On the Connection between the Complexation and ... - ACS Publications

J. Phys. Chem. B 2008, 112, 15691–15700

15691

On the Connection between the Complexation and Aggregation Thermodynamics of Oxyethylene Nonionic Surfactants Gloria Tardajos,† Teresa Montoro,‡ Montserrat H. Vinãs,‡ Mauricio A. Palafox,† and Andre´s Guerrero-Martıńez*,§ Departamento de Quı´mica-Fı´sica I, Facultad de Ciencias Quı´micas, UniVersidad Complutense de Madrid, 28040 Madrid, Spain, EUIT Forestales, UniVersidad Politécnica de Madrid, 28040 Madrid, Spain, EUIT Informa´tica, UniVersidad Politécnica de Madrid, 28031 Madrid, Spain, and Physikalisches Institut, Westfa¨lische Wilhelms-UniVersita¨t Mu¨nster, Mendelstrasse 7, D-48149 Mu¨nster, Germany ReceiVed: August 1, 2008; ReVised Manuscript ReceiVed: September 17, 2008

Density and sound velocity data for aqueous solutions containing nonionic surfactants of the homologue series of polyoxyethylene(n) nonyl phenyl ethers (NPEn, n ) 5 and 40) were analyzed in the absence and presence of β-cyclodextrin (β-CD) at 298 K. Thus, the critical micelle concentration of the surfactants and their apparent and partial molar volumes and compressibilities were measured. From a pseudophase separation model, the partial molar volumes and compressibilities of both pure surfactants in the micelle state and those of NPE40 in the monomer phase have been determined directly. For the ternary systems, increases of the molar volumes and compressibilities of NPE5 and NPE40 at infinite dilution and shifts of the cmc were observed compared to the binary systems. Luminescent measurements of the complexation process between NPE40 and β-CD showed 1:1 + 1:2 (NPEn/2β-CD) stoichiometries for the complexes, with thermodynamic equilibrium constants that were in good agreement with previous results for NPE5 in the presence of β-CD. This resemblance allowed us to use these results to indirectly determine the molar partial properties of NPE5 in the monomer state and understand the changes in the thermodynamic properties of NPE5 due to aggregation. From the aggregation and complexation data, a folding of the surfactants at the monomer state, in which the hydrophobic moieties of NPEn are surrounded by the EO chain, has been found. The oxyethylene group contributions at the monomer and micelle state of the NPEn homologue series have been estimated. The values of the transfer thermodynamic properties of both surfactants and β-CD at infinite dilution conditions have been discussed in terms of a new extended model, in which the balance between the released water from the cavities of two β-CDs and the different hydrophobic moieties of the surfactant that enter the macrocycle was considered. Introduction The main feature that makes cyclodextrins (CDs) of interest is their ability to form inclusion complexes with a wide variety of organic guest molecules in aqueous solution.1–3 This property offers interesting applications in many chemical fields, which have been extensively described in the literature.4,5 These macrocycles are oligomers of R-D-(+)-glucopyranose linked by R-1,4 glycosidic bonds, and the three major CDs, R-, β-, and γ-CD, are formed by six, seven, and eight glucose units, respectively (Figure 1).6 In aqueous solution, the cavity of CD presents a slight hydrophobic character, whereas the rims, consisting of the primary and secondary hydroxyl groups of the glucose units, are hydrophilic.7 This amphiphilic balance is responsible for the formation of complexes in water through noncovalent interactions with guest molecules that fit, total or partially, in the cavity. There are several factors that influence the complexation of CDs, such as the relief of conformational strain of the macrocycle, the release of high-energy water from the cavity, hydrophobic interactions, and induction and dispersion forces.8 Among them, the hydration changes that hosts undergo during the complexation process have been the subject

Figure 1. Chemical structures of β-cyclodextrin (β-CD) and polyoxyethylene(n) nonyl phenyl ethers (n ) 5 and 40).

* To whom correspondence should be addressed. E-mail: aguerrero@ quim.ucm.es. Phone: +49 251-5340-6838. Fax: +49 251-5340-6102. † Universidad Complutense de Madrid. ‡ Universidad Polite ´ cnica de Madrid. § Wesfa ¨ lische Wilhelms-Universita¨t Mu¨nster.

of continuous studies.9,10 Prime guest candidates to understand this hydration process are surfactants since they allow modulation of the binding and stoichiometry of their complexes with

10.1021/jp806883x CCC: $40.75  2008 American Chemical Society Published on Web 11/12/2008

15692 J. Phys. Chem. B, Vol. 112, No. 49, 2008 CDs by changing structural parameters of the amphiphile, such as the head group or the length of the hydrocarbon tail.11–14 These structural differences of the surfactants affect not only the complexation but also the aggregation properties in water, which are directly related to noticeable changes in their hydration states as well.15–17 Volumetric and, particularly, compressibility properties of solutes are known to be sensitive to the degree and nature of solute hydration, and many studies have been carried out on different compounds containing hydrophobic and hydrophilic groups, such as alcohols, monosaccharides, surfactants, or polymers.18–21 For surfactants, the micellization phenomenon, in which molecules move from the full hydrated monomer state to the hydrocarbon-like core of a micelle, can be readily monitored by the analysis of these thermodynamic properties. Analogously, the remarkable changes in molar volumes and compressibilities upon complexation of CDs are useful for the determination of the transfer process of guest molecules from bulk water to the nonpolar cavity of the host.22–25 These changes are mostly due to alteration of the hydration of both host and guest molecules since the CD releases the inclusion water molecules to allow the entrance of the guest, which loses completely or partially the hydration shell. Nonionic surfactants show characteristic temperature- and concentration-dependent phases in water that may start strongly to scatter light at the so-called cloud point of the surfactant.26,27 This cloudiness is related to a phase separation process driven by noncovalent interactions between the hydrophilic and hydrophobic parts of the surfactant and the surrounding water.28 Thus, these amphiphilics are interesting hosts for the study of the role that hydration water has in the thermodynamics of CD complexation. We have recently reported the complexation of the surfactant polyoxyethylene(5) nonyl phenyl ether (NPE5, Figure 1) in the presence of β-CD by measuring photophysical and NMR properties.29 The formed complex is strong enough to disrupt the formation of aggregates and shifts the critical micelle concentration (cmc ) 3 µM) and the cloud point at 25 °C (mc ) 0.45 mM) of the surfactant to 3.0 and 3.5 mM, respectively, when the concentration of the macrocycle is 6.0 mM. These measurements pointed out the formation of a complex of dominant 1:2 stoichiometry (NPE5/2β-CD), in which the hydrophobic alkyl and phenyl moieties of the surfactant thread two CDs, whereas the oxyethylene (EO) chain does not interact with the macrocycles. Such results encouraged us to continue the investigation of these systems, paying more attention to the role that water hydration has in the inclusion of polyoxyethylene(n) nonyl phenyl ethers, NPEn, that bear different numbers of EO groups (n ) 5 and 40). Although some reports have been published on the study of the hydration balance between cationic surfactants with CDs,30–32 proper hydration studies of the encapsulation of conventional nonionic surfactants with CDs in water have not yet been achieved so far since the characteristic low cmc values (1-100 µM) make these investigations very difficult. This renders the determination of the molar properties of surfactants at the monomeric phase difficult, even by using pseudophase separation models for the micelle formation.33 We have analyzed the thermodynamic properties of the aggregation of NPE5 and its complexation with β-CD by comparison with those observed for the surfactant NPE40 (Figure 1). This comparison is supported by two general and well-reported observations: (i) for nonionic surfactants of the EO type, there is a moderate increase in the cmc as the polar head becomes larger,34 and (ii) β-CD shows weak interactions with EO chained molecules in

Tardajos et al. aqueous solution, whereas R-CD or derivatives of β-CD form stable complexes with them.35–37 Therefore, we show how the analysis of the complexation thermodynamics of the surfactant NPE40 with β-CD can help to understand the aggregation thermodynamics of NPE5. Thus, the density and speed of sound have been measured in a wide range of concentrations for both surfactants, in the absence and presence of the macrocycle, and from these measurements, the partial molar volumes and adiabatic compressibilities have been calculated. These experiments give us information about the nature of the complexes at a molecular level and also about their stoichiometries and the effect that β-CD has on the micellization by using a simple model, which takes into account the released water molecules from the cavity as well as the part of the guest that enters the macrocycle. Experimental Methods Chemicals and Sample Preparation. Nonionic surfactants NPE5 and NPE40, and β-CD were purchased from Aldrich and used without further purification. A water content of 13.5% in weight for β-CD, determined by thermogravimetric analysis, was considered in the calculation of the molality of the solutions. Stock solutions of the binary and ternary systems were prepared by weighting of the different components. Freshly deionized water from a Millipore Q-System, with conductivities lower than 15 µS cm-1, was used in the preparation of the solutions. Density and Speed of Sound Measurements. Measurements of the speed of sound, u, and density, F, were performed simultaneously with a homemade computerized technique, in which u and F were measured with a pulse-echo type technique that makes use of a 13 MHz transducer excited with pulses of the same frequency38 and a vibrating tube densimeter, respectively.39 Temperature control was achieved with a water bath using a temperature controller, where the ultrasonic cell and the densimeter were immersed. To change the concentration of solute during the experiments, an amount of a stock solution was weighed and added directly to the measuring cell. The ultrasonic cell and the densimeter were calibrated with pure water at 298.15 K and 1 bar (u0 ) 1496.739 m s-1 and F0 ) 997.045 kg m-3),40,41 and with dry air,42 immediately prior to the measurement. All measurements were carried out at 298.15 K, with a stability of (1 × 10-3 K. At these conditions, the precision of the speed of sound and density are (2 × 10-3 m s-1 and (1 × 10-3 kg m-3, respectively. The apparent molar volumes of a solute in water, υφ,s, can be determined from F, according to the relation

υφ,s )

Ms (F - F0) F msFF0

(1)

where Ms and ms are the molar mass and the molality of the solute, respectively, and the zero subindex stands for the initial state, in which the molality of the solute is zero. Assuming that the sound wavelength at 13 MHz is much larger than the particle size of the aggregates and independent of the frequency,43 velocity dispersions can be considered negligible, and the adiabatic compressibilities, β ) 1/(Fu2), of a solute in water can be readily determined. The apparent molar compressibility κφ,s can be therefore calculated from the relation

Thermodynamics of Oxyethylene Nonionic Surfactants

κφ,s ) βυφ,s +

(β - β0) msF0

J. Phys. Chem. B, Vol. 112, No. 49, 2008 15693

(2)

From υφ,s and κφ,s, the corresponding partial molar volume, υs, and compressibility, κs, of the binary system can be readily obtained by multiplying and taking the derivatives of eqs 1 and 2 with the molality

υs )

d (υ m ) dms φ,s s

(3)

κs )

d (κ m ) dms φ,s s

(4)

Analogously, in a ternary system such as that studied herein, in which the molality of the solute i is kept constant, the apparent molar volume and compressibility of the solute s in water can be related to F and u from the relations

υφ,s )

Ms (1 + miMi)(F - F0) F msFF0

κφ,s ) βυφ,s +

(1 + miMi)(β - β0) msF0

(5)

(6)

where Mi and mi are the molar mass and the molality of the solute, whose concentration is kept constant. The corresponding partial molar properties, υs and κs, for the ternary system can be obtained analogously to the binary system by determining the derivatives of eqs 5 and 6 multiplied by ms, taking into account that the molality of one of the components is not changed. Absorption and Fluorescence Spectroscopy. All experiments were carried out at 298 K, using quartz cuvettes with optical paths of 1 cm. UV absorption spectra were registered using an UVICON XL spectrophotometer (Bio-Tex Instruments). Steady-state fluorescence spectra were recorded on an AMINCO Bowman series 2 spectrofluorimeter, with a 2.0 nm bandwidth for excitation and emission. The excitation wavelength was fixed at 276 nm. The fluorescence quantum yields of NPEn, φNPEn, were measured using phenol in water as the standard (φphenol ) 0.14 at an excitation wavelength of 275 nm and 23 °C).44 Results and Discussion Binary Systems. The study of the complexation between CDs and surfactants demands a previous analysis of the binary system. The cmc of a surfactant may be calculated through any property which changes sharply around its critical concentration. Among these properties, the density and speed of sound are clear examples that allow the cmc determination when they are plotted versus the molality of surfactants, mNPEn (see the F and u measurements of the nonionic surfactants NPE5 and NPE40 in the Supporting Information). The changes observed in u show that this technique is more sensitive to the formation of aggregates for both surfactants than use of F.45 The cmc values have been determined by obtaining the derivatives of u with respect to mNPEn, provided that many measurements at close intervals of molalities were available. This determination gives an inflection point in the first derivative and a minimum in the

Figure 2. (a) Second derivative of the speed of sound measurements for the NPE5 binary system (O, the inset shows a zoom around the cmc) and the β-CD + NPE5 mixture at a fixed concentration of β-CD (b, mβ-CD ) 10.0 mmol kg-1). (b) Second derivative of the speed of sound measurements for the NPE40 binary system (O), and the β-CD + NPE40 mixture at a fixed concentration of β-CD (b, mβ-CD ) 5.0 mmol kg-1). Dotted lines point out the mβ-CD for the different ternary systems.

second derivative that can be assigned to the cmc of the surfactant. Figure 2a,b shows that the cmc’s for NPE5 and NPE40 surfactants are 0.02 and 0.4 mmol kg-1, respectively, in good agreement with previous results for NPE5 and literature values for nonionic surfactants.29,46 The apparent and partial molar volumes and compressibilities of NPE5 and NPE40 versus the mNPEn are plotted in Figures 3a,b and 4a,b, respectively. In a general micellization process, these properties change smoothly below the cmc and increase above this concentration as a result of aggregation until a constant value is reached. This change is more noticeable in the case of the partial properties. However, the low values of the cmc of both nonionic surfactants do not allow a direct analysis of monomers, and only the molar volumes and compressibilities at the micelle state can be directly determined (Table 1). The thermodynamic properties reach a plateau above the cmc of both surfactants, a region that was analyzed through a pseudophase separation model for the micelle formation.33 This model considers the cmc as the solubility of the surfactant by defining two different monomer and micelle phases. Below the cmc, the concentration of monomers corresponds with mNPEn, and the concentration of NPEn in the micelle state is equal to zero; above the cmc, the concentration of monomers is equal to the cmc, and the concentration of the surfactant in the form of micelles is mNPEn - cmc. If it is assumed that the molar volume or compressibility of the surfactant remains constant in each phase,

15694 J. Phys. Chem. B, Vol. 112, No. 49, 2008

Tardajos et al. For NPE40, both apparent molar properties decrease linearly with cmc/mNPEn in a manner consistent with the pseudophase micellization model. The resulting values of the linear fit are M M υNPE ) 1710 × 10-6 m3 mol-1, ∆υNPE ) 21 × 10-6 m3 40 40 -1 M 15 -1 3 -1 M mol , κNPE40 ) 180 × 10 Pa m mol , and ∆κNPE ) 183 40 15 -1 3 -1 × 10 Pa m mol (Table 1). The goodness of the applied model can be checked by comparison of the calculated apparent molar properties, obtained by substitution of the fitting parameters at different mNPE40 in eq 7 with the experimental data M (Figure 4, Table 1). A comparison between ∆υM NPE40 and ∆κNPE40 values and the aggregation properties of ionic surfactants with a similar alkyl chain, such as sodium decanoate (∆υsM ) 10 × 10-6 m3 mol-1 and ∆κsM ) 118 × 1015 Pa-1 m3 mol-1)47 or -6 m3 mol-1 decyltrimethylammonium bromide (∆υM s ) 5 × 10 and ∆κsM ) 103 × 1015 Pa-1 m3 mol-1),14,22 shows higher changes upon micellization in the case of the nonionic surfactant. This evidence can be explained in terms of a strong release of the initial hydration of the EO chain of the surfactant when the micelles are formed and suggests that not only the hydrophobic tail and the aromatic group are located in the micellar core but M also part of the EO hydrophilic chain. As expected, υNPE n increases with increasing EO content from NPE5 to NPE40, with a slope of 36.4 × 10-6 m3 mol-1 of the EO unit, assuming a linear increase of the thermodynamic properties with the number of EO units in the micelle state. This value is in good agreement with that obtained for the increase in υφ,s of the series of ethylene glycol (37.2 × 10-6 m3 mol-1),48 oxyethylene gemini surfactants (38.8 × 10-6 m3 mol-1),49 and C12EOn nonionic surfactants

Figure 3. (a) Apparent (circle) and partial (square) molar volumes for the NPE5 binary system (opened symbols) and the β-CD + NPE5 mixture at a fixed concentration of β-CD (closed symbols, mβ-CD ) 10.0 mmol kg-1). (b) Apparent (circle) and partial (square) molar compressibilities for the NPE5 binary system (opened symbols) and the β-CD + NPE5 mixture at a fixed concentration of β-CD (closed symbols, mβ-CD ) 10.0 mmol kg-1). Dotted lines point out the mβ-CD for the ternary system.

the respective apparent molar property, pφ,NPEn, can be expressed according to the relation

M pφ,NPEn ) pNPE n

cmc ∆pM mNPEn NPEn

(7)

where pM NPEn is the partial molar property of NPEn in the micelle M phase and ∆pNPE is the property change due to micelle n 0 formation. The molar property of monomers at the cmc, pNPE , n M M . Figure can be determined by the subtraction pNPE ∆p NPEn n 5a,b shows the variation of pφ,NPEn versus the ratio cmc/mNPEn above the cmc of both surfactants. From these plots, it is evident that in the studied concentration range, the pseudophase separation model fits well with the micellization behavior of surfactant NPE40 but cannot be applied to the aggregation of NPE5 as a consequence of its low cmc. From eq 7, the properties M of the micelle state of NPE5 have been estimated to be υNPE ) 5 15 Pa-1 m3 mol-1 435.0 × 10-6 m3 mol-1 and κM ) 127 × 10 NPE5 (Table 1). The molar volumes and compressiblities of NPE5 in the monomer phase will be determined after the analysis of the complexation process (see the Model of Complexation subsection) and will show how complexation with cyclodextrins can help to understand the aggregation of surfactants with very low values of the cmc.

Figure 4. (a) Apparent (circle) and partial (square) molar volumes for the NPE40 binary system (opened symbols) and the β-CD + NPE40 mixture at a fixed concentration of β-CD (closed symbols, mβ-CD ) 5.0 mmol kg-1). (b) Apparent (circle) and partial (square) molar compressibilities for the NPE40 binary system (opened symbols) and the β-CD + NPE40 mixture at a fixed concentration of β-CD (closed symbols, mβ-CD ) 5.0 mmol kg-1). Dotted lines point out the mβ-CD for the ternary system. Solid lines show the theoretical values of the apparent molar properties of the binary system obtained from substitution of linear fitting parameters in eq 7.



TABLE 1: Thermodynamic Parameters for the Aggregation of NPE5 and NPE40 in Water at 298.15 K, in the Absence and Presence of β-CD NPE5

cmc (mmol kg-1) cmc*/mβ-CD 0 υNPE × 106 (m3 mol-1) n M υNPE × 106 (m3 mol-1) n M ∆υNPEn × 106 (m3 mol-1) 0 κNPE × 10-15 (Pa-1 m3 mol-1) n M κNPEn × 10-15 (Pa-1 m3 mol-1) M ∆κNPE × 10-15 (Pa-1 m3 mol-1) n

NPE40

binary system

ternary systemc

binary system

ternary systemc

0.02 405 ( 4e 435.0 ( 0.2a, 435.0 ( 0.3b 30 ( 4e -77 ( 13e,f 127 ( 1a, 126 ( 2b 204 ( 14e,g

7.1d 0.71 434.0 ( 0.5b 130 ( 5b -

0.4 1688.4 ( 0.6a 1709.8 ( 0.1a, 1710 ( 1b 21.4 ( 0.5a -3 ( 5a 180 ( 1a, 180 ( 10b 183 ( 4a

4.0d 0.80 1710 ( 1b 180 ( 5b -

a Determined from the pseudophase separation model (eq 7). b Determined from the partial molar properties. c mβ-CD ) 10.0 mmol kg-1 and 5.0 mmol kg-1 for NPE5 and NPE40, respectively. d cmc in the presence of β-CD, cmc*. e Estimated from the transfer properties of NPE40 0 M (Table 2). f κNPE is possibly overestimated due to the structural differences between NPE5 and NPE40. g ∆κNPE is possibly underestimated due 5 5 to the structural differences between NPE5 and NPE40.

Figure 5. (a) Apparent molar volumes for the NPE5 (O) and NPE40 (0) binary systems versus cmc/mNPEn. (b) Apparent molar compressibilities for the NPE5 (O) and NPE40 (0) binary systems versus cmc/ mNPEn. Solid lines are the linear fits to eq 7.

(37.1 × 10-6 m3 mol-1).50 The contribution of the EO unit to the apparent molar compressibility of the surfactants in the M micellar state derived from κNPE data is 1.5 × 1015 Pa-1 m3 n -1 mol . We did not find in the literature direct measurements of the compressibility EO group contribution in water. However, this result seems to agree well with the measurement of the molar compressibilities of polyethylene glycols carried out by Seimiya et al.,51 which points to a small EO group contribution, on the order of 1 × 1015 Pa-1 m3 mol-1. Ternary Systems. The NPEn + β-CD + water ternary systems have been measured at constant β-CD concentrations of 10.0 and 5.0 mmol kg-1 for NPE5 and NPE40, respectively

(see F and u measurements of the ternary systems in the Supporting Information). The characteristic cloudiness of concentrated NPE5 solutions instantly disappeared in the presence of β-CD, which showed initial evidence for the disruption of the surfactant aggregates upon complexation. In the presence of β-CD, a shift of the aggregation process to higher values of molalities has been observed for both surfactants, thus indicating the formation of complexes between the amphiphiles and the macrocycle. The cmc in the presence of the macrocycle, the so-called cmc*, corresponds to a minimum in the second derivative of u (Figure 2a,b) and shows the stoichiometry of the complexation. The new cmc*’s for NPE5 and NPE40 are observed at 7.1 and 4.0 mmol kg-1 (Table 1), respectively, which corresponds to ratios of cmc*/mβ-CD ) 0.71 and 0.80, respectively. The analysis of the cmc* of the ternary system requires a comparison between the thermodynamics of micellization and that of complexation. According to the classic Anianson and Wall analysis,52 the equilibrium constant for the incorporation of a monomer n into 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 the selfassociation equilibrium constant, Kn ) kn/kn-1 ) 1/cmc, provided that the n steps in the process have the same equilibrium constant. From this approximation, the Kn constants are 5.0 × 104 and 2.5 × 103 mol-1 kg for NPE5 and NPE40, respectively. Recently, we observed from fluorescence studies that NPE5 forms complexes of 1:1 and 1:2 stoichiometries with β-CD, with the calculated complexation constants of the equilibria NPE5 T NPE5/β-CD and NPE5/β-CD + β-CD T NPE5/2β-CD being K11 ) (1.9 ( 0.2) × 104 L mol-1 and K12 ) (1.1 ( 0.1) × 103 L mol-1, respectively.29 From these stepwise binding constants, the overall association constant can be estimated to be β12 ) K11K12 ) 2.1 107 L2 mol-2. Therefore, the explanation for the shifts of the aggregation in the presence of the macrocycle is evident in terms of the larger value of β12 compared to Kn for NPE5. The cmc*’s point to a mixture of 1:1 and 1:2 stoichiometries of the complexation (one molecule of surfactant per two molecules of β-CD) for both surfactants and imply that the competitive equilibrium due to the different affinities of the monomers for the micelles or the β-CD is resolved in favor of the complex formation. The comparison between the complexation and aggregation of the surfactant NPE40 demands a detailed calculation of the complexation constants with β-CD (see next subsection).


Tardajos et al.

TABLE 2: Thermodynamic Parameters for the Complexation of NPE5 and NPE40 with β-CD in Water at 298.15 K, Keeping the Concentration of the Macrocycle or Surfactant Constant NPE5

NPE40

mβ-CD ) 10.0 mmol kg-1 1:2 υNPE × 10-6 (m3 mol-1) n 1:2 ∆υNPEn × 10-6 (m3 mol-1) 1:1 ∆υNPE × 10-6 (m3 mol-1) n 1:2 κNPEn × 1015 (Pa-1 m3 mol-1) 1:2 ∆κNPE × 1015 (Pa-1 m3 mol-1) n 1:1 ∆κNPEn × 1015 (Pa-1 m3 mol-1)

mβ-CD ) 5.0 mmol kg-1 1719 ( 31 ( 4a 14 ( 2a 17 ( 3a -

436 ( 1 31 ( 4b -60 ( 10a 17 ( 3b,c a

a Determined from extrapolation of the apparent molar properties. underestimated due to the structural differences between NPE5 and NPE40.

The apparent and partial molar volumes of NPE5 and NPE40 versus mNPEn are plotted in Figures 3a and 4a, respectively. Some remarkable differences can be observed along the studied concentration range in contrast with the binary systems. For both surfactants, when the concentration of the amphiphile is below mβ-CD, the apparent and partial volumes are above the curve for pure NPEn in water. Such a difference between the surfactant in the monomer state and that in the complexed form is only possible if the water molecules that are located inside of the cavity of the macrocycles are involved in the complexation process. The extrapolated values of the apparent molar volumes at infinite dilution give molar volumes of 436 × 10-6 and 1719 × 10-6 m3 mol-1 for NPE5 and NPE40, respectively, which correspond to the molar volumes of the surfactants in 1:2 the complex of higher stoichiometry 1:2, υNPE (Table 2, see n the Model of Complexation subsection). Regarding micellization, the curve of the ternary system is shifted, and the volume of the surfactant in the micelle form is the same irrespective of the presence of β-CD (Table 1). This result has been observed with different ionic surfactants,14,47 and it indicates that the complexes are isolated and that β-CD does not take part in the micelle structure. This evidence is in agreement with the appearance of the cloudiness in the solution after the cmc* that shows the formation of large aggregates. An analogous behavior is observed with the apparent and partial adiabatic compressibilities (Figures 3b and 4b). The molar compressibilities for the 1:2 complex were obtained by extrapolation of the experi1:2 mental data at infinite dilution, κNPE ) -60 × 1015 Pa-1 m3 5 -1 1:2 15 -1 mol and κNPE40 ) 14 × 10 Pa m3 mol-1 (Table 2). For NPE40 at infinite dilution, κ1:2,NPE40 reaches a value slightly 0 higher than that calculated for the monomer, κNPE , thus 40 indicating that the extent of the change of compressibilities due to the formation of complexes is much less pronounced than that registered for the micellization. At concentrations above the cmc for NPE5 and NPE40, the κs curves of the binary and ternary systems coalesce, and the effect of the new cmc* is analogous to that observed for the volumes. Estimation of the Binding Constants. In the case of luminescent molecules that form aggregates, the fluorescence emission spectroscopy has been used as a useful technique to estimate the complexation constants with CDs.53 The binding constants of the association process between NPE40 and β-CD have been determined by measuring the luminescence properties of the surfactant at a concentration below the cmc, in the presence of different concentrations of macrocycle. The UV absorption spectrum of NPE40 below the cmc shows two maxima, at 222 and 282 nm, with molar absorptivities of 9.5 × 103 and 8.8 × 102 L mol-1 cm-1, respectively. Figure 6a shows that the addition of β-CD to a 0.02 mM solution of surfactant induces a nonsignificant red shift of 1 nm. There are

b

mNPE40 ) 5.0 mmol kg-1 16 ( 3b 6 ( 4b

3a

Determined from NPE40 measurements.

c

1:2 ∆κNPE is possibly n

Figure 6. (a) Absorption spectra of NPE40 ([NPE40] ) 0.02 mM) in the absence (s) and presence (- - -) of β-CD ([β-CD] ) 0.1 mM). (b) Emission spectra of the NPE40 + β-CD system at different β-CD concentrations (excitation at 282 nm, [NPE40] ) 0.02 mM). (c) Intensity ratios of NPE5 (O, ref 29) and NPE40 (b) versus [β-CD] at 298 nm (solid lines are fits to eq 8). (d) Job plot for the NPE40 + β-CD system at 298 nm (dash lines point out the 1:1 and 1:2 stoichiometries).

no significant changes in the overall absorbance intensity at molar ratios of r ) [β-CD]/[NPE40] < 15, which indicates that the free guest and the surfactant in the complexed form have the same molar absorptivity. At higher values of r, the absorption contribution of the β-CD to the overall absorbance cannot be considered negligible (molar absorptivity of 15.0 L mol-1 cm-1 at 280 nm), and the increase observed in the absorption patterns is associated with the macrocycle. The emission spectrum of NPE40 in the monomer state is independent of the excitation wavelength and consists of a broad and nonstructured band, with a maximum centered at 298 nm. The fluorescence emission of the ternary system has been



studied, keeping the concentration of the surfactant constant below the cmc ([NPE40] ) 0.02 mM). When variable amounts of macrocycle are added, an increase of the intensity is observed (Figure 6b). Considering the chemical structure of NPEn surfactants, consisting of two differentiated hydrophobic regions (an aliphatic tail and an aromatic fluorescent moiety), and previous results found in the case of NPE5, the coexistence of 1:1 and 1:2 stoichiometries can be considered. In the general case of a mixture of 1:1 + 1:2 equilibria,54 in which the complexes and the free guest are fluorescent, the variation in intensity is given by the relation

1 + aK11[β-CD](1 + K12[β-CD]) I ) I0 1 + K11[β-CD] + K11K12[β-CD]2

(8)

where I is the measured fluorescence at each β-CD concentration of the ternary system, I0 is the fluorescence of the pure surfactant, and [β-CD] is the concentration of free macrocycle. The parameter a is a function of the quantum yields, φi, and absorptivities, εi, of NPE40 in its free and complexed forms, a ) εcompφcomp/εNPE40φNPE40. This quotient considers the same ratio for the absorption and emission coefficients of the 1:1 and 1:2 complexes with respect of the free monomer, an assumption that is reasonable in terms of the identical values of the free molecule and complex absorptivities and the chemical structure of NPEn. The binding constants have been obtained by applying a nonlinear fitting (Benesi-Hildebrand method)55 of the I/I0 experimental data versus the total concentration of the macrocycle (Figure 6c), which is based on the general mass action law for a two-step equilibrium. The fitted curve is plotted in Figure 6c, and the resulting parameters are a ) 1.78, K11 ) (1.4 ( 0.2) × 104 L mol-1, and K12 ) (1.9 ( 0.2) × 103 L mol-1, with an overall binding constant of β12 ) K11K12 ) 2.7 107 L2 mol-2. The stability of these parameters has been tested by using different initial values, and the 1:1 + 1:2 stoichiometries have been corroborated by the Job method (Figure 6d).56 The fitting parameters obtained for NPE40 are in good agreement with those obtained previously for NPE5 (a ) 1.86, K11 ) (1.9 ( 0.2) × 104 L mol-1, and K12 ) (1.1 ( 0.1) × 103 L mol-1),29thus indicating analogous complexation modes for both surfactants. From the quantum yields of both surfactants (φNPE5 ) 0.18 and φNPE40 ) 0.21) and the fitting parameter a, the quantum yields corresponding to the complexes can be obtained, φcomp(NPE5) ) 0.33 and φcomp(NPE40) ) 0.34, which are in agreement with the higher luminescence of the surfactants under complexation. The complexation avoids the exposure of the aromatic moiety to the solvent, which decreases the effectiveness of the nonradiative pathways through solute-solvent interactions. Additionally, the higher value of the quantum yield in the case of NPE40 at the monomer state could indicate that the EO chain protects the aromatic moiety from the solvent. From these results and the analogous hydrophobic moiety of NPE5 and NPE40, a reasonable comparison between the thermodynamic aggregation processes of both nonionic surfactants can be ascertained. Moreover, the fact that EO chains do not interact favorably with β-CD in water due to the highly hydrophilic character of the EO groups35–37 makes the complexation of both surfactants analogous and reinforces the relation between their aggregation and complexation processes. Model of Complexation. The apparent and partial molar properties offer information about the complexation process at a molecular level. In an experiment in which the concentration

of the macrocycle is kept constant and the concentration of the surfactant is increased, the transfer volume and compressibility are defined as the change in these properties for the surfactant in the presence and absence of β-CD and are directly related to the release of water molecules from the cavity of the macrocycle. In the case of two equilibrium steps of complexation coexisting with a micellization process, in which the concentration of the surfactant is above the cmc, the apparent molar properties for the surfactant can be expressed according to the relation 0 M 1:1 p0 + χNPE pM + χNPE p1:1 + pφ,NPEn ) χNPE n NPEn n NPEn n NPEn 1:2 χNPE p1:2 (9) n NPEn 1:1 1:2 where pNPE and pNPE are the partial molar properties of the n n surfactant at complexes of 1:1 and 1:2 stoichiometries and χ 0NPEn, M , χ1:1 , and χ1:2 are the molar fractions of surfactant in χNPE NPEn NPEn n the form of the monomer, micelle, 1:1 complex, and 1:2 complex, respectively. The concentrations of all of the components in solution are connected by the corresponding mass balances and mass action law. It is not difficult to prove that when mNPEn f 0, and according to the obtained binding constants in which β12 . Kn, the concentration of the surfactant at the 1:2 complexed form is the majority, and the value of the 1:2 . Thus, at these apparent molar properties is pφ,NPEn f pNPE n diluted conditions, the transfer properties are defined as ∆υ1:2 NPEn 0 1:2 1:2 0 ) υ1:2 NPEn - υNPEn and ∆κNPEn ) κNPEn - κNPEn. The partial molar properties of the 1:2 complex have been determined previously by extrapolation of the respective apparent molar properties at infinite dilution in the case of the ternary systems for both surfactants (Table 2). On the other hand, only the thermodynamic properties corresponding to the monomer of NPE40 could be directly determined in Figure 5. Thus, the transfer properties for NPE40 are ∆υ0t ) 31 × 10-6 m3 mol-1 and ∆κ0t ) 17 × 1015 Pa-1 m3 mol-1 (Table 2). These changes in the transfer properties indicate that the molecular environment of the surfactant, when the β-CD is present, differs strongly from the monomer in water and shows that complexation has taken place. A different experiment has been carried out in order to obtain the thermodynamic properties for the 1:1 complex formed between NPE40 and β-CD. The ternary system has been studied, keeping the surfactant concentration constant above the cmc ([NPE40] ) 5.0 mM) and increasing the concentration of the macrocycle. For comparison, the apparent molar volumes and compressibilities of this ternary system are plotted in Figure 7, together with the corresponding values of the binary system 0 0 β-CD + water (υβ-CD ) 704 × 10-6 m3 mol-1 and κβ-CD ) 15 -1 3 -1 57 -2.6 × 10 Pa m mol ). The apparent molar properties for the β-CD depend on the coexistence of two different complexes of 1:1 and 1:2 (one molecule of surfactant per two molecules of β-CD) stoichiometries and the free host and can be expressed according to a relation

0 0 1:1 1:1 1:2 1:2 pφ,β-CD ) χβ-CD pβ-CD + χβ-CD pβ-CD + 2χβ-CD pβ-CD (10) 0 1:1 , and p1:2 are the partial molar properties of where pβ-CD , pβ-CD β-CD the macrocycle at free form and complexes of 1:1 and 1:2 1:2 stoichiometries and χ 0β-CD, χ1:1 β-CD, and χβ-CD are the molar fractions of β-CD in the form of the free host, 1:1 complex, and 1:2 complex, respectively. At low concentrations of β-CD and in accord with β12 . Kn, the value of the apparent molar properties of the macrocycle is the result of two contributions, (i) the release of the monomer from the micelle and (ii) the subsequent


Figure 7. (a) Apparent (circle) and partial (square) molar volumes for the β-CD binary system (opened symbols, ref 57) and the β-CD + NPE40 mixture at a fixed concentration of NPE40 (closed symbols, mNPE40 ) 5.0 mmol kg-1). (a) Apparent (circle) and partial (square) molar compressibilities for the β-CD binary system (opened symbols, ref 57) and the β-CD + NPE40 mixture at a fixed concentration of NPE40 (closed symbols, mNPE40 ) 5.0 mmol kg-1). Dotted lines point out the mNPE40 for the ternary system.

formation of the complex of lower stoichiometry (the concentration of surfactant at the 1:1 complexed form is higher than that at the 1:2 stoichiometry). At these conditions, it is possible to relate the aggregation of the surfactant and the complexation of the macrocycle and define the extrapolated value of the molar 0 properties at infinite dilution of β-CD as pφ,β-CD ) pβ-CD + 1:1 M , where ∆p1:1 ∆pNPE ∆p is the value of the transfer NPEn NPEn n properties when the complex of the 1:1 stoichiometry is formed. The transfer volumes and compressibilities of the 1: 1 complex 1:1 1:1 thus obtained are ∆υNPE ) 16 × 10-6 m3 mol-1 and ∆κNPE 40 40 ) 6 × 1015 Pa-1 m3 mol-1, respectively (Table 2). The result of the volume is in good agreement with that obtained for the 1:2 /∆υ1:1 1:2 stoichiometry complex (∆υNPE NPE40 ≈ 2.0), and they 40 are slightly smaller than those observed for ionic surfactants that form complexes with β-CD of 1:1 (for sodium decanoate and decyltrimethylammonium bromide, ∆υ1:1 are 20 × 10-6 and 19 × 10-6 m3 mol-1, respectively) and 1:1 + 1:2 (for tetradecyltrimethylammonium bromide, ∆υ1:2 is 36 × 10-6 m3 mol-1) stoichiometries.14,47 In the case of the compressibility 1:2 /∆κ1:1 (∆κNPE NPE40 ≈ 3.0), we found that the transfer compress40 ibilities for the 1:1 and 1:2 complexes are significantly smaller than those characteristic for surfactants that form 1:1 (for sodium 1:1 decanoate and decyltrimethylammonium bromide, ∆κNPE are 40 69 × 1015 and 67 × 1015 Pa-1 m3 mol-1, respectively) and 1:1 1:2 + 1:2 (for tetradecyltrimethylammonium bromide, ∆κNPE is 40 15 -1 3 -1 14,47 87 × 10 Pa m mol ) complexes with β-CDs. This evidence suggests that in the monomer state, there is a partial folding of the surfactant, in which the hydrophobic moieties of NPE40 are surrounded by the EO chain. This structural conformation of the monomer could decrease the water contact

Tardajos et al. of the alkyl chain and, especially, the phenyl group and could lead to higher values of the compressibility for the monomer and lower values of the transfer compressibilities for the 1:1 and 1:2 complexes. This plausible explanation is in good agreement with the measured transfer volumes and the higher value of the quantum yield observed in the case of NPE40 with respect to NPE5 for the monomer state in water, which shows that the aromatic moiety is less exposed to the solvent in the case of the surfactant with a longer EO tail. The analogy observed between the complexation of NPE5 and NPE40 with β-CD from the photophysical measurements allows consideration of the same values of the transfer properties for the NPE5 complexation and estimation of the thermodynamic properties of NPE5 at the monomer state (Table 1). From these results, the change in the properties under micellization can be M M estimated, ∆υNPE ) 30 × 10-6 m3 mol-1 and ∆κNPE ) 204 × 5 5 15 -1 3 -1 10 Pa m mol , which are significantly higher than those obtained for the surfactant NPE40 (Table 1). According to the M transfer compressibilities, the value of ∆κNPE could be under5 estimated due to a higher exposure to water of the hydrophobic part of the NPE5 monomer, which presents a smaller size of the EO chain compared to NPE40. The higher values of both micellization properties with respect to NPE40 can be related to the formation of larger aggregates that are characteristic of nonionic surfactants above their cloud points. In these large aggregates, the hydration of the hydrophilic tail is lower than that in the case of conventional micelles or monomers. This decrease of the hydration exposure that undergoes the EO surface increases the internal core size of the aggregates and implies that the surfactants are expanded and more compressible in this situation. The determination of the EO unit contribution to the thermodynamic properties at the monomer state, suppos0 0 ing a linear increase of υNPE and κNPE with the EO content, n n -6 3 -1 gives slopes of 36.7 × 10 m mol and 1.1 × 1015 Pa-1 m3 mol-1, results that are in good agreement with those obtained in the case of micelles in the absence of β-CD. The resulting values of molar properties, assuming that all of the water molecules of the cavities of two CDs are expelled, can be explained according to the following reaction scheme

NPEn(l) + 2CD(m + n) T NPEn(l - s)/2CD(m) + 2n (11) where l is the total hydration water of the surfactant, m is the number of water molecules that hydrates the external surface of CD, n represents the molecules of water inside of the cavity, and s is the number of water molecules that the surfactant loses upon complexation. Due to the geometry of the guest and host molecules, we can assume that in the complexation, there are changes in the hydration water of the β-CD cavity and in the hydration shell that coats the hydrophobic region of the surfactant. The change in volume or compressibility of the reaction according to this model can be calculated from the relation 1:2 0 0 ∆pNPE ) pw0nw - pCH n - pCH n - p0aromnarom + n 2 CH2 3 CH3 NPEn w - pβ-CD ) (12) (pβ-CD

where pw0 is the molar property of 1 mol of water (υw0 ) 18.068 × 10-6 m3 mol-1 and κw0 ) 8.081 × 1015 Pa-1 m3 mol-1), nw is the number of water molecules expelled from the cavity of 0 0 0 the β-CD, which is 6.5,58 pCH , pCH , and parom are the molar 2 3 properties of the methylene, methyl, and aromatic groups in

Thermodynamics of Oxyethylene Nonionic Surfactants 0 0 water, respectively (υCH ) 15.8 × 10-6 m3 mol-1,14,23 κCH ) 2 2 0 15 -1 3 -1 14,59 -6 -1.5 × 10 Pa m mol , υCH3 ) 26.2 × 10 m3 0 0 mol-1,60 κCH ) -2.5 × 1015 Pa-1 m3 mol-1,61 υarom ) 83.1 × 3 -6 3 -1 48 15 -1 3 0 10 m mol , κarom ) -4.6 × 10 Pa m mol-1),62 and nCH2, nCH3, and narom are the number of methylene, methyl, and NPEn - pw aromatic groups buried in the β-CDs. The (pβ-CD β-CD) contribution accounts for the changes of the thermodynamic properties of the β-CDs when they are threaded by the surfactant or filled with water. This term is equal to zero in the case of the volume because of the negligible difference in the volume of the β-CD cavity when the macrocycle is filled with water or with the surfactant. We can use eq 12 to determine the number of CH2 groups that enter the cavities. By substituting ∆υ0t into eq 12, we obtain that nCH2 is 6.0 when nCH3 ) 1 and narom ) 1, which is consistent with the chemical structure of NPEn. These results are in good agreement with the number of methylene groups obtained for the 1:1 complexation between β-CD and ionic surfactants with similar lengths of the aliphatic tail, such as sodium decanoate (nCH2 ) 6.1)47 or decyltrimethylammonium bromide (nCH2 ) 6.2),23 and with the height of the β-CD (7.9 Å) that corresponds theoretically to 6.3 CH2 groups, assuming the length of a C-C bond with C in sp3 hybridization.63 The analysis of the compressibility is more difficult, and it can be done by considering the sum of different contributions, which are some of the driving forces in the complex formation with CDs. The water molecules that are inside of the cavity are highly structured and present a rather low compressibility with respect to the bulk water. Additionally, the surfactant is exposed to a more hydrophobic environment in the complexed form compared to the monomer state. Thus, we cannot assume that the differences of the cavity upon complexation are negligible. The last term in eq 12 considers this effect, and by substitution of the number of water molecules expelled and the number of CH3, CH2, and phenyl groups of NPE40 that enter in two β-CDs, s - κw ) 15 -1 (κCD CD cavity has been determined to be -72 × 10 Pa 3 -1 m mol . This value is possibly underestimated for NPE5, in which the hydrophobic groups of the monomer are more exposed to the solvent due to the smaller size of the EO chain compared to NPE40. A positive value for the compressibility of the cavity should indicate that the cavity of β-CD will be easier to compress when it is filled with the nonionic surfactant than with water. The negative value could be explained by the high and negative value of the compressibility of NPE40 at the monomer state due to a partial folding of the molecular structure and by strong van der Waals contacts between the interacting surfactant and β-CDs atomic groups in the cavities. Moreover, the existence of intense hydrogen bond interactions between the hydroxyl groups of the β-CDs that are forming head-tohead dimeric units and a contribution due to interactions between the hydroxyl groups placed at the rims of β-CD and the EO chain of the surfactants cannot be excluded.

Conclusions By examining the thermodynamics of the complexation process between β-CD and oxyethylene nonionic surfactants with very different lengths of the hydrophilic chain in aqueous solution, we were able to understand the micellization process for a nonionic surfactant with a low value of the cmc. The complexation was independent of the EO chain length due to the low affinity of β-CD for these highly hydrophilic and hydrated groups. We believe that this analysis could contribute not only to the understanding of the complexation between surfactants and CDs but also to the determination of the aggregation thermodynamic properties of nonionic oxyethylene

J. Phys. Chem. B, Vol. 112, No. 49, 2008 15699 surfactants with low values of the cmc, according to previous measurements of the complexation and aggregation thermodynamics of analogous surfactants of the homologue series. Acknowledgment. Financial support by the Ministerio de Educación y Ciencia (A.G.M. and CTQ2006-14933/BQU). Supporting Information Available: Additional experimental measurements. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Wenz, G.; Han, B. H.; Muller, A. Chem. ReV. 2006, 106, 782. (2) Suksai, C.; Figueiras-Go´mez, S.; Chhabra, A.; Liu, J.; Skepper, J. N.; Tuntulani, T.; Otto, S. Langmuir 2006, 22, 5994. (3) Jeon, W. S.; Moon, K.; Park, S. H.; Chun, H.; Ko, Y. H.; Lee, J. Y.; Samal, S.; Selvapalam, N.; Rekharsky, M. V.; Sindelar, V.; Sobransingh, D.; Inoue, Y.; Kaifer, A. E.; Kim, K. J. Am. Chem. Soc. 2005, 127, 12984. (4) Szejtli, J. Cyclodextrins and Their Inclusion Complexes; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988. (5) Duchene, D. New Trends in Cyclodextrins and DeriVatiVes; Editions de Sante´: Paris, 1991. (6) Atwood, J. L.; Davies, J. E. D.; Macnicol, D. D.; Vo¨gtle, F. C. ComprehensiVe Supramolecular Chemistry Volume 3:Cyclodextrins; Szejtli, J., Osa, T., Eds.; Pergamon: Tarritown, NY, 1996. (7) Guerrero-Martıńez, A.; Berger, S.; Tardajos, G. ChemPhysChem 2006, 7, 2074. (8) Connors, K. A. Chem. ReV. 1997, 97, 1325. (9) Ross, P. D.; Rekharsky, M. V. Biophys. J. 1996, 71, 2144. (10) Shikata, T.; Takahashi, R.; Satokawa, Y. J. Phys. Chem. B 2007, 111, 12239. (11) De Lisi, R.; Milioto, S.; Muratore, N. J. Phys. Chem. B 2002, 106, 8944. (12) De Lisi, R.; Lazzara, G.; Milioto, S.; Muratore, N. J. Phys. Chem. B 2003, 107, 13150. (13) Wilson, L. D.; Verrall, R. E. Langmuir 1998, 14, 4710. (14) Kudryashov, E.; Kapustina, T.; Morrisey, S.; Buckin, V.; Dawson, K. J. Colloid Interface Sci. 1998, 203, 59. (15) Fisicaro, E.; Compari, C.; Duce, E.; Contestabili, C.; Viscardi, G.; Quagliotto, P. J. Phys. Chem. B 2005, 109, 1744. (16) Lazzara, G.; Milioto, G.; Muratore, N. J. Phys. Chem. B 2008, 112, 5616. (17) Juarez, J.; Taboada, P.; Valdez, M. A.; Mosquera, V. Langmuir 2008, 24, 7107. (18) Hanke, E.; Schulz, U.; Kaatze, U. ChemPhysChem 2007, 8, 553. (19) Chalikian, T. V. J. Phys. Chem. B 1998, 102, 6921. (20) Senkow, S.; Mehta, S. K.; Douheret, G.; Roux, A. H.; RouxDesgranges, G. Phys. Chem. Chem. Phys. 2002, 4, 4472. (21) Chalikian, T. V. J. Phys. Chem. B 2008, 112, 911. (22) Gaitano-Gonza´lez, G.; Crespo, A.; Tardajos, G. J. Phys. Chem. B 2000, 104, 1869. (23) Gaitano-Gonza´lez, G.; Crespo, A.; Compostizo, A.; Tardajos, G. J. Phys. Chem. B 1997, 101, 4413. (24) Taulier, N.; Chalikian, T. V. J. Phys. Chem. B 2006, 110, 12222. (25) Taulier, N.; Chalikian, T. V. J. Phys. Chem. B 2008, 112, 9546. (26) Blom, A.; Warr, G. G.; Wanless, E. J. Langmuir 2005, 21, 11850. (27) Toerne, K.; vonWandruszka, R. Langmuir 2002, 18, 7349. (28) Holmberg, K.; Jo¨nsson, B.; Kronberg, B.; Lindman, B. Surfactants and Polymers in Aqueous Solution; Wiley: Chichester, U.K., 2003; pp 97118. (29) Guerrero-Martıńez, A.; Montoro, T.; Montserrat, H. V.; Gonza´lezGaitano, G.; Tardajos, G. J. Phys. Chem. B 2007, 111, 1368. (30) Wilson., L. D.; Verrall, R. E. J. Phys. Chem. B 1997, 101, 9270. (31) Guerrero-Martıńez, A.; Domıńguez-Gutie´rrez, D.; Palafox, M. A.; Tardajos, G. Chem. Phys. Lett. 2007, 446, 92. (32) Wilson, L. D.; Verrall, R. E. J. Phys. Chem. B 2000, 104, 1880. (33) Desnoyers, J. E.; De Lisi, R.; Perron, G. Pure Appl. Chem. 1980, 52, 433. (34) Atwood, D. J. Phys. Chem. 1968, 72, 339. (35) Harada, A. AdV. Polym. Sci. 1997, 133, 141. (36) Harada, A. Polym. News 1993, 18, 358. (37) González-Gaitano, G.; Brown, W.; Tardajos, G. J. Phys. Chem. B 1997, 101, 710. (38) Tardajos, G.; Gonza´lez-Gaitano, G.; Montero de Espinosa, F. ReV. Sci. Instrum. 1994, 65, 2933. ´ lvarez, J.; Gonza´lez-Gaitano, G.; Tardajos, G. ReV. Sci. (39) Herrero-A Instrum. 1997, 68, 3835. (40) Kroebel, W.; Mahrt, K. H. Acustica 1976, 35. (41) Brown, I.; Lane, J. E. Pure Appl. Chem. 1976, 45, 1.

15700 J. Phys. Chem. B, Vol. 112, No. 49, 2008 (42) The air density can be calculated by FA ) (0.001293/(1 + 0.00367T))(P/760), where T is the temperature in °C and P the pressure in mm Hg. See: Kohlrausch, Praktische Physik; Teubner: Stuugart, Germany, 1968; Vol. 3. (43) Kaatze, U.; Hushcha, T. O.; Eggers, F. J. Solution Chem. 2000, 29, 299. (44) Rahavendran, S. V.; Karnes, H. T. Anal. Chem. 1996, 68, 3763. (45) Wen, X. G.; Verrall, R. E. J. Colloid Interface Sci. 1997, 196, 215. (46) Tringali, A.; Kim, S.; Brenner, H. J. Lumin. 1999, 81, 85. (47) Gonza´lez-Gaitano, G.; Sanz-Garcıá, T.; Tardajos, G. Langmuir 1999, 15, 7963. (48) Cabani, S.; Gianni, P.; Mollica, V.; Lepori, L. J. Solution Chem. 1981, 10, 563. (49) Wettig, S. D.; Li, X.; Verrall, R. E. Langmuir 2003, 19, 3666. (50) Maccarini, M.; Briganti, G. J. Phys. Chem. A 2000, 104, 11451. (51) Seimiya, T. J. Colloid Interface Sci. 2003, 266, 422. (52) 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.

Tardajos et al. (53) Smith, V. K.; Ndou, T. T.; DelaPena, A. M.; Warner, I. M. J. Inclusion Phenom. Macrocyclic Chem. 1991, 10, 471. (54) Connors, K. A. Binidng Constants: The Measurement of Molecular Stability; John Wiley & Sons: New York, 1987; Chapter 4. (55) Hirose, K. J. Inclusion Phenom. Macrocyclic Chem. 2001, 39, 193. (56) Dykes, G. M.; Smith, G. M. Tetrahedron 2003, 59, 3999. (57) Gonza´lez-Gaitano, G.; Compostizo, A.; Sańchez-Martıń, L.; Tardajos, G. Langmuir 1997, 13, 2235. (58) Zabel, V.; Saenger, W.; Mason, S. A. J. Am. Chem. Soc. 1986, 108, 3664. (59) Vikingstad, E. J. Colloid Interface Sci. 1979, 72, 75. (60) Gianni, P.; Lepori, L. J. Solution Chem. 1996, 25, 1. (61) Hedwig, G.; Hoiland, H. Phys. Chem. Chem. Phys. 2004, 6, 2440. (62) Kharakoz, D. P. J. Phys. Chem. 1991, 95, 5634. (63) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley: New York, 1973.

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