Inclusion Complexes betweenâ-Cyclodextrin and a Gemini Surfactant in AqueousSolution: An NMR Study

Andres Guerrero-Martı nez,† Gustavo Gonzalez-Gaitano,‡ Montserrat H. Vin as,§ andGloria Tardajos* ,†

Departamento de Quı´mica-Fısica I, Facultad de Ciencias Quı´micas, UniVersidad Complutense de Madrid,28040, Madrid, Spain, Departamento de Quı´mica y Edafologı´a, UniVersidad de NaVarra, 31080 Pamplona,NaVarra, Spain, and EUIT Informa´ tica, UniVersidad Politecnica de Madrid, 28031 Madrid, Spain

ReceiVed: March 14, 2006; In Final Form: May 22, 2006

1H NMR spectra, diffusion-ordered NMR (DOSY), and 2D rotating-frame Overhauser enhancementspectroscopy (ROESY) experiments for aqueous solutions at 298 K containing the gemini surfactant, bis(dodecyl dimethylammonium)diethyl ether dibromide (12-EO1-12), in the absence and presence ofâ-cyclo-dextrin (â-CD) were used to characterize the surfactant and to determine the effects of the complexation inthe micellization. For the binary system, the critical micelle concentration (cmc), the aggregation number,the stepwise micellization constant, and the size of the monomer have been obtained by studying the dependenceof the chemical shifts and the self-diffusion coefficients with the concentration of surfactant. For the ternarysystem, the analysis of the1H NMR spectra and the self-diffusion coefficients reveal the formation of complexesof 1:1 and 2:1 stoichiometry (â-CD:gemini), with a calculated stability constant for the second binding stephigher than that of the first. The values of the hydrodynamic radii of the complexes were obtained from thecalculated diffusion coefficients. The presence ofâ-CD modifies the cmc in an extension that indicates mainlythe formation of a 2:1 complex. The analysis of the chemical shifts of the surfactant indicates thenonparticipation of the complexes into the micelles. ROE enhancements depend substantially on the amountof the macrocycle added and therefore on the stoichiometry; at low concentrations ofâ-CD, one of thehydrocarbon chains binds favorably with the cavity whereas the other interacts with the outer face. By contrast,at higher concentrations ofâ-CD, the two hydrocarbon tails are included in two different macrocycles.

Introduction

The microencapsulating effects of organic hosts on theinherent properties of guest molecules as well as their interac-tions have been studied extensively over the last few decades.1

Cyclodextrins (CDs) have often been used for such studiesbecause of their marked ability to form inclusion complexeswith a wide variety of guests in solution.2 These macrocyclesare cyclic oligosaccharides formed by units (six, seven, or eight)of R-D-(+)-glucopyranose namedR-, â-, or γ-CD, respectively.They form a doughnut-shaped structure, with a hydrophobiccavity and two hydrophilic rims in which the primary andsecondary OH groups are inserted (Figure 1). Thus, a CDconstitutes a singular microenvironment where molecules withsuitable size and hydrophobic character can be housed. Thisproperty renders their study of great interest and calls for adetailed investigation of their inclusion process, with all thepotential applications that this fact implies.3

Of particular interest is the effect of CDs on the self-organization process of surfactants in which the presence ofthese macrocycles introduces a new equilibrium which competeswith the aggregation.4 These amphiphilic molecules are usedas probes to understand the phenomenon of complexation, sincetheir molecular structures (e.g., polar nature of the head, charge,

length of the hydrocarbon tail, etc.) affect the binding process.Recently, a new class of double-chained surfactants, calledgemini surfactants, has been introduced.5 In contrast to theirmore traditional single-chain counterpart analogues, these novelsurfactants are made of two hydrophobic tails and two hydro-philic headgroups linked by a spacer chain. In colloid science,these molecules have gained recent attention because of theirexceptional properties,6 such as low critical micelle concentra-tions and a stronger efficacy in decreasing the surface tensionof water.7

The possibility of synthesizing a whole variety of gemini-type architectures,7 by selecting the number, hydrophobic nature,

* To whom correspondence should be addressed. E-mail: tardajos@quim.ucm.es.

† Universidad Complutense.‡ Universidad de Navarra.§ Universidad Polite´cnica de Madrid.

Figure 1. Chemical structures ofâ-cyclodextrin (â-CD) and bis(dodecyl dimethylammonium)diethyl ether (12-EO1-12) dibromide.

13819J. Phys. Chem. B2006,110,13819-13828

10.1021/jp0615813 CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 06/28/2006

and flexibility of the hydrocarbon tails and spacers, and alsothe ionic character of the headgroups, offers new ways to explorethe intermolecular forces responsible for the inclusion processeswith CDs. A battery of experimental techniques has been usedto investigate the micellization of gemini surfactants in water,including, among others, surface tension,8 electrical conductiv-ity,9 time-resolved fluorescence,10 SANS,11 microcalorimetry,12

NMR,13 and volumetric measurements.14 However, there arefew references in the literature dealing with the encapsulatingproperties of CDs with these amphiphilic molecules.15

In this study, we have chosen a gemini surfactant, bis (dodecyldimethylammonium)diethyl ether dibromide (12-EO1-12), toinvestigate host-guest interactions withâ-CD in conditionsabove and below the critical micellar concentration (cmc). Thissurfactant presents two quaternary ammonium headgroups aswell as a flexible hydrophilic oxyethylene spacer (Figure 1). Inparticular, we have studied the effects of the complexation withâ-CD in the micellization of the gemini surfactant by differentNMR experiments, such as1H NMR spectra, diffusion-orderedNMR (DOSY), and rotating-frame Overhauser enhancementspectroscopy (ROESY).16 DOSY experiments have been previ-ously used for the analysis of a wide variety of complexprocesses, providing basic information on the diffusion char-acteristics of molecules.17 With DOSY, it is possible to obtainthe self-diffusion coefficients,D, of individual compounds froma mixture according to the differences in their effective sizes.18

In addition, the ROESY technique can provide detailed informa-tion on the structure of the complexes, always keeping in mindthe dynamic character of these systems.19 These studies,combined with those obtained via1H NMR titrations, give usinformation at a molecular level of the nature and structure ofthe complexes, their stoichiometries, and the effect that themacrocycle has on the micellization process, and represent thefirst investigation of the interaction between ionic geminisurfactants andâ-CD.

Experimental Methods

Chemicals. â-CD was purchased from Aldrich, having awater content of 13.5%, as determined by thermal analysis. Allthe NMR samples were prepared in D2O (Aldrich ChemicalCo., 99.9% minimum in D). Bis (dodecyl dimethylammonium)-diethyl ether dibromide was synthesized according to theprocedure described by Bhattacharya et al.11 Phosphorus tri-bromide,n-dodecylbromide, diethylene glycol, and dimethyl-amine were purchased from Aldrich Chemical Co. Commonreagents and solvents used in the synthesis were obtained fromcommercial suppliers, without further purifications.

1H NMR Spectra. In the study of the gemini system in water,a stock solution of 12-EO1-12 was added to vials containingdifferent volumes of water. In the case of the1H NMR andDOSY experiments of the ternary systems, different CD/geminimolar ratios were prepared from stock solutions of surfactant,by weighing increasing amounts of CD in suitable vials. Theconcentration of surfactant in these experiments was keptconstant at 0.6 mM (under this condition, the concentration ofsurfactant is always below the cmc). The studies on the shiftingof the cmc were performed using virtually the same procedure,but in this case, the concentration of macrocycle was keptconstant at 6.0 mM (above the cmc) and the concentration ofsurfactant was changed. All the mixtures were sonicated andtransferred to NMR tubes (final volume 0.5 mL).

The proton spectra were recorded at 298 K in a BrukerAvance AV-500 spectrometer (11.7 T) by averaging 32 scans,with a digital resolution of 0.30 Hz. The HDO signal was used

as the reference.20 The signal assignment of the surfactant wasestablished by conventional NMR methods (COSY, TOCSY).

DOSY NMR Spectra. For the binary and ternary systems,the samples were prepared in the same conditions as thosedescribed in the previous section. A stimulated echo sequenceincorporating bipolar gradients (BPPLED),21 with a longitudinaleddy current delay of 5 ms, was used for acquiring DOSYspectra. The duration of the magnetic field pulse gradients andthe diffusion times were optimized for each sample to observethe complete signal decay with the maximum gradient strength.Gradient strengths of 2.0-2.5 ms were incremented in 32 stepsranging between 2% and 95% of the total gradient using a linearramp. An exponential window function with 1 Hz line broaden-ing was applied before Fourier transformation. All the measure-ments were carried out at 298 K.

ROESY Experiments. A Bruker Avance DPX-300 spec-trometer (7.05 T) was used, by applying the pulse sequencedefined in the literature.22 Different spin-lock mixing times(ranging between 200 and 800 ms) were applied to ensure thevalidity of the linear approximation for the ROE cross-peaksand to obtain the best signal-to-noise ratio, which was achievedwith 600 ms. Thirty-two scans were collected in each spectrum.Before the subsequent Fourier transformation and 2D phasetuning, linear prediction in F1 and cosine square apodizationin both dimensions were applied to the free induction decays(FIDs). The temperature was kept constant in these experimentsat 298 K.

Results and Discussion

System Gemini Surfactant+ Water. Chemical Shifts.Themicellization process of 12-EO1-12 has been investigated byNMR spectroscopy. The cmc of a surfactant may be determinedthrough any property that changes sharply around the criticalconcentration, for example, from the plots of chemical shift ordiffusion coefficient vs the surfactant concentration. Two setsof signals can be distinguished in the1H NMR spectra of thegemini according to its structure (Figure 2). Regarding thehydrophobic tail region,23 it is noted that, for the surfactant inmonomeric form, a broad signal composed of two superimpos-ing resonances atδHλ ) 1.268 (br, 28H, (CH2)14) andδHγ )1.336 (br, 8H, (CH2)4) can be unambiguously identified as thecorresponding nine nonequivalent methylene groups of the alkylchains. As for the oxyethylene region, the two broad multipletsat δHR′ ) 3.572 (br, 4H, (N(CH2))2) andδHâ′ ) 3.941 (br, 4H,((CH2)O)2) are assigned to the spacer. At low concentrations,the chemical shifts change smoothly with the gemini concentra-tion, and the extrapolations at infinite dilution provide theproperty corresponding to the monomer. The relative values ofthe chemical shifts with respect to the extrapolations vs thesurfactant concentration have been plotted in Figure 3. The cmcof the pure surfactant is observed at 1.0 mM, in good agreementwith the literature values.24 At concentrations above the cmc,the chemical shifts increase as a result of micelle formation, upto reaching a constant value. All the resonances undergoremarkable downfield shifts in which we can observe twodifferent trends. The relative changes inδ show that protonslocated close to the head ionic groups undergo larger changes,in a maximum extent of+0.150 ppm for HR at 18.0 mM. Incontrast, protons of the alkyl chains change scarcely, in aminimum extent of+0.034 ppm for Hλ.

Under fast exchange in the NMR time scale,25 the measuredchemical shifts for the corresponding protoni, δexp

i , can beexpressed as the sum of the chemical shift of the free surfactant,δSF

i , and the aggregated form,δSN

i , each one averaged with its

13820 J. Phys. Chem. B, Vol. 110, No. 28, 2006 Guerrero-Martı´nez et al.

respective molar fractions, that is

with N being the aggregation number of the micelles. If a massaction law model,NSF T SN, and the corresponding self-association equilibrium,K ) |SN|/|SF|N, are assumed, then theconcentration of free monomers and micelles can be expressedas

with |ST| being the total concentration of gemini. Thus, it ispossible to calculate using an iterative nonlinear fitting thechemical shifts of the surfactant in both forms and get valuesof N and logK, provided these properties remain constant withinthe fitting interval. The properties thus calculated for thedifferent protons of the surfactant are collected in Table 1. Theresult for the aggregation number,N ) 34, agrees well withdata of Verrall et al.,24 obtained by light scattering measurements(N ) 33). In the case of micelles formation that involves anaggregation number smaller than 100,26 we can obtain, fromNand log K ) 98.0, the corresponding stepwise associationconstant throughKn ) K 1/N, resulting in 763 M-1. This valueis intermediate between those obtained for ionic surfactants withhigher alkyl chains, tetradecyltrimethylammonium bromide(TTAB, Kn ) 263 M-1) and hexadecyltrimethylammoniumbromide (CTAB,Kn ) 1087 M-1),27 which indicates the higherhydrophobicity of the gemini surfactants with respect to itssingle-chain counterpart analogues.

NMR Diffusion Measurements.Further information about theaggregation process can be attained by using data from DOSYexperiments through the analysis of the self-diffusion coef-

ficients. These measurements provide qualitative and quantita-tive information about the molecular association since themicellization involves changes in the hydrodynamic radii of thedifferent surfactant states. These changes can be monitored ifthe NMR time scale of the diffusion and aggregation processmatch.28 The expansions of the DOSY spectra at differentconcentrations of surfactant in water, within the chemical shiftrange of the Hλ proton, are shown in Figure 4a. One of thefeatures of the DOSY spectra of 12-EO1-12 is that all the spinsthat belong to the molecule have the same diffusion coefficientat different concentrations. The simple inspection of these plotsreveals that the surfactant diffuses more slowly than in themonomer region above the cmc, as a result of self-aggregation,with implications on its effective size. The experimental self-diffusion coefficients for the surfactant in water solution as afunction of the concentration are plotted in Figure 4b. The shapeof the curve resembles that of chemical shifts giving the samecmc, and the extrapolation at infinite dilution for the surfactant

Figure 2. 1H NMR spectra and proton assignment for 12-EO1-12 inD2O at different concentrations of surfactant.

δexpi ) øSF

δSF

i + NøSNδSN

i (1)

|SF| ) |ST| - NK|SF|N (2)

Figure 3. Increment in the chemical shifts vs concentration ofsurfactant for selected protons of 12-EO1-12. Solid lines are the bestfit to eq 1. The experimental error of the chemical shifts is(1 × 10-3

ppm.

TABLE 1: Micellization Parameters of 12-EO1-12 Obtainedby Non-linear Fitting Analysis of the Chemical Shifts andSelf-diffusion Coefficients

N log K δSF

i /ppm δSN

i /ppm δSN

i - δSF

i /ppm

Hω 34 98.4 0.832 0.880 0.048Hλ 32 90.0 1.268 1.302 0.034Hγ 33 91.0 1.336 1.382 0.046Hâ 34 98.0 1.747 1.787 0.040Hn 35 99.9 3.092 3.193 0.101HR 34 97.0 3.328 3.490 0.162HR′ 34 97.3 3.572 3.675 0.103Hâ′ 34 97.7 3.941 4.034 0.093

N log K DSF 10-10/m2 s-1 DSN10-10/m2 s-1

D 34 99.1 3.40 0.51

â-Cyclodextrin and a Gemini Surfactant J. Phys. Chem. B, Vol. 110, No. 28, 200613821

in the monomer region yields the diffusion coefficient of themonomer.

Due to the fact that aggregation is a dynamic process fasterthan the NMR time scale, in the limit of the fast exchange, theexperimental diffusion coefficient is a weighed average of thecoefficient in the monomer and micelle form. The measuredvalue at each concentration can be expressed as

that is, the sum of the contributions due to the unimer,DSF, andto the micelle,DSN, weighed each one by its mole fraction. Toestimate the change in the diffusion coefficient of the unimersupon micellization, we have used the same iterative procedureemployed with the chemical shifts. The values of the aggregationnumber, N, and the micellization constant,K, are in goodagreement with those obtained by the former method (Table1).

In the well-known approach of a small spherical particle underno-slip boundary conditions, the hydrodynamic relation betweenthe self-diffusion coefficient,D, and the viscosity,η, is givenby the Stokes-Einstein equation

whereRh is the hydrodynamic radius of the diffusing particle.The hydrodynamic radius of the monomer,Rh ) 5.7 Å, hasbeen obtained combining the diffusion coefficient of the freemonomer,DSF ) 3.4× 10-10 m2 s-1, and the viscosity of D2Oat 25°C, η ) 1.132 cP, in the preceding equation.29 The changein the diffusion coefficient of 12-EO1-12 with the concentrationhas contributions, mainly from the fact that the monomer isincorporated into the micelles but also from the overall changein viscosity.30 We have not detected significant changes in thediffusion coefficient of the solvent in the range of concentrationsstudied,31 which proves that the contribution of the viscosity inthe measured diffusion coefficients of the surfactant is smallcompared with the increase in its effective size.

Systemâ-Cyclodextrin + Water. Diffusion Measurements.The diffusion coefficients forâ-CD solutions in D2O as afunction of the molarity are plotted in Figure 4b. The experi-mental points were fitted to the following equation

where the zero superindex stands for the property at infinitedilution and theBD coefficient accounts for the solute-soluteinteractions. A negativeBD is indicative of a rather slight globalincrement of the viscosity and/or the formation of low concen-

Figure 4. (a) Expansions of the1H DOSY spectra at the chemical shift range of the Hλ, at different concentrations of surfactant. (b) Self-diffusioncoefficients of the binary systems, 12-EO1-12 (b) andâ-CD (O). Solid lines are the best fits to eqs 3 and 5. The experimental error of the diffusioncoefficients is(5.0 × 10-12 m2 s-1.

Dexp ) DCD0 + BD|CD| ) 2.71× 10-10 -

6.7× 10-10|CD| (m2 s-1) (5)

Dexp ) øSFDSF

+ NøSNDSN

(3)

D )kBT

6πηRh(4)

13822 J. Phys. Chem. B, Vol. 110, No. 28, 2006 Guerrero-Martı´nez et al.

tration of labile aggregates.32 The small value of the slope is inaccordance with the nonsignificant changes observed in thediffusion coefficient of water. The value forDCD

0 is in goodagreement with previous results,33 yielding a hydrodynamicradius of theâ-CD, Rh ) 7.1 Å, that is reasonable in the lightof the known dimensions of CDs from X-ray diffraction andlight scattering measurements.34

System Gemini Surfactant+ â-CD + Water. Estimationof the Binding Constants: Chemical Shifts.The effect ofmicellization in the chemical shift of gemini resonances hasbeen avoided using a fixed concentration of surfactant belowthe cmc (0.6 mM). The concentration ofâ-CD was varied toobtain different molar ratios,r ) [â-CD]/[12-EO1-12], rangingfrom pure CD to pure surfactant in water. Representative resultsof 1H NMR spectra for mixtures at differentr values are shownin Figure 5. Upon addition of variable amounts ofâ-CD, theresonances of all the guest protons undergo shifting (see Figure1 for notation). HR′ cannot be resolved due to the overlap withthe H4 proton ofâ-CD. Whereas protons far from the methylgroup of the alkyl chains Hγ, Hâ, Hn, and Hâ′ move upfield, theresonances of protons located close to the edges, Hω and someof the Hλ, move upfield up tor ) 2 and then conversely shiftdownfield when r > 2. Since chemical shifts reflect thesurrounding chemical environment, the direction and displace-ment of the signals suggest that the interaction between thesurfactant and the CD undergoes a substantial dependence inthe stoichiometry upon addition of macrocycle. A similarbehavior between other surfactants andR-cyclodextrin has beenreported previously,35 in which the deshielding of these nucleiis attributed to the formation of 2:1 channel type complexes indifferent single-chain surfactants. At the same time, the protonsH3 and H5 of â-CD, located in the cavity of the macrocycle,

move upfield, and protons H2 and H4, placed in the externalpart of the CD, shift downfield. Also, H6, at the rim made upof the primary hydroxyls, undergoes a slight shift to higherfields. The maximum changes registered in some of theseresonances reach-0.166 ppm in the case of H5 and -0.075ppm for Hγ.

Assuming stoichiometries 1:1+ 2:1 and a fast exchange onthe NMR time scale,36 the measured chemical shifts,δexp

i , forthe host (CD) or the guest (S) can be expressed as the sum ofthe contributions of the chemical shifts due to the free molecule,δF

i , to the 1:1 complex,δ1:1i , and to the 2:1 complex,δ2:1

i , eachone weighted by its mole fraction, that is

whereøF, ø1:1, andø2:1 refer to the molar fraction of the moleculewhose chemical shifts are being observed in the differentsituations andn is a stoichiometric factor equal to 2 for CDand 1 for the gemini. The concentrations of all the componentsin solution are connected by the corresponding mass balanceand mass action law. The development in terms of theconcentration of free host,|CD|, leads to a cubic polynomialequation in the form

where the T subindex refers to the corresponding total concen-tration andK1 andK2 are the association constants for the firstand second binding step, respectively. The binding constantscan be estimated by using a multivariable analysis, fitting thewhole set of resonances of the host and guest molecules,imposing the condition that the binding constants must be thesame for each proton.37

The chemical shifts for the protons of 12-EO1-12 have beenplotted vs the molar ratio in Figure 6. This plot suggests a 2:1stoichiometry, that is, two molecules ofâ-CD per one ofsurfactant, as deduced from the intercept between the extrapola-tions from high and low molar ratios. We have excluded fromthe regression analysis the protons Hλ of 12-EO1-12, which are

Figure 5. Expansion of the1H NMR spectra of 12-EO1-12 + â-CDmixtures at different molar ratiosr ) [â-CD]/[12-EO1-12], with [12-EO1-12] ) 0.6 mM.

Figure 6. Molar ratio plots for selected protons of 12-EO1-12 in thepresence ofâ-CD, with [12-EO1-12] ) 0.6 mM. Solid lines are themultivariable fit to a three-site model (eqs 6 and 7). The experimentalerror of the chemical shifts is(1 × 10-3 ppm.

δexpi ) øFδF

i + ø1:1δ1:1i + nø2:1δ2:1

i (6)

|CD|F3 + (2|S|T - |CD|T + 1K2

) |CD|F2 +

1K2

(|S|T - |CD|T + 1K1

) |CD|F -|CD|TK1K2

) 0 (7)

â-Cyclodextrin and a Gemini Surfactant J. Phys. Chem. B, Vol. 110, No. 28, 200613823

poorly resolved, and the protons Hω, whose chemical shifts donot converge along the binding isotherm due to a change in thestoichiometry. In addition, the whole proton set of CD has notbeen included because more data at highr ) [â-CD]/ [12-EO1-12] should be necessary for a reasonable fit. The results of theregressions are collected in Table 2, yielding binding constantsK1 ) (8 ( 5) × 103 L mol-1 andK2 ) (2.8 ( 0.9) × 104 Lmol-1. When dealing with multiple equilibria, the standarddeviations of the parameters exhibit a comparatively highervalue with respect to those obtained for systems with a 1:1stoichiometry, because of the increased number of variables.36

The higher value ofK2 reveals that this complexation processdoes not follow a simple statistic model.38 From the fittedchemical shifts of the complexes (Table 2), we observe thatprotons located in the hydrocarbon chains, Hγ and Hâ, havecomparatively higher relative changes of the chemical shiftsfrom the monomer to the 2:1 complex,δ2:1,j

i - δji, than those

registered for protons located close to the headgroups, Hn, HR,and Hâ′. If one compares these results with the calculatedchanges upon micellization, then we come to the conclusionthat, in the formation of complexes with different stoichiom-etries, the surrounding chemical environment of the headgroupsis slightly influenced by complexation. Thus, the CDs must befound remote from the charged quaternary ammonium groups.

Estimation of the Binding Constants and Molecular Sizes:Diffusion Measurements.Determination of self-diffusion coef-ficients in a multicomponent system is a very helpful tool forextracting information about the complexation process.32 Justlike chemical shifts, a fixed concentration of surfactant belowthe cmc (0.6 mM) was used and the concentration ofâ-CD wasvaried. In a similar analysis as that described above, themeasured diffusion coefficient,Dexp, can be expressed as

whereDF refers to the diffusion coefficient of the free molecule(CD or S) andD1:1 andD2:1 stand for the diffusion coefficientof the 1:1 and 2:1 complexes, respectively. Figure 7 shows theDOSY plot of a mixture 0.6 mM 12-EO1-12 and 3.0 mMâ-CDobtained according to the procedure described in the NMRExperiments section. Both groups of resonances that correspondto the host or guest molecule have the same diffusion coefficient.The simple inspection of the DOSY spectrum reveals somefeatures of the system under study by comparison with thediffusion coefficient of the pure gemini and CD (Figure 4b).Upon addition of the CD, the surfactant diffuses more slowlythan in its free form, which can be attributed to an increase in

its effective size due to the inclusion. The diffusion coefficientsof the surfactant and the macrocycle vs the surfactant concentra-tion have been plotted in Figure 8. The addition ofâ-CD slowsdown the movement of the surfactant. In the case ofâ-CD, theeffect of the complexation on the diffusion coefficients is lessmarked. A concomitant decrease of the diffusion occurs up to1.2 mM pointing to a change in the stoichiometry, in accordancewith the 1H NMR experiments. We observe largely a 1:1stoichiometry at low concentrations of CD, which diffuses faster,and a 2:1 stoichiometry when the concentration ofâ-CDincreases, with a slower diffusion. At higher CD concentrations,the diffusion coefficient of the macrocycle becomes higher asa result of an increase in the CD concentration in free form,and the curve in the absence (binary mixture) and presence ofsurfactant coalesces, indicating that, when the complex forms,it does not interact with other complexes or free macrocycles.The analysis of the self-diffusion coefficient of water signalconfirms that there are not significant changes in the globalviscosity of the solutions.

The stoichiometry, binding constants, and diffusion coef-ficients of the different complexes can also be determinedapplying the multivariable analysis previously described to thediffusion coefficient of the surfactant and CD vs the concentra-tion of the macrocycle, given by eqs 7 and 8.36 The fitted bindingconstants and diffusion coefficients of the different complexes

TABLE 2: Multivariable Non-linear Fitting Analysis of the Chemical Shifts and Self-Diffusion Coefficients for the Complexâ-CD:12-EO1-12 and Chemical Shifts at Infinite Dilution, δ2:1

i,0 , in the cmc* Calculations

δFi /ppm δ1:1

i /ppm δ2:1i /ppm δ2:1

i - δFi / ppm δ2:1

i,0 /ppm

Hγ 1.337 1.377 1.414 0.077 1.409Hâ 1.748 1.777 1.803 0.055 1.799Hn 3.088 3.092 3.108 0.020 3.105HR 3.328 3.342 3.364 0.036 3.360Hâ′ 3.940 3.944 3.954 0.014 3.948

K1 ) (8 ( 2) × 103 L mol-1

K2 ) (2.8( 0.9)× 104 L mol-1

DF/ppm D1:1/ppm D1:2/ppm

D12-EO1-12 3.40 2.45 2.01Dâ-CD 2.62

K1 ) (1.0( 0.5)× 103 L mol-1

K2 ) (5 ( 3) × 104 L mol-1

Dexp ) øDF + ø1:1D1:1 + nø2:1D2:1 (8)

Figure 7. 1H DOSY plot for the ternary system: [â-CD] ) 3.0 mM(CD) + [12-EO1-12] ) 0.6 mM (S)+ water (W).

13824 J. Phys. Chem. B, Vol. 110, No. 28, 2006 Guerrero-Martı´nez et al.

are compiled in Table 2, yieldingK1 ) (1.0 ( 0.5) × 103 Lmol-1 andK2 ) (5 ( 3) × 104 L mol-1. These values followthe same trend as those obtained from the chemical shifts butwith higher relative errors. For the rest of the paper, we willuse the calculated constants of the previous section due to themuch higher experimental points of the fit. The results of thediffusion coefficient of complexes,D1:1 ) 2.45× 10-10 m2 s-1

andD2:1 ) 1.90× 10-10 m2 s-1, reveal a plausible decrease insize for the complex, owing to the change in the stoichiometry,that correspond to hydrodynamic radii of 7.9 and 10.1 Å,respectively. Cabaleiro-Lago et al.32 have examined the com-plexation ofâ-CD and alkyltrimethylammonium bromide sur-factants by diffusion measurements using pulse-gradient spin-echo proton NMR. These authors found, in the case ofdodecyltrimethylammonium bromide (DoTAB), a 1:1 equilib-rium with a constant value and diffusion coefficients of thesurfactant and complex ofK1 ) (1.9 ( 0.4) × 104 L mol-1,DDoTAB ) 4.96× 10-10 m2 s-1, andD1:1 ) 2.52× 10-10 m2

s-1, respectively. These results are in good agreement with ourvalues, taking into account the higher size of the gemini(D12-EO1-12 ) 3.40 × 10-10 m2 s-1). It should be mentionedthat the diffusion coefficient of our 1:1 complex,D1:1, is slightlylower than that obtained for DoTAB. This observation couldbe explained in terms of a partial folding of the free hydrocarbonchain in the external part of the macrocycle, which would leadto a diminution of the expected hydrodynamic radii.

cmc* Calculations: Chemical Shifts.A different experimenthas been carried out to study the effect of CD on the aggregationof the surfactant. The ternary system has been studied keepingtheâ-CD concentration constant in 6.0 mM and increasing theconcentration of surfactant. As a comparison, chemical shiftsof representative protons of the surfactant in these ternarymixtures, together with the corresponding values in the binarysystem, are plotted in Figure 9. Since at infinite dilution ofsurfactant the interactions between 12-EO1-12 molecules arenegligible, the chemical shift of the different resonances in thislimit, δ2:1

i,0 , corresponds to the interaction between the CD andthe surfactant in the complex of the highest stoichiometry (Table2). These values can be compared with those obtained by themultivariable analysis of the experiments in which the concen-tration of surfactant was kept constant. An inspection of these

results confirms the coherence ofδ2:1i,0 with the values of the

complex of 2:1 stoichiometry,δ2:1i , and shows the goodness of

the applied model.The interpretation of Figure 9 in the case of HR and Hn is

quite evident. At low concentrations of surfactant, a complexof dominant 2:1 stoichiometry is observed, in agreement withthe higher value ofK2. The new cmc value, cmc*, is reached atconcentrations above that for the pure surfactant. This valuecan be quantitatively obtained when the concentration of freesurfactant in the presence ofâ-CD reaches the value of 1.0mM.39 For this purpose,K1 and K2 from the chemical shiftshave been used, and the resulting cmc* is 4.4 mM. This shiftindicates a mixture of 1:1+ 2:1 stoichiometries and confirmsthat the competitive equilibrium due to the affinity of themonomer for the micelle or for theâ-CD is resolved in favorof the latter. The analysis of the Hâ proton shows an analogousresult, in which the chemical shift of the surfactant in the micelleform is between that of the complex and monomer. Thisresonance is evidence that the curves of the chemical shift ofthe micellization process in the presence and absence of CDcoalesce, providing that the complex does not have any influenceon the micelles. It should be mentioned that higher surfactantconcentrations would be necessary to detect this behavior inthe case of HR and Hn.

Structure of the Complexes.For the 2D ROESY experimentson the ternary mixtures, the concentration of gemini was fixed

Figure 8. Self-diffusion coefficients for the ternary system, 12-EO1-12 (b) and â-CD (O) ([12-EO1-12] ) 0.6 mM). Solid lines are thebest fit to eqs 7 and 8. Dotted line corresponds to the linear fit of theCD binary system. The experimental error of the diffusion coefficientsis (5.0 × 10-12 m2 s-1.

Figure 9. Selected chemical shifts for 12-EO1-12 in water and mixtureswith â-CD vs 12-EO1-12 molarity: [â-CD] ) 0 mM (open symbols);[â-CD] ) 6.0 mM (close symbols). Dotted line indicates the cal-culated cmc*. The experimental error of the chemical shifts is(1 × 10-3 ppm.

â-Cyclodextrin and a Gemini Surfactant J. Phys. Chem. B, Vol. 110, No. 28, 200613825

below the cmc (0.6 mM) and those ofâ-CD were 0.12, 0.96,and 3.3 mM (molar ratios CD/surfactant,r ) 0.2, 1.6, and 5.5,respectively). At 300 MHz, the1H NMR of the differentmixtures is crowded and not all the signals can be used in abidimensional integration without overlap. Figure 10 shows anexpanded region of the 2D ROESY spectra that correspond tor ) [â-CD]/ [12-EO1-12] of 0.2 and 5.5, respectively. Theinspection of these bidimensional spectra reveals intense cross-peaks between the inner protons ofâ-CD and some of thegemini surfactant, where a concomitant increment of the CD-gemini contacts occurs with the increase of the macrocycleconcentration. These results are consistent with the observedchanges in the chemical shifts and diffusion coefficients andconfirm that the gemini binds favorably into the cavity. Repre-sentative numerical values of the relative volume integrals withrespect to the ROE cross-peak Hλ{H5} are given in Table 3.

From inspection of Figure 10a atr ) 0.2, the resonancecorresponding to the methyl protons, Hω, only exhibits a ROEeffect with the external proton H4. Also, Hλ shows a stronginteraction with H3 and especially with H6. In the spectral regionof H2 and H5, there is a signal correlating with Hλ, which rendersa quantitative assessment more difficult. However, from theabove-mentioned results, the presence of ROE enhancementsfor the pairs Hω{H4} and Hλ{H6} suggests that these Hλmethylene protons can bind favorably with both H2 and H5.

Moreover, these results and the simultaneous absence of ROEvalues for Hγ, Hâ, HR, Hn, HR′, and Hâ′, as expected by theinduced chemical shifts, indicate a preference of the cavity forthe methylene moiety far away from the charged headgroups.On the basis that the calculated concentrations of complexes atr ) 0.2 areC1:1 ) 0.28 mM andC2:1 ) 0.15 mM, the measuredROEs suggest a possible geometry for the inclusion complexwith a main 1:1 host/guest stoichiometry. The lack of inter-molecular ROEs between the terminal methyl group and theinner of the macrocycle, together with the interaction that thisgroup undergoes with the external part of the CD, can only beexplained in terms of a complete inclusion of one of thesurfactant chains, whereas the other tail must be interacting withthe exterior of the macrocycle. The cross-peaks point to acomplex structure in which the terminal Hλ methylene groupsof one chain must be found at the narrower rim, whereas theHλ remaining methylenes are directly interacting with the widerrim (Figure 11a).

The trend of the relative volume integrals indicate that therelationship of CD and surfactant has a remarkable effect onthe ROE transfer. The experiment shows that the relativeintensities of the ROEs differ with each other to some extent at

Figure 10. Partial view of the 2D ROESY spectra for the [â-CD]/[12-EO1-12] system ([â-CD] ) 0.6 mM): (a) r ) [â-CD]/[12-EO1-12] ) 0.2 and (b)r ) 5.5.

TABLE 3: Normalized Cross-Peaks Intensities forIntermolecular Homonuclear ROE between 12-EO1-12 andâ-CD Protons (600 ms mixing time)

H3+6 H5 H4

r ) 0.2Hω 1.64Hλ 2.61 1.00a

HγHâ

r ) 1.6Hω 0.67Hλ+γ 2.70 1.00b

Hâr ) 5.5

Hω 0.27 0.06 0.28Hλ+γ 3.30 1.00b

Hâ

a Signal overlap of H2, H5, and Hλ. b Signal overlap of H5 and Hλ.

Figure 11. Proposed structures of the complexes of (a) 1:1 and (b)2:1 stoichiometries.

13826 J. Phys. Chem. B, Vol. 110, No. 28, 2006 Guerrero-Martı´nez et al.

different concentrations ofâ-CD, and this might reflect a changein the site-specific interactions as a result of a modification ofthe stoichiometry. The situation at higher concentrations of CD,r ) 5.5, exhibits some differences with respect tor ) 0.2,showing ROE effects between the cavity protons H3+6 and theresonances Hγ and Hω (Figure 10b) and an important decreaseof the interaction between the proton Hω and the external partof â-CD. On the basis of these results and the calculatedconcentrations of complexes atr ) 5.5,C1:1 ) 0.001 mM, andC2:1 ) 0.021 mM, we can associate this finding with thecomplexation of the free chain at lowr values by a second CD,which would lead to a close contact of the first complexed CDwith Hγ. These evidences are compatible with two possiblegeometries for the inclusion complex without any preferencein the orientation of the second macrocycle (Figure 11b). It mustbe noticed that these structures account for the remarkablechanges in the chemical shifts of Hγ (more than 0.07 ppm) andwith the fact that Hω first moves upfield tor ) 2 and thenconversely shifts downfield whenr > 2.

Conclusions

Different NMR experiments have been conducted to studythe micellization process of the gemini 12-EO1-12 and itsinclusion complex formed withâ-cyclodextrin, as well as thepure â-CD in solution. The aggregation number, stepwisemicellization constant, self-diffusion coefficients, and the chemi-cal shifts for different resonances of the free monomer and theaggregated form were determined by using a nonlinear fitting.

The structure and binding of the inclusion complexes betweengemini andâ-CD have been studied by 1D proton NMR, DOSY,and 2D ROESY experiments. When the surfactant concentrationis lower than the cmc, the system is a mixture of two complexes,CD:S and CD2:S. From the calculated diffusion coefficients ofthese complexes, it is concluded that the 2:1 complex issignificantly larger than the 1:1 complex. The two bindingconstants obtained by a multivariable nonlinear regressionanalysis of the chemical shifts areK1 ) (8 ( 5) × 103 L mol-1

andK2 ) (2.8 ( 0.9) × 104 L mol-1. The fact thatK2 > K1

means that the complexation of both CDs are not independentprocesses and that a pure statistical model is not followed.ROESY experiments reveal an evolution of the ROE contactswith the stoichiometry of the complexes. This is also evidencedby the changes of the chemical shifts. At lowr values (r )[â-CD]/[12-EO1-12]), the ROESY spectrum shows the forma-tion of a 1:1 complex in which one tail of the surfactant entersthe cavity through the wide rim, with the other chain interactingwith the external surface of the macrocycle. All the spectradisplay no contacts between the protons close to the chargedheadgroups with theâ-CD and a strong interaction between theinternal cavity protons and the Hλ and Hω. Whenr increases, anew cross-peak with Hγ rises. In addition, the diminution ofthe interaction between the aliphatic chain and the external partof the macrocycle is in good agreement with the increment ofthe concentration of the 2:1 complex. These experimentalevidences indicate that the second included CD induces amovement to a deeper position of the first CD in the geminihydrophobic moiety. This result shows a cooperative effect andan interaction between both CDs resulting in a higher value ofK2.

The presence of the macrocycle shifts the aggregation of thegemini to higher concentrations of surfactant. The calculatedvalue of the cmc* using the obtained binding constants is inagreement with the experimental results confirming that theinclusion of both hydrophobic tails is not independent. Further

thermodynamic studies to elucidate the changes in the hydrationstate of the surfactant hydrocarbon chains andâ-CD arecurrently in progress.

Acknowledgment. The authors acknowledge financial sup-port from the U.C.M. (PR1/06-14507) and Ministerio de Cienciay Tecnologı´a (BQU2001-1426-CO2-01).

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