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J. Phys. Chem. B 2001, 105, 430-435
Dependence of Water Dynamics upon Confinement Size J.-B. Brubach,†,‡ A. Mermet,†,‡ A. Filabozzi,†,§ A. Gerschel,†,‡ D. Lairez,⊥ M. P. Krafft,∞ and P. Roy*,†,‡ LURE, UMR CNRS n°130, baˆ t. 209 D, and LCP, UMR CNRS n°8611, baˆ t. 490, UniVersite´ Paris-Sud, 91405 Orsay Cedex, France; Dipart. Fisica, UniVersita` Roma “Tor Vergata” and INFM, Via Ricerca Scientifica 1, 00133 Roma, Italy; Laboratoire Le´ on Brillouin, Commissariat a` l’Energie Atomique-CNRS, Centre d’Etudes de Saclay, 91191 Gif-sur-YVette, France; and Institut Charles Sadron, UPR CNRS n°22, 6 rue Boussingault, 67083 Strasbourg Cedex, France. ReceiVed: August 17, 2000; In Final Form: October 30, 2000
Water confined in nonionic fluorocarbon reverse micelles was investigated through mid-infrared spectroscopy (OH stretching and bending modes), in combination with quasielastic light scattering data. The characteristic OH stretching band is seen to exhibit significant changes upon decreasing water core size. An analysis in terms of three different levels of water connectivity has allowed the estimation of the extent of perturbation of water dynamics as a function of confining size.
I. Introduction The collective dynamics of water is often thought to provide fast communication pathways between biological objects or within various parts of a single complex biological system. However, the identification of this unique property is a nontrivial task because water is found in a wide variety of biological environments, whose diverse chemical natures may screen the underlying physical properties that ensure the transmission of information between remote objects in an aqueous medium. In particular, very little is known about the effect of confinement size on the water molecules arranged into H-bonded networks. The aim of this study is to quantitatively evaluate the extent of perturbation of water organization using a well-controlled confining medium. Reverse micelle systems are especially well adapted in this context, as they are potentially able to host either small or significant amounts of water.1 Moreover, they can be considered as intermediate between complex biological water cavities and rigid wall pores in solid media. As in biological objects, the reverse micelles are soft nonrigid cavities, which may host solute ions and/or polar molecules. As in rigid pores, the micelles present a rather well-defined closed geometry, with a finite size and single constituent walls, as opposed to biological cavities whose walls may be composed of very diverse constituents. The microemulsion studied here by infrared spectroscopy is a water-in-fluorocarbon system. In contrast with already studied similar micellar systems (like sodium bis(2-ethylhexyl) sulfosuccinate (AOT), for instance), the hereby investigated microemulsion is made of nonionic surfactants, which allows the preclusion of headgroup charge effects onto the encapsulated water. Besides, the micelle mean size has been precisely measured, thereby allowing the first determination of the behavior of water as a function of confining size. The degree of organization of water trapped inside droplets of about 10
nm radius was assessed through measurements of the OH stretching mode and bending mode. II. Experiment A. Surfactant Synthesis. The emulsifying agent belongs to a homologous series of (F-alkyl)alkyl dimorpholinophosphate surfactants (FnCmDMP, where DMP ) dimorpholinophosphate); in our case the surfactant chosen is F8C11DMP. This single-tailed nonchiral amphiphilic molecule is composed of a half-fluorinated half-hydrogenated hydrophobic carbon chain, ended with a nonionic hydrophilic polar headgroup (DMP).2,3
The synthesis of this surfactant is performed in two steps.2 The first step is a phosphorylation of the fluorinated alcohol in a mixture of triethylamine and dry ether with a solution of phosphorus oxytrichloride in dry ether. The mixture was stirred at 0 °C for 1 h; all the synthesis was carried out under dry nitrogen. In a second step, a solution of morpholine and triethylamine in ether was added to ([(F-octyl)undecyl)]phosphoryldichloride, under the same conditions. The reaction mixture was maintained free from oxygen and cooled with an ice bath. After stirring for 18 h, the mixture was allowed to warm to room temperature. The clear oil residue was dried under reduced pressure and finally purified by chromatography.
* Corresponding author. † LURE, Universite ´ Paris-Sud. ‡ LCP, Universite ´ Paris-Sud. § Universita ` Roma “Tor Vergata” and INFM. ⊥ Centre d’Etudes de Saclay. ∞ Institut Charles Sadron.
10.1021/jp002983s CCC: $20.00 © 2001 American Chemical Society Published on Web 12/20/2000
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B. Preparation of the Micellar Solutions. The reverse micelles were formed in perfluoroctyl bromide (PFOB, C8F17Br) as the fluorocarbon continuous phase. The DMP surfactants have a high interfacial activity. They can lower the surface tension of water much more than the usual purely hydrocarbon chain surfactants. They also strongly decrease the interfacial tension between water and fluorocarbons and are characterized by a low critical micellar concentration. These compounds were found to exhibit a strong ability to self-assemble into vesicles and microtubules and into stable reverse emulsions.2,3 Microemulsions of several concentrations were prepared as follows: F8C11DMP was dispersed into perfluoroctyl bromide by gentle stirring, well-defined microamounts of doubly distilled water (conductivity < 10-7 Ω1- cm-1 at 25 °C) were then added, and the mixture was shaken manually. The water content is characterized by the water/surfactant concentration ratio W0
W0 )
[H2O] [surfactant]
(1)
All samples were prepared at concentrations allowing a single stable and transparent isotropic phase to be formed at room temperature, in agreement with partial ternary phase diagrams of the water/PFOB/F8C11DMP system.4 Our study focuses on W0 values ranging between 1.51 and 25.3, i.e. microemulsions with droplet sizes on the order of 10 nm. These values correspond to water weight concentrations between 0.1% and 1.6% and a surfactant weight concentration of 3%. C. Micelle Size Characterization. To evaluate the average sizes of the reverse micelles, quasielastic light scattering (QELS) measurements were performed in self-breathing mode, using an Ar ion laser (λ ) 488 nm, 300 mW) device.5 The timeaveraged autocorrelation function of the scattered intensity was calculated using a Malvern 7032 multicorrelator. The diffusion coefficient was measured at several angles (90°, 120°, and 150°) and confirmed the monodispersity of the samples. The hydrodynamic radii (Rh) of the reverse micelles was thus determined for various concentrations of water (W0), using the StokesEinstein equation:
kT D) 6πηsRh
(2)
where D is the diffusion coefficient, ηs is the experimentally determined viscosity of the pure PFOB sample, and Rh is the hydrodynamic radius. All measurements were conducted at T ) 25.0 ( 0.1 °C. As shown in Figure 1, the detected micelle hydrodynamic radius increases linearly with increasing water amount, from 7.5 nm up to 27 nm for W0 values ranging from 1.85 up to 35.6, respectively. As reported elsewhere,6 the extrapolation of these data to W0 ) 0 has no physical meaning since, for very low water contents the variation of Rh is no more linear. The time stability of these systems was checked by recording a same sample within an interval of 3 days (see the two overlapping points at W0 ) 27.6). The temperature stability of Rh was assessed between 15 and 35 °C. D. Infrared Measurements. The transmission spectra of the microemulsions were recorded using a Bomem DA8 Fourier transform spectrometer, at the SIRLOIN beamline at SuperACO, LURE, University of Paris-Sud, Orsay, France.7,8 This device can equally operate with infrared synchrotron radiation or regular internal sources. For the hereby reported study, the mid-infrared region (500-9000 cm-1) was investigated thanks to a Globar source, in combination with a KBr beam splitter
Figure 1. Variation of the reverse micelle hydrodynamic radius (Rh) versus water content (W0), as determined from QELS. The line was obtained by a best fit procedure and was used to determine Rh. The filled point corresponds to a measurement performed after a period of 3 days. The overlap demonstrates the time stability of the sample.
and a MCT wide-range detector. The spectra were recorded with a resolution of 4 cm-1 with 300 scans per spectrum, and no mathematical correction (e.g., smoothing) was performed. All spectra displayed below have a reproducibility larger than 0.1%. The spectrum of PFOB alone was used as a reference in the absorbance calculations, to extract the bands of water and of the amphiphile. Transmission measurements of both reference and samples were performed using a variable path cell. The thickness of the liquid film, and therefore the irradiated amount of sample, was fixed by the thickness of a spacer ring (∼75 µm) placed between CaF2 windows. The temperature of the cell was controlled; all measurements were made at 25.0 ( 0.2 °C. III. Results and Discussion A. Surfactant Signal. Spectroscopic measurements on a sample containing only PFOB and F8C11DMP, with no added water, were made to identify the spectral contribution coming from the surfactant in the micellar solution spectra. The aim of this preliminary investigation was to further track the possible changes of the surfactant signal, on encapsulating increasing amounts of water. The assignment of the most prominent peaks arising from the PFOB and/or surfactant is reported in Table 1.9 The most intense peaks arise from the C-H stretching vibration, for which the asymmetrical and the symmetrical modes occur at 2927 and 2856 cm-1 respectively, and from the C-H bending mode at 1454 cm-1. Strong bands from the CF2 and the CF3 groups appear at 931 and 2500 cm-1. For these large absorption bands no frequency nor intensity modifications were observed on adding water to the system. The most evident frequency shift observed upon water encapsulation is seen for the band initially at 1147 cm-1 shifting toward higher frequency as W0 increases, then reaching a constant value (1170 cm-1) from W0 ∼ 8, i.e. Rh ≈ 13 nm. From literature data,9 this band is assigned to the asymmetric motion of the C-O-C bond, featured in the surfactant DMP headgroup. The C-O-C band shift, observed in this concentration range, most likely reflects the fact that the hydrophilic environment, associated with the inner wall of the micelles, progressively reaches a steady conformation. The observed
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TABLE 1: Infrared Band Positions and Assignments for the Anhydrous PFOB + F8C11DMP Spectrum frequency (cm-1)
attribution
931 1045 1080 1147 1205 1236 1255 1370 1454 1550 2425 2856 2899 2927 2964
stretching C-F symmetric stretching PdO and P-O-C symmetric stretching C-O-C asymmetric stretching C-O-C symmetric stretching CF2 + CF3 asymmetric stretching PdO symmetric stretching CF2 + CF3 vibration wag CH2 and C-O-C bending scissoring -CH2vibration -CF2-CF2vibration -N-CH2- and -(CF2-CF2)symmetric stretching -CH2symmetric stretching -O-CH2asymmetric stretching -CH2asymmetric stretching -O-CH2-
spectral changes reflect the compromise between headgroupheadgroup interactions and water-headgroup interactions. B. OH Stretching Band versus Water Content. The confined water was studied by following the stretching mode of the OH bond, culminating around 3400 cm-1. Figure 2a displays the OH stretching band for several water concentrations. The signal arising from the surfactant, namely the CH symmetric and asymmetric stretching modes, remains approximately constant as only the water concentration is changed. The total OH band area was found to linearly increase with increasing W0 and thus increasing Rh. Figure 2b compares the OH band shapes for bulk water and for water encapsulated in a low-W0 microemulsion and in a high-W0 microemulsion, of micelle hydrodynamic radii ∼ 9 and 15.5 nm, respectively. Clearly, the OH band shape evolves considerably with increasing water content. It appears that the confinement essentially affects the low-frequency side of the OH stretching band (the small Rh OH band is not homothetical to that of the large Rh). Besides, we observed that for much larger micelles (i.e. Rh ) 26.5 nm) this band shape is very similar to that of bulk water, indicating that for such large micelles the encapsulated water can be considered as unaffected bulk water. For the investigated Rh range, the OH stretching band maximum was found to shift from 3437 cm-1 down to 3401 cm-1 upon Rh increase. Such a finding is in agreement with the downward shift observed with AOT-based micellar systems.10-12 Moreover, it is important to note that 75% of the observed frequency shift occurs for micelles sizes with Rh between 9 and ∼13 nm. To provide a quantitative evaluation of the observed changes, the OH band was decomposed into three Gaussians (Figure 3), three being the least number of Gaussians allowing a satisfactory fit of the whole band. Following previous studies on both bulk water13 and water encapsulated in AOT micelles,10,14,15 each of the Gaussians was ascribed to a “particular type” of water molecules: “network water” molecules (NW), “intermediate water” molecules (IW), and “multimer water” molecules (MW). The first type, NW, which is assigned to the lower energy Gaussian (∼3310 cm-1), is expected to arise from water molecules involved in transient networks that break and form continuously.16 These water molecules are most likely connected tetrahedrally, almost as in ice, thus generating instantaneous H-bonded low-density pathways, extending over a supermolecular level. The second type of water molecules, IW (intermediate energy Gaussian, at ∼3455 cm-1), is ascribed to water molecules that are somewhat connected to other water molecules, though unable to develop fully connected patches. These water molecules, with distorted H-bonds, may be those located
Figure 2. (a) OH stretching band for various micelle sizes, Rh. The two low energy side peaks arise from the ν1 and ν3 CH modes, from the surfactant. (b) Band shape comparison of bulk water (solid line), water encapsulated in a low-Rh microemulsion (W0 ) 1.85 T Rh ) 9 nm, dotted dash line), and water encapsulated in a high-Rh microemulsion (W0 ) 15.4 T Rh ) 15.5 nm, dotted line). Each band was normalized with respect to its maximum intensity.
at the interface of the aforementioned long distance networks or those arranged in short-lived water aggregates.17 Finally, the third kind of water molecules, MW (higher energy Gaussian, at ∼3570 cm-1), corresponds to water molecules that do not feature the kind of supermolecular connectivity of NW or IW, standing as free monomers or as dimers or trimers.18 This latter assignment is supported by the fact that, frequency-wise, these MW molecules are close to those found in the vapor phase, just as the NW Gaussian is positioned at a frequency close to that of the OH band in ice. According to this pattern, free fits of the data were performed, yielding different proportions of the three Gaussian areas, as the micelle size is increased. These results are plotted in Figure 4. The positions and widths of the Gaussians were found to remain constant with micelle size. Since the OH stretching band shape evolves continuously toward that of bulk water, the three Gaussian picture was also applied to bulk water, giving levels of contribution close to those found for the biggest micelle system investigated. Figure 4 unveils that only water involved within supermolecular connectivity schemes (NW and IW) is
Water Dynamics and Confinement Size
Figure 3. Gaussian decomposition of the OH band for Rh) 15.5 nm. The lower energy Gaussian is ascribed to “network water” molecules, the medium energy Gaussian is ascribed to “intermediate water” molecules, and the higher energy Gaussian is ascribed to “multimer water” molecules (see the text).
J. Phys. Chem. B, Vol. 105, No. 2, 2001 433 long distance connectivity networks, favoring the restricted connectivity structures (this may stem from the molecularly rugged headgroup wall structure, as opposed to smooth walls), and only reaching a minimum radius of curvature Rhlim can restore the maximum proportion of network water inherent to the bulk water structure. Using a simple model, one can evaluate the amount of water affected by the confinement from the various changes in water proportions. For such purpose, one needs to evaluate the micelles water core sizes. Since the W0 ) 0 extrapolation is not realistic, we estimated the water core radii of the micelles by subtracting a calculated amphiphile length of 2.6 nm19 from the hydrodynamic radii. The water core (of radius Rtot) is assumed to consist of an inner core (of radius Rinn) surrounded by an affected water shell (of thickness Rtot - Rinn). While the inner core includes the three types of water molecules (whose relative contributions should, in the limiting case of large radii, be those of bulk water), the affected water layer is assumed to consist only of intermediate water (neglecting smaller contributions from the multimer water). It follows from this picture that at a given total core radius Rtot, the different water type contributions within the inner core are given by MW(Rtot), NW(Rtot), and IW(Rtotf∞), while the remaining quantity IW(Rtot) - IW(Rtotf∞) forms the affected water layer. Hence the percentage of water affected, represented by the ratio p of the water layer volume to the total core volume, is expected to scale with the quantity IW(Rtot) IW(Rtotf∞) according to
p)
4/3π(Rtot3 - Rinn3) 4/3πRtot3
) 1 - (Rinn/Rtot)3
or
Rtot - Rinn ) Rtot[1 - (1 - p)1/3]
Figure 4. Respective fractions of the different OH band Gaussian areas as a function of the micelle hydrodynamic radius (Rh): triangles, lower energy Gaussian (network water); circles, medium energy Gaussian (intermediate water); squares, higher energy Gaussian (multimer water). The arrows indicate the equivalent fractions for bulk water.
affected by the confinement, while the MW contribution remains practically unchanged throughout the investigated interval. Even though “network water” always dominates, its proportion increases considerably, passing from 56% to 67% as the hydrodynamic radius increases from 9 to 13 nm. Meanwhile, the intermediate water contribution decreases from a proportion of 39% to 27%. Interestingly, these modifications essentially occur until a certain size, Rhlim ∼13 nm, is reached, beyond which further growing of the micelles barely affects the relative contributions. It is remarkable that the value Rhlim matches that inferred from the onset of a constant value for the C-O-C band position, suggesting that the C-O-C band is a reliable probe of the confining conditions. The exactly opposite variations observed for the two types of water reveal that there is an interchange between the two as the confining dimensions increase: the loss of IW occurs in favor of NW. In other words, the confinement destabilizes the
(3)
The so-obtained affected water layer thickness (Rtot - Rinn) was found to decrease, within the error bars, from 3.5 Å down to 1.5 Å for respective values of Rtot of 6.7 and 11.9 nm. The observation of a nonconstant thickness layer of affected water suggests that the micelle formation is not solely governed by the water-headgroup interactions but also by the radius of curvature of the confining geometry. C. Comparison with Ionic Systems. To evaluate the role of polar versus ionic headgroups, we compared our data with the counterpart values obtained for AOT reverse micelles.10,14 As in the case of the presently studied DMP systems, the OH stretching band in AOT is centered around 3400 cm-1. However, the Gaussian fits deduced in these works show systematic deviations as far as the Gaussian positions are concerned. Nevertheless, the Gaussians intensities are comparable in both ionic and polar systems, therefore allowing qualitative comparisons. In the extensive study of water encapsulated in AOT, by Onori et al,10 the OH components as a function of W0 show strong differences with the present data. However, the W0 range investigated therein corresponds to much smaller water core radii, according to the size evaluation study from van Dijk et al.1 In contrast, the comparison of the relative intensities of the various water types, for water core sizes as close as available (i.e. 6.8 nm for DMP systems and 5.3 nm for AOT), shows that in AOT the lowest energy Gaussian contribution remains always greater than that at intermediate energy, while that from the highest energy Gaussian still has the lowest contribution, with very close ratios for all of them. Besides, as in DMP
434 J. Phys. Chem. B, Vol. 105, No. 2, 2001
Figure 5. H2O bending mode for various hydrodynamic radii, Rh, indicated by the figures on top of the bands. The inset shows a fourGaussian decomposition of the lowest Rh band shape. The oblique line stands for the background contribution.
systems, the confinement in AOT preferably affects water molecules relevant from the two lower energy Gaussians, that is, according to our interpretation, those involving supermolecular connectivity. These results suggest that the electrostatic nature (polar or ionic) of the amphiphile headgroup appears not to be a major factor in the level of perturbation, at least in the presently studied confinement range. D. H2O Bending Motion. The effect of confinement was also studied by following the H2O bending mode arising around 1650 cm-1. As displayed by Figure 5, the intensity of this band increases (proportionally) to the water content, in a very similar fashion as that found for the OH stretching band. No frequency shift of the overall peak was detected. The Figure 5 inset shows a close up view of the lowest water content bending band, together with a corresponding four-Gaussian decomposition. From the comparison with the anhydrous PFOB/surfactant spectrum, the two satellite peaks at 1580 and 1705 cm-1 turn out to be already present in the PFOB/surfactant spectrum. Therefore, only the two Gaussians at ∼1625 and ∼1660 cm-1 can be assigned to water. This is supported by Figure 6, showing the respective fractions of the different Gaussians deduced from free fits of the data. While the weak contributions from the two extreme Gaussians remain approximately constant, those observed for the main bands are very similar to the NW and IW variations. However, while in the case of the OH stretching band, the lower energy Gaussian contribution is the one to increase with Rh, in the case of the bending mode, it is the higher energy Gaussian. From there, one can conclude that the lower energy H2O bending component reflects the “intermediate” type of water molecules, while the higher Gaussian is associated with “network” water molecules. A more detailed investigation of the H2O bending vibrational band upon water encapsulation, particularly as a function of temperature, will be reported in a forthcoming paper. IV. Conclusion The combined use of infrared spectroscopy and quasielastic light scattering allowed us to quantitatively evaluate the extent of perturbation of water encapsulated in fluorocarbon reverse microemulsions. The investigation of the low water content
Brubach et al.
Figure 6. Respective fractions of the different H2O bending mode Gaussian areas as a function of the micelle hydrodynamic radius (Rh): circles, third highest energy Gaussian (G3 see Figure 6 inset); triangles, second highest energy Gaussian (G2); squares, lowest energy Gaussian (G1); diamonds, highest energy Gaussian (G4).
region showed that, in these systems, the characteristics of water confined in the core radii lower than ∼10 nm strongly deviate from those of its bulky state, all the more so as the size is reduced. Using a three-Gaussian decomposition of the OH stretching band data, we found that confinement essentially affects the two lower energy components, assigned to water molecules involved in different supermolecular bonding schemes, that differ from each other through their respective mean degrees of connectivity. In other words, confinement does perturb the short-lived water networks. A quantitative interpretation of these results showed that the thickness of the water layer (or the socalled hydration water), interacting with the surfactant polar headgroups, and thus affected by it, decreases from 3.5 to 1.5 Å for water core radii growing from 7 up to 12 nm, respectively. Such finding goes against the initial guess ,according to which the layer thickness of water affected by the confinement is independent of the micelle size. From the first ever comparison of these nonionic systems with already published data on ionic AOT micellar systems, we found that the confinement-induced modifications are very similar, whether counterion (AOT) or not (DMP). This suggests that the solute ions from the AOT surfactants add no further perturbation to that inherent to the confinement. Eventually, the H2O bending mode was also found to bear significant modifications upon the level of confinement. The two components found from a Gaussian decomposition of this mode show very similar behaviors with increasing micelle size, as those observed for the OH stretching band. The results obtained here call for further exploration of the connectivity properties of confined water. With this respect, molecular dynamics simulations are particularly well suited, as they are able to reliably reproduce the confining conditions studied here. Further experimental work, for instance the investigation of the H-bond stretching mode, lying in the farinfrared, will provide a direct probing of the state of connectivity of encapsulated water. Acknowledgment. The authors are thankful to V. Sadtler for her expertise in preparing the samples.
Water Dynamics and Confinement Size References and Notes (1) Dijk, M. A. V.; Joosten, J. G. H.; Levine, J. K.; Bedeaux, D. J. Phys. Chem. 1989, 93, 2506 and references therein. (2) Krafft, M. P.; Vierling, P.; Riess, J. G. Eur. J. Med. Chem. 1991, 26, 545. (3) Krafft, M. P.; Riess, J. G. Biochimie 1998, 80, 489. (4) Sadtler, V.; doctorate thesis, Universite´ Nice-Sophia Antipolis 1997. (5) Chu, B. In Laser Light Scattering, 2nd ed.; Academic Press: Boston, 1991. (6) Laia, C. A. T.; Brown, W.; Almgren, M.; Costa, M. B. Langmuir 2000, 16, 465. (7) Roy, P.; Mathis, Y.-L.; Lupi, S.; Nucara, A.; Tremblay, B.; Gerschel, A. Synchrotron Radiation News 1995, 8 (5), 415. (8) Mathis, Y.-L.; Roy, P.; Tremblay, B.; Nucara, A.; Lupi, S.; Calvani, P.; Gerschel, A. Phys. ReV. Lett. 1998, 80 (3), 1220. (9) Lin-Vien, D.; Colthup, N. B.; Fateley, W. G.; Grasselli, J. G. In The Handbook of Infrared and Raman Characteristic Frequencies of Organic Molecules; Academic Press: New York, 1991. (10) Onori, G.; Santucci, A. J. Phys. Chem. 1993, 97, 5430.
J. Phys. Chem. B, Vol. 105, No. 2, 2001 435 (11) Li, Q.; Weng, S.; Wu, J.; Zhou, N. J. Phys. Chem. B 1998, 102, 3168. (12) Fioretto, D.; Freda, M.; Mannaioli, S.; Onori, G.; Santucci, A. J. Phys. Chem. B 1999, 103, 2631. (13) Gigue`re, P. A. J. Chem. Phys. 1987, 87, 4835. (14) Jain, T. K.; Varshney, M.; Maitra, A. J. Phys. Chem. 1989, 93, 740. (15) MacDonald, H.; Bedwell, B.; Gulari, E. Langmuir 1986, 2, 704. (16) Stanley, H. E.; Teixeira, J. J. Phys. Chem. 1980, 73, 3404, and references therein. Texeira, J. In Correlation and ConnectiVity; Stanley, H. E., N. Ostrowsky, Eds.; Kluwer Academic Publishers: Norwell, MA, 1990; p 167. Considering the amount of literature devoted to this subject, it is not possible to present a complete list of the relevant references. (17) Rousset, J. L. Duval, E.; Boukenter, A. J. Chem. Phys. 1990, 92, 2150. (18) Walrafen, G. E. In Hydrogen Bonded SolVent Systems; Covington, A. K., Jones, P., Eds.; Taylor and Francis: London, 1968. (19) Israelachvili, N. J. In Intermolecular and surface force with applications to colloidal and biological systems; Academic Press: London, 1985.
