J. Phys. Chem. 1991, 95, 5931-5936
5931
Structural Slmllarltles between the L3 and Bicontinuous Cubic Phases in the AOT-Brine System Balin BalinovJ Ulf Olsson,* and Olle merman Division of Physical Chemistry 1. Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden (Received: December 3, 1990; In Final Form: February 28, 1991)
The molecular self-diffusion coefficients of water and surfactant were measured in the isotropic liquid L3 and bicontinuous cubic phases of the ternary sodium bis(2-ethylhexyl) sulfosuccinate (A0T)-water-NaC1 system. It is demonstrated that the selfdiffusiondata from the L3phase is consistent with a multiply connected bilayer microstructure,of low average coordination number, but inconsistent with a discrete particle, i.e., micellar, structure. The self-diffusion constants of water and surfactant decrease smoothly with increasing surfactant concentration,even as one passes from the L3 to the cubic phase. This observation lends strong support to the view that the microstructures of the L3 and bicontinuous cubic phases are topologically related and that the liquid L3 phase, which lacks long-range order, may be pictured as a disordered, or melted, cubic phase.
1. Introduction
Surfactant systems show a rich phase behavior, involving a number of liquid and liquid crystalline phases.'I2 A considerable amount of interest has recently been focused on the so-called L3 phase.'-la This isotropic liquid phase appears rather generally in surfactant systems and ma be found in systems rich in water'*'* as well as rich in oil,18JJmost often adjacent to a swollen lamellar phase. The L3 phase may join up continuously with other liquid phases, and its significance has therefore not always been recognized. An example is the narrow tongue extending from the L2 phase toward the water comer in several water-fatty acidsoap systems,lO**'first reported in 1935.1° The first recognition of its particular character probably arose from the observation of a second dilute liquid phase at higher temperatures, above the clouding temperature, in the water-C12E, systemU and of a narrow isotropic liquid region in the sodium bis(Zethylhexy1) sulfosuccinate (A0T)-water-NaCI system.I1 The L3 phase has also been termed, among other names, yanomalous",12owing to its particular macroscopic appearance. It may show strong opalescence and flow birefringence, in particular a t high dilution. Experimental r e s u l t ~ , ~ * as ~ . well ~ . ~ as J~ theoretical considerations? point toward a microstructure where a surfactant bilayer of multiply connected topology forms a 3D continuous dividing surface separating two solvent domains. However, it has also been suggested that the structure consists of disklike discrete micelles, the size of which decreases with increasing surfactant c ~ n c e n t r a t i o n . ~ ~ Bicontinuous bilayer structures are also present in certain cubic liquid crystalline phases.2c29 It has been suggested that the microstructure of the L3 phase should be recognized as a disordered, or melted, cubic phase, obviously lacking long-range order."* Indeed, in some systems the L3 phase is a t high surfactant concentration in equilibrium with a bicontinuous cubic phase."JO One such system, the AOT-water-NaCI system, was investigated in the present study. AOT is an asymmetric anionic double-chained surfactant that, from a phase behavior point of view, exhibits the usual properties of double-chained surfactants. Due to its bulky hydrophobic part, the water-rich liquid phase, LI,can solubilize only a minor amount of surfactant, and the binary system with water is dominated by a lamellar which extends from approximately 10 vol 6 surfactant up to slightly less than 70 vol 6. At higher concentrations a bicontinuous cubic phase, V2, and a reversed hexagonal phase, H2, are f ~ r m e d . ~Adding ',~~ small amounts of NaCl to the binary system causes the Occurrence of a L3phase that extends over a wide range of water-to-surfactant volume ratios, but its stability is very sensitive to the concentration of NaC1.I' In Figure 1 we show a partial isothermal (20 "C) phase 'On leave from: The Institute of Physical Chemistry, Bulgarian Academy of Science, Sofia, Bulgaria. *To whom correspondence should be addressed.
0022-3654/91/2095-593 1$02.50/0
diagram of the AOT-water-NaC1 system (redrawn from ref 11) in the plane defined by the surfactant volume fraction, a, and the aqueous NaCl concentration, e, represented in weight percent. The cubic phase swells to @ E 0.6 when t is allowed to increase. From @ E 0.55 the L3 phase is stable which subsequently can be diluted to about @ = 0.05. In a bicontinuous bilayer structure, the average mean curvature (1) 157. . . (2) (3) (4)
Ekwall, P.; Mandell, L.; Fontell, K. Mol. Crys?. Liq. Crys?. 1%9,8,
Ekwall, P. Adv. Liq. Crysr. 1975, 1. 1. Nilsson, P.-G.; Lindman, B. J. Phys. Chem. 1984,88, 4764. Miller. C. A.: Ghash, 0. Lunmw" 1986. 2. 321. ( 5 ) Cates,'M. E.; Roux, D.; Anddman, D.; Milner, S. T.; Safran, S . A. Europhys. Lett. 1988,5, 733. (6) Porte, G.; Marignan, J.; Bassereau, P.; May, R. J. Phys. (Paris) 1988, 49, 511. (7) Strey, R.; Jahn, W.; Porte, G.; Bassereau, P. Lungmuir 1990,6, 1635. ( 8 ) Anderson, D. M.; WennerstrBm, H.; Olsson, U. J. Phys. Chem. 1989, 93. 4243. (9) Gazeau, D.; Bellccq, A. M.; Roux, D.; Zemb, T. Europhys. Lerr. 1989, 9, 447. (10) Strey, R.; Schomiicker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990,86, 2253. (1 1) Fontell, K. In Colloidal Dispersions and Micellar Behavior; ACS Symposium Series No. 9; American Chemical Society: Washington, DC, 1975; p 270. (12) Lang, J. C.; Morgan, R. D. J. Chem. Phys. 1980, 73, 5849. (13) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bastock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. I 1983, 79, 975. (14) Bellocq. A. M.; Roux, D. In Microemulsions: Srrucrure and Dynamics; Fribcrg, S.,Bothorel, P., Eds.; CRC Press: Boca Raton, FL, 1987; p 33. (15) Benton, W. J.; Miller, C. A. J. Phys. Chem. 1983, 87, 4981. (16) Porte, G.; Gomati, R.; El Haitamy, 0.;Appell, J.; Marignan, J. J. Phys. Chem. 1986,90, 5746. (17) Marignan, J.; Gauthier-Fournier, F.; Appell, J.; Akoum, F.; Lang, J. J . Phys. Chem. 1988,92, 440.
(18) Olsson, U.; StrBm, P.; Sijderman, 0.;WennerstrBm, H. J. Phys. Chem. 1989, 93, 4572. (19) Kunieda, H.; Shinoda, K. J . Dispersion Sci. Technol. 1982, 3, 233. (20) McBain, J. W.; Field, M. C. J. Am. Chem. Soc. 1935, 55, 4776. (21) Ekwall, P.; Mandell, L. Kolloid Z . 1969. 233, 938. (22) Harusawa, F.; Nakamura, S.;Mitsui, T. Colloid Polym. Sci. 1974, 252, 613. (23) Miller, C. A.; Gradzielski, M.; Hoffmann, H.; Kriimer, U.; Thunig, C. Colloid Polym. Sci. 1990, 268, 1066. (24) Lindblom, G.; Larsson, K.; Johansson, L.; Fontell, K.; Forsdn, S.J . Am. Chem. Soc. 1979, 101, 5465. (25) Longley, W.; McIntosh. T. J. Narure (London) 1983, 303, 612. (26) Hyde, S.T.; Anderson, S.;Ericsson, B.; Larsson, K. 2.Krisrallogr. 1984, 168, 213. (27) Charvolin. J.; Sadoc, J. F. J . Phys. (Paris) 1987, 18, 1559. (28) Lindblom, G.; Rilfors, L. Biochim. Biophys. Acra 1989, 988, 221. (29) Fontell, K. Prog. Colloid Polym. Sci. 1990, 268, 264. (30) Craig, D. A.; Durrant, J. A,; Lowry, M. R.; Tiddy, G. J. T. J . Chem. Soc., Faraday Trans. I 1984,80. 789. (31) Rogers, J.; Winsor, P. A. Narure (London) 1967, 216, 477. (32) Ekwall, P.; Mandell, L.; Fontell, K. J. Colloid Interface Sci. 1970, 33, 215.
0 1991 American Chemical Society
5932
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 0.05
I
I
I
I
Balinov et al.
1
0.2
li I 0;
La 1
1
1
0.2
0.4
0.6
\\ \I 11 0.8
0.1
I 1.0
0
@ Figure 1. A schematic partial phase diagram of the AOT-water-NaCI system. Q! denotes the volume fraction of surfactant, and e denotes the weight fraction of NaCl in the water.
of the bilayer midplane vanishes by symmetry. However, the average mean curvature of the polar-apolar interface, Le., a surface through the surfactant head groups, is toward the solvent and varies with dilution as8
(H)
y(%i,aye,2/6)
t 1
(1)
where OPbilawis the bilayer volume fraction, 6 is the bilayer thickness, and y is a number of the order of unity that depends only weakly on the topology. The narrow existence region of the L3 phase, Le., the observation that it has in practice one degree of freedom rather than two, according to Gibb’s phase rule under the given circumstances, is a characteristic property of L3 phases. As suggested by Anderson et a1.t the constraint that reduces the number of degrees of freedom from two to one is the condition where Hois the spontaneous, or preferred, mean that (H)= Ho, curvature of the surfactant monolayer. Also, the phase behavior can be understood by considering the mean curvature of the surfactant monolayers and how its spontaneous value is expected to vary with the salinity. Addition of salt screens electrostatic interactions. Screening of the lateral headgroupheadgroup interactions in the monolayer lowers the spontaneous mean curvature (counting curvature toward water as negative) and triggers a transition from L, to L3. Due to the presence of salt, interbilayer interactions are weakened and the liquid L3 phase is stable relative to the cubic phase. However, the interactions become stronger with increasing surfactant concentration and the liquid type structure crystallizes at higher surfactant concentration into a cubic phase. In the present study we investigate the L3 and cubic phases of the AOT-water-NaCI system by measuring the self-diffusion constants of water and surfactant. Multicomponent self-diffusion measurements is now a well-established technique for studying microstructure in surfactant systems.3F3s It has been suggested that the structure of the L3 phase is topologically related to bicontinuous bilayer cubic phases.8 The AOT-water-NaCI system hence offers an interesting opportunity to investigate this relationship. The self-diffusion properties of some triply periodic bicontinuous structures were recently ~alculated,’~ allowing for a quantitative analysis of self-diffusion data in bicontinuous L3 and cubic phases. The outline of the paper is as follows. After describing the experimental method we present the experimental results. Since the main arguments for a bilayer continuous microstructure of the L3phase come from transport properties, in particular from the high conductivity measured in an oil-rich L3 phase? we examine our self-diffusion data explicitly both in terms of particle, (33) Lindman, B.;stih p. In Micmemulsions: StrUCtUfe and Dynamics; Friberg, s.,Bothorel, P.. Ws.; CRC Press: Boca Raton, FL, 1987; p 119. (34) Lindman, B.; Shinoda. K.; Olson, U.;Anderson, D.;Karlstrbm, G.; Wennerstrbm, H. Colloids Surf. 1989, 38, 205. (35) Olsson, U.; Lindman, 8. In The Structure, Dynamics and Equilibrium Properties of Collidal Systems; Wyn-Jones, E., Bloor, D. M.,Eds.; Kluwcr Academic Publishers: The Netherlands, 1990; p 233. (36)Anderson, D.M.;Wennerstrbm, H. J. Phys. Chem., in press.
0.1 0.2
0 . 3 0 . 4 0.5
0.6
0.7
0.8
@S
Figure 2. Variation of the reduced water self-diffusion coefficient with the volume fraction of surfactant. Data correspond to the L3 phase (tilled symbols) and the V, phase (open symbols). The solid line is a linear least-squares fit to the data from the L3 phase corresponding to Dw/DWo = 0.65 - 0.77@#.
i.e. micellar, structures and in terms of a bicontinuous structure. 2. Experimental Section MateMs. Sodium bis(2-ethyIhexyl) sulfosuccinate (AOT) was obtained from Sigma and used without purification. Sodium chloride (p.a.) was obtained from Merck. The water used was triply distilled. Heavy water was obtained from Norsk Hydro and was enriched to 99.8% in deuterium. Samples for the NMR studies were prepared in 5-mmNMR tubes that were immediately flame-sealed. For sensitivity reasons in the NMR experiments, the samples in the cubic phase were prepared with water (H,O), while the samples in the L3 phase were prepared with heavy water (D20).If the compositions of the AOT-heavy water-NaCl samples were converted into molar ratios, no significant effects on the phase behavior were detected if ordinary water was replaced with heavy water. Methods. The self-diffusion coefficients were measured with the Fourier transform pulsed field gradient spin echo (FTPGSE) Two NMR spectrometerswere used. The first one, a JEOL FX-60spectrometer, was used for measuring samples with an AOT concentration exceeding 15 wt %. The second one was a home-built spectrometer, equipped with a 2.3-T iron magnet. For both spectrometers the strength of the field gradients was calibrated by using standards with known diffusion coefficients. The accuracy in the determined diffusion coefficients is better than f5%, as determined by repeated measurements. Explicit care was undertaken to ensure that unrestricted threedimensional diffusion was measured under the present experimental conditions. This was done by varying the observation time, and thereby the observed mean-squared displacement of the molecules, by varying the time between the two field gradient pulses. A11 experiments were carried out at 25 f 0.5 OC as measured by a calibrated copper-constantan thermocouple. 3. Results The results of the water self-diffusion measurements in the L3 and cubic phases are shown in Figure 2. Here we have plotted the reduced diffusion constant, Dw/Dwo,as a function of the surfactant volume fraction, e,. D, is the observed diffusion constant, and DWorefers to the bulk diffusivity of water in NaCI brine of the same salinity. In Figure 3 we show the variation of the surfactant self-diffusion constant, D,, with 0, in the L3 and cubic phases. A characteristic and immrtant feature of the Dresent results is the smooth variation of t‘he water and surfacta; self-diffusion coefficients as one the L3-cubic transition. D,/D,O delinearly with and approaches a of about 0.65 at infinite dilution. A linear fit to the data from the L3 _ _phase, (37) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987. 19, 1. (38) Callaghan, P. T. Aust. J . Phys. 1984, 37, 359.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5933
L3 and Bicontinuous Cubic Phases of AOT-Brine 3 10'1
2 10"
L
I
d 1101'
0
0.1 0 . 2
0.3
0 . 4 0.5 0 . 6 0 . 7 0.8 @s
Figure 3. Variation of the surfactant self-diffusion constant with the volume fraction of surfactant in the L3 (filled symbols)and V, (open symbols) phases. The broken line is the variation predicted for a bicontinuous structure where the surfactant bilayer midplane forms a Schwartz' P minimal surface, assuming that the lateral self-diffusion constant equals 4.0 X m2s-I (see text).
the result of which is shown in Figure 2, gives Dw/Dwo= 0.65 0.77+,,. D, shows a minor decrease with a,, The decrease is less than a factor of 6 over an order of magnitude change in CP8. In what follows we will analyze these results in terms of two separate classes of microstructures. First we will examine whether or not the results from the L3 phase are consistent with a discrete particle, i.e. micellar, structure. We will then proceed and analyze the results from the L3 and cubic phases in terms of a bilayer continuous (bicontinuous) microstructure. 4. Analysis in Terms of a Particle Structure in the L3Phase
The self-diffusion coefficient of a spheroidal particle in a viscous medium is related to the particle size and shape according to the Stokes-Einstein and Perrin equation^.'^ For a spherical particle Dmphere = k B T/6?r?b (2) Here, kBis the Boltzmann constant, Tis the absolute temperature, 7 is the viscosity of the continuous medium, and b is the radius of the sphere. The corresponding equation for a prolate spheroid is
trations slightly above cmc. The value quoted is D = 7 X IO-" m2 s-l. In agreement with the conclusion of the present work, Stilbs and Lindman conclude that this value is not consistent with spherical micelles. In a corresponding analysis in terms of prolate or oblate spheroids, it is reasonable to set the length of the minor semiaxis to the length of the AOT molecule, b = 10 A, which is roughly half of the bilayer thickness (19 A) determined in the binary water-AOT Laphase?2 In the case of prolates, D, = 2.7 X IO-" m2 s-I then corresponds to an axial ratio of rpmhte= 34:1, and the corresponding ratio in the case of oblates is rOMak= 12:l. The next step in the analysis is to examine whether prolates and oblates of these dimensions are compatible with the water diffusion data. From data on solvent diffusion in solutions of colloidal particles one may draw conclusions regarding particle shape and size. The obstruction effect on solvent diffusion in solutions of particles of various size and shape has been calculated by Jbnsson et al." The obstruction depends on the particle volume fraction and, in the case of oblate or prolate spheroids, on their axial ratio as well. Turning to the water diffusion data, we note that Dw/Dwoa p proaches 0.65 at high dilution. At this low surfactant concentration we can neglect the surfactant headgroup hydration. For a solution of spheroidal particles the treatment in ref 43 implies that 2/3 IDw/D$ 5 1, where the actual value of Dw/D$ depends on size, shape, and volume fraction of particles. The experimental value given above, Dw/Dwo= 0.65 (at CP = 0.05), equals roughly the lower limit and corresponds to very large oblates, having an axial ratio of over 100. At 0 = 0.05, large prolates would give Dw/Dwo= 0.97 and oblates with an axial ratio of 12:l would give Dw/Dwo= 0.90 (spheres would give Dw/Dwo= 0.98). We may therefore conclude that a structure of discrete particles fails to simultaneously explain the surfactant and water self-diffusion, at least at high dilution. At higher surfactant concentration the analysis of water and surfactant self-diffusion data becomes more complicated. We can no longer neglect the effect of hydration of the surfactant headgroups on the water self-diffusion. Moreover, for the self-diffusion of particles one has to take into account the particle obstruction. Nevertheless, some qualitative remarks can be made. To first order in the particle volume fraction, 0,particle obstruction can be accounted for by Dpanicle
(3)
and for an oblate spheroid (4)
In eqs 3 and 4, b is the length of the minor semiaxis and r = a / b (21) is the axial ratio, where a is the length of the major semiaxis.
Equations 2-4 are valid in the absence of interparticle interactions, i.e. at infinite dilution. We may now use the equations above to evaluate a particle size in the L3phase from the D, data at high dilution. The cmc of AOT in water is low (reported cmc data cover the range (2.5-6) X IO-' M),'O and additions of salt decrease the monomer concentration even further. We may therefore safely assume that D, indeed reports on the aggregated state of the surfactant. At high dilution we measure D, = 2.7 X lo-" m2 s-l. From eq 2 we may then calculate that, in the case of spherical micelles, this value corresponds to a radius of 70 A. However, since this dimension is much larger than the length of the AOT molecule (being roughly 10 A), a structure of spherical micelles can be ruled out. In this context it is worth mentioning the study of Stilbs and Lindman$I who report diffusion data for AOT micelles formed at concen(39) Hicmenz, P. C. Prlnciples of Colloid and Surface Chemisrry, 2nd ai.; Marcel Dekker: New York. 1986. (40) Mukerjee. P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfacranr Sysrems; NSRDS-NBS 36; US.Government Printing Office: Washington, DC, 1971. (41) Stilbs, P.; Lindman, 8. J . Colloid Interface Sci. 1984, 99, 290.
@'&rticdl
- a@)
(5)
where @wlticlc is the particle diffusion constant at infinite dilution. a is a numerical constant with the value a = 2 for a system of hard spheres without hydrodynamic interaction^.^*'^ The corresponding correction for the case of hard prolate or oblate spheroids has, to our knowledge, not been derived. On analogy with hard spheres, Jbnsson et al. have proposed the estimate CY = 2(RH/b)3, where RHis the hydrodynamic radius of the particle.& Hence, with this approximation, a value of a 2 2 is expected, depending on particle shape and size. Turning again to the surfactant self-diffusion data, we note that the observed concentration dependence of D, is significantly weaker than what is expected from eq 5 . Hence, if D, would correspond to a particle diffusion constant, the particle size must decrease significantly with increasing surfactant concentration. Such a decrease in size is, however, not consistent with the water selfdiffusion data. From comparisons with previous studies of water self-diffusion in micellar solutions of various surfactant^,"*^ we (42) Fontell, K. J . Colloid Interface Sci. 1973, 44, 318. (43) Jdnsson. B.; WennerstrBm, H.; Nilsson, P.-G.; Linse, P. Colloid Polym. Sci. 1986, 264, 77. (44) Othsuki, T.; Okano, K. J . Chem. Phys. 1982, 77, 1443. (45) Lekkerkerker, H. N. W.; Dhont, J. K. G. J . Chem. Phys. 1984,80, 5790. (46) Jonrtrdmer, M.; Jdnsson, B.; Lindman, B. J . Phys. Chem. 1991, 95, 3293. (47) Lindman, B.; Puyal, M.-C.; Kamenka, N.; RymdCn, R.; Stilb, P. 1. Phys. Chem. 1984,88, 5048. (48) Faucompr€, B.; Lindman, B. J . Phys. Chem. 1987, 91, 383. (49) Nilsson, P.-G.;Wennerstrdm, H.; Lindman, B. J . Phys. Chem. 1983, 87, 1377.
5934 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
may conclude that unreasonably large hydration numbers have to be invoked in order to bring the water self-diffusion data for this system in consistency with small particles. For example, at a, = 0.25 we obtain D,/DWo= 0.44. This value is significantly smaller than the value 0.76 obtained in a micellar solution of sodium octanesulfonate (the same polar headgroup as AOT) at the same surfactant-to-water ratio. In this micellar solution the micelles are likely to be spherical, but in the case of small oblate Note micelles (say r = 3) the obstruction effect would be ~imilar.4~ also that the value 0.76is even higher than the value of D,/DWo at high dilution in the L3 phase. Molecular exchange between aggregates may enhance the effective surfactant diffusion in the case of large aggregates and sufficiently high concentrations and when the lateral diffusion constant is much larger than the particle diffusion constant. Exchange occurs via monomers in bulk (there is a finite molecular lifetime in aggregates), a mechanism which has been treated in detail by Jijnsson et al.“ In the present system the effect can be neglected due to the very low monomer concentration. Direct exchange through collisions may also occur if the repulsive interactions are sufficiently weak. This mechanism, even if exchange at contact is facile, has a small impact on the effective diffusion. For disks, contact regions can be seen as highly obstructing regions for lateral diffusion, and this additional diffusion process is expected to have low effect relative to the lateral diffusion constant. In order for this mechanism to reach an effective diffusion of the order of the lateral diffusion, a complete network (without loose ends) has to be formed in case of cylindrical aggregates and, in the case of two-dimensional aggregates, a multiply connected surface. In the present system the observed surfactant diffusion constant is of the order of the lateral diffusion constant, which has been measured to 2.7 X 10-I’ m2 s-l in the binary AOT-D20 L, phase,50 a t 60 wt 9% AOT. To summarize this section, we have shown that a model based on a discrete particle structure fails to explain the experimental data. Below, we will analyze our results in terms of a multiply connected bilayer structure.
5. Analysis in Terms of a Bilayer Continuous Structure The recent introduction of differential geometry to the field of microstructure in surfactant-water41 has provided us with a tool to quantify some properties of multiply connected surfaces (bilayers and monolayers) in three-dimensional space. Recently, the surfactant and solvent diffusion properties were calculated for some model cubic phase microstructures.x In what follows we will investigate how these results compare with our experimental D values. An important result of the present study is the observations of a smooth variation of D, and D, across the L3 to V2 transition. These observations in combination with the observation that D,/DWoapproach the theoretically predicted value of about 0.65 at high dilution allow us to draw the following initial conclusions. (i) They show that the disordered L3 phase microstructure is topologically related to the ordered microstructure of the V2phase. Hence, this supports the view that the L3 phase microstructure consists of a multiply connected bilayer and that the L3phase can be seen as a melted, or disordered, cubic phase. (ii) The geometrical obstruction effects calculated for the solvent and surfactant self-diffusion in some cubic phase model structures also describe the diffusion in the disordered L3 phase. (iii) The geometrical obstruction depends on the coordination number of the obstructing surface. This, being a fundamental result of the ~ a l c u l a t i o n s was , ~ ~ also recently experimentally verified in a selfdiffusion study performed on the sequence of cubic phases occurring in the didodecyldimethylammonium bromide (DDAB)-water-styrene system.s4 In this system clear jumps (50) Lindblom, G.; Wcnncrstrom, H.Biophys. Chem. 1977, 6, 167. (51) Scrivcn. L. E. Nafure 1976, 263, 123. (52) Helfrich. W. 2.Naturforsch. 1973. -. -2812 .- . 693. - (53j Anderson, D.M.:D a d , H.T.; &riven, L. E.;Nitsche, J. C. C. Adu. Chem. Phys. 1990, 77, 331.
Balinov et al. layer of bound water
free water @tv
surfa&t
I/-
bilayer
0s
Figure 4. An illustration of the spatial decomposition into surfactant bilayer, bound water, and free water.
in 0, and 0,were observed at the transitions between various cubic microstructures. The absence of such jumps in the present system, Le. the smooth variation of D, across the L3 to V2transition, hence indicates that the average coordination number of the L3 phase microstructure, at least at higher 4, is similar to the coordination number of the V2 phase microstructure. X-ray results from the V2 phase are only available from the binary water-AOT axis, where the space group of Ia3d was determined.5s The underlying microstructure is believed to be assoCiated with the Gyroid minimal surface, having a coordination number of three. We cannot exclude, at this point, that the V2 region consists of more than one cubic phase. However, the smooth variation of D, and D, with 9, in this region indicates that this is not the case. To summarize, the data indicate that the L3 phase microstructure consists of a multiply connected bilayer of lower coordination number (possibly ~ 3 ) . Proceeding to a quantitative analysis, we consider first the L3 phase. At lower surfactant concentration (9, I0.4) the variation of water (D,) and surfactant (0,)self-diffusion coefficients with the bilayer volume fraction can be approximated by36
Here, Owoand 0: are the bulk diffusion constant of water and the lateral diffusion constant of surfactant, respectively, and af, b’, a”, and b” are constants. a’= 0.65 and roughly independent of the topology. b’, on the other hand, is more strongly topology dependent and increases with increasing coordination number. b’ i= 0.27 for the “D” and b’= 0.39 for the “P” family of constant mean curvature surfaces. a” is related to the surface (lateral) diffusion on a minimal surface and is analytically proven to equal 2/3.36 The calculations of Anderson et al. were restricted to families of lower coordination numbers, relevant for the type of cubic phase microstructures observed in surfactant systems, and for bilayer structures we are limited to compare our results to the ‘D”(coordination number of 4) and the up” family (coordination number of 6). However, this is not necessarily a serious restriction since, as stated above, the L3phase microstructure appears to have a low average coordination number. Below we will analyze the water and surfactant diffusion separately. Water Diffusion, Effect of Hydration. Turning to the water diffusion (Figure 2), we note firstly that when extrapolating to infinite dilution we obtain D,/D$ = 0.65 which is consistent with a bilayer continuous structure. We measure a slope of -0.77, which is steeper than the s l o p calculated for the D and P families of surfaces, respectively. However, as previous studies of water diffusion in surfactant solutions have shown, a quantitative analysis requires that hydration of the surfactant headgroups is taken into account. The simplest way of achieving this is to apply a two-site discrete exchange model. Here, the water is described as being in either one of the two sites, bound (b) and free (f), respectively, where we allow different diffusivities in the two sites. The bound water hydrates the surfactant headgroups while the free water is unperturbed by the surfactant film and possesses bulk water (54) StrBm, P.; Anderson, D.M. Submitted for publication. ( 5 5 ) Fontell, K.J. Colloid Inferface Sci. 1973, 43, 156.
L3and Bicontinuous Cubic Phases of AOT-Brine
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5935
properties. This spatial decomposition is illustrated in Figure 4. Assuming that the number of bound water molecules (nbw)is proportional to the number of surfactant molecules (n8),then the fraction of bound water molecules is given by
where we also have identified Df$ = DWo.Noting that, experimentally, D W / L ois roughly linear in as,the slope being 4.77, it is of interest to expand eq 14 to first order (we refrain from analyzing the second order term, but note that it appears to be small)
-= a’D W
where n, = nbw+ nfwis the total number of water molecules, n, is the number of surfactant molecules, and A is the number of bound water molecules per surfactant molecule, A = nbw/ns.p and M refer to density and molecular weight, with index s and w indicating surfactant and water, respectively. The volume fraction of bound water, ab,, becomes abw= Xbw@w = Xbw(l - 9,) = kQ, (8) where
k = A(P,Mw/PwM,) (9) In a FTPGSE e~periment,~’J*a macroscopic mean-squared displacement in one dimension is measured. This quantity is related to the diffusion constant (0) and the observation time (T) through (x2) = 2Dr (10) Microscopic heterogeneities, for example involving bound and free water, are averaged out on the experimental time scale (TE 0.1 s), and an average diffusion constant is measured. The observed D value can be modeled as a population-averaged mean. With fast exchange (lifetime much shorter than 7 ) between two discrete sites (bound and free) the averaged D value is given by Dw XbwDbw + (1 - xbw)Dfw (11) The bound and free water experience different geometrical obstructions as well as having different local diffusion constants. Dbw
(124
@bDbwo
Dfw = BfDfWO ( 1 2b) Measurements of residual quadrupolar couplings and spin relaxation of 2Hand I7O water nuclei in colloidal systems imply that the perturbation of molecular reorientation of water, induced by the surfactant film, is s h ~ r t - r a n g e d . ~In ~ . this ~ ~ respect, the bound water corresponds roughly to the primary hydration layer plus counterions. It is reasonable to assume that a similar short-range perturbation also holds for the translational diffusion. We may then describe the bound water as being limited to diffusion on a surface. The free water, on the other hand, should be treated as volume diffusion. Applying the twesite model to the results of ref 36, we associate the bound water with the bilayer when evaluating the obstruction factor, 81. That is, the free water experiences a geometrical obstruction from a multiply connected bilayer structure of volume fraction a’ = as ab,. The bound water will be approximated as diffusing on a surface of constant mean curvature spanning the middle of the bound water layer. This corresponds to a surface diffusion on a bilayer of volume fraction 9”= Q, Qbw/2.With these assumptions we may write the obstruction factors as & = 0 ” - b ” ( q ‘/2@bw)2 (13a)
+
+
+
@f 0 ’ - b’(@,+ 9 pbw) (1 3b) Combining q s 6-9 and 11-13, we can write the full expression for the observed water diffusion in terms of diffusion of bound and free water, respectively:
(1
- k&)[a’-
b’(1
+ k)Q,]DWo(14)
(56) Womner, D. E. J . Magn. Reson. 1980, 4, 297. (57) CarlstrBm, G.: Halle, E. Longmufr 1988, I , 1346.
[
b‘+ k( a ‘ + b ‘ - a ’ ‘ S ) ] @ ,
(15)
DWO
This leaves us with two unknowns, k and Dbwo,beside some uncertainty regarding the coefficient b’. (Recall that a’and d’can be considered as topology independent, and b” appears first in the third-order term.) The different parameters contained in the slope can of course not be determined independently from the data. However, the state of the “bound” water can be estimated from other experiments. NMR data, e.g. spin relaxations7 and quadrupolar line s p l i t t i n g ~ ~indicate * * ~ ~ that roughly 15 water molecules per AOT molecules are perturbed, with respect to their reorientational properties, by the plarapolar interface. Moreover, the magnitude of the perturbation appears to be weak. In the “bound” state, the reorientation dynamics is less than a factor of 10, possibly a factor It is reasonable that the perturbation of 3, slower than in of the lateral translational properties has similar range and magnitude. With A = 15, and using the coefficients for the “P” family of = 0.71. For the same surfaces (b’= 0.39), we obtain Dbwo/Dwo value of A, the “D” family (b’ = 0.27) yields Dbwo/Dwo = 0.28. Hence, the data support the view that the L3 phase microstructure has a low average coordination number (if the perturbation of rotational and translational degrees of freedom in the “bound” state are similar in range and magnitude). The properties of the “bound” water molecules may also be estimated from the data at higher as.For A = 15 the fraction of “free” water molecules reaches zero at 9, E 0.57, which corresponds to the most dilute sample in the cubic phase. An approximate representation of the cubic phase structure, originally due to Luzzati,6O is in terms of the so-called interconnected rod model (ICR).Having only “bound” water, the water diffusion can be considered as volume diffusion only. (The surface diffusion approximation, used above, would give a very similar result at these low water contents.) For the interconnected rod (ICR) model Anderson et al.36give the following approximate formula Dw/DwoE 0.636 - 0.2649,
(16)
valid when Q, < 0.8. With eq 16 we obtain Dbwo/,DWo = 0.4 at 9,= 0.57 (corresponding to nw/n, = IS), assuming all water molecules to be “bound”. At Q8 = 0.7 (n,/n, = 9) the corresponding number is L 0 / D $ = 0.2. Note that bo is an average diffusion coefficient in the bound state. When nw/n, decreases below A (which was assumed to equal 15 above), the water molecules are expected to experience an increased average perturbation and hence the average lateral mobility is expected to decrease. Surfactant Diffusion. Turning to the variation of the surfactant self-diffusion with Q, in the L3 and V2 phases, these data are presented in Figure 3. We note again the important observation that no discontinuity in the diffusion behavior is observed when passing from the L3 to the cubic phase. For a bicontinuous structure, D, is reduced by a factor of 2 / 3 at infinite dilution as compared to the lateral diffusion constant, D,O, Extrapolating our data to Q, = 0, we obtain D? = 4.2 X lo-” m2 s-I (=(3/2)2.8 X lo-” m2 d),which is slightly higher than the value 2.7 X lo-’’ m2 s-’ measured in the binary water-AOT L, phase at 60 wt % AOT; 60 wt % AOT corresponds roughly to the most dilute of our Sam les in the cubic phase. Here we measure D, = 1.25 X lo-’’ mPs-I, which within the ICR model (58) SWerman, 0. Unpublished results. (59) Quist, P.-0. Unpublished results. (60) Luzzati, V.;Tardieu, A,; Gulik-Krzywicki, T.; Rivas, E.; Rei=Husson, F. Narure 1968, 220, 485.
5936
J . Phys. Chem. 1991, 95, 5936-5942
corresponds to D,O = 2.5 X lo-" m2 s-I, in excellent agreement with the 0,"value measured in the L, a t the same surfactant Concentration. From this we may conclude that D: is concentration-dependent. With increasing asin the cubic phase there is a strong decrease in D,,which within the ICR model is due mainly to a decrease in 0:. (The change in geometrical obstruction is only about 10% in this a, range.) The data point on the binary axis corresponds m2 s-l. The concentration dependence of D: to D: = 8 X becomes stronger as 9, increases. We note that similar strong concentration dependence of the surfactant diffusion constant was recently observed in the Vi phase of the water-dodecyltrimethylammonium chloride (DOTAC) system.61 In that system the surfactant diffusion constant decreases by a factor of 2 when the surfactant volume fraction increases from 0.84 to 0.88. In the L3 phase, D, is less concentration dependent. The fact that 02 is concentration dependent complicates a quantitative analysis by the introduction of additional parameters, and we refrain from a quantitative fit. However, some general remarks can be made. A general result of ref 36 is that the geometrical obstruction on the surfactant diffusion has only a weak dependence on as(cf. eq 6b). In Figure 3 we show the D, vs ascurve for the "P" family : = 4.2 X m2 s-l. The surfactant diffusion in the with 0 case of the "D" family was not calculated; however, the concentration dependence here is expected to be even weaker than for (61) Siiderman, 0.;Olsson, U.; Wong, T. C. J . Phys. Chem. 1989, 93, 7474.
the "P" family-this however is not yet firmly established. (b" appears to increase with increasing coordination number.) Hence, assuming a weak concentration dependence of the geometrical obstruction, the concentration dependence of D, in the L3.phase is to a large extent due to a concentration dependence in D:. 6. Conclusion We have demonstrated that self-diffusion data from the L3 phase in the AOT-water-NaCl system are inconsistent with a model based on a structure of discrete micellar aggregates. On the other hand, the data are consistent with a multiply connected bilayer structure. Data imply that the L3 phase microstructure consists of a multiply connected bilayer of low average coordination number (possibly 3 or 4). This is implied by the smooth variation of D, and D, when going from the L3 phase to the cubic phase (coordination number 3). Also, the concentration dependence D, in the L3 phase is consistent with a low average coordination number if the range and the magnitude of the perturbation of water molecules induced by the polampolar interface are similar in the cases of molecular reorientation and lateral diffusion. Furthermore, contrary to what has been claimed by Miller et al.,23we show that self-diffusion data indeed may discriminate between continuous and discontinuous bilayer structures.
Acknowledgment. We acknowledge David Anderson for stimulating discussions. This work was supported by the Swedish Natural Sciences Research Council (NFR). B.B. acknowledges a grant from the Swedish Institute. Registry No. AOT,577-1 1-7; NaCI, 7647-14-5; water, 7732-18-5.
Dipole Oriented Anion Binding and Exchange in Zwitterionic Micelles Mauricio S. Baptists and Mario J. Politi* Departamento de Bioqujmica e Laboratbrio Interdepartamental de Cinetica Rbpida, Instituto de Quimica, Universidade de Siio Paulo, Caixa Postal 20780, SiS.0 Paulo, S.P., CEP 01498, Brazil (Received: April 25, 1990: In Final Form: January 28, 1991)
The binding of 8-hydroxy-l,3,6-pyrenetrisulfonateanion (POH)to zwitterionic interfaces of 3-(N-hexadecyl-N,N-dimethy1ammonium)propanesulfonate (HPS),lysolecithin (lysPC) micelles, or lecithin sonicated vesicles was measured by steady-state fluorescence emission of POH. The addition of inert salts displaced bound FQH in the three systems, showing the electrostatic nature of the binding. IH NMR spectra, degree of polarization of fluorescence (P), and emission intensities due to the excited-state prototropic dissociation of POH together pointed to a dipolspotential-drivenanion binding and exchange in these formally neutral surfaces.
Introduction The binding of ions to zwitterionic interfaces is well kn0wn.l The driving forces for ion binding, however, are not clear. Recent studies report surface enrichment of anions in sulfobetaine aqueous micelles and exchange with bulk aniom2 An accepted description of the driving force for binding in the case of betaines, and analogous monomer-forming aggregates, is the larger surface positive charge density. This distinct radial charge separation, although elcctroneutral, generates a dipole moment that, in turn, can attract charged species. This reasoning, in the case of aqueous (1) (a) Hauser, H.;Hinchley, C. C.; Krebs, J.; Levinc, B. A,; Philip, M. C.; Williams, R. J. P. Blochem. Biophys. Acra 1977, 468, 364. (b) Chrzeszczyk, A.; Wishia, A. Blochem. Biophys. A d a 1981, 618,28. (2) (a) Bunton, C.A.; Mhala, M. M.;Moffatt, J. R. J. Phys. Chem. 1989, 93, 854. (b) /bid. 1987, 52, 3836. (c) Pillersdrof, A.; Katzhcndler, J. Isr. J . Chem. 1979, 18. 330. (d) Pottel, R.; Kaatzc, U.; Muller, St. Eer. Eunsen-Ges. Phys. Chem. 1978, 82, 1086. (e) Clunie, J. S.; Corbill, J. M.; Goodman, J. F.; Ogden, C. P. Trans. Faraduy Soc. 1%7, 63, 505. (0 Brochsztain, S.;Berci, P. F.; Toscano, V. G.; Chaimovich, H.; Politi. M.J. J . Phys. Chcm. 1990, 94,6781.
0022-3654191 12095-5936$02.50/0
micelles, presumes a radial distribution of the monomers in a spherical aggregate. Thus in the case of betaine headgroups the positive charge should remain closer to the micelle core. Support for this rationale can be found in the work of Chevallier on phosphobetaine micelles, which pictures the individual dipoles pointing out radially in a spherical micelle, at least for monomers having from one to four methylene spacers between the charged groupsS3 In the present work we investigated the binding and exchange of a triply negatively charged probe in sulfobetaine and lysolecithin micelles and in lecithin vesicles. The extent of probe binding could be monitored due to the decreased excited-state acid dissociation rate constant upon probe binding. Probe binding to the sulfobetaine micelle interface clearly demonstrated a dipolar electrostatic nature of the binding. Furthermore, the binding of the probe to lysolecithin (lysPC) micelles will be discussed in terms of either a specific binding of the probe or a dipole configuration inversion (3) Chevalier, Y . ;Germanauk, L.; Perchec, P. Colloid Polym. Sci. 1988, 266, 44 1.
1991 American Chemical Society
