Thermodynamic and Spectroscopic Study of a Molecular Rotaxane

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Thermodynamic and Spectroscopic Study of a Molecular Rotaxane Containing a Bolaform Surfactant and β-Cyclodextrin G. Gonza´lez-Gaitano,† A. Guerrero-Martıńez,‡ F. Ortega,‡ and G. Tardajos*,‡ Departamento de Quı´mica y Edafologıá, Facultad de Ciencias, Universidad de Navarra, 31080 Pamplona, Spain, and Departamento de Quı´mica-Fı´sica I, Facultad de Ciencias Quı´micas, Universidad Complutense, 28040 Madrid, Spain Received August 25, 2000. In Final Form: November 17, 2000

A thermodynamic and proton NMR spectroscopy study of a bolaform type surfactant, docosane 1,22bis(trimethylammonium bromide), has been carried out in water and in the presence of β-cyclodextrin (β-CD) at 298 K. Density and sound velocity data for the aqueous solutions of the bolaform in both systems were analyzed to calculate the molar apparent and partial volumes and adiabatic compressibilities. For the binary system, the molar partial compressibilities and volumes of the bolaform in water as a function of concentration have been obtained. Compressibility data indicate that the surfactant, both in monomer or in micelle form, is partially folded. For the ternary system, a remarkable increase of the thermodynamic properties of the surfactant is observed at infinite dilution with respect to the value in water and a shift of the critical micelle concentration in an extension that points to complexes of predominantly 2:1 stoichiometry. The values of the transfer properties of the bolaform at infinite dilution, discussed in terms of a simple model which takes into account the balance between the released water from the cavity and the methylene groups of the substrate that enter into the macrocycle, prove the formation of a molecular rotaxane in which three β-CDs are threaded by one molecule of surfactant under conditions of excess of β-CD, which turns to 2:1 when the surfactant concentration increases. 1H NMR in D2O experiments have been performed in order to elucidate the molecular structure of the rotaxane in solution. Analyses of the induced chemical shifts corroborate the thermodynamic results and prove that the β-CD is located preferentially on the surfactant chain, being the cationic heads scarcely involved in the complex.

Introduction Cyclodextrins are a group of well-known cyclic sugars, with the capability of forming reversible noncovalent complexes with a wide variety of guests.1 These macrocycles are structurally based on glucose, consisting of several R-D-glucopyranose residues (six, seven, or eight rings, named R-, β-, and γ-CD, respectively) linked by glycoside bonds R-1,4. They form a doughnut-shaped structure in which the cavity has a hydrophobic character compared to water, whereas the rims, in which the primary and secondary OH groups are inserted, are hydrophilic. The cavity size and the nature of the substituents can be modulated, according to the nature of the particular guest (mainly its shape, hydrophobicity or the electronic density), to obtain the most suitable binding, stoichiometries, etc.2,3 As a consequence of the binding process, some properties of the target molecule can be dramatically changed. This is the case of amphiphiles forming micelles or any other type of aggregates, in which the presence of CDs introduces a new equilibrium into the medium which competes with the self-assembly process, normally inducing the destruction of the aggregates.4,5 If the guest is a linear chain of * To whom correspondence should be addressed: e-mail, [email protected]. † Universidad de Navarra. ‡ Universidad Complutense. (1) D’Souza, V. T.; Lipkowitz, K. B. Chem. Rev. 1998, 98, 1741. (2) Connors, K. A. Chem. Rev. 1997, 97, 1325. (3) Raymo, F. M.; Stoddart F. J. Chem. Rev. 1999, 99, 1643. (4) Gonza´lez-Gaitano, G.; Sanz-Garcıá, T.; Tardajos, G. Langmuir 1999, 15 (23), 7963. (5) Gonza´lez-Gaitano, G.; Compostizo, A.; Sańchez-Martıń, L.; Tardajos, G. Langmuir. 1997, 13 (8), 2235.

atoms (a surfactant, for instance), the CD is threaded in a structure known as rotaxane, in which the surfactant constitutes the molecular axis.6 The case of a surfactant having two hydrophilic ends (bolaform surfactants) is of special interest due to the balance between several intermolecular forces: on one hand, the hydrophobic effect which tends to protect the alkyl chain from the aqueous environment; on the other hand, the hydration of the stoppers, which need to lose the water molecules prior to the complex formation, and the esteric hindrances. All these changes in the hydration water of all the involved molecules must be reflected in thermodynamic properties related to the volume and compressibility, of the solutes.4-8 In this paper an investigation of a bolaform surfactant, docosane 1,22-bis(trimethylammonium) bromide (C22Me6), with β-CD is presented, in conditions above and below the critical micellar concentration (cmc), using density and speed of sound measurements. The hydrophilic/hydrophobic balance in the complexation is compared with the homologous series of the alkyl trimethylammonium bromide (CnMe3), which is known to form stable inclusion complexes with β-CD with increasing stoichiometry when the surfactant length increases.9 With a simple model that takes into account the released water molecules from the β-CD and the methylene groups of the guest that enter the cavity, the stoichiometry is easily obtained. 1H NMR studies in D2O have been carried out together with the (6) Nepogodiev, S. A.; Stoddart, J. F. Chem. Rev. 1998. (7) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 2000, 104, 1880. (8) De Lisi, R.; Milioto, S.; Pellerito, A. Langmuir 1998, 14, 6045. (9) Gonza´lez-Gaitano, G.; Crespo, A.; Tardajos, G. J. Phys. Chem. B 2000, 104 (8), 1869.

10.1021/la001235r CCC: $20.00 © 2001 American Chemical Society Published on Web 02/10/2001

Study of Bolaform Surfactant with Cyclodextrin

Langmuir, Vol. 17, No. 5, 2001 1393

thermodynamic studies to reinforce the conclusions about the structure of the complex.

Table 1. Properties of Monomers and Micelles for C22Me6

Materials and Methods Materials. β-CD was purchased from Sigma, with a water content of 13.5%, as determined from thermal analysis. Tetramethylammonium bromide (TMAB) was purchased from Fluka, with purity better than 99%, and it was used as received. Docosane 1,22-bis(trimethylammonium bromide), bolaform C22Me6, has been obtained from docosane 1,22-dibromide by reaction with trimethylammine in dry ethanol.10 The reaction mixture was kept under reflux for 6 h, and the product was recrystallized from MeCN-Et2O. The critical micelle concentration (cmc) yielded 2.8 × 10-3 M at 25 °C by surface tension measurements. The solutions were prepared in all cases by weight in redistilled, deionized (Millipore super-Q system), and degassed water. Density and Speed of Sound Measurements. Measurements of speed of sound, u, and density, F, have been performed simultaneously with a computerized technique in which the speed of sound is measured with a pulse-echo type technique which makes use of a 13 MHz transducer excited with pulses of the same frequency.11 For the density it uses a vibrating tube densimeter designed by us.12 Temperature control is maintained with a water bath using a homemade temperature controller, where the ultrasonic cell and the densimeter are immersed. To change the concentration in the cell, a stock solution was added from a digital buret Metrohm 665 or by directly weighing an amount of the solution. Before the experiments, the ultrasonic cell is calibrated with pure water (u ) 1496.739 m s-1, ref 13) and the densimeter with water (F ) 997.045 kg m-3, ref 14) and air.15 All the measurements were carried out at 298.15 K, with a stability better than 1 mK. In these conditions the precision in speed of sound and density is 2 × 10-3 m s-1 and 1 × 10-6 g cm-3, respectively. From F and u the apparent and partial molar volumes and adiabatic compressibilities can be deduced. In ternary systems as the studied, in which the CD molality is kept constant, the apparent molar volume of the surfactant is related to the density of the solution, F, through

νφ,s ) Ms/F - (1 + mCDMCD)(F - F0)/msFF0

(1)

where Ms, ms and MCD, mCD are the molar masses and molalities for the surfactant and β-CD, respectively, and F0 is the density of the solution when ms is zero. Provided that the speed of sound, u, is known, the apparent molar compressibility can be calculated as

κφ,s ) βνφ,s + (1 + mCDMCD)(β - β0)/msF0

(2)

where β ) 1/Fu2 is the adiabatic compressibility of the solution (Laplace equation) and β0 that of the system when ms is zero. From vφ,s and κφ,s, the corresponding partial molar properties can be readily obtained taking derivatives with ms:

νs )

( ) ∂V ∂ns

)

nw,nCD

( ( ))

κs ) -

∂ ∂V ∂ns ∂P

d (ν m ) dms φ,s s

S n ,n w CD

)

d (κ m ) dms φ,s s

(3)

(4)

1H NMR Measurements. The samples for the NMR experiments were prepared in D2O (S.d.S., France, with deuteration

(10) Cipiciani, A.; Fracassini, M. C.; Germani, R.; Savelli, G.; Bunton, C. A. J. Chem. Soc., Perkin Trans. 2 1987, 547. (11) Tardajos, G.; Gonza´lez Gaitano, G.; Montero de Espinosa, F. Rev. Sci. Instrum. 1994, 65 (9), 2933. (12) Herrero, J.; Gonza´lez-Gaitano, G.; Tardajos, G. Rev. Sci. Instrum. 1997, 68 (10), 3835. (13) Kroebel, W.; Mahrt, K. H. Acustica 1976, 35. (14) Brown, I.; Lane, J. E. Pure Appl. Chem. 1976, 45, 1. (15) Kohlrausch. Praktische Physik (vol. 3); Teubner: Stuttgart, 1968.

mol-1)

vs × vsm × 106 (m3 mol-1) ∆vm × 106 (m3 mol-1) κs0 (PPa-1 m3 mol-1) κsm (PPa-1 m3 mol-1) ∆κm (PPa-1 m3 mol-1) 0

106

(m3

C22Me6 + H2O

C22Me6 + β-CD + H2O

522.2 ( 0.2 532 ( 1 8(1 -22 ( 1 149 ( 4 165 ( 4

580 533 ( 1 9(1 109 146 ( 6 160 ( 6

degree better than 99.9%), keeping the concentration of β-CD approximately constant at 15 mM for all the molar ratios and varying that of the surfactant. A VARIAN VXR 300S spectrometer operating at 300 MHz and equipped with a thermostat was used for the recording of the spectra. The experiments were run at 20.0 ( 0.1 °C, with 64 accumulations in each spectrum, and taking the HDO signal of the solvent as the reference, at 4.63 ppm. Data were treated in a PC with the 1D WIN-NMR program.16

Results and Discussion Bolaform + Water. The results of density and speed of sound for the binary and the ternary systems are plotted in Figure 1a. We have determined the cmc from the u plot, since this property changes more sharply around the cmc than F. The method consisted in obtaining the derivatives with respect to ms, provided many measurements at close intervals of concentration are available. This should give an inflection point in the first derivative, ∂u/∂ms, and a minimum in ∂2u/∂ms2 plots (Figure 1b). The cmc thus obtained is 0.0030 mol kg-1, in good agreement with literature average value of 0.0028 ( 0.0003 mol L-1 (ref 17). In Figure 2 we have plotted the apparent and partial molar volumes of C22Me6 versus ms. The molar volumes and compressibilities of monomers and micelles are collected in Table 1. To calculate the volume change upon micellization, we have taken the volume of the monomer in micelle form from the partial molar property, vsm equal to (532 ( 1) × 10-6 m3 mol-1, and subtracted the volume at the cmc. This renders ∆vm ) (8 ( 1) × 10-6 m3 mol-1. Zana et al. report (6 ( 2) × 10-6 m3 mol-1. This value would be equivalent to that of tetramethylammonium bromide (TTAB) and less than twice the volume change upon micellization of DTAB.9 This can be understood if a folding of the alkyl chain in the micelle is considered, which seems reasonable taking into account the length of the surfactant. Chemical relaxation studies seem to support this conclusion also.17 The change in the surfactant compressibility upon micellization can be calculated from Figure 3 in the same way as the volume. From the partial molar compressibility, κsm ) 149 ( 4 PPa-1 m3 mol-1 and subtracting the compressibility at the cmc, we obtain ∆κm ) 165 ( 4 PPa-1 m3 mol-1. The extrapolated value at infinite dilution gives the molar volume of the monomer, (522.2 ( 0.2) × 10-6 m3 mol-1. This value agrees with the literature value,17 523.4 × 10-6 m3 mol-1, at the cmc. To perform an analysis of group contributions, the monomer volume should be 22v(CH2) + 2v(TMAB) - 2vCH3, and the same would stand for the compressibility. To this purpose, we have measured the speed of sound and density of tetramethylammonium bromide (TMAB) in water. The calculated apparent molar volume and compressibility for TMAB are plotted in Figure (16) WIN-NMR, Bruker-Franzen Analytic GmbH. Version 960901. (17) Zana, R.; Yiv, S.; Kale, K. M. J. Colloid and Interface Sci. 1980, 77 (2), 456.

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Gonza´ lez-Gaitano et al.

Figure 1. (a) Density and speed of sound plots for C22Me6 and C22Me6 + β-CD solutions. (b) Plot of the second derivative of sound velocity versus the surfactant molality for C22Me6 and C22Me6 + β-CD solutions.

4. Both properties have been fitted to an equation of the form

Yφ,TMAB ) YTMAB0 + AYmTMAB1/2 + BYmTMAB + CYmTMAB3/2 (5) where AY is the Debye-Hu¨ckel limiting slope and BY and CY are deviation parameters of the limiting law of the Y property. For the volume, Av ) 1.865 × 10-6 m3 kg1/2 mol-3/2 at 25 °C for a 1:1 electrolyte. To our knowledge, there are no numerical estimations of the limiting law parameter for the adiabatic compressibility, Aκ. Hence, we have used Aκ ) 2.55 PPa-1 m3 kg1/2 mol-3/2, that is, the same as the isothermal compressibility.18 From the fit to eq 5 we obtain vTMAB0 ) (114.43 ( 0.01) × 10-6 m3 mol-1 and κTMAB0 ) -3.76 ( 0.03 PPa-1 m3 mol-1, with coefficients Bv ) (-2.5 ( 0.4) × 10-6 m3 kg mol-2, Cv ) (1.5 ( 0.7) × 10-6 m3 kg3/2 mol-5/2, Bκ ) 11.1 ( 0.6 PPa-1 m3 kg mol-2 , and Cκ ) -12 ( 1 PPa-1 m3 mol-5/2 kg3/2. The results are in good agreement with literature data from Perron et al.19 of (114.35) × 10-6 m3 mol-1 for vTMAB0 and -4.1 PPa-1 m3 mol-1 for κTMAB0 from Mathieson and Conway.20 Taking the calculated volume of TMAB, that of a CH2 group as 15.8 × 10-6 (ref 18), and that of a CH3 group in water 26.2 × 10-6 (ref 21), the volume in water of the (18) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71, 147. (19) Perron, G.; Desnoyers, J. E. J. Chem. Eng. Data 1972, 17, 136. (20) Mathieson, J. G.; Conway, B. E. J. Solution Chem. 1974, 3, 455. (21) Gianni, P.; Lepori, L. J. Solution Chem. 1996, 25, 1.

Figure 2. Apparent and partial molar volumes for C22Me6 and C22Me6 + β-CD solutions (solid circles, mCD ) 1.814 mmol kg-1).


Figure 3. Apparent and partial molar compressibilities for for C22Me6 and C22Me6 + β-CD solutions (solid circles, mCD ) 1.814 mmol kg-1).

Figure 4. Apparent molar volumes and compressibilities for TMAB and fit curves to eq 5.

C22Me6 would be 524.1 × 10-6 m3 mol-1, practically the same as the measured value. The coincidence of these values would not indicate a possible folding of the C22Me6. Since it is well-known that the compressibility is more sensitive to structural changes, we have tried also with this property. The molar compressibilities are plotted in Figure 4. From the fit to ms in the premicellar region, κs0 ) -22 ( 1 PPa-1 m3 mol-1. Unlike the volumes, we have not found measurements of this property in the literature

Langmuir, Vol. 17, No. 5, 2001 1395

for the bolaform, but it is possible to do a group contribution analysis of κs0 with the compressibilities of the molecule fragments as we have done with vs0. Thus, taking κs0(TMAB) ) -3.76, κs0(CH2) ) -1.5, and κs0(CH3) ) -3.1 PPa-1 m3 mol-1 (ref 9), the compressibility of the bolaform would be -34.3 PPa-1 m3 mol-1, which is smaller than -22 ( 1 PPa-1 m3 mol-1. This value is more negative than the measured one, and it could indicate that, in the monomer form, the C22Me6 is less exposed to water and, therefore, suggesting that a partial folding occurs, in agreement with ultrasonic relaxation experiments.17 Bolaform + β-CD + Water. The ternary system has been measured at a constant β-CD concentration mCD ) 0.001814 mol kg-1. In Figures 2 and 3 the apparent molar and partial molar volumes versus the bolaform molality are plotted. From the vφ,s plot, remarkable differences can be observed along the range of concentrations studied. For the ternary system, vφ,s is always well above the curve for the pure bolaform in water, and only when the partial molar volume is plotted do the curves merge at concentrations above the cmc. It can be stated, therefore, that the volume of the surfactant in the micelle form will be the same irrespective of the presence of β-CD. This same behavior has been observed with alkyltrimethylammonium bromides9 and sodium alkanoates4 and it is an indication that the β-CD does not take part into the micelle structure. Another interesting consideration is that the cmc in the ternary system (cmc*) is reached at higher concentrations (Figures 1b, 2, and 3). The shift implies that the competitive equilibrium due to the affinity of the monomer for the micelle or the β-CD must be resolved in favor of the latter, that is, only when all the available cavities are occupied can the monomers aggregate to form the micelles. According to the Anianson and Wall analysis,22 the equilibrium constant for the incorporation of a monomer n to a forming micelle with aggregation number n - 1 is related to the kinetic constants of the entrance and release of the monomer, kn and kn-1, respectively, by Kn ) kn/kn-1 ) 1/cmc, provided the n steps in the process have the same equilibrium constant. Zana et al.17 have studied the micellization kinetics of this surfactant, obtaining 2 × 109 M-1 s-1 for kn and 7 × 106 s-1 for kn-1. This means that Kn is about 285 M-1. Binding constants of surfactants with β-CD usually increase with the chain length. For instance, for alkyltrimethylammonium bromides the binding constant for the 1:1 complex ranges between 103 for DTAB (ref 9) and ca. 105 for CTAB (ref 23). In light of the plots of vφ,s versus ms, it is clear that the binding constants must be larger compared to Kn. Moreover, the shift is approximately cmc + mCD/2, which is better appreciated in the plot of the partial property. This fact points to a 2:1 stoichiometry, i.e., two β-CDs per molecule of surfactant. The height of the β-CD is about 7.9 Å, which is going to be, at most, the surfactant length included in its allstaggered conformation. This length is equivalent to 6.3 CH2 (ref 24). This would permit a maximum number of three threaded CDs, assuming the hydrocarbon chain of the bolaform is completely extended. The volume of the monomer in the presence of CD, v0s,CD, obtained from the extrapolation at infinite dilution of vφ,s or vs is 580 × 10-6 m3 mol-1, much higher than that for (22) Anianson, E. A. G.; Wall, S. N.; Almgrem, M.; Hoffman, H.; Keilman, I.; Ulbritch, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905. (23) Gonza´lez-Gaitano, G.; Crespo, A.; Compostizo, A.; Tardajos, G. J. Phys. Chem. B 1997, 101, 4413. (24) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Krieger: Malabar, FL, 1991.

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the surfactant in water. The difference between both is the transfer volume at infinite dilution, ∆vr0. In a previous paper,23 a simple model has been applied to conventional ionic surfactants to calculate the number of CH2 groups that are complexed. The goal is to relate the transfer volume to the released molecules of water from the cavity and the number of methylene groups that enter the CD. That is

∆νr0 ) nwνw0 - nCH2νCH20

(6)

where vw0 is the volume of 1 mol of pure water (18.068 × 10-6 m3), nCH2 is the number of CH2 groups buried into the CD, and νCH20 is the volume of a methylene group in water (15.8 × 10-6 m3 mol-1 from ref 18). Note that in this equation an equilibrium completely displaced to the products is assumed, that is, a complete complex formation, and that the complex formed in conditions of excess β-CD is that of maximum stoichiometry (in this case, 3:1). Both conditions are reasonable and they have been confirmed in the CnTAB (n ) 10-16) + β-CD + water systems.9 Substituting in eq 6 the transfer volume, 58 × 10-6 m3 mol-1 and considering that 6.3 CH2 groups release 6.5 water molecules, that is, the number of molecules found by X-ray diffraction25 and neutron diffraction26 for the solid β-CD, we obtain about 20.4 methylene groups included. Of course, this model is rather simple and sensitive to the volume of a methylene group but the results are consistent with the length of the surfactant when it is completely extended. It is worthy to mention that the complex is formed despite the hydration state and charge of the head, that is, for a cyclodextrin to be threaded by the alkyl chain, it must overpass the cationic ends. This implies a desolvation and a latter resolvation, once the complex has formed, which does not seem to be a drawback for the rotaxane formation. An analogous behavior is observed with the apparent adiabatic compressibility (Figure 3). At infinite dilution, κφ,s reaches a value of 109 PPa-1 m3 mol-1, positive and considerably higher than -22 PPa-1 m3 mol-1 for the pure surfactant, yielding a transfer compressibility at infinite dilution, ∆κr0 ) 131 PPa-1 m3 mol-1. At concentrations beyond the cmc, the curves of the binary and ternary systems get together, and the cmc of the C22Me6 is shifted (better perceived in the κs plot). In the previous study of ternary systems CnTAB + β-CD + water,9 the same trend in κs0 than that for C22Me6 has been observed, and κs0 increases steeply with n. We have plotted in Figure 5 the transfer compressibilities and volumes of these systems, ∆κr0 and ∆vr0, together with the C22Me6 value versus n. Although this surfactant does not belong to the homologue series due to the presence of the extra -N+(CH3)3 group, the points are quite well aligned, a clear indication that, in the formation of a complex with CD, the hydrophilic part is not such an important contribution as the hydrophobic one. The interpretation of the compressibility can be done considering the sum of several contributions. First, there is the effect of the hydration water. When the complex forms, the released water molecules that were inside the cavity become bulk water. We can consider the water molecules included within the cavity as highly structured water, having a rather low compressibility compared to the bulk water. Second, the surfactant feels a more

where κw0 is the compressibility of the bulk water and κCH20 is that of a CH2 group in water. Equation 7 relates the change in the transfer compressibility at infinite dilution to the difference between the compressibility of the water released when the complex forms, which is incorporated to the bulk, and the compressibility of the included surfactant moiety in water, nCH2κCH20. The last contribution in the above equation accounts for the different compressibility of the CD or CDs when they are threaded by the bolaform or filled with water. When dealing with volumes, a term analogous to the latter should be included, but it can be assumed that the difference in volume when the β-CD is filled with water or with the surfactant is negligible, so we did not consider it in eq 6. By substitution in eq 7 of the water molecules expelled (having κw0 ) 8.081 PPa-1 m3 mol-1) and the CH2 groups that enter, which are known from ∆vr0 and eq 6, the compressibility per methylene group, -1.5 PPa-1 m3 mol-1 (ref 9), together with the measured ∆κr0, it is possible to estimate the last term, resulting in (κCDs - κCDw)cavity ) -70 PPa-1 m3 mol-1. It is negative, which seems striking considering that, in the case of a surfactant which forms a 1:1 complex as it is the case of DTAB, (κCDs - κCDw)cavity is positive and equal to 9 PPa-1 m3 mol-1 (ref 9). The negative value can be ascribed to other factors not included in eq 7, such as the formation of hydrogen bonding between the hydroxyl groups of the adjacent threaded CDs. In fact, these interactions occur in polyrotaxanes,6 molecules in which the molecular axis is a polymer, and they are supposed to be partially responsible for their stability, since CDs with all the OH groups completely substituted by -CH3 groups do not form these structures.28

(25) Lindner, K.; Saenger, W. Carbohydrate Res. 1982, 99, 103. (26) Zabel, V.; Saenger, W.; Mason, S. A. J. Am. Chem. Soc. 1986, 108, 3664.

(27) Rekharsky, M. V.; Inoue, Y. Chem. Rev. 1998, 98, 1875. (28) Gonza´lez-Gaitano, G.; Tardajos, G.; Brown, W. J. Phys. Chem. B 1997, 101 (5), 710.

Figure 5. Transfer volumes and compressibilities for CnTAB + β-CD systems and C22Me6 + β-CD.

hydrophobic environment when it is forming the complex compared to water, which is one of the driving forces in the complex formation.27 If the surfactant becomes longer, we will have more conversion to bulk water of the molecules that are inside and an increasing surface or volume of hydrophobic cavity for the surfactant. The explanation for the compressibility behavior can be done quantitatively, in a similar way than that the volume. If we consider a complex that forms completely, in which nCH2 groups are threading one or more CDs, we have

∆κr0 ) nwκw0 - nCH2κCH20 + (κCDs - κCDw)cavity (7)


Langmuir, Vol. 17, No. 5, 2001 1397

Figure 7. 1H NMR spectra showing the β-CD protons for C22Me6 + β-CD systems at different molar ratios of surfactant/ β-CD.

Figure 6. 1H NMR spectra in D2O for C22Me6 below the cmc (a) and above the cmc (b) and β-CD (c).

With regard to the binding constants for the different complexes, the only thing that can be said is that they must be large. In the cited paper9 we have used Young’s rule29 to estimate the binding constants and reaction parameters from the apparent volume or apparent compressibility. This can be done whenever the micellization begins after the complex has formed completely, as in DTAB or sodium alkanoates up to sodium dodecanoate,30 surfactants with a cmc reasonably high to fulfill this condition. If the cmc is low, the analysis of the thermodynamic properties is complicated by the presence of the aggregation of the surfactant, and data cannot be obtained over a range of concentration wide enough. The binding constants for the two-step equilibrium in CTAB are K1 ) 67 700 L mol-1 and K2 ) 9600 from emf measurements,31 so we can expect them to be about this order of magnitude in C22Me6. Probably emf measurements with selective electrodes of the surfactant or microcalorimetric measurements could shed light on the subject. 1H NMR Studies. In Figure 6 the proton spectra corresponding to the β-CD and to the bolaform (both in monomer and in micelle form) are shown, together with the signal assignment. The most important protons to study in the CD are those inserted in the inner face, H3 and H5, since these are the probes to detect the inclusion complex. The other protons, H1, H2, and H4, point to the exterior of the CD. H6 protons are positioned at the narrower rim of the β-CD. In the surfactant, the protons under study are those of the head, (CH3*)3-N+ and -CH2*-N+, which we will denote hereafter as CH3 and CH2(1), and those of the chain, -CH2*-CH2-N+ and -(CH2*)n-, denoted as CH2(2) and CH2(n), respectively. (29) Young, T. F.; Smith, M. B. J. Phys. Chem. 1954, 58, 716. (30) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 1997, 101, 9270. (31) Mwakibete, H.; Crisantino, R.; Bloor, D. M. Langmuir 1995, 11, 57.

Beside the broad singlet of the latter CH2(n), there is a small peak which integrates for eight protons and that can be assigned to the two methylene groups next to CH2(2). Taking into account the symmetry of this surfactant, each one of these four signals represents a double contribution of protons, since they are chemically equivalent (e.g., the signal for CH3 represents the two sets of methyl groups of both heads, 2 × 9 protons, that of CH2(1) represents 2 × 2 protons, and so on). In the ternary system, remarkable upfield shifts of the protons of the β-CD, H3, H5, and H6 are observed (Figure 7). The H1 signal changes scarcely, in a maximum extent of -0.02 ppm. H2 and H4 resonances do not change their positions although a loss of the symmetry in the H2 doublet and H4 triplet is noticed, probably due to the distortion of the β-CD structure. The greatest changes in the inner protons signals occur with high molar ratios, R ) C22Me6/β-CD. Although it is difficult to follow the resonances due to the overlapping, H5 protons suffer maximum changes of ∆δ ) (δ0 - δ)CD ≈ 0.19 ppm, H3 of ∆δ ≈ 0.10 ppm, and H6 of ∆δ ≈ 0.07 ppm. This seems reasonable considering that H5 protons, at the narrower part of the cavity are more protuberant than H3, and these are more than the seven H6, which are inserted in the edge of the CD. In Figure 8 plots of ∆δ versus the molar ratio for the ternary system are shown. Since the outer H1 protons do not seem to be affected in the complexation, their signal has been used as an internal standard in the spectra to calculate the changes in δ upon the complexation. The chemical shifts of the host protons decrease monotonically up to a constant value around R ) 0.5, which indicates a predominant stoichiometry of 2:1, in good agreement with the observed cmc shifting, and a strongly bound complex since the saturation of the plot is reached sharply. The shifts to high field of these protons display an increasing shielding during the complex formation, as a result of the release of the water molecules from the cavity which are replaced by the nonpolar alkyl chain of the bolaform.

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Figure 8. Plot of the change in the chemical shifts for some β-CD protons versus the molar ratio.

Figure 9. 1H NMR spectra showing the surfactant protons for C22Me6 + β-CD systems at different molar ratios of surfactant/ β-CD (asterisks represent systems in which the concentration of free surfactant is higher than the cmc).

Binding constants could be obtained from these plots, by applying the Benesi-Hildebrand method modified for NMR applications.32 In the present case it would be necessary to use a four-site model, that is, to divide the measured δ into the contribution of the free CD and each complex, 1:1, 2:1, and 3:1, and the use of six parameters. However, the use of so many parameters, together with binding constants that seem to be very high according to the plots of the thermodynamic properties and δ versus R, would lead to misleading values. As far as the changes in the resonances for the surfactant protons are concerned, they are smaller in absolute value than those of the host and depend on the protons considered. In Figure 9 we have plotted the different spectra obtained with different molar ratios C22Me6/βCD. To ascribe the changes in δ only to the complex equilibrium, measurements must be performed at concentrations below the cmc*, since the micellization (32) Bergeron, R. J.; Channing, M. A.; Gibeley, G. J.; Pillor, D. M. J. Am. Chem. Soc. 1977, 99, 5146.


produces a broadening of the signals which could mask the effects of the binding. We have included spectra at molar ratios 1.70 and 2.30 in the plot, in which the free bolaform is at concentrations above the cmc*, to illustrate this effect. The most remarkable change due to the β-CD presence is the splitting and broadening of the CH2(n) signal which precludes a quantitative investigation of the individual components. The presence of this asymmetry when the β-CD is in the solution indicates nonequivalent molecular environments attributable to complexes of different stoichiometry. This has been observed in a proton NMR study on alkylcarboxylates with β-CD,33 where NaD (sodium decanoate), which is short enough to form only a 1:1 complex, lacks the broadening and asymmetry, whereas in NaL (sodium dodecanoate, or laurate) the effect is manifested. The resonances of the methyl protons, CH3, and the adjacent protons, CH2(1) and CH2(2), change their positions in -0.040, -0.060, and -0.025 ppm significantly less than the changes for the inner protons of the β-CD, which suggests that they are little involved in the complex, and the CDs will have a preference for covering the middle part of the chain, instead of the bulky and charged ends. No complex has been observed by NMR when measuring the system TMAB + β-CD, as a confirmation of the low affinity of the CD for the stoppers. Conclusions The system docosane 1,22-bis(trimethylammonium bromide) + β-CD in aqueous solution has been studied by density and speed of sound measurements and proton NMR spectroscopy at 298 K. From the speed of sound and density, the molar partial compressibilities and volumes of the bolaform in water and of the ternary system as a function of the surfactant concentration have been obtained. For the C22Me6 + water system, compressibility data, together with measurements on TMAB, indicate that the surfactant is partially folded when it is in its monomeric form. For the ternary system, C22Me6 + β-CD + water, a notable increase of the thermodynamic properties of the surfactant at infinite dilution is observed. The quantitative treatment of the transfer properties, according to the released water molecules from the cavity and the methylene groups of the bolaform that enter, prove the formation of a molecular rotaxane in which three β-CDs are threaded per molecule of surfactant in conditions of excess β-CD. The rotaxane forms despite the hydration state of the cationic heads at both ends. The comparison of the transfer properties with a series of alkyltrimethylammonium bromides proves that the tendency to form the complexes is mainly controlled by the length of the hydrophobic alkyl chain. The shift of the cmc points to a predominant stoichiometry of 2:1, although in excess of CD, a 3:1 stoichiometry is revealed. 1H NMR experiments have been performed to elucidate the molecular structure of the rotaxane. The trends of the chemical shifts point to very high binding constants, confirm the main 2:1 stoichiometry, and indicate that the bulky charged ends of the surfactant are not included inside the β-CD. Acknowledgment. The authors acknowledge the financial assistance provided by the M.E.C. through DGES (Grant Number PB970324) and by the U.C.M. (Grant Number PR486/97-7489) and wish to thank Dr. J. R. Isasi for the revision of the original manuscript. LA001235R (33) Wilson, L. D.; Verrall, R. E. Can. J. Chem. 1998, 76, 25.

Thermodynamic and Spectroscopic Study of a Molecular Rotaxane

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