; [BS]0 = 3.95 x 10᎑5 M; [MO10]0 = 3.35 x 10᎑5 M; [MY10]0 = 4.33 x 10᎑5 M; [C]0 = 3.20 x 10᎑4–2.00 x 10᎑2 M. The wavelength is chosen such that ∆A, the absorbance with cyclodextrin minus the absorbance in the absence of cyclodextrin, shows highest values.

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In the Laboratory Academic Publishers: Dordrecht, The Netherlands, 1994. 8. Clarke, R. J.; Coates, J. H.; Lincoln, S. F. Adv. Carbohydr. Chem. Biochem. 1988, 46, 205. 9. Maury, M.; Roque, J. Biofutur 1986, 49, 17. 10. New Trends in Cyclodextrins and Derivatives; Duchêne, D., Ed.; Editions de Santé: Paris, 1991. 11. Valero, M.; Arco-Gómez, A.; Rodríguez, L. J. J. Inclusion Phenomena and Macrocyclic Chem. 2002, 42, 121. 12. Laidler, K. J.; Meiser, J. H. Physical Chemistry, 3rd ed.; Houghton Mifflin: Boston, 1999. 13. McQuarrie, D. A.; Simon, J. D. Physical Chemistry: A Molecular Approach; University Science Books: Sausalito, CA, 1997. 14. Atkins, P. Physical Chemistry, 7th ed.; Oxford University Press: Oxford, 2001. 15. Silbey, R. J.; Alberty, R. Physical Chemistry, 3rd ed.; John Wiley: New York, 2001. 16. Indivero, V. M.; Stephenson, T. A. In Physical Chemistry, De-

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17. 18. 19. 20. 21. 22. 23. 24.

veloping a Dynamic Curriculum; Schwenz, R. W., Moore, R. J., Eds.; American Chemical Society: Washington, DC, 1993. Valero, M.; Rodríguez, L. J.; Velázquez, M. M. J. Chem. Educ. 1999, 76, 418. Moyá, M. L.; Izquierdo, C.; Casado, J. J. Phys. Chem. 1991, 95, 6001. Casado, J.; Izquierdo, C.; Fuentes, S.; Moyá, M. L. J. Chem. Educ. 1994, 71, 446. Hernández Benito, J.; González Mancebo, S.; Calle, E.; García Santos, M. P.; Casado, J. J. Chem. Educ. 1999, 76, 419. Hernández Benito, J.; González Mancebo, S.; Calle, E.; García Santos, M. P.; Casado, J. J. Chem. Educ. 1999, 76, 422. Szejtli, J. Cyclodextrins and Their Inclusion Complexes; Akademiai Kiado: Budapest, Hungary, 1982. Cramer, F.; Saenger, W.; Spatz, H.-Ch. J. Am. Chem. Soc. 1967, 89, 14. FAO Nutrition Meetings, Series No. 46, A. WHO/Food AAD/ 70.36.


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A Practical Integrated Approach to Supramolecular Chemistry III

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