Langmuir 1997, 13, 3331-3337
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Surface Forces in Bicontinuous Microemulsions: Water Capillary Condensation and Lamellae Formation Plamen Petrov, Ulf Olsson, and Ha˚kan Wennerstro¨m* Division of Physical Chemistry 1, Chemical Center, P.O. Box 124, S-221 00 Lund, Sweden Received December 10, 1996. In Final Form: March 17, 1997X We present results from measurements of forces between macroscopic mica surfaces immersed in a bicontinuous microemulsion (AOT/n-decane/brine). At separations of 40-60 nm a force barrier appears, followed by two or three more. These indicate the presence of lamellar-like structures. The relative position of the sample within the phase diagram (at constant surfactant volume fraction) has profound impact on the transition region. Moving closer to the excess water phase boundary, we observe, apart from the layered structure, water droplets condensing out from the bulk phase, leading to an attractive background in the force profile due to the capillary forces. This attraction becomes more and more dominant over the repulsive barriers closer to the microemulsion/water phase boundary. Finally, on the border, only a longrange (∼120 nm) attraction remains. In contrast to other examples of capillary condensation, when it leads to an immediate jump of the two surfaces into contact, we could, because of the low microemulsion surface tension, measure the whole force profile, on both approach and separation. In a simple thermodynamic model we explain the observed phenomena.
Introduction Systems with oil, water, and surfactant form isotropic homogeneous solutions, microemulsions. Depending on the value of the spontaneous curvature of the surfactant film, the solution can consist of oil droplets in water or water droplets in oil or form a bicontinuous structure. The latter occurs when the spontaneous curvature is close to zero.1 For an ionic surfactant like AOT the value of the spontaneous curvature can be tuned by varying the salt content of the aqueous region.2 In the bicontinuous microemulsion the surfactant film extends in a topologically complex three-dimensional network with water on one side and oil on the other. When such an isotropic three-dimensional network is constrained by a surface or interface, structural deformations must occur. Such structural changes also have consequences for the interfacial energy. The influence on structure and thermodynamic quantities becomes even more pronounced when the solution is confined between two surfaces. In previous papers3,4 we studied the properties of an L3 (sponge) phase confined between two surfaces in a surface force apparatus. This phase consists of a topologically similar bilayer network. We found structural order from the bulk solution and surface-induced transition to a lamellar phase. In the present paper we pose the same questions for the bicontinuous microemulsion, but we get a different answer. Materials and Method Forces between mica surfaces are measured using a Mark IV surface force apparatus, described in full elsewhere.5,6 This technique allows for direct measurement of the interaction force, F(D), between two molecularly smooth surfaces as a function of their separation, D. The experimental procedure has been well * To whom all correspondence should be addressed. X Abstract published in Advance ACS Abstracts, May 15, 1997. (1) Strey, R. Colloid Polym. Sci. 1994, 272, 1005. (2) Chen, S. H.; Chang, S.-L.; Strey, R. J. Chem. Phys. 1990, 93, 1907. (3) Petrov, P.; Olsson, U.; Christenson, H.; Miklavic, S.; Wennerstro¨m, H. Langmuir 1994, 10, 988. (4) Petrov, P.; Miklavcic, S.; Olsson, U.; Wennerstro¨m, H. Langmuir 1995, 11, 3928. (5) Israelachvili, J. N. J. Colloid. Interface Sci. 1973, 44, 259. (6) Parker, J. L.; Christenson, H. K.; Ninham, B. W. Rev. Sci. Instrum. 1989, 60, 3135.
S0743-7463(96)02085-9 CCC: $14.00
Figure 1. Partial phase diagrams of the ternary systems AOT/ water/NaNO3/n-decane. The microemulsion phase region (µE) is neighboring two-phase regions with excess brine and a lamellar (LR) phase. The compositions at which surface force measurements are performed are denoted by crosses (× ) (equal volumes of water and oil). established and documented over the years. Two equally thick mica sheets are silvered on the backside to allow multilayer interferometric distance determination. The surfaces are glued on supporting silica cylinders and then mounted, respectively, to a piezoelectric tube and double cantilever spring in crossed cylinder geometry. A natural mechanical instability occurs whenever the gradient of the force, ∂F/∂D, becomes larger than the spring constant. In this situation the surfaces jump to the next stable position where ∂F/∂D is again less than the spring constant. With the SFA assembled, the surface-surface contact in air is determined and a microemulsion phase injected (∼30 cm3). The first force run is performed some hours after injection, as soon as the thermal drifts are sufficiently low to ensure a stable calibration (i.e., 99%), and n-decane, by Sigma (99+% pure). Deionized and distilled water used in all experiments is passed through a Millipore Water System consisting of an ion-exchange cartridge, Organex-Q, activated charcoal filter, and nucleopore filters. The samples are prepared by weighing the components and mixing until homogeneity and later inspected in transmitted light and scattered light and between crossed polarizers to confirm the existence of a single homogeneous and isotropic phase.
Experimental Results We have measured the interaction forces in samples of bicontinuous microemulsions from different positions on the phase diagram. Figure 2 shows the force normalized by the radius of curvature of the surfaces as a function of the separation in the presence of microemulsions of constant salt content (0.55% NaNO3), but different volume fractions AOTsfrom 15% to 24%. In our previous study4 of the L3 phase (of similar to the bicontinuous microemulsion surface topology), we have observed long-range oscillatory forces due to the short-range order in the system. In the present case no such forces are observed. In some of the experiments the long-range part of the force profile shows some irregularities, larger than the noise level, but they cannot be resolved and reproduced quantitatively. The 15% system exhibits a long-range linear attractive regime (Figure 2a) not seen on the other figures from that group, but for other samples (vide infra). All force curves from Figure 2 show some common behavior. At separations around 40 nm a force barrier appears on approach. It is followed by additionally two or three barriers separated by mechanically unstable regions. The magnitude of the barriers increases with decreasing separation. Similar to our observations in the L3 phase, the exact magnitude at which a jump to the next barrier occurs cannot be reproduced quantitatively between the separate force runs. The forces measured on separation complement the data recorded on approach. All features of the force profile in that region make us confident to conclude that the structure leading to the observed behavior is of a lamellar character. In contrast to the lamellae nucleated from the L3 phase, which is oilfree, now we have alternating layers of water and oil, separated with surfactant monolayer. The magnitude of the very last barrier is much higher than that of the other, and even at extreme pressure the surfaces cannot be brought into molecular contact. The mica surface is hydrophilic, and we may expect that there should be a water wetting layer between the surfaces. Neutron reflection studies of the bicontinuous microemulsion/water interface have shown that even at a hydrophobic surface (air) there is a water layer of substantial thickness.7 Our measurement of the refractive index in that region gives values close to the expected ones for water-rich media (approximately 1.34). The pulloff force needed to separate the surfaces from the minimum separation around 5 nm is about 0.5-2 mN/m, much weaker than in pure water. The fact that we see only two to three repulsive barriers in the lamellar region makes it difficult to extract accurately the interlamellar spacing. In Figure 3 we show how the period of the oscillations λ (calculated from the positions of the minimum of the force barriers when (7) Zhou, X.-L.; Lee, L.-T.; Chen, S.-H.; Strey, R. Phys. Rev. A 1992, 46, 6479.
Figure 2. Normalized force versus distance measured on approach (b) and separation (O) for bicontinuous microemulsions at constant salt content (0.55% NaNO3) and different surfactant concentrations: 15% (a); 17.5% (b); 20% (c); 24% (d). Arrows indicate the positions of jumps in/out between the repulsive barriers.
measured on separation8) depends on the surfactant volume fraction. The data can be fitted with an acceptable accuracy to the hyperbolic functional form λ ) -11.6 + 5.8/φ, nm. The other line on the phase diagram, which we have followed in our SFA experiments, is the one at constant surfactant volume fraction. Figure 4 represents the force versus separation data for a series of bicontinuous microemulsions at 17.5% AOT and salt content from 0.42% to 0.66%. The sample with low salt lies close to the border with the two-phase region with excess lamellar phase, (8) Richetti, P.; Ke´kicheff, P.; Barois, P. J. Phys. II Fr. 1995, 5, 1129.
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Figure 3. Spacing between the repulsive barriers (measured from the minimum in the force profile) as a function of the surfactant volume fraction. The line is a hyperbolic fit to the measured data: λ ) -11.6 + 5.8/φ, nm.
while on the other end we reach the excess water line. First glance at the data reveals the familiar oscillation from the lamellar-like region at short separations. Increasing the salt concentration we see the emergence of an attractive background of a longer range, up to 120 nm, and increasing magnitude. The oscillation gets weaker and less developed and finally disappears completely at the highest measured salt concentration (0.66%). Even at 0.63% (Figure 4d) the second barrier is quite unstable and poorly reproduced. The gray circles on the plot represent a force run when the surfaces jumped into a final contact directly from the attractive region. A most important observation from this series of experiments is that of the shape of the interference fringes, used to monitor the separation between the surfaces.9 Together with the onset of the attraction, one can see a discontinuity in the shape of the fringesa sharp spike at the center indicating that the material between the surfaces is no longer homogeneous in the lateral direction. Decreasing the separation, we observe initial rapid broadening of the spike and then a more steady increase of its size. Similar behavior has been reported previously9 and interpreted as the appearance of inhomogeneity in the gap with lower refractive index than that of the surrounding medium. Unfortunately, precise determination of the refractive index is not possible with the resolution of our current experimental setup. However, an estimate from the shift of the wavelength of the fringe gives values close to that of water. This leads us to the conclusion that for samples close to the excess water phase boundary there is a condensation of water in the center between the surfaces. The attraction seen in Figure 2a (15% AOT, 0.55% NaNO3) has the same origin as the one described here, but the distortion of the fringes is much less pronounced. Another consequence of the condensation of an aqueous phase between the surfaces is that the force is measurable also when separating the surfaces. In contrast to the other samples there is no major jump to a large separation from the adhesive minimum when the surfaces are separated. In Figure 4e we see that the force measured on separation is, at small distances between the surfaces, nearly the same as on approach, indicating close to equilibrium conditions. The larger the separation the larger is, on a relative scale, the difference between the force on approach and on separation. The shape of the fringes follows the same evolution as seen on approach, but even after separating the surfaces to micrometer distances, the water droplet does not disappear instantly. It takes a few minutes (for the 0.60% sample) and up to 20-30 min at 0.66% until the water diffuses away from the surfaces and the fringes restore (9) Christenson, H. K. J. Colloid Interface Sci. 1985, 104, 234.
Figure 4. Normalized force versus distance for microemulsions at constant surfactant volume fraction (17.5%), but different salt contents: 0.42% (a); 0.55% (b); 0.60% (c); 0.63% (d); 0.66% (e). Arrows mark the positions of jumps between the repulsive barriers. The straight lines in (d) and (e) and the dotted line in (e) are theoretical fits, using eqs 9 and 10, respectively. See text for details.
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their original shape. The rate-limiting step in the equilibration appears to be the diffusional transport of oil and water to and from the aqueous meniscus between the surfaces. Discussion We identify four characteristic features of the measured force curves: (i) absence of oscillatory forces occur beyond a separation of 50 nm; (ii) for some compositions there is an attractive force that varies nearly linearly with separation and that can extend to 100 nm separation; (iii) one to three force barriers with mechanically unstable regions and attractive minima in between exist at separations between 10 and 50 nm; (iv) a steep repulsion appears at separations less than 5 nm. Below we discuss these observations one at a time. No Long-Range Oscillatory Force. In our previous study of a sponge phase from the same system3,4 we have found oscillatory forces measurable up to separations larger than 100 nm. These have been interpreted as signifying a local periodic order in the bulk liquid. In the present system the surfactant bilayer of the sponge phase is replaced by a monolayer of a similar topology. The periodicity of the surfactant film is determined by volume constraints, and for the same surfactant concentration the microemulsion film should show a periodicity half of that in the sponge phase. However, we have alternatively aqueous and oil domains and the periodicity in the liquid should be the same, as in the sponge phase. The fact that we, for, e.g., the sample with 20% AOT, do not see a periodic force at longer range indicates that the correlation length is shorter in the microemulsion than for the sponge phase. The latter with a bilayer film has, roughly, twice as a high bending constant, resulting in a less flexible film, allowing for more correlations. Furthermore, in the composition region where measurements were made, the spontaneous curvature of the surfactant film is slightly negative. This generates a curvature energy frustration in the bicontinuous structure, presumably adding to the disorder. Force Barrier at Short Range. At separations of less than 5 nm we observe a steep repulsive force. At these separations we can estimate the refractive index for the liquid in the small patch between the crossed cylinders and we obtain a value of approximately 1.34. Thus, the liquid in this region is an electrolyte solution and the observed repulsion is a double-layer repulsion. In contrast to measurements in bulk sodium salt solutions, the aqueous region is a lens of finite width between the surfaces. There is also a force component from the region where the aqueous part goes over into the microemulsion. As we will discuss in more detail below, this contributes an additional attractive component and there is an adhesive minimum around a separation of 5 nm, amounting to 0.5-2 mN/m. In Figure 5 we show the last two force barriers for the bicontinuous microemulsion of 15% AOT (Figure 2a). The smooth lines are fits to the data points using a numerical solution of the Poisson-Boltzmann equation combined with a van der Waals interaction (Hamaker constant of 2.2 × 10-20 J). The fitted decay length of 1.2 nm corresponds well with the one expected for that salt concentration (0.065 M). The experimental data lie closer to the constant charge solution of the DLVO equation. The strong repulsive force, preventing the surfaces from coming into primary adhesive minimum, is consistent with measurements of sodium salt solutions10,11 that show an absence of adhesive contact above concentrations of about 10 mM. (10) Pashley, R. M. J. Colloid Interface Sci. 1981, 83, 531. (11) Petrov, P.; Miklavic, S. J.; Nylander, T. J. Phys. Chem. 1994, 98, 2602.
Figure 5. Forces at short separations for a sample of 0.55% NaNO3 and 15% AOT, together with DLVO fit (constant charge and constant potential). The decay length, obtained from the fit, is 1.2 nm.
Force Barriers at Separations of 10-50 nm. For all systems, except one, we observe one to three force barriers in the region of 10-50 nm separations. When multiple barriers occur, they become higher and steeper the shorter the separation. The period is approximately the same for a given surfactant composition and it becomes shorter the higher the concentration, as shown in Figure 3. In the case of the sponge phase, we observed repulsive barriers at approximately the same separations, but these were stronger and preceded by a mechanically unstable region signaling a first-order transition. In the present case we have no signs of such a preceding unstable region and the barriers appear more continuously. Thus, there is no basis for concluding that there is a bicontinuous microemulsion-to-lamellar phase transition in the confined space between the surfaces. There seems to be a layered structure that could also exist outside the single surface, and the barriers would then represent changes in the number of layers with breakthroughs of the films. Another alternative is that the layering is further reinforced in the confined space, but in a continuous way without a transition behavior. The mica surface has a strong preference to be wet by water rather than oil; so in a microemulsion it is the aqueous regions that meet the mica surface. In the vicinity of the surface, the microemulsion will not show the isotropy of the bulk solution. When a second surface approaches, the deviation from isotropy will increase and the local structure will, most likely, be that of a lamellar phase, with fewer and fewer hole defects the smaller the separation. For samples with a composition closer to a lamellar phase, more force barriers are observed. Furthermore, the estimated distance between the force barriers decreases with increasing surfactant concentration, in accordance with the expectations for the lamellar phase,12 but the magnitude does not match the expected repeat distance in such a bulk phase. Note also that the observed period deviates from the characteristic distance of the bulk microemulsion phase. Force from Capillary Condensation. We will concentrate our discussion of the capillary force on the most simple case, when the force is purely attractive and almost linear down to a few nanometers separation (Figure 4e). Observations of the shape of the interference fringes and estimates of the refractive index of the solution in the gap show nonequivocally that a water droplet of micrometer size radius condenses between the surfaces and (12) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces and Membranes; Addison-Wesley: Reading, MA, 1994.
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our SFA experiment this approximation is more than excellent (see below). The change of the total free energy of the system due to the emergence of a water droplet out from the homogeneous microemulsion phase can be written as the sum of bulk (∆Gbulk) and surface (∆Gsurf) terms:
∆Gtot ) ∆Gsurf + ∆Gbulk
Figure 6. Illustration of the model system consisting of a drop of water condensing from the microemulsion bulk phase in the gap between sphere and a plane. h0 is the distance between the sphere (with radius R0) and the plane. Rm denotes the maximum radial extent of the water drop. All relative dimensions are highly exaggerated for clarity.
grows bigger with decreasing separation. In this way an area of microemulsion-mica contact is replaced by the energetically more favorable water-mica contact. This gives rise to an attractive force, the magnitude of which depends on the interfacial tension between the condensed aqueous phase and the bulk microemulsion. Similar behavior is observed when a liquid is condensing out of its saturated vapors13,14 or from a mixture with another (immiscible) liquid.9,15 In those cases, due to the high surface tension between the drop and the surrounding liquid/vapor, the attractive force is extremely high and, as soon as the droplet is formed, the mica surfaces jump into deep adhesive contact. In our system, the surface tension of the microemulsion/water interface is very low16,17 and we could explicitly measure the capillary force from when the condensate is formed down to the point when the interaction is overcome by the repulsive doublelayer force. Let us now try to analyze the water capillary condensation in greater detail. The classical approach in dealing with this phenomena is to assume the validity of the Kelvin equation,18 which gives the equilibrium curvature of the liquid meniscus, and then calculate the attractive force from the Laplace pressure across the interface.9,19 Both the equilibrium case (constant Kelvin radius throughout all separations) and a nonequilibrium one (constant drop volume) have been analyzed and applied to several sets of experimental data. In what follows we will demonstrate another approach, based on simple thermodynamic calculations, which we think illustrates better the driving force behind the observed phenomena. Suitable geometry, equivalent to the crossed cylinders in the SFA, is that of a sphere against plane, as illustrated on Figure 6. We will consider water drop with radius Rm surrounded by a bicontinuous microemulsion phase. The radius of the sphere is R0 and the minimal distance to the plane is h0. There is a wetting film of water on both surfaces, but we consider this as a part of the microemulsion phase. The circumference of the droplet is approximated to a cylinder (dashed line on Figure 6) instead of the more correct concave one. Numerical computations, using the exact geometry, show that for the typical dimensions of the surfaces and separations in (13) Fisher, L. R.; Israelachvili, J. N. Colloids Surf. 1981, 3, 303. (14) Christenson, H. K. J. Colloid Interface Sci. 1988, 121, 170. (15) Christenson, H. K.; Fang, J.; Israelachvili, J. N. Phys. Rev. B 1989, 39, 11750. (16) Aveyard, R.; Binks, B. P.; Lawless, T. A.; Mead, J. Can. J. Chem. 1988, 66, 3031. (17) Kegel, W. K.; Bodna`r, I.; Lekkerkerker, H. N. W. J. Phys. Chem. 1995, 99, 3272. (18) Evans, D. F.; Wennerstro¨m, H. The colloidal domain: where physics, chemistry, biology and technology meet.; VCH Publishers: New York, 1994. (19) Fisher, L. R.; Israelachvili, J. N. J. Colloid Interface Sci. 1981, 80, 528.
(1)
The surface free energy term is due to different surface tensions of the mica/water and mica/microemulsion interfaces plus the energy of the perimeter of the water drop:
∆Gsurf ) A1(γmica/water - γmica/µE) + A2γ where A1 and A2 are the areas of the water/mica and water/ microemulsion interfaces and γ is the surface tension of the latter one. Taking into account the presence of water wetting layers on the mica surfaces, we can simplify the above expression by assuming that γmica/water - γmica/µE ) -γ or equivalently there is a zero contact angle according to the Young equation. In this case
∆Gsurf ) (-A1 + A2)γ
(2)
The bulk free energy term reflects the difference in the chemical potentials of the condensed water and the water in the microemulsion phase:
∆Gbulk ) Vw∆µ
(3)
where Vw is the volume of the droplet. The surface areas A1 and A2 and the volume Vw are (after expansion up to first order in the curvature 1/R0)
A1 ) 2πRm2
( (
) )
Rm2 A2 ) 2πRm h0 + 2R0 Vw ) πRm2 h0 +
(4)
Rm2 4R0
The radius of the water droplet has to be determined from the condition of giving minimum to the total free energy. ∆Gtot also has to be negative in order to favor water condensation:
∂∆Gtot )0 ∂Rm
(5)
∆Gtot(Rm) < 0 Typical dimensions and operational distances in the SFA are R0 ∼ 10-2 m, h0 ) 0-10-7 m, and Rm ∼ 10-5 m, i.e.
R0 . Rm . h0
(6)
In this approximation we can derive the following expression from eq 5, using eqs 1-4:
x (
Rm = 2
R0RK 1 -
)
h0 2RK
where RK is a constant with dimension as length:
RK ≡
γ ∆µ
(7)
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Table 1. Fitted Parameters for Microemulsion-Water Surface Tension, γ, Chemical Potential Difference, ∆µ, Aqueous Solution-Microemulsion, and the Kelvin Radius RK AOT conc, %
NaNO3 conc, %
γ, µN/m
∆µ, J/m3
RK, nm
17.5 17.5 15
0.66 0.63 0.55
46 9.6 14
1100 195 290
42 49 48
If we compare (7) with the result obtained in the “classical” capillary theory approach,13 we see that we get the same quantitative result with a Kelvin radius being the constant RK. From eq 7 it is clear that the water droplet cannot appear if the separation between the surfaces is larger than a critical one (2RK). The interaction force can be calculated from the free energy expression:
F)-
∂∆Gtot ) -(2πγRm + π∆µRm2) ∂h0
(8)
having the radius of the drop at its optimal value for each particular separation. In the above mentioned approximation, eq 6, we can get the following expression by substituting (7) into (8):
(
F = -4πR0γ 1 -
h0 + 2RK
x(
)) (
RK h0 1R0 2RK
=
-4πR0γ 1 -
)
h0 (9) 2RK
Again, the same approximate result could be derived, using the Kelvin radius approach.13 In the force measurements of Figures 2a and 4d,e, we observe long-range attractions and they all obey the linear force versus separation relation predicted by eq 9). The straight lines in the figures are fits with this equation, and the resulting parameters are presented in Table 1. However, the force is monotonically attractive only for the force curve of Figure 4e, for which we could assume that the phase separating out between the surfaces is a pure aqueous phase. For the other two systems we observe a force barrier at intermediate separations, showing that some surfactant and probably oil remain in the meniscus. This explains the low values of γ and, particularly, ∆µ for these samples. For the sample at 17.5% AOT, 0.66% NaNO3 the deduced surface tension is in qualitative agreement with previous direct measurements for the AOT-NaCl system.16 One should note that bulk equilibrium surface tension measurements necessarily involve compositions on the phase boundary, while we in the present case have compositions inside the one-phase area. We are not aware of any independent measurements of the difference in chemical potential ∆µ. If we ignore the contribution from the electrolyte, ∆µ ) 1100 J/m3, corresponding to 8 × 10-6 kT per water molecule. This illustrates the really small deviations of the chemical potentials in microemulsions from the values in the corresponding locally homogeneous phases. Figure 7 shows the result of exact numerical computation for the radius of the water droplet versus separation dependence (5) using the more correct concave cylindrical shape of the meniscus. On the insert we compare it to the approximated equation (7) (shown by dotted line). The only small discrepancy comes at large separations, when the approximated theory predicts a slightly shorter critical water nucleation distance. The steplike appearance of the water condensate with non-zero radius is a manifest
Figure 7. Radius of the water droplet as a function of the distance between surfaces calculated numerically using the exact eq 5 and concave cylinder geometry. The dotted line on the insert is calculated using the approximated eq 7. The numerical constants are R0 ) 1.64 cm, γ ) 46 µN/m, and ∆µ ) 1100 J/m3 (reflecting the experiment at 17.5% AOT and 0.66% NaNO3 (Figure 4e)).
of the first-order character of the capillary condensation caused by the surface free energy associated with the area A2 between the meniscus and the bulk phase. At shorter separations the difference between both models is nondistinguishable. We are not in a position to make direct comparison of the theoretical curve from Figure 7 to the experimental observation of the diameter of the water droplet, since the error in the latter one is too big for a quantitative comparison. The order of magnitude, though, and the way it depends on the separation are in good qualitative agreement with the calculated ones. In Figure 4e we see that a weak attraction appears for distances larger than 2RK, in conflict with eq 9. We do not have a definite explanation for this observation, but it appears that instead of an abrupt first-order process the aqueous meniscus is formed more gradually. The oil and surfactant concentrations are in this picture substantially lower than the bulk values but still non-zero at large separation. When the surfaces are separated, the force is still measurable in Figure 4e at a range of separations and it is slightly more attractive than on approach. Since we observe that the meniscus remains for some considerable time (30 min) even at large separations (1 µm), a simple assumption is that the volume of the aqueous drop remains constant during the time of the measurement. We can then use the same arguments as those that led to the force of eq 9 but with the meniscus volume constant. At contact
Vw )
πRm4 ) 4πR0RK2 4R0
from eq 4. As the surfaces separate, the radius Rm of the meniscus decreases and at constant volume
((
Rm2 ) 2R0h0 1 + and the force is
( (
) )
4RK2 h02
F = -4πR0γ 1 - 1 +
1/2
-1
) )
4RK2 h02
-1/2
(10)
which for small values of h0, h0 , 2RK, gives the same dependence as eq 9 but for larger h0 values has substantial
Surface Forces in Bicontinuous Microemulsions
deviations. The dotted line in Figure 4e shows the predicted force on separation. Considering that there is no adjustable parameter, we find the agreement satisfactory. Conclusions We investigated the interfacial behavior and the surfaceinduced phase transitions of bicontinuous microemulsions at different compositions within the phase diagram. Our experimental findings and theoretical analysis can be summarized as follows: (i) The bicontinuous microemulsion and the L3 phase are two surfactant systems of similar topology but with different interfaces dividing the space into equal volume domainssmonolayer in the first case and bilayer in the second. As a consequence of their different flexibilities, when such systems are confined between solid surfaces, they give rise to an oscillatory force in the bilayer case but show almost no resistance in the monolayer case. (ii) Bicontinuous microemulsions exhibit repulsive force barriers under confinement due to the overlap of the layered, lamellae-like structures present between the mica surfaces.
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(iii) For microemulsion samples close to the phase boundary with the two-phase region with excess water the repulsive barriers are superimposed on attractive background due to water capillary condensation between the center of the surfaces. At the border with excess water phase only a long range (∼120 nm) attraction remains. (iv) The transition to lamellar structure or water condensation is driven by the lower surface energy of the LR-mica or water-mica interface, relative to the microemulsion. (v) The attractive forces measured both on approach and on separation can be quantitatively described by considering surface free energies and bulk chemical potentials. Acknowledgment. We are grateful to Hugo Christenson for helpful discussions. This work was supported by grants from the Swedish Natural Science Research Council (NFR), the Swedish Council for Planning and Coordination of Research (FRN), and the Go¨ran Gustafsson Foundation. LA962085G
