Molar Partial Compressibilities and Volumes, 1H NMR, and Molecular

Langmuir 1999, 15, 7963-7972

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Molar Partial Compressibilities and Volumes, 1H NMR, and Molecular Modeling Studies of the Ternary Systems β-Cyclodextrin + Sodium Octanoate/Sodium Decanoate + Water G. Gonza´lez-Gaitano,† T. Sanz-Garcıá,‡ and G. Tardajos*,‡ Departamento de Quı´mica-Fı´sica I, Facultad de Quı´micas, Universidad Complutense, 28040 Madrid, Spain, and Departamento de Quı´mica y Edafologıá, Facultad de Ciencias, Universidad de Navarra, 38080 Pamplona, Spain Received December 4, 1998. In Final Form: July 26, 1999 The thermodynamic behavior of the ternary systems β-cyclodextrin (β-CD) + sodium octanoate (NaO) or sodium decanoate (NaD) + water has been studied from density and speed of sound measurements in a broad concentration range at 298 K and at natural pH. The molar partial compressibilities and volumes of the pure surfactants in water as a function of concentration have been obtained and compared with the literature data. For the ternary systems, a remarkable increase of the molar partial compressibility of the surfactant at infinite dilution with respect to the value of the surfactant in water is observed, whereas it does not change in the micelle region, and the same behavior is found with the partial volume. The changes in the transfer properties of the surfactants at infinite dilution, molar partial compressibilities, and volumes can be discussed in terms of a simple model in which it is considered the balance between the released water from the cavity and the methylene groups of the substrate that enter into the macrocycle. The positive molar compressibility of the surfactant when it is forming the complex, as a difference with the negative value when it is in pure water, prove the hydrophobic component of the interaction and permits estimating from this property the binding constants by application of Young’s rule. 1H NMR studies on the systems permit us to elucidate the complex structure and corroborate the thermodynamic data. The association constants and stoichiometry have been deduced from volumes, compressibilities, and 1H NMR data, yielding consistent values that agree with other literature results obtained at fixed pH. Molecular mechanics calculations have been performed to shed light on the structure of the complex in solution. The results confirm the NMR data and indicate that the polar head in the complex is at the wider rim of the macrocycle, protruding in the cavity, with the surfactant tilted within the β-CD.

1. Introduction Cyclodextrins (CDs) are cyclic oligosaccharides having six, seven, or eight glucopyranose units linked by glycosidic bonds R-1,4 (R, β, and γ-cyclodextrins, respectively). They have a toroidal or hollow, truncated cone shape with a nonpolar, hydrophobic inside and two hydrophilic rims, formed by the primary (narrower rim) and secondary (wider rim) OH groups. Their unusual structure gives the CDs the ability to form inclusion complexes through noncovalent interactions with molecules that fit into the cavity. Cyclodextrins are consequently of great interest in a variety of fields.1 There are many works in the literature dealing with the encapsulating properties of CDs with many different compounds and the calculation of stoichiometries and equilibrium constants.2 However, little attention has been paid to the role that hydration water has in these systems and its effect in the thermodynamics of complexation. Volumetric and, particularly, compressibility properties of solutes are known to be sensitive to the degree and nature of the solute hydration, and many studies have * To whom correspondence should be addressed. † Universidad de Navarra. ‡ Universidad Complutense. (1) (a) Szelti, J. Cyclodextrins and Their Inclusion Complexes; Akademiai Kiado: Budapest, Hungary, 1982. (b) Bender, M. L.; Komiyama, M. Cyclodextrin Chemistry; Springer-Verlag: Berlin, 1978. (2) Mwakibete, H.; Crisantino, R.; Bloor, D. M.; Wyn-Jones, E.; Holzwarth, J. F. Langmuir 1995, 11, 57. (3) Wurzburger, S.; Sartorio, R.; Elia, V.; Cascella, C. J. Chem. Soc., Faraday Trans. 1990, 86, 3891.

been carried out on more or less simple compounds containing hydrophobic and hydrophilic groups, such as alcohols,3 carboxylic acids,4 carbohydrates,5 nucleotides,6 amino acids,7 etc. In the case of a hydrophobic molecule (e.g., a surfactant) dissolved in water, the solvent reorganizes around it and this results in a negative value of the molar partial adiabatic compressibility. If this molecule is transferred to the nonpolar cavity of a CD, it is reasonable to expect remarkable changes in compressibility, as are observed, for instance, in micellization processes, in which a hydrophobic molecule passes from water to the hydrocarbon-like core of a micelle. Since the formation of an inclusion complex between a substrate and a CD involves changes in the hydration water of both host and guest molecules, it must be reflected in thermodynamic properties related to the volume and compressibility of the implicated species. If the guest is a surfactant, the complex formation should modify dramatically parameters such as critical micelle concentration (cmc), monomer compressibility, or volume, due to the presence of a competitive equilibrium between micellization and complexation. Thus, properties such as molar compressibilities or volumes could be used with advantage to explain these processes, or even to estimate the association constant between the monomer and the CD, provided an adequate model is assumed and fairly precise (4) Shahidi, F.; Farrell, P. G. J. Solution Chem. 1978, 7, 459. (5) Nomura, H.; Onoda, M.; Miyahara, Y. Polym. J. 1982, 14, 249. (6) Buckin, V. A.; Kankiya, B. I.; Kazaryan, R. L. Biophys. Chem. 1989, 34, 211. (7) Kharakoz, D. P. J. Phys. Chem. 1991, 95, 5634.

10.1021/la981678j CCC: $18.00 © 1999 American Chemical Society Published on Web 11/09/1999

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measurements of the corresponding properties are available. In a previous work,8 the authors have observed this behavior studying the molar partial volumes and compressibilities in sodium cholate + β-CD + water, proving that, although the transference volumes are almost zero, it is possible to observe the formation of the complex via the compressibilities. Later on, a simple model was developed in which by studying a cationic surfactant, decyltrimethylammonium bromide (DTAB), we gave the interpretation of the molar partial properties at a molecular level in terms of the transfer volumes and compressibilities at infinite dilution.9 To our knowledge, only a few papers take up volumetric studies in systems CD + alkylcarboxylates + water, using natural10 or modified cyclodextrins,11,12 but none of these deals with compressibilities. In this work we have measured the speed of sound and density for the ternary systems β-CD + sodium octanoate (NaO) or decanoate (NaD) + water in the premicellar and micellar regions at natural pH, and from these measurements, the molar partial volumes and adiabatic compressibilities have been calculated. To obtain these properties with the required precision, a very precise technique has been employed to measure simultaneously density and speed of sound. It has the advantage, in relation to common experiments of this kind, that the sweep in concentration is performed in a continuous way, so that between two consecutive points of very close concentration the system is not perturbed, and the property and its changes can be obtained with higher precision. These experiments give us information at a molecular level of the nature of the complex, the binding constants, the stoichiometry, and the effect that the CD has on the micellization. A molecular modeling and 1H NMR study has been done in addition to the thermodynamic study to reinforce the conclusions regarding to the microscopic structure of the complex. 2. Materials and Methods Materials. β-CD was purchased from Sigma, with a purity of 99% and a water content of 13.5%, as determined from thermal analysis. Sodium alkanoates (NaO and NaD) were obtained from Sigma, with purities between 99 and 100%. All the reactants were used as received without further purification, and the solutions were prepared in redistilled, deionized (Millipore super-Q system), and degassed water. Measurements of Density and Speed of Sound. Measurements of density, F, and speed of sound, u, have been performed simultaneously with a technique designed in this laboratory and described extensively elsewhere.13 For the density we have utilized two different vibrating tube densitometers, a commercial one (Anton Paar DMA 601 HT with frequency meter DMA 60) and a new prototype designed by us.14 The first one was used in the NaO + β-CD + water system, and the second one in the NaD + β-CD + water system. The ultrasonic cell is immersed in the thermostat in both the assemblies, where (8) Gonza´lez-Gaitano, G.; Compostizo, A.; Sańchez-Martıń, L.; Tardajos, G. Langmuir 1997, 13, 2235. (9) Gonza´lez-Gaitano, G.; Crespo, A.; Compostizo, A.; Tardajos, G. J. Phys. Chem. B 1997, 101, 4413. (10) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 1997, 101, 9270. (11) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 1998, 102, 480. (12) De Lisi, R.; Milioto, S.; Pellerito, A.; Inglese, A. Langmuir 1998, 14, 6045. (13) Tardajos, G.; Gonza´lez Gaitano, G.; Montero de Espinosa, F. Rev. Sci. Instrum. 1994, 65 (9), 2933. (14) Herrero, J.; Gonza´lez-Gaitano, G.; Tardajos, G. Rev. Sci. Instrum. 1997, 68 (10), 3835.

Gonza´ lez-Gaitano et al.

a TRONAC PTC41 and a cryostat achieve a temperature stability better than 1 mK. The molar properties that can be calculated from F and u are apparent and partial molar volumes and adiabatic compressibilities. In ternary systems as those 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

vφ,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. The molality in this formula is defined as mole of solute per kilograms of water. If the speed of sound, u, is known, the apparent molar adiabatic compressibility can be calculated as

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

(2)

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

vs )

( ) ∂V ∂ns

)

nw,nCD

( ( ))

κs ) -

∂ ∂V ∂ns ∂P

d (v m ) dms φ,s s

S n ,n w CD

)

d (κ m ) dms φ,s s

(3)

(4)

All the experiments were carried out at 298.15 K, keeping mCD fixed in the ternary systems. The concentration range was swept in two experiments, at high and low molalities, to minimize errors in concentration. Before the experiments the ultrasonic cell was calibrated with pure water (1496.739 m s-1)15 and the densimeter with pure water (997.045 kg m-3)16 and air.17 Precision in speed of sound and density are 2 × 10-3 m s-1 and 1 × 10-3 kg m-3 (1.5 × 10-3 kg m-3 with the Anton Paar), respectively. 1H NMR Spectra. The NMR samples were prepared using D2O as the solvent (S.d.S., France, with deuteration degree better than 99.9%), keeping the concentration of β-CD constant at 15 mM for all the molar ratios and varying that of the surfactant always below the critical micellar concentration (cmc) to avoid effects due to the self-aggregation of the alkanoates. All the solutions and samples were prepared by weight, in the molality scale. To record the 1H NMR spectra, we utilized a Varian VXR 300S spectrometer operating at 300 MHz and equipped with a thermostating unit. The experiments were recorded 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.18 Molecular Modeling. The software for the molecular mechanics calculations was Insight II program,19 implemented in an IRIS 4D/310VGX workstation of Silicon Graphics. Energy minimization of the isolated host and guest molecules was performed with the Discover module, employing the CVFF force field,20 and with several algorithms (at first a steepest descents, finishing with a modified Newton-Raphson to refine the structures) until (15) Kroebel, W.; Mahrt, K. H. Acustica 1976, 35. (16) Brown, I.; Lane, J. E. Pure Appl. Chem. 1976, 45, 1. (17) Kohlrausch. Praktische Physik; Teubner: Stuttgart, 1968; Vol. 3. (18) WIN NMR; Bruker-Franzen Analytic GmbH. Version 960901. (19) Insight II (3.0.0); Biosym Technologies, San Diego, 1995. (20) Dauber-Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J. Proteins: Struct., Funct., Genet. 1988, 4 (1), 31.

Compressibilities in Ternary Systems

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Figure 1. Apparent molar volume, vφ,s, and partial molar volume, vs, for NaO in water (open points) and NaO plus β-CD in water (solid points).

Figure 2. Apparent molar compressibility, κφ,s, and partial molar compressibility, κs, for NaO in water (open points) and NaO plus β-CD in water (solid points).

the root mean squares of the derivatives were less than 0.0004 kJ Å-1. Afterward, molecular dynamics of the system were run at 298 K, and the process of minimization was repeated to find the absolute minimum of energy. The alkanoates were fitted in the cavity by rigid docking with the refined structures. An XY plane was defined by the O4 atoms of the β-CD, and the coordinate origin as the center of mass of the seven O4. The Z-axis is perpendicular to this plane, with positive orientation to the wider rim. The center of the alkanoate is the C atom of the carboxylate group. The interaction energies were calculated with the docking module of the program, approximating the guest along a vector in the Z direction by the head toward the β-CD, with 0.5 Å steps and starting in 7 Å from the center of the β-CD. A cutoff distance of 100 Å for the Coulomb and van der Waals energies was chosen to include all the possible interactions, and cross terms and Morse potentials were considered in the force field. For the minimization of the complexes, the structure of minimal docking energy in each case was taken as the starting point, following strategies similar to those employed for the isolated hosts, with a convergence criterion of 0.004 kJ Å-1 in the derivatives. To account for the solvent effects, a distancedependent dielectric constant was introduced into the electrostatic term of the force field. 3. Results and Discussion Thermodynamic Properties of the Surfactants in Water. The thermodynamic properties are plotted in Figures 1-4. The apparent molar volume of the pure alkylcarboxylates in water in the premicellar region has been fitted to the equation

vφ,s ) vs0 + Avms1/2 + Bvms

Figure 3. Apparent molar volume, vφ,s, and partial molar volume, vs, for NaD in water (open points) and NaD plus β-CD in water (solid points).

deviation parameter. The results of the fit for the alkylcarboxylates in monomer form are summarized in Table 1. De Lisi et al. give for NaD a monomer volume of 164.08 × 10-6 m3 mol-1 (ref 21) and 164.89 × 10-6 m3 mol-1 (ref 12). Vikingstad et al.22 report 132.4 and 164.2

(5)

where vs0 is the monomer volume, Av is the Debye-Hu¨ckel limiting slope (1.865 cm3 kg1/2 mol3/2 at 25 °C), and Bv a

(21) De Lisi, R.; Perron, G.; Desnoyers, J. E. Can. J. Chem. 1980, 58, 959. (22) Vikingstad, E.; Skauge, A.; Høiland, H. J. Colloid Interface Sci. 1978, 66, 240.

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Figure 4. Apparent molar compressibility, κφ,s, and partial molar compressibility, κs, for NaD in water (open points) and NaD plus β-CD in water (solid points). Table 1. Thermodynamic Parameters for the Pure Surfactants in Water in Monomer and Micelle Form at 298.15 Ka cmc

vs0

Bv

vsm

∆vm

κs0

Bκ

κsm

∆κm

NaO 0.403 133.30 -0.48 143.6 8.8 -70.7 44 40.4 93.6 NaD 0.111 165.5 0 175.4 9.8 -71.1 115 57.2 117.6 a cmc in mol kg-1; volumes in m3 mol-1 × 106; compressibilities in PPa-1 m3 mol-1; Bv in m3 mol-2 kg; Bκ in PPa-1 m3 mol-2 kg.

× 10-6 m3 mol-1 for NaO and NaD, whereas Kale et al.23 find 164.0 × 10-6 m3 mol-1 for NaD. More recent data come from Wilson et al.,10 who give 133.0 and 165.1 × 10-6 for NaO and NaD, obtained at constant pH ) 10.5. As far as the Bv coefficient is concerned, calculations from eq 5 yield -0.48 × 10-6 and 0 m3 mol-2 kg for NaO and NaD, respectively. De Lisi et al.,24 for NaD, find 2.7 × 10-6 m3 mol-2 kg, although they do not calculate the value of the parameter for NaO. In that paper, other analogues of the series yield values that range between -0.9 (for sodium heptanoate) and 1.1 × 10-6 (sodium hexanoate), but no conclusion can be extracted about the dependency with the number of carbon atoms, nC. Since we have measured only two components of the analogue series, it is difficult to say anything conclusive, but Bv seems to increase with nC, which indicates that the longer the chain is (the hydrophobicity) the larger are the deviations from the limiting law. The cmc’s can be estimated from F or u measurements. Since u changes more sharply around the cmc, we have used this property, defining the critical concentration as the intercept of the two lines that fit the u points in the premicellar or micellar regions. The change in the micellization volume, ∆vm, has been calculated as the difference between the molar partial property at the beginning of the aggregation (cmc) and the value ex(23) Kale, K. M.; Zana, R. J. Colloid Interface Sci. 1977, 61, 312. (24) De Lisi, R.; Ostiguy, C.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1979, 71, 147.

trapolated from high concentrations to the cmc (Table 1). The micellization volumes thus measured are in good agreement with literature data: 8.9 × 10-6 m3 mol-1 for NaO and for NaD 9.6 × 10-6 m3 mol-1 (ref 22) and 10.6 × 10-6 m3 mol-1 (ref 23). As for the molar partial compressibilities, the only available data for sodium alkanoates are those of Vikingstad et al.22 Their κs0 values for the monomer lie between -71 and -82 PPa-1 m3 mol-1 for a series from sodium heptanoate to sodium myristate. The values they obtain for these surfactants are -74 and -78 PPa-1 m3 mol-1, slightly different than ours, and the contribution per CH2 group is, considering the whole series, -1.6 PPa-1 m3 mol-1. From our NaO and NaD data (Table 1), the compressibility per CH2 group would be -0.2 PPa-1 m3 mol-1, smaller in absolute value than that of Vikingstad. Kudryashov et al. in a recent paper25 obtain for a homologue series of alkyltrimethylammonium bromides (n ) 8 to n ) 16) -0.87 PPa-1 m3 mol-1, and Buwalda et al.26 obtain -0.54 PPa-1 m3 mol-1 for the shorter homologues of the same series (n ) 3-6). In view of these results, although we have measured only two homologues, it seems that the contribution per methylene group should be less than the reference value. For the molar apparent compressibility we have used an equation similar to eq 5. To our knowledge, there are no numerical estimations of the limiting law parameter for the adiabatic compressibility, Aκ. Hence, we have considered Aκ ) 2.55 PPa-1 m3 mol-3/2 kg1/2, that is, the same as that of the isothermal compressibility, since the plots of both properties have the same shape.24 With this assumption, Bκ results in 44 PPa-1 m3 mol-2 kg for NaO and 115 PPa-1 m3 mol-2 kg for NaD, which seems to follow the same trend with nC as the Bv coefficient of eq 5. The change in the compressibility of micellization, ∆κm, is calculated in the same way as ∆vm, resulting in 93.6 PPa-1 m3 mol-1 and 117.6 PPa-1 m3 mol-1, in fair agreement with literature data22 (92 and 114 PPa-1 m3 mol-1, respectively). Thermodynamic Properties of the Systems β-CD + Surfactant + Water. The molar apparent and partial properties for NaO and NaD in the presence of β-CD are plotted in Figures 1-4. The fixed β-CD concentrations in each case were 0.01532 and 0.01209 mol kg-1. The behavior of the molar properties when the β-CD is present is analogous to that observed with cationic surfactants at infinite dilution: both the apparent volume and compressibility are higher than those of the pure surfactant in water.9 The apparent cmc (cmc*) is reached at concentrations above the cmc of the pure surfactant, in an extension apparently equal to the cmc plus the fixed mCD (Figure 5). It can be observed in Figures 1-4 that, after a certain value of ms, the molar partial properties of the surfactant are displaced in an amount approximately equal to the CD concentration and have the same value in absence or presence of CD, indicating that the complex does not take part into the micelles. In Figure 3, the values of the molar partial volumes are indicated in the cmc’s. In Table 2 are collected the transfer properties at infinite dilution. The shift of the cmc implies that the competitive equilibrium between micellization and complexation is resolved in favor of the latter: only when all the available “holes” (CDs) are occupied can the monomers aggregate to form the micelles. According to the Anianson and Wall (25) Kudryashov, E.; Kapustina, T.; Morrisey, S.; Buckin, V.; Dawson, K. J. Colloid Interface Sci. 1998, 203, 59. (26) Buwalda, R.; Engberts, J.; Høiland, H.; Blandamer, M. J. J. Phys. Org. Chem. 1998, 11, 59.


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between the water expelled from the cavity, which is incorporated into the bulk, and the hole occupied by the segment of the surfactant that is included. Assuming a 1:1 stoichiometry and the above reaction scheme, the reaction volume would be

∆v1:10 ) vw0nw - nCH2vCH20

Figure 5. Speed of sound for NaD in water (open points) and plus β-CD (solid points) showing the cmc and the stoichiometry of the complexes. Table 2. Transfer Parameters and Equilibrium Constants for Sodium Alkanoate + β-CD + Water at 298.15 Ka ms*/mCD

vs0

∆vr0 ∆v1:10

NaO

0.97

150.1 16.8

18.7

NaD

0.94

185.5 20

20.3

c

κs0

∆κr0 ∆κ1:10

-11.8 58.9

-2

69.1

74

74.3

Kb 400 ( 200c 660 ( 60 240 ( 20 1.100 ( 500c 2300 ( 600 1500 ( 100

where vw0 is the volume of 1 mol of pure water, nCH2 the number of CH2 groups buried into the CD, and vCH20 the volume of a methylene group in water. In eq 6 it is assumed that the volume of the cavity filled with water or with the surfactant is the same, so it does not produce an observable change in the molar volume of the monomer when it forms the complex. It is interesting to consider the relationship between the measured transfer volume, ∆vr0, and the change in the volume of the surfactant when it is in free state or when it is totally bound to the CD, a parameter that we have named ∆v1:10. This parameter gives us direct information about the water molecules involved in the process, and it would correspond to the measured value of the property if the reaction were totally displaced to the complex formation. Indeed, both parameters, ∆vr0 and ∆v1:10, are going to be related through the equilibrium constant and the fixed CD concentration in the system. Let us call K1 the binding constant of the equilibrium S + CD S S:CD. Since we are dealing with dilute concentrations, we can fairly approximate the activities to molalities, so that the equilibrium constant can be expressed as

a Units as in Table 1. b From 1H NMR, v φ,s and κφ,s respectively. Obtained at 293 K.

analysis,27 the equilibrium constant for the incorporation of a monomer to a forming micelle with n - 1 monomers is Kn ) kn/kn-1) 1/cmc (assuming all the n steps in the process have the same equilibrium constant). For these surfactants, Kn values would be 2.5 and 9 M-1, values which are small enough to justify the preference of the monomer to form the complex rather than joining to another monomer to construct the micelle. The volume of the monomer at infinite dilution, vs0, increases with the chain length from 16.8 to 20 × 10-6 m3 mol-1 (Table 2). The big changes at infinite dilution in the monomer volume and, especially, in the compressibility, ∆vr0 and ∆κr0, prove that the molecular surroundings of the surfactant in absence or presence of CD are quite different due to the formation of the inclusion complex. The resulting values of the transfer properties at infinite dilution can be explained according to the following reaction scheme9

CD(m + n) + S(l) f CD(m):S(l - s) + n + s where m stands for the number of outer water molecules of hydration, n the molecules of water that are inside the cavity, l the hydration water of the surfactant, and s the molecules of water that the surfactant loses when it is included in the cavity. Due to the geometry of the CD, we can assume that the only water which is going to be involved in the process is the water of the cavity and the part of the hydration shell that covers the surfactant and that will be lost in the inclusion. The change in the volume of the reaction according to this model is the difference (27) 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. (28) Young, T. F.; Smith, M. B. J. Phys. Chem. 1954, 58, 716.

(6)

K1 )

mscx (mCD - mscx)(ms - mscx)

(7)

This equation stands for each point of the plot of vφ,s versus ms in the premicellar zone. Here mCD is the fixed CD molality and mscx that of the surfactant-forming complex. It can be assumed, according to Young’s rule,28 that the apparent volume can be split in the contributions due to the free monomer, vs0, and to the monomer-forming complex, v1:10. In the case of a 1:1 complex (or two site model), the measured apparent molar volume is

vφ,s ) χsvs0 + χ1:1v1:10 )

msf 0 mscx v + v 0 ms s ms 1:1

(8)

where each volume is weighed by its mole fraction in solution, χi, ms being the total surfactant molality at each point, msf the molality of the free surfactant, and mscx the molality of the surfactant in complex form. This equation is valid whatever the range of concentration considered and assuming there are no aggregation processes, such as micelle formation. However, at infinite dilution mCD will be much larger than mscx and eq 7 is simplified, allowing us to express mscx as a function of K1 and mCD, thus

mscx )

K1msmCD 1 + K1mCD

(9)

which can be introduced into eq 9 to give

K1mCD vφ,s ) vs0 + (v1:10 - vs0) 1 + K1mCD

(10a)

7968


∆vr0 ) vφ,s - vs0 ) ∆v1:10


K1mCD 1 + K1mCD

(10b)

which relates the measured transfer volume to the change in the monomer volume, ∆v1:10. Note that only if the product K1mCD is much higher than 1 will both volumes ∆vr0 and ∆v1:10 will be the same and that ∆v1:10 is independent of the CD concentration. In view of eq 10b, it is clear that ∆v1:10 must be always higher than ∆vr0. Of course, we need to know K1 beforehand to perform the calculation. However, both parameters, K1 and ∆v1:10, can be obtained together from the plots of vφ,s versus ms. In the case of a surfactant like decyltrimethylammonium bromide (DTAB), which is known to form 1:1 complexes, no dependency with mCD has been observed for transfer properties at infinite dilution (molar partial volumes and compressibilities)9 at the CD concentrations employed. With NaO, which has a smaller K, De Lisi et al.12 report this dependence from volume and heat capacity measurements when studying complexes with hydroxypropyl-β-CD (HPβ-CD). If a 2:1 stoichiometry is possible, then the model can be extended, and eq 8 becomes

vφ,s ) χsvs0 + χ1:1v1:10 + χ2:1v2:10

(11)

It is not difficult to prove that, when ms f 0

∆vr0 ) ∆v1:10

K1mCD 1 + K1mCD + K1K2mCD2 ∆v2:10

+

K1K2mCD2 1 + KsmCD + K1K2mCD2

(12)

where K1 and K2 are the association constants for the first and second binding of the surfactant to the CD, ∆v1:10 ) v1:10 - vs0 and ∆v2:10 ) v2:10 - vs0. In a recent paper, Wilson et al.10 apply Young’s model to estimate the binding constant and extend the model to higher stoichiometries (three-site model, that is, two CDs per one of the guest). We have used the two-site binding strategy with our volumes, since as a difference to data of Wilson et al. they have been measured at natural pH. The numerical problem can be solved by a nonlinear leastsquares fitting (NLSF) with the Levenberg-Marquardt algorithm (LM), in which v1:10 (or ∆v1:10, since vs0 is known) and K1 are adjustable parameters and vφ,s is the measured volume at each ms. The binding constants thus obtained are 660 ( 60 M-1 and 2300 ( 600 M-1, together with the parameters ∆v1:10 ) (18.7 ( 0.3) × 10-6 and (20.3 ( 0.4) × 10-6 m3 mol-1 for NaO and NaD, respectively. Wilson et al. obtain 622 and 2140 M-1 for the same surfactants from apparent molar volumes10 and 660 and 5100 M-1 from spectroscopic measurements (spectral displacement technique with phenolphthalein29). Palepu et al.,30 from conductivity experiments, give for this series 370 and 740 M-1, reporting a participation of a 2:1 stoichiometry for NaO but not with NaD. Gelb et al.31 from emf data report 683 and 7500 M-1 and detect a ternary complex with both surfactants, reporting constants for the 2:1 stoichiometry of 32 and 9.6 M-1, at 293 K. (29) Wilson, L. D.; Siddall, S. R.; Verral, R. E. Can. J. Chem. 1997, 75, 927. (30) Palepu, R.; Richardson, J. E.; Reinsborough, V. C. Langmuir 1989, 5, 219. (31) Gelb, R. I.; Schwartz, L. M. J. Inclusion Phenom. Mol. Recognit. Chem. 1989, 7, 465.

When eq 6 was first applied to the DTAB + β-CD + water system, we used the measured transfer properties, ∆vr0, although in a general case ∆v1:10 must be considered since it does not depend on the CD concentration or on K1. 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. It corresponds to 6.3 CH2 groups, taking the length of a C-C bond with C in sp3 hybridization.32 In the study with DTAB using the transfer volume of this surfactant which is well-known to form a 1:1 complex and by application of this model, we calculated that approximately 6.5 water molecules are expelled when the complex forms, exactly the number of molecules found by X-ray diffraction33 and neutron diffraction34 for the solid β-CD inside the cavity that remains within the CD when it is dissolved. Considering that 6.3 CH2 groups displace 6.5 water molecules, it can be proposed according to eq 6 that, when the surfactant is forming the complex

nCH2 )

∆v1:10 vw06.5/6.3 - vCH2

)

∆v1:10 2.84

(13)

See that now ∆vr0, as a difference to eq 6, is replaced by ∆v1:10. Applying eq 13 to the volumes obtained for the homologues in complex form, the number of CH2 groups included into the CD are 6.6 and 7.1 respectively, taking the volume of a CH2 group in water as 15.8 × 10-6 m3 mol-1 (ref 24). Table 2 shows the molar ratios, expressed as the ratio ms*/mCD, that is, the stoichiometric concentration of surfactant measured divided by the fixed molality of CD. As we did for the cmc, ms* can be calculated by intercepting the extrapolations of the u points in the complex region. Since the concentration range is short, the determination of the intercept can be done with more accuracy than for the cmc (in NaO, for instance, the cmc is relatively high and the micellization occurs in a wide range of ms). The ratio is nearly 1 in both cases, although a decrease with the chain length is noticed, which would indicate a small participation of the 2:1 complex for the longer homologue that is also noticed in the slight increase of the number of methylene groups included when passing from NaO to NaD. With the aim of calculating this 2:1 participation, we have applied the tree site model to our NaD data according to eq 12. A better fit is achieved than with the two site model, and we have obtained K1 ) 4800 ( 800 M-1, K2 ) 55 ( 30 M-1, v1:10 ) (185.0 ( 0.1) × 10-6 m3 mol-1, and v02:1 ) (187 ( 1) × 10-6 m3 mol-1. These values seem reasonable with the definitions and with the literature data. However, the estimate of K2 is quite sensitive to the points used for the fit and values thus obtained can be even lower than those reported and with higher errors. From all this evidence we conclude that the 2:1 complex forms but its proportion is meaningless due to the low K2 value. It is easy to prove from eqs 11 and 12 that the proportion between 2:1 and 1:1 complex when ms f 0 is χ2:1/χ1:1 ) K2mCD. Thus, if K2 is low enough, the proportion of 2:1 complex could be small, even in this situation in which the 2:1 complex is favored. The longer homologues of the series, sodium laurate and sodium myristate, give clearly the 2:1 stoichiometry, as expected.10 All the above considerations help us to understand the data in the literature about the observed dependency of the transfer volumes with the number of carbon atoms of (32) Tanford, C. The hydrophobic effect, 2nd ed.; Wiley: New York, 1973. (33) Lindner, K.; Saenger, W. Carbohydrate Res. 1982, 99, 103. (34) Zabel, V.; Saenger, W.; Mason, S. A. J. Am. Chem. Soc. 1986, 108, 3664.


Langmuir, Vol. 15, No. 23, 1999 7969

Figure 6. Plot of ∆v1:10 versus nC (number of carbon atoms in the chain) for sodium alkanoates with β-CD (open circles, ref 10) and HP-β-CD (open triangles, ref 11; solid triangles, ref 12).

the chain, nC. Data of Wilson et al.10 are the most appropriate for the comparison, since they utilize the same cyclodextrin as we use. In their studies they obtain an almost linear dependency of the transfer volume with nC (Figure 6). If instead of plotting this property we plot ∆v1:10, considering their calculated constants and the concentration of CD fixed in the experiments, a plateau region is observed which levels off at nC ) 8. Beyond this chain length, the value increases, since the 2:1 stoichiometry becomes possible. Actually, ∆v1:10 should be constant and approximately equal to 20 × 10-6 m3 mol-1, but the application of the two-site scheme makes it higher since in ∆v1:10 it is included the effect of the 2:1 complex when the chain is long enough. It is possible to calculate this contribution from the fit to the three-site model of eq 12. The plateau region up to nC ) 8 indicates that the cavity is full with the surfactant in any of the cases. Only with a longer chain is another CD able to “attack” the protruding tail, thus giving the 2:1 stoichiometry, as seems to occur with nC ) 10. The same shape of these plots is perceived with other macrocycles, e.g., HP-β-CD with sodium alkanoates, systems which have been studied foremost by Wilson et al.11 with CnOONa (n from 6 to 14) and lately by De Lisi et al.12 (n from 2 to 10). We have plotted in the same figure both data for comparison (Figure 6). Now the macrocycle is longer than β-CD but the results make sense considering the lengths of both the host and the guest. The plateau seems to extend between 8 and 12 and only a 1:1 complex is observed, whereas the 2:1 binding arises with the longest homologue, sodium myristate, which is long enough to give such stoichiometry. Up to nC ) 8, ∆v1:10 increases regularly since the cavity is losing the water molecules at the same time as the surfactant enters in the macrocycle. The scheme proposed for the transfer volumes can be applied to the compressibility, although a careful analysis of the inclusion process must include more contributions:

∆κ1:10 ) κw0nw - nCH2κCH20 + (κCDs - κCDw)cavity (14) This equation states that the change in the compressibility of the reaction is the difference between the compressibility of the water expelled from the cavity, which is incorporated to the bulk having the same compressibility as that of bulk water (8.081 PPa-1 m3 mol-1), and the compressibility of the included surfactant moiety in water, nCH2κCH2. The last contribution in eq 14 accounts for the different compressibility of the cavity when it is filled with the alkyl chain or with water. When we are dealing with volumes,

Figure 7. Apparent adiabatic compressibility for NaD + β-CD versus ms. The solid line is the fit to eq 14. The dashed lines represent the mole fraction of complex and free β-CD.

we can presuppose that the differences in volume of the cavity when it is filled with water or with the surfactant are going to be negligible. This is the reason we do not consider this effect in eq 6. Substituting in this equation the water molecules expelled and the CH2 groups that enter, data known from the molar volumes, together with the transfer compressibilities in the limit of ms f 0, it is possible to estimate the last contribution, provided the compressibility per methylene group is known. Taking -0.2 PPa-1 m3 mol-1 for κCH20 from our compressibility data for NaO and NaD, we obtain 17.7 and 13.7 PPa-1 m3 mol-1 for (κCDs - κCDw)cavity. Although the result is sensitive to the κCH20 considered, it is positive in any case. This indicates that the cavity is more compressible when it is filled with the guest than with water. This positive value is consistent with the formation of an inclusion complex: the free volume in the cavity is higher when the CD is filled with an alkyl chain than with water and it is expected that the higher the free volume, the larger the compressibility. Young’s model can be extended to the apparent adiabatic compressibilities in the same way as for the volumes if the compressibility of the monomer in water is known. Thus

κφ,s ) χsκs0 + χ1:1κ1:10

(15)

where κs0 and κ1:10 are the adiabatic molar compressibilities of the monomer in free or in complex form. By applying the method to this property the association constants and ∆κ1:10 can be estimated (Table 2). As can be seen, the constants are lower than those resulting from the volumes but remain within the same order of magnitude. The fitted curve is plotted in Figure 7 for the apparent compressibility of NaD; in the same figure have been simulated the mole fractions of complex and free monomer calculated from the K value as a function of ms. As can be seen, the complex concentration increases stepwise, and at concentrations almost twice the fixed mCD all the surfactant is in its complex form. Consequently, the amount of free CD decreases and, when micelles form, all the CDs in the solution are forming complexes with the surfactant. This explains that the apparent cmc is reached at a point which is approximately cmc (in absence of β-CD) + mCD. This also explains why the molar partial properties do not change in the micelles region, since all the CD molecules are forming complexes and do not take part into the micelles. As for the change in the compressibility of the

7970



Figure 9. Chemical shift increments for the H5 protons of β-CD versus the molar ratio surfactant/cyclodextrin.

and assuming a 1:1 stoichiometry, the measured chemical shifts, δ, are the sum of the contributions of the chemical shifts due to the complex, δCD:S, and to the host, δS, averaged with the molar fraction. That is

δ)

Figure 8. 1H NMR spectra for NaD with β-CD at different molar ratios of surfactant/cyclodextrin.

monomer when forming complex, ∆κ1:10, it results in 74 ( 2 and 74.3 ( 0.6 PPa-1 m3 mol-1 for NaO and NaD, respectively. The relative changes when compared to those in volumes are higher, and the compressibility of the monomer passes from a low negative value to be almost zero, indicating the sensibility of the property to detect the complex formation. 1H NMR and Molecular Modeling. The resonances in the 1H NMR spectra corresponding to the six types of protons of the β-CD can be easily assigned.35 When the alkanoate is present, upfield shifts of the inner protons, H5 and H3, are observed (Figure 8), whereas H1 (not shown in the figure), H2, and H4, that is, the protons inserted in the outer face of the cavity and at the narrower rim (H6), are scarcely shifted (less than 0.025 ppm). Movements in the H5 resonances are more pronounced than the less protuberant H3, a fact that would indicate a major contact with the former protons (∆δH3 ≈ 0.5∆δH5). ∆δ for the H5 protons (the chemical shift in absence of guest molecule minus the observed δ) versus the molar ratio (surfactant/CD) are plotted in Figure 9. The stoichiometry is 1:1, being the changes larger for NaD than for NaO (overall increments of 0.180 and 0.160 ppm respectively for H5 protons). This fact reflects more interactions between the CD and the longer homologue, being the equilibrium more displaced to the formation of the complex than otherwise. The binding constants can be calculated from the Benesi-Hildebrand method for NMR applications.36 Thus, for the reaction S + CD S S:CD, if the equilibrium is fast on the NMR time scale37 (35) Demarco, P. V.; Thakkar, A. L. Chem. Commun. 1970, 2. (36) Bergeron, R. J.; Channing, M. A., Gibeley, G. J.; Pillor, D. M. J. Am. Chem. Soc. 1977, 99, 5146.

mCDf mCDcx δCD + δ mCD mCD CD:S

(16)

The binding constant can be estimated by a nonlinear fit of the increments in the chemical shifts, ∆δ, versus R (molar ratio). Notice that the method is essentially the same as the one described in the preceding section for the thermodynamic properties and that it can be applied to protons of the host or the guest. The binding constants for NaO and NaD calculated in this way using the H5 resonances are 460 and 1100 M-1, respectively, at 293 K. Wilson et al.,10 from 1H NMR experiments, obtain 650 and 5200 M-1 for NaO and NaD with H5 protons, working at constant p(H + D) ) 10.5. This prudence measure is taken to avoid solubility problems due to the free acid, which could be present if the salts are not pure enough. If such is the case, it results in a slight turbidity of the solutions, turbidity that we have not observed with the studied substances in our conditions. Working at fixed pH helps also to control the potential hydrolysis of the CD that could be enhanced by increasing temperature. However, within the temperature range studied and at the natural pH of these soaps, this risk seems improbable. Our 1H NMR constants seem to be closer to the values deduced from the adiabatic compressibilities (Table 2). Anyway, the data are in fair agreement, even though they have been obtained with techniques based on different physical chemical principles, e.g., densities, compressibility, and NMR. As far as the resonances for the surfactant protons are concerned, they are not as large as those of H5 and they undergo downfield shifts. For instance, for NaO the relative maximum changes of the resonances corresponding to CH3-, -(CH2)n-, -CH2-, and -CH2-COO- protons are 0.055, 0.040, 0.010, and 0.007 ppm, respectively, at a molar ratio S/β-CD ) 1, and for NaD they are 0.100, 0.0450.008 (signal split), 0.021, and 0.004 ppm, with the same molar ratio as in NaO + β-CD. It is possible to evaluate from NMR experiments the thermodynamic parameters of the reaction by measuring (37) Connors, K. A. Binding Constants. The measurement of Molecular Complex Stability; John Wiley & Sons: New York, 1987.


Langmuir, Vol. 15, No. 23, 1999 7971

Figure 11. Potential energy wells for NaD and β-CD when the surfactant enters (a) from the tail to the narrower rim and (b) from the tail to the wider rim.

Figure 10. (a) Saturation plots for NaD + β-CD at different temperatures. (b) van’t Hoff plot for the complex between NaD and β-CD.

the temperature dependence of the equilibrium constant,38 according to the van’t Hoff equation

ln K )

∆S0 ∆H0 R RT

(17)

with the assumption that both the entalphy and entropy are not temperature dependent within the considered range. We have recorded the spectra for different surfactant/CD molar ratios at 21, 26, 36, and 41 °C and from each series the association constant calculated from the H5 protons. The results are plotted in Figure 10 for NaD. From slope and the intercept we obtain ∆H0 ) -15 ( 2 kJ mol-1 and ∆S° ) 9 ( 7 J mol-1 K-1. If the last point in the plot (26 °C) which seems to deviate is rejected, the parameters are ∆H0 ) -11.9 ( 0.8 kJ mol-1 and ∆S° ) 19 ( 2 J mol-1 K-1. The deviation could be ascribed to temperature dependence of the heat capacity. In any of the cases, the reaction is exothermic and enthalpy driven, as usually happens with inclusion complexes with CDs,39 and the change in entropy is positive but not large. The values do not differ much from potentiometric data of Gelb et al. for this surfactant31 (∆H 0) -20.5 ( 2 kJ mol-1 and ∆S° ) 1.3 ( 1.8 J mol-1 K-1). The complex formation, as we have seen, involves the dehydration of both the CD cavity and the guest molecule, leading to a more hydrophobic environment for the alkanoate tail (∆S > 0). However, the surfactant will be more constrained in the complex, confined to the size of the cavity, resulting in a loss of rotational degrees of freedom around the C-C (38) Zhu, C. Y.; Bradshaw, J. S.; Oscarson, J. L.; Izatt, R. N. J. Inclusion Phenom. 1992, 12, 275. (39) Rekharsky, M. V.; Inoue, Y. Chem. Rev. 1998, 98, 1875.

bonds. Both effects can compensate each other to give such low entropy values.40 To find out the molecular structure of the complex, the interaction energy (electrostatic and van der Waals) between NaD and β-CD has been calculated, as explained in the methods section. The guest molecule has been approximated to the CD in two ways: from the head toward the wider rim and from the head toward the narrower rim of the cavity, and the van der Waals and electrostatic contributions to the interaction energy have been calculated. We have not considered the rotation of the alkanoate since, for other surfactants with β-CD as decyltrimethylammonium bromides, there is almost no dependence of the energy with the rotation angle of the guest (the width of the cavity is enough for the surfactant to “rattle” inside).9 Figure 11 shows the calculated energy wells with their different contributions for the two considered geometries. The van der Waals energy is negative in both cases, but a strong electrostatic repulsion arises when the carboxylate group passes through the cavity. The minimal energy conformation is shown in Figure 12a, in which the carboxylate group is outside the CD, at the secondary rim. However, this energy barrier can be overcome, since inclusion complexes between CDs and dicarboxylic acids have been reported, even with the narrower macrocycle, R-CD.41 This structure is compatible with the observed changes in the chemical shifts of the protons of the surfactant, suggesting a major contact of the guest with the H5 protons rather than with H3, and larger changes in the chemical shifts for the tail protons in the guest molecule. This structure can be used as the starting point for a minimization in order to find out the molecular structure of the complex. In this minimization the solvent effects are comprised into a dielectric constant of 80 dependent on the distance, as is usual in this kind of calculation.42 Note that when the complex forms, there are no water molecules inside the cavity but only outside, and these will not feel influenced by the inclusion (according to the reaction scheme given at the beginning of the section). Thus, although the calculation may be too simplistic to give reliable absolute values of the energy, it can permit discrimination between conformations close in energy. The (40) Connors, K. A. Chem. Rev. 1997, 97, 1325. (41) Watanabe, M.; Nakamura, H.; Matsuo, T. Bull. Chem. Soc. Jpn. 1992, 65, 164. (42) Leach, A. R. Molecular Modelling. Principles and Applications; Addison-Wesley Longman Limited: Edinburgh, 1996.

7972



The calculated energies for the complexes by this strategy are -85.3 and -93.0 kJ mol-1 for NaO and NaD, respectively, implying that the enthalpy increases with the number of carbons in the chain, the same trend as observed with the binding constants. 4. Conclusion

Figure 12. (a) Structure of minimal energy according to the docking procedure for decanoate ion with β-CD. (b) Minimized structure of the complex between decanoate ion and β-CD.

structure, for NaD with the CD, is depicted in Figure 12b. The difference between this and the structure in Figure 12a is that the surfactant is tilted within the cavity, with a considerable freedom of movement. This fact favors a 1:1 stoichiometry and increases the theoretical number of methylene groups that can be lodged into the cavity. This justifies too the observations of 2:1 stoichiometries with the R-CD that become 1:1 with the β-CD, e.g., dodecyltrimethylammonium bromide (DoTAB) which is known to form 1:1 complexes with β-CD, whereas it forms 2:1 with the R-CD.43 With the six glucose macrocycle the fit is more tight for a hydrocarbon chain than with the β-CD, making easier a second CD to reach the protruding tail. (43) Wan Yunus, W. M. Z.; Taylor, J.; Bloor, D. M.; Hall, D. G.; WynJones, E. J. Phys. Chem. 1992, 96, 8979.

The apparent and partial molar volumes and adiabatic compressibilities of the ternary systems β-CD + NaO or NaD + water have been obtained from density and speed of sound measurements in a broad concentration range at 298 K and at natural pH. The molar partial compressibilities and volumes of the pure surfactants in water as a function of concentration have been obtained and compared with the literature data. For the ternary systems, the magnitudes of the molar partial compressibility and volume of the surfactant at infinite dilution are greater than that in pure water (especially κφ,s), but they are coincident in the micelle region. The changes in the transfer properties of the surfactants can be discussed in terms of the balance between the released water from the cavity and the methylene groups of the substrate that enter into the macrocycle, resulting in 6.6 and 7.1 CH2 groups for NaO and NaD, respectively. The thermodynamic properties have been used to deduce the binding constants using Young’s rule. The values calculated from compressibilities are lower than the estimated from the apparent molar volumes but remain within the same magnitude order and are consistent with literature data. The stoichiometry of the complexes is predominantly 1:1, although a slight participation of the 2:1 complex for NaD is reported, as evidenced from the methylene groups lodged in the cavity, the equilibrium values assuming a two-step reaction and from the stoichiometric points. The compressibility data can be explained in the same way as the volume data, and they indicate that the CD becomes more compressible when it is filled with the guest than with structured water. 1H NMR and molecular modeling strategies have permitted us to elucidate the complex structure and corroborate the thermodynamic data, showing that the polar head in the complex has preference for the wider rim of the macrocycle, protruding from the cavity, with the surfactant inclined within the β-CD, making possible a 2:1 stoichiometry with NaD that is prohibitive with NaO. Acknowledgment. Authors are grateful to the M.E.C. of Spain for financial support through DGES Grant Number PB970324, to the U.C.M. (Grant Number PR486/ 97-7489), and to the Centro de Espectroscopıá of the U.C.M. They also thank J. R. Isasi for his valuable suggestions. LA981678J

Molar Partial Compressibilities and Volumes, 1H NMR, and Molecular

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