In the Laboratory
W
Chemical Equilibrium in Supramolecular Systems as Studied by NMR Spectrometry
Gustavo González-Gaitano* Departamento de Química y Edafología (sección de Química-Física), Universidad de Navarra, 31080, Pamplona, Spain; *
[email protected] Gloria Tardajos Departamento de Química-Física I, Facultad de Ciencias Químicas, Universidad Complutense, 28040, Madrid, Spain
The objective of this experiment is to expose undergraduate students to the use of proton NMR spectrometry to analyze chemical equilibria in systems that cannot be studied by optical–spectroscopic techniques. Supramolecular assemblies, structures in which the interacting species are held together by noncovalent forces, are studied. Specifically the inclusion complexes formed between cyclic oligosaccharides (β- or γcyclodextrin) and sodium alkanoates (sodium octanoate, NOc, or sodium decanoate, NDe) are examined. Students assign the NMR spectra and, from the relative changes in the resonances of both the host and guest molecules, deduce the topology of the complex. The binding constants between the cyclodextrin and guest molecules are calculated from the nonlinear least-squares fitting of some proton signals. The effects of the surfactant hydrophobicity and the cyclodextrin cavity size on the stability of the supramolecular association are discussed in view of the numerical results. This experiment assumes that the students have completed physical chemistry and know the basics of chemical equilibrium and NMR (chemical shifts, peak assignment, and instrumentation), along with some knowledge of data fitting. The experiment can be carried out as a “dry lab” experiment if the student is supplied with the spectra previously recorded by the supervisor. Supramolecular Systems The discipline known as supramolecular chemistry deals with the organized assemblies formed between two or more interacting species held together by noncovalent forces, such as van der Waals interactions and hydrogen bonding. It has been defined as the “chemistry beyond the molecule”, in contrast to the term “molecular chemistry”, which refers to the chemistry based on the covalent bond (1, 2). The associations found in supramolecular systems are weaker than those corresponding to ordinary chemical bonds and, as a consequence, their properties are more dynamic and can be easily modulated by the effect of external variables, which constitutes the cause of their functionality. As a consequence, supramolecular chemistry is a continuously growing interdisciplinary field that involves aspects of physical chemistry, organic synthesis, coordination and bioinorganic chemistry or biochemistry, among others, leading to a number of interesting applications (3). An example of an application is the microencapsulation of small molecules in organic host molecules. Microencapsulation is an effective medium to change some of the properties of the guest molecule (solubility, bioavailability, resistance against radiation, or the attack of reactants, etc.), 270
Journal of Chemical Education
•
without modifying its chemical identity. A popular class of host molecules are cyclodextrins (CDs), a family of cyclic oligosaccharides containing six, seven, or eight α-D-glucopyranose residues, linked by α-1,4 glycosidic bonds (referred to as α-, β-, and γ-CD, respectively). This class of carbohydrates exhibits a doughnut shape where the cavity has a hydrophobic character compared to water and the rims, bearing the primary and secondary OH groups, are hydrophilic (Figure 1A and 1B). Thus, a CD constitutes a singular microenvironment where molecules with a suitable size and hydrophobic character can be housed, forming an inclusion complex (4). The mechanism of the inclusion comprises the transfer of a molecule, or part of it, to the cavity of a CD. In this process, several effects dependent on the species involved must be considered. In aqueous media, the release of the water molecules contained within the CD cavity and the dehydration of the substrate, with the subsequent changes in entropy and enthalpy, seem to play an important role in the binding (5). The chemical education literature contains some experiments describing inclusion complexes of CDs as examples of supramolecular systems. They deal with structural aspects (6), the thermodynamics of the binding (7, 8), or the kinetics (9). All the association studies are based on the change of some property of the guest molecule, host molecule, or both, upon the inclusion, such as the fluorescence emission or the absorbance (10, 11). However, there are cases in which the A
B
H4 H6' OH H6''
secondary rim
(
HO OH
O H2
HO
H5
H1
OH H3
O)
n
primary rim
OH
n = 6, 7, 8
C
O O
octanoate
ⴚ
O O
ⴚ
decanoate
Figure 1. Structures of cyclodextrins (CDs) showing (A) the position numbering of the protons and (B) emphasizing the cavity shape; (C) structures of the sodium alkanoates.
Vol. 81 No. 2 February 2004
•
www.JCE.DivCHED.org
In the Laboratory
guest neither absorbs nor emits optical radiation and other techniques must be used. This is the case of many surfactants, lipids, and carbohydrates. In this experiment the guest molecule is an anionic surfactant (NOc or NDe) and the host molecule is a CD (β- or γ-CD). In the complex formed the hydrocarbon chain of the surfactant is lodged in the hydrophobic cavity of the CD. The inner protons of the CD, H3 and H5, act as the “probe” for the inclusion (Figure 1A). The chemical environment of these protons changes upon the inclusion when the water filling the CD is replaced by the surfactant. The outer protons are not modified. The induced chemical shifts on complexation give information about the stoichiometry and structure of the assembly. A nonlinear least-squares fitting of chemical shifts in the NMR spectra is used to find the association constant and other thermodynamic parameters of the binding.
A
B
R=0
R = 0.4
H6' ,H6'' H3 H2
H5
H4
Chemical Shift (ppm)
C
D
R = 1.7
R = 3.1
Experimental Procedure H3
Chemicals and NMR Spectrometer All the chemicals were purchased from Aldrich with purities greater than 98% and used as received. Deuterium oxide (D2O) was purchased from SdS (France) with a deuterium degree greater than 99.9%. The spectra were recorded with a Varian VXR 300S (300 MHz) with a thermostating unit coupled to a SUN SPARK workstation. Sample Preparation and Recording of the Spectra Different surfactant兾cyclodextrin molar ratios (R = [S]兾[CD]) are prepared from stock solutions of β-CD and γ-CD in D2O, by weighing increasing quantities of surfactant in suitable vials and adding the stock solution afterwards. The samples are then transferred to the resonance tubes. Molar ratios varied between 0 and 5, with 12 mM in CD (under these conditions the surfactant is always below the critical micelle concentration, cmc). We collected 64 accumulations per spectrum. The HDO signal of the solvent at 4.63 ppm was used as the reference. The temperature was kept constant at 20.0 ± 0.1 ⬚C. Hazards Although the experiment does not present any particular hazards, the use of a mask and gloves is advisable when handling the alkanoates (in the form of fine, irritant powder that can be easily inhaled). When recording the spectra, people having an implanted pacemaker or a metal prosthesis must keep out the measurement zone, which should be conveniently indicated, owing to the intense magnetic fields generated by NMR spectrometers. CD Spectrum Assignment The one-dimensional 1H NMR spectrum of β-CD, at 300 MHz, is displayed in Figure 2A. The assignment of some resonances can be deduced from the areas of the signals and their multiplicity (12). The H1 signal (doublet, centered at 4.89 ppm; not shown in the figures) is the least deshielded because of the two neighboring oxygen atoms. It is coupled to only one other proton, H2, and integrates for 7 protons. www.JCE.DivCHED.org
•
H5
Chemical Shift (ppm)
Figure 2. 1H NMR spectra of β-CD and NDe at several molar ratios (R = [NDe]/[β-CD])
The H2 must be a doublet of doublets, owing to the different coupling to H1 and H3, and must integrate for seven protons also. As a result of the similar chemical environments, the coupling constants H2–H3 and H3–H4 must be similar in magnitude. The same situation occurs with H4 (Figure 1A). Thus, both H3 and H4 must be triplets of area equal to 7, but the former is more deshielded, owing to the neighbor OH, in position 3. Hence, H3 must correspond to the signal at 3.78 ppm, and H4 to the signal at 3.39. The remaining protons, H5, H6′, and H6″ appear overlapped, yielding an area of 21. The most important resonances for the experiment are those of H3 and H5 since these protons are located inside the cavity of the CD and, consequently, are sensitive to changes in the microenvironment upon inclusion. H2 and H4 point outwards, whereas H6′ and H6″, whose signal integrates for twice than the rest of resonances, is located at the narrower rim of the CD (Figure 1B). The spectrum of γCD (not shown) is virtually the same as that of β-CD. When the surfactant is added an upfield shift is observed for the inner H3 signal. The H5 signal, which was partially overlapped by the H6′ and H6″ signal, undergoes even more pronounced upfield changes than H3, and becomes well resolved when the molar ratio [S]兾[CD] increases (Figure 2B– D). The signal is unambiguously assigned to H5 since its area gives seven protons, whereas that of H6 yields double the area. The considerable changes in both H3 and, especially, H5 (inserted at the narrower rim of the cavity and more pro-
Vol. 81 No. 2 February 2004
•
Journal of Chemical Education
271
In the Laboratory
lent environments. In the limit of fast interchanging, the measured frequency is a weighed average of the frequencies in each site, and the chemical shift can be used to measure the extent in which the equilibrium is displaced (13). The chemical shift δ at each R can be expressed as;
0.20
H5
∆δ (ppm)
0.15
H5
δ = χi δ i + χ cx δ cx
0.10
H3 0.05
H3
0.00 0
1
2
3
4
5
[S]/[β-CD]
that is, as the sum of the contributions of the chemical shifts due to the complex, δcx, and to the free host or guest, δi (i = CD or S), each one averaged by its mole fraction. In this experiment, the cyclodextrin concentration is kept constant, [CD]0, and the resonances of the CD protons are monitored. In this case, eq 1 becomes,
δ = 1 −
0.15
= δ CD
∆δ (ppm)
H5 0.10
[S:CD] δ [CD]0 CD [S:CD] (δ + [CD]0 cx
H5 0.00 1
2
3
4
5
∆δ =
[S]/[γ-CD] Figure 3. Chemical shift increments (∆δ = δ0 − δ) for the inner protons of β-CD (top) and γ-CD (bottom). Closed symbols correspond to NDe and open symbols to NOc, respectively.
tuberant than H3), are an indication of a close contact with the guest molecule. On the contrary, H1, H2, H4, and H6, are scarcely shifted, which indicates that there are no important changes in their magnetic environments on complex formation. The resonances of the surfactant protons do not change significantly on complexation. Only the protons belonging to the center of the tail, –(CH2)n–, which give a single resonance in water, undergo a broadening, an indication of the nonequivalence of the different parts of the tail. The chemical shift of a CD proton in D2O minus the measured chemical shift upon addition of surfactant (∆δ) have been plotted against the molar ratio [S]/[CD] in Figure 3. These plots represent a binding isotherm in which saturation is reached when all the available CDs are filled with the surfactant. The stoichiometry is clearly 1:1 with β-CD. The overall changes in δ with β-CD are larger for NDe than for NOc (Table 1). For the complex between γ-CD and NOc, the changes in δ upon complexation are small, indicating a poor affinity of the surfactant for the γ-CD. The 1:1 stoichiometry is not evident in this case. Chemical Equilibrium Examined by NMR The use of NMR for the study chemical equilibrium is based on the chemical shift change that results when the nucleus interchanges between two magnetically nonequiva272
Journal of Chemical Education
•
+
[S:CD] δ [CD]0 cx (2)
− δ CD )
where [S:CD] is the concentration of bound surfactant. Defining ∆δ as the difference between the chemical shift of the CD alone and that measured at each concentration, and ∆δ0 as the difference in the limit when all the surfactant is complexed, eq 2 can be written as:
0.05
0
(1)
[S:CD] ∆δ [CD]0 0
(3)
If the quantity of added surfactant, S0, is large, the equilibrium shifts towards the formation of the complex, and δ → δcx. Notice that this method can be applied to protons of the guest molecule as well, although we have focused on the CD protons, since they undergo the greatest changes in this case. The concentration of the complex is given by the mass action law, K =
[S:CD] [S][CD]
=
[S:CD] ([S]0 − [S:CD]) ([CD]0 − [S:CD])
(4)
where K is the binding constant. Developing this expression in terms of [S:CD], a quadratic equation is obtained that can be solved and expressed as a function of K and the molar ratio R = [S]0兾[CD]0 as:
[S:CD]
=
1 1 [CD]0 1 + R + 2 [CD] 0 K
±
1+ R +
1 [CD]0 K
2
− 4R
(5)
From the two possible solutions, only that obtained using the minus sign in front of the square root has physical meaning. For a series of R, by introducing this result in eq 1, a set of calculated chemical shifts, δcal, is obtained. The procedure for deducing the binding constant consists in finding a vector (K, ∆δ0) that minimizes the sum of
Vol. 81 No. 2 February 2004
•
www.JCE.DivCHED.org
In the Laboratory
squares of the residuals for the n points measured: E =
n
∑ (δ i
i =1
− δ cal )2
Table 1. Maximum Changes in δ (ppm) upon Complex Formation for β-CD Protons
(6)
Since eq 5 implies a nonlinear dependency of [S:CD] with the fitting parameters, K and ∆δ0, the data cannot be analyzed with the method of linear least-squares. It is necessary to apply a nonlinear least-squares fitting procedure of the ∆δ versus R plots; that is, employing a numerical method that finds the minima of a function of several variables (the two unknown parameters in this case). In this routine an initial guess is used as the starting point for the algorithm to search for the minimum. The fundamentals of nonlinear analysis and its application to laboratory practice have been described in this Journal (14, 15, and references therein). In the Supplemental MaterialW we include a MATLAB (16) function that performs this task. There are other software packages that can be used as well, such as Microsoft Excel, Microcal Origin, or Mathcad. The binding constants and ∆δ0 values are shown in Table 2. Discussion The relative changes in the chemical shifts of the nuclei contain valuable structural information. Firstly, the fact that the inner protons of the CD change extensively with the addition of the surfactant, whereas the outer protons remain practically unchanged indicates that the complex is not a mere association but an inclusion of the surfactant within the CD cavity. The minor changes of H5 and H3 of γ-CD when compared to those of β-CD imply a less efficient contact between the surfactant and the cavity (i.e., less shielding of these protons), which indicates weaker van der Waals interactions. This agrees well with the values of the binding constants (Table 2). For the case of NOc with γ-CD the interaction is so weak that K cannot be estimated (the algorithm does not converge). Thus, it is shown that an important parameter in the formation of the inclusion complex with CD is the fitting of the surfactant within the cavity: if it is too wide, the complex does not form, or it forms scarcely. On the contrary, if the cavity is too narrow the complex will not form either. The hydrophobicity of the surfactant is another significant factor. For the β-CD, K increases with the tail length; that is, the longer the surfactant (hydrophobicity), the higher the affinity for the CD. This can be understood when comparing the inclusion to the formation of a micelle. Micellization takes place because the environment the hydrocarbon chains feel inside the micelle is similar to that of the pure hydrocarbon. The longer the lipophilic tail, the smaller the value of the cmc (critical micelle concentration); that is, less concentration of surfactant is required to form the micelle. In this process, a substantial factor is the entropy gain owing to the loss of the hydration shell that covers the surfactant. Something similar happens with the entrance of the surfactant into the CD. The hydrophobic cavity of a CD offers the surfactant a favorable environment. The process also results in the dehydration of the guest molecule, ∆S > 0. At the same time strong van der Waals interactions occur between the surfactant and CD, ∆H < 0, more intensely when the contact between both molecules is closer. www.JCE.DivCHED.org
•
Change in δ/ppm
Proton H1
NDe ᎑0.008
NOc +0.001
H2
᎑0.034
᎑0.028
H3 H4
᎑0.098 +0.012
᎑0.046 +0.036
H5
᎑0.174
H6
᎑0.004
᎑0.131 +0.009
Table 2. Binding Constants, K (L/mol), and ∆δ δ0 Calculated from the H5 NMR Shifts Surfactant Compound NOc
NDe
β-CD
K = (4.6 ± 0.7) ×102 ∆δ0 = 0.137 ± 0.003
K = (1.1 ± 0.6) ×103 ∆δ0 = 0.166 ± 0.005
γ-CD
___
K = (3.0 ± 0.7) ×101 ∆δ0 = 0.19 ± 0.02
Oⴚ O
Figure 4. Schematic structure of the inclusion complex NDe:CD.
The length of the hydrocarbon tail (in Å), assuming it is in a all-trans conformation, can be calculated from the empirical formula given by Tanford (17), l tail = 1.50 + 1.26 nC
(7)
where nC is the number of C atoms. Since the cavity in a CD is about 7.9 Å in height, the minimum number of –CH2– groups that can be lodged within the cavity, according to eq 7, is 5. However, since the width of β-CD and γ-CD allows coiling of the surfactant chain and a possible tilting of the surfactant within the cavity, the number of methylene groups accommodated can be higher (18). The changes in the chemical shifts for the tail protons are too small to obtain quantitative information. Shifts in the –CH3 and the –(CH2)n– signals almost double (ca. 0.05 ppm) those of the methylenes closest to the carboxylate group, for both of the surfactants. This can indicate that the anionic head is, either outside the cavity, or at one of the rims. The complex structure deduced from all the facts explained above has been depicted in Figure 4. In this scheme a fully extended alkyl chain has been assumed.
Vol. 81 No. 2 February 2004
•
Journal of Chemical Education
273
In the Laboratory
Expanding the Experiment and Variants
Literature Cited
The experiment can be expanded by recording the spectra at different temperatures (for example, at 15, 25, 35, and 45 ⬚C). In this way, the binding constant can be obtained as a function of the temperature and, by applying the van’t Hoff equation, the enthalpy and entropy of the inclusion process deduced. This permits a discussion of the role of the hydrophobic effect in the binding. Surfactants other than NOc and NDe can be used, for example, sodium alkylsulphates, or cationic surfactants such as alkyltrimethylammonium bromides. In this way, the effect of the charge of the ionic head can be discussed. In any case, surfactants with no more than ten methylene groups should be used. Otherwise, higher stoichiometries are observed (i.e., S2:CD), and the mathematical model and the fit procedure become more complicated, beyond the scope of the experiment. An additional complication when increasing the tail length is that the cmc lowers, and micelle formation could interfere with the binding.
1. Atwood, J. L.; Davies, J. E. D.; Macnicol, D. D.; Vögtle, F. Comprehensive Supramolecular Chemistry; Szejtli, J., Osa, T., Eds.; Pergamon: Tarritown, NY, 1996; Vol 2. 2. Gellman, S. H., Ed. Chem. Rev. 1997, 97, 1231–1734 and thematic issues contained herein. 3. Atwood, J. L.; Davies, J. E. D.; MacNicol, D. D.; Vögtle, F. Comprehensive Supramolecular Chemistry; Szejtli, J., Osa, T., Eds.; Pergamon: Tarritown, NY, 1996; Vol 3. 4. Szejtli, J. Cyclodextrins and Their Inclusion Complexes; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988. 5. Connors K. A. Chem. Rev. 1997, 97, 1325. 6. Varneck, A. A.; Dietrich, B.; Wipff, G.; Lehn, J. M.; Boldyreva, E. V. J. Chem. Educ. 2000, 77, 222. 7. Hernández-Benito, J.; González-Mancebo, S.; Calle, E.; García-Santos, M. P.; Casado, J. J. Chem. Educ. 1999, 76, 419. 8. Valero, M.; Rodríguez, L. J.; Velázquez, M. M. J. Chem. Educ. 1999, 76, 418. 9. Hernández-Benito, J.; González-Mancebo, S.; Calle, E.; García-Santos, M. P.; Casado, J. J. Chem. Educ. 1999, 76, 422. 10. Zarzycki, P. K.; Lamparczyk, H. J. Chem. Educ. 1996, 73, 456. 11. Wagner, B. D.; MacDonald, P. J.; Wagner, M. J. Chem. Educ. 2000, 77, 178. 12. Schneider, H.-J.; Hacket, F.; Rüdiger, V. Chem. Rev. 1998, 98, 1755. 13. Connors, K. A. Binding Constants. The Measurement of Molecular Complex Stability; Wiley: New York, 1987; pp 189–192. 14. Zielinski, T. J.; Allendoerfer, R. D. J. Chem. Educ. 1997, 74, 1001. 15. Machuca-Herrera, J. O. J. Chem. Educ. 1997, 73, 448. 16. MATLAB, version 4.2. The Mathworks, Inc. 17. Tanford, C. The Hydrophobic Effect; Willey: New York, 1980. 18. Park, J. W.; Song. H. J. J. Phys. Chem. 1989, 93, 6454.
W
Supplemental Material
A student handout, notes for the instructor, and MATLAB functions are available in this issue of JCE Online. Acknowledgments The authors acknowledge financial support from the Gobierno de Navarra and the Ministerio de Ciencia y Tecnología y Cultura (fund num. BQU2001-1426-C02-02), and thank J. R. Isasi for his help in the revision of the manuscript.
274
Journal of Chemical Education
•
Vol. 81 No. 2 February 2004
•
www.JCE.DivCHED.org
