J. Phys. Chem. 1980, 84, 1895-1899
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Structural Features of Water-in-Oil Microemulsions C. Kumar Department of Chemistry, Indian Instlfufe of Technology, Kanpur 2080 16, India
and D. Balasubramanlan" School of chemistry, University of Hyderabad, Hyderabad 50000 1, India (Received December 3, 1979)
The structural features of water-in-oil microemulsions of Triton X-100, 1-hexanol,and water in cyclohexane have been studied by NMR relaxation and ESR spin probe methods. The mobility of the water molecules, the extent of hydration of the surfactant, and the mobility of the poly(oxyethy1ene) segment and the nonpolar segment of the amphiphile have been monitored and analyzed in terms of the molecular processes occurring in the microemulsion system. Comparison of these results with those on simple reverse micelles in nonpolar mediia indicates considerable similarities between water-in-oil microemulsions and reverse micelles.
Introduction Micelles are formed when surfactant molecules aggregate in aqueous solution, with their nonpolar tails associating through the hydrophobic effect. The hydrophobic core of the micelle thus formed can solubilize significant amounts of nonpolar molecules. Tanfordl has discussed the basic features of micellar aggregation, and Menger2has recently reviewed the structure, fluidity, and spectroscopic properties of micelles in agueous medium. Several arnphiphiles are able to aggregate when dispersed even in nonpolar organic solvents, to produce reverse micelles, wherein the structural organization is the inverse of that of aqueous micelles. The polar core of these reverse micelles is able to solubilize significant amounts of water. These reverse micellar systems are thought to resemble pockets of water included in bioaggregates such as membranes, the rnitochondrial matrix, etc., and considerable attention has been paid to reverse micellar systems in recent yearsa3 There is yet another class of aggregates, commonly referred to as microemulsions, wherein microdroplets (size 10-100 nm) of a hydrocarbon are solubilized in water (the oil-in-water or o/w type) via a 20-60 thick interfacial sheath of a surfactant-cosurfactant m i ~ t u r e .The ~ alternative arrangement of a pool of water in a continuous oil phase (the water-in-oil or w/o type microemulsion) is also possible, and frequently realized. Such microemulsions commonly consist of four components: a surfactant (ionic or nonionic), a cosurfactant (usually alkanols, e.g., l-hexanol), water, and an organic liquid (oil). These are optically transparent, ossentidly monodisperse, and thermodynamically stable and, depending on the water:oil ratio, undergo phase transitions from isotropic spheres of the w/o type through anisotropic birefringent lamellae to clear isotropic spheres of the o/w type. A pedagogic example of such microemulsions and their features has been recently givenas The recent monographs by Prince6 and by Shah and Schechte? highlight,the basic features of microemulsions and their applicatioris. Because of their ease of formation, stability, and the ease with which reactants can be organized at the molecular level within them, microemulsions have been used for a variety of applications, two of which are the photoregulation of the activity of an imbedded enzyme* and the photovoltaic conversion of energy involving a compartmentalized redox pair.g Microemulsions offer several advantages over micelles and reverse micelles in that: (i) the hydrophile-lipophile balance (HL13) is adjustable by a proper choice of the
a
0022-3654/80/2084-1895$01 .OO/O . .
relative amounts of the surfactants and cosurfactants so that a variety of surfactants can be made to aggregate in nonpolar media; (ii) the aggregation number of the surfactant in microemulsions is far larger than those usually encountered in reverse micelles; (iii) the amount of water solubilized inside a w/o microemulsion is larger than that in comparable reverse micelles; and (iv) in several instances, it is possible to convert a microemulsion from the w/o isotropic phase to the lamellar liquid crystalline arrangement to the o/w type by changing the water:oil ratio continuously. This makes a comparative study of the structural features of the various aggregates possible. In studying these systems as biological models, it is of particular interest to use nonionic amphiphiles so as to avoid electrostatic effects due to charged head groups, and here microemulsions, with their high aggregation numbers, are of greater advantage since nonionic qmphiphiles do not generally aggregate beyond oligomers in reverse micelles. We have recently characterized the w/o microemulsions and lamellae formed by the nonionic surfactant Triton X-100 and 1-hexanol in cyclohexane.lOJ1Up to about 10% water solubilized (v/v), this system exists as a clear, isotropic, spherical assembly, whereas further addition of water (between 10 and 18% v/v) causes a phase transition into a stable, anisotropic, optically birefringent, lamellar liquid crystalline phase, when the Triton X-100:hexanol ratio is 4:l (w/w). We report here on the IH nuclear magnetic resonance (NMR) and allied spectroscopic studies on this system that provide information on the nature of the water in the central pool, the interactions at the interface, and the fluidity of the surfactant sheath. These studies afford a comparison between the structural details of microemulsions and reverse micelles, a point of interest in light of the controversy in the literature on this subject.12 The results presented here suggest that water-in-oil microemulsions are similar to reverse micelles, both in structural features and in the nature of the water pools they encapsulate. The role of the cosurfactant is also clarified to some extent.
Experimental Section All solvents used where dried with standard drying agents and distilled. The water used was double distilled. Triton X-100, whose chemical structure is as follows:
0 1980 American Chemical Society
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The Journal of Physical Chemistty, Vol. 84, No. 15, 1980
was purchased from the C.S.I.R. Biochemicals Unit, New Delhi, India, and used after exposure to high vacuum for 3 h at 70 “C in order to remove any low-boiling impurities. The electron spin resonance (ESR) spin probe, 2,4-dinitrophenylhydrazone of 2,2,6,6-tetramethylpiperidinyl1-oxy, referred to as compound I, was synthesized and
purified according to published ~r0cedures.l~ The NMR line-width measurements were done on a Varian XL-100 spectrometer, at 100-MHz operating frequency (protons), by using D20 external lock and with due attention to homogeneity conditions. The spin-lattice relaxation times Tl for the protons of interest were measured with a JEOL FX-100 Fourier transform spectrometer of operating frequency 100 MHz by the inversion recovery method. DzO was the external lock. The inversion recovery experiments, using a 18Oo-~-9O0sequence, were carried. out under the control of the dedicated computer of the instrument, which also calculated the TIvalues, using the “Autostacking” program. The ESR spectra were run with a JEOL FE-3X spectrometer, operating in the X band. Electronic absorption spectra were obtained with a Cary Model 17D spectrophotometer. All the spectral measurements were done at ambient temperature, 28 f 1 “C.
Results and Discussion One of the systems investigatedlOJ1was a 20% (w/v) solution of Triton X-100-1-hexanol in the weight ratio 3:2 in cyclohexane, hereafter referred to as the 3:2 system. This system solubilized up to 10% (v/v) water, existing as a clear, isotropic, spherical w/o microemulsion, as monitored by light scattering, viscosity, conductivity, and fluorescence probe methods. Addition of water beyond 10% leads to turbid macroscopic emulsions. A second system was a 20% (w/w) solution of Triton X-100 and 1-hexanol in the weight ratio 4:l in cyclohexane, hereafter referred to as the 4:l system. Here, solubilization up to 10% (v/v) water occurs in the form of a clear isotropic spherical w/o microemulsion, and when further water is added, the system changes into an optically birefringent lamellar liquid crystalline phase. Addition of water beyond 18% leads to macroscopic emulsions. A comparative study of the spherical micellar form and the lamellar phase is thus possible, which we present here. Chemical Shifts of the OH and CH2CHz0Protons. In the 3:2 system, the chemical shift of the surfactant backbone ethylene oxide protons appeared as a single sharp line at 3.84 6. Triton X-100 appears to exist as molecularly dispersed in dry cyclohexane; and as water is added, the ethylene oxide groups are removed into the interface of the microemulsion that is formed, and the small change in the chemical shift seen reflects the changed solvent environment. These observations are similar to those obtained with the reverse micelles of the poly(oxyethy1ene) ether surfactant Tween 80 in xylene, reported by Gentile et al.14 The signals due to the OH groups appeared as a single peak, reflecting a fast exchange between the protons of water and the OH protons of hexanol and Triton X-100. The OH proton chemical shift was seen to change downfield from an initial value of 4.2 6 at 1% water to a final value of 5.0 6 (bulk water value) at 7% water and beyond. We have interpreted this downfield shift of the OH protons in these systems as due to changes in the environment of the water molecules.’l Similar trends are seen in the
Kumar and Balasubramanian
I
I
1
3
5
WATER
7
D
ADDED, o/n
11
’fi
13
Figure 1. The variation in the spin-lattice relaxation times, TI, of OH protons (circles) and of CH,CH,O protons (triangles) as a function of added water. The open data points refer to the system containing a weight ratio of 3:2 TrRon X-lOO:l-hexanol, whereas the filled data points refer to the system with a 4:l ratio. The bulk phase is cyclohexane.
chemical shifts of the ethylene oxide protons and the OH protons in the 4:l system as well. There are no sharp changes seen here as one moves from the isotropic spherical phase to the lamellar phase, suggesting that the molecular environments of the concerned protons do not change significantlyduring this phase transition. And, the presence of a single OH signal suggests that the residence time of protons in the water pool and in the interfacial sites s. is shorter than T1Measurements. A study of the spin-lattice relaxation times T1of the CHzCHzOand the OH protons has given us some insight into the hydration profile of the surfactant and the fluidity of the microemulsions. In Figure 1 is displayed the variation of the T1values of the backbone ethylene oxide protons of Triton X-100 as water is solubilized by the 3:2 and the 4:l systems. The relaxation times drop in both cases from an initial value of about 1.1 s to about 0.3-0.4 s by the time 3% water is taken in, and stay constant beyond. There is no significant change in the Tl value even as the transition from the isotropic phase to the lamellae is completed in the 4:l system. It is to be noted that although it was possible to partly resolve signals and TI values due to the different oxyethylene protons of Triton X-100 micelles in aqueous solution,15such a separation was not obtained in the present experiments on the w/o microemulsions with the 100 MHz instrument used. The T1values reported here are thus weighted averages of the ethylene oxide protons of the entire surfactant chain. The OH protons due to water, 1-hexanol, and the terminal hydroxyl of Triton X-100 also gave a single relaxation time at all compositions reported, suggesting an exchange of the OH protons between various sites with a rate faster than 1/T,, and the observed TIis thus a weighted average of the different TIvalues of these sites.16 The TI values for the OH proton display a linear increase through the isotropic microemulsion region in both of the systems. In the 4:l system, the TIdrops from a value of 1 s at 9% water to 0.75 s at and above 11% water. This change is coincidental with the microemulsion to liquid crystalline phase transition. The initial increase in TIsuggests a greater mobility for the OH protons as water is progressively added until the lamellar phase is reached, where a slight reduction in the mobility is apparent. Although it cannot be rigorously delineated, it does not appear unreasonable to assign a major part of the contributions to T1 as arising from water protons, since even at 2% water
The Journal of Physical Chemistry, Vol. 84, No. 15, 1980
Structural Featuires of Water-in-Oil Microemulsions 1
TABLE I: Reorientational Correlation Time, T ~ of, OH Protons and Microviscosity, q , of the Environment in the w/o Microemulsions of Triton X-100-Hexano1:Water in Cyclohexanea amt of H,O added (v/v)
q , cp
1 0 " ~ ~ ~eq 2 3:2 System 0.29 7.4 0.23 5.7 0.19 4.9 0.16 4.0 4 : l System 0.39 9.7 0.30 7.7 0.26 6.6 0.19 4.8 0.18 4.4 0.23 5.9 0.22 5.5
1 I
I
L 1
3
5
W A T E R ADDFD,".
'/v
Figure 2. Estimation of the amount of water bound to the ethylene oxide groups of l'rton X- 100 in the w/o micrcemulsionsof Triton X-100, 1-hexanol and water in cyclohexane. Open circles refer to a Triton X-100:hexanol weight ratio of 3:2,whereas the closed circles refer to a ratio of 4: 1 The malar ratio of water bound per ethylene oxide residue was calculated by using eq 1; see related discussion in the text. Each 1 % v/v of water added corresponds to 0.23 and 0.31 mol of H,O/mol of ethylene oxide in the 4:l and 3:2 cases respectively.
added, the concentr,ations of OH protons due to water, hexanol, and Triton X-100 are in the ratio 9:1.6:1,and at higher water compositions this ratio is even higher in favor of water protons. Interestingly, the T1values observed for the OH protons in these systems are about the same as those observed for the water protons in the water pools of the reverse micelles of the anionic surfactant Aerosol OT in heptane,17suggesting that the status of water in w/o microemulsions and in Aerosol OT water pools are comparable. The drop seen in the Tl values of the OH protons during and after the spherical-to-lamellar phase transition in the 4:l system is not observed with the ethylene oxide protons. This indicates that the transition affects the arrangement and mobility of the water molecules more significantly than that of the omyethylane backbone of the surfactant. Surfactant- Water Interactions. Complementary to the above discussion, it is also possible to analyze the variations in T1 of the OH protons in the spherical microemulsion region in terms of the changes in the hydration of the surfactant at the interface, using the approach suggested by Hansen.lg Consider the OH protons to consist of two fractions, a fraction fA bound to the surfactant and relatively immobile with a relaxation time T1A and a fraction fB that is more akin to free or bulk water protons with a relaxation time Tl13, Fraction fA includes in itself the exchangeable protons of the interface. If exchange of protons between the two fractions fA and fB is fast, then
If one assumes that T1B has a value of 3.6 s, that of bulk liquid water,Ig and TIAcan be obtained by extrapolating the initial linear portion of the curves in Figure 1 to zero water concentration (0.5 s in the 3:2 system and 0.4 s in the 4:l system), fA and fB can be calculated from eq 1. From the values of fA thus calculated, the concentration of bound water molecules can be arrived at by subtracting the concentrations (of hexanol and Triton X-100 groups: concentration of bound water = l/z(fAIOH]t,,, [OH](,,ib, + hsxanol). The ratio of the moles of water molecules bound per mole of ethylene oxide residue of the surfactant calculated in this fashion is shown in Figure 2 for both the (3:2and the 4:l systems. The curves reveal that the hydration of the surfactant increases slowly as water is added, leveling off to a value of about 0.5, suggesting a limiting ratio of one molecule of water bound per two oxyethylene unils. A similar value for the hydration
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3 5 7
1 3 5 7 9 12 15
eq 4 4.2 3.3 2.8 2.3 5.5 4.4 3.8 2.7 2.5 3.4 3.1
a Constants used: b = 1.58 X lo-' cm;a = 1.5 X lo-' cm;No = 6.75 X lo2,. According to eq 2 of text.
of the oxyethylene moieties in a related polyethylene oxide surfactant (Igepol CO-530) reverse micelle has been rep ~ r t e d .It~ is noteworthy that this value of hydration in reverse micelles and w/o microemulsions is in marked contrast to the value of unity or more seen in the case of aqueous micelles of poly(oxyethy1ene)-typesurfactants in water.z0-22 Mobility of the Water. Analysis of the T1 values of the OH protons using the Bloembergen, Purcell, and Pound approachz3leads to a characterization of the ease of molecular motion in the core of the microemulsions. T1 is related to the reorientational correlation time, r,, as:
--1
- 9~~y~h'No~/5kT (3) TIinter (4) 1/T1 = 1/T1 intra + 1/T1 inter where TIintra and Tlinterare the intramolecular and intermolecular parts of the dipolar relaxation mode of the spin system, y the magnetogyric ratio, b the proton-proton distance in the water molecule, r, the reorientational correlation time, w the resonance frequency, q the viscosity of the surrounding medium, and No the concentration of the spins per cm3. If one were to assume the Debye-Stokes equation to be valid here, then rc = 4?rqa3/3kT
(5) where a is the radius of the molecule approximated to a sphere and q the microviscosity experienced. It is then possible to estimate the r, and the microviscosity of the environment of the water molecules either according to the intramolecular relaxation mechanism alone or allowing the intermolecular mode as well. The values so calculated are listed in Table I. I t can be seen from the table that (i) r, values for water in these microemulsions are comparable to those of water in Aerosol OT reverse micelles,17 i.e., 0.2 X 10-lo-0.4 X s, and suggest that the motion of the molecules of water in the water pool is not coupled to the overall tumbling of the spherical microemulsion (which is expected to be in the range of about s) and (ii) the microviscosity calculated from the intramolecular mode alone is an overestimate, whereas that using both modes is an underestimate. The true value lies probably between the two. It is also seen from Table I that the microviscosity falls from an initial high value as water is added. In the
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The Journal of Physical Chemistry, Vol. 84,No. 15, 1980
Kumar and Balasubramanlan
w
I , 1
3
5
WATER
7
9
11
13
I
A D D E D YO /v'
Flgure 3. Variation in the spln-spin relaxation times, T,, of OH protons (circles) and of CH,CH,O protons (triangles) as a function of added water. The open data points refer to the system containing the weight ratio of 3:2 Triton X-lOO:l-hexanol, whereas the filled data points refer to the system with a 4:1 ratio. The bulk phase is cyclohexane.
4:l system, the value of 77 increases abruptly at the point where the transition from the spherical to the lamellar phase occurs. Nevertheless, even in the lamellar phase, the q value is significantly smaller than the bulk viscosity of the medium.1° T2 Measurements. In Figure 3 are given the variations with water addition of the spin-spin relaxation times T2 of the OH and CHzCH20protons in the microemulsions, obtained from the corresponding signal line widths. The changes in the T2values roughly parallel those in the T1 values, with the following differences: (i) The magnitudes of T2are consistently lower than T1,suggesting the presence of modes of relaxation other than dipolar interactions alone. In the case of the OH protons, a large part of the difference between T I and T2values might be due to the alcohol-water proton exchange process, whereas that in the case of the oxyethylene protons could be possibly due to changes in the orientation of the surfactant at the interface, changes which have been shown to affect T1 and T2differently.% (ii) The values of T2in the 4 1 system start decreasing at around 8% water, whereas the transition to the lamellar phase occurs at 10% water. This suggests that some of the molecular rearrangements necessary for the phase transition start anticipatory to the transition itself. (iii) The values of T2of the OH protons observed here are again comparable to those of the Aerosol OT reverse micelle~.~~ ESR Spin Probe Study. The NMR results discussed above are concerned with the motional features of the trapped water and of the ethylene oxide segment of the surfactant. Since it has not been possible for us to look a t the alkyl and phenyl protons of Triton X-100because of interference from the hexanol and cyclohexane protons, we have adopted the method of YoshiokaZ0to monitor the mobility of the nonpolar end of the surfactant by utilizing the stable free radical probe, 2,4-dinitrophenylhydrazone of 2,2,6,6-tetramethylpiperidinyl-l-oxy (compound I). Molecule I serves at once as an ESR probe and as an absorption spectral probe, since its electronic absorption band near 360 nm is sensitive to the environmental polarity. Yoshioka20has established, on the basis of its absorption band position, that molecule I positions itself near the nonpolar (dodecyl group) region of the surfactant C12H25(OCH2CH2)z10H. Probe I, when incorporated into our 3:2 and 4:l systems displays an absorption band at 358 nm at 0% water (and red shifts only by 2 nm even at 15%
1
3
5
7
9
WATER ADDED,%
11
13
"/v
Flgure 4. The variation in the reorientational correlation time, T ~ of, the ESR spin probe I as a function of added water in the microemulsions. The open circles refer to the system with a Triton X-100:l-hexanol weight ratio of 3:2,whereas the filled circles refer to the system with a 4:l ratio. The bulk phase is cyclohexane.
water addition), which suggests an environmental polarity somewhat less than that of ethylene glycol dimethyl ether.20 This indicates that I is positioned close to the alkyl phenyl ether end of the ethylene oxide chain of Triton X-100 in the microemulsion. This affords a possibility of using I as an ESR probe to monitor the motional features of this segment of Triton X-100in the microemulsions. From the ESR spectral details of I in the microemulsions, its reorientational correlation time was computed from eq 6,25where A is a constant set equal to 6.6 X 10-lo,after 7, = AAHm=l([Im=l/Im=-~]1~2 - 11 (6) Griffith et a1.,26AHm=,the peak to peak width in gauss of the peak to peak the low-field line, and ImZ1and Im=-l heights of the low-field and high-field lines, respectively, of the ESR spectrum. The variation in the 7,of I is plotted in Figure 4 as a function of water in both the 3:2 and the 4:l systems. Since the probe I is not spherical in shape, an estimation of the microviscosity of its immediate medium from the 7,values is not straightforward. Thus we have restricted ourselves to a nonquantitative discussion of the trends seen in T~ In the initial region of 0-1 % water addition, 7, increases, reflecting an increased hindrance to the motion of I. Since the probe appears to be positioned near the alkyl phenyl ether end of Triton X-100, this might suggest a restriction in the mobility of this region of the surfactant. We have already noted a restriction in the mobility of the ethylene oxide end of the amphiphile, as seen from the T I variation. This restriction of the motion of Triton X-100is to be expected as microemulsions start forming from true molecular solutions upon water addition. In the region 1-3% water, while the polyethylene glycol region is progressively immobilized (as seen from NMR results), the drop in the 7, of spin probe I appears to indicate a greater degree of mobility near the nonpolar region of the surfactant. The increase in the interfacial area accompanying the formation of an ordered surfactant sheath at the polar end of the molecule seems to result in an enhanced mobility of the nonpolar end after 1%water addition. In the range of water beyond 3%, hydration of the surfactant extends up to the ether end of the ethylene oxide chain, reducing the mobility of the entire surfactant molecules, as evidenced by the low TI values of the CHzCHpOprotons and increased 7, of the spin probe. That the initial hydration leads to an immobilization of the added water is also seen when one monitors the optical
Structural Features of Water-in-Oil Microemulsions
absorption band of dissolved Coz+ions in these systems. CoC1,.6Hz0, which is pink in color, when added to the 3:2 or 41 systems, dissolves and becomes intensely blue ,A( 655 nm), characteristic of tetrahedral complexation. The absorptivity at 655 nm decreases slowly up to 190water addition, after which it is lost, suggesting that beyond 1% free water is available to interact with Co2+ions to produce the octahedral complex (with no band near 655 nm), in a fashion similar to that reported by Wellsn for phosphatidyl choline reverse micelles in diethyl ether.
Conclusions The spectroscopic results so far discussed suggest that there is considerable similarity between the processes occurring in these microemulsions and the reverse micellar systems of Aerosol OTI7 and of phosphatidyl choline,27 even though the microemulsions differ from the latter in important properties like size, components, total water uptake, etc. In the present microemulsions of the nonionic surfactant, electrostriction of the water or ion-dipolar interactions are absent, making them somewhat more convenient to study. Because of the many attractive properties of such w/o microemulsions discussed above, we believe that the results presented here and further spectral characterization of such systems will be of further interest and utility. It may adso be noted here that both the NMR and the ESR data reveal a higher surfactant mobility at the interface in the 3:2 system than in the 4:l system, consistent with Schulman’s postulationz8of the role of the alcohol cosurfactant as a promoter of disorder at the interfacial sur Factant film.
Acknowledgment. This work was supported by a grant from the Science & Engineering Research Council of the Department of Science and Technology, India, to whom we owe thanks. We thank Dr. Surjit Singh of the Indian Institute of Technology, Madras, for the use of the Varian XL-100 NMR spectrometer.
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References and Notes (1) C. Tanford, “The HydrophobicEffect”, Wiiey-Interscience, New Yak, 1973. (2) F. M. Menger, Acc. Chem. Res., 12, ill (1979). (3) J. H, Fendler, Acc. Chem. Res., 9, 153 (19761, (4) C. E. Jones, C. A. Jones, and R. A. Mackay, J. Phys. Chem., 83, 805 (1979); R. A. Mackay, K. Letts., and C. Jones in “Miceliization, Solubilization, and Microemulsions”, Voi. 2, K. L. Mittal, Ed., Plenum Press, New York, 1977, p 801. (5) S. E. Friberg and B. Bendiksen, J. Chem. €doc., 56, 553 (1979). (6) L. M. Prince, ”Microemukions-Theory and Practice”, Academic Press, New York, 1977. (7) D. 0. Shah and R. S. Schechter, “Improved Oil Recovery by Surfactant and Polymer Floodina”. Academic Press, New York. 1977. (8) D. Balasubremanian,S..Subramani, and C. Kumar, Nature (London), 254, 252 (1975). (9) I. Wittner, W. E. Ford, J. W. Otwos, and M. Calvin, Nature(London), 280, 823 (1979). (10) C. Kumar and D. Baksubramanian,J. ColloMInterface Sci., 69, 271 (1979). (11) C. Kumar and D. Balasubramaian,J. ColloM Interface Sci., 74, 64 (1980). (12) L. M. Prince, J. ColloMInterface Sci., 52, 182 (1975); D. G. Rance and S. Friberg, J. Colloid Interface Sci., 60, 207 (1977). (13) E. G. Rozantsev and M. B. Neiman, Tetrahedron,20, 131 (1964). (14) F. P. Gentile, F. Ricci, F. Podo, and P. E. Gna, Gazz. Chim. Ita/., 108, 423 (1976). (15) F. Podo, A. Ray, and G. Nemethy, J. Am. Chem. SOC.,95, 6164 (1973). (16) D. E. Woessner and J. R. Zimmerman, J . Phys. Chem., 67, 1590 (1963). (17) M. Wong, J. K. Thomas, and T. Nowak, J. Am. Chem. SOC.,99, 4730 (1977). (18) J. R. Hansen, J. Phys. Chem., 78, 256 (1974). (19) K. Krinicki, Physica (Amsterdam), 32, 167 (1966). (20) H. Yoshioka, J. ColloM Interface Sci., 63, 378 (1978). (21) D. I. D. El Ani, B. W. Barry, and C. T. Rhodes, J . Colloidlnterface Sci., 54, 348 (1976). (22) P. Becher and H. Aral, J . Colloid Interface Sci., 27, 634 (1968). (23) N. Bioembergen, E. M. Purceil, and R. V. Pound, Phys. Rev., 73, 679 (1948). (24) E. J. Staples and G. J. T. Tiddy, J. Chem. SOC.,Faraday Trans. 7 , 74, 2530 (1978). (25) J. Martinie, J. Michon, and A. Rassat, J. Am. Chem. Soc., 97, 1818 (1975). (26) 0. H. Griffith, D. W. Cornell, and H. M. McConneil, J. Chem. Phys., 43, 2909 (1965). (27) M. A. Wells, Biochemistry, 13,4937 (1974). (28) J. H. Schulman and T. S. McRoberts, Trans. Faraday SOC.,42B, 165 (1946).
