The Confinement-Induced Sponge to Lamellar Phase Transition

The Confinement-Induced Sponge to Lamellar Phase Transition ... the isotropic phase since it displays a bulk first-order transformation to the lamella...
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The Confinement-Induced Sponge to Lamellar Phase Transition David A. Antelmi,*,† Patrick Ke´kicheff,‡ and Philippe Richetti§,| Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia, Institut Charles Sadron, CNRS, 6 rue Boussingault, F-67083 Strasbourg, France, and Centre de recherche Paul Pascal, CNRS, Avenue du Docteur-Schweitzer, F-33600 Pessac, France Received March 17, 1999. In Final Form: July 1, 1999 The behavior of an isotropic fluid near its first-order phase transition to an ordered phase is investigated when confined between two macroscopic walls. The sponge (L3) phase of the system sodium bis(2-ethylhexyl)sulfosuccinate/brine was used as the isotropic phase since it displays a bulk first-order transformation to the lamellar (LR) phase upon reaching the transition temperature TLR. When confined, measurement of the interactions between the two confining walls with a surface force apparatus showed that over a limited temperature range below TLR the confined L3 phase transformed to the LR phase at a specific wall separation. This confinement-induced transformation was signaled by the existence of two distinct oscillatory force regimes. Structural characteristics of either the L3 or the LR phase were observed in the oscillatory profiles including the characteristic length or reticular spacing, the nature and topology of structural defects, the order parameter correlation length (for the L3 phase), and the elastic compressibility modulus (for the LR phase). The force-distance profiles also allowed the interfacial tension of the L3/LR interface to be evaluated.

Introduction When a fluid is in contact with a solid interface or confined between two solid interfaces, its properties will be different from those of the same fluid in the infinite or bulk state. In his pioneering studies on nematic liquid crystals, Sheng demonstrated how a single isolated surface exerting an ordering potential on a semi-infinite system may induce a first-order phase transition at the phase interface.1,2 The so-called boundary layer phase transition that was introduced is none other than the prewetting transition3 and is a rather general phenomenon that occurs when two phases near their critical point are influenced by a third phase.4 Such an effect is further exaggerated upon introduction of a second interface that restricts the intervening fluid to exist in a confined geometry. The well-known phenomenon of capillary condensation of simple liquids results from such a configuration where the presence of the walls promotes adsorbed film thickening or liquid phase nucleation.5 The curved interface of the wetting liquid filling the pore or slit then allows the induced liquid condensate to coexist with an undersaturated bulk vapor.6 The presence of interfaces therefore provides additional contributions to the fluid’s free energy density. First is the existence of wall-fluid interactions which can impose an ordering potential on the fluid and also determine the * To whom correspondence should be addressed. † Autralian National University. ‡ Institut Charles Sadron. § Centre de Recherche. | Present address: Department of Chemical Engineering, University of California, Santa Barbara 93106 CA. (1) Sheng, P. Phys. Rev. Lett. 1976, 37, 1059. (2) Sheng, P. Phys. Rev. A 1982, 26, 1610. (3) Sluckin, T. J.; Poniewierski, A. Fluid Interfacial Phenomena; John Wiley: 1986. (4) Cahn, J. W. J. Chem. Phys. 1977, 66, 3667. Ebner, C.; Saam, W. F. Phys. Rev. Lett. 1977, 38, 1486. (5) Wanless, E. J.; Christenson, H. K. J. Chem. Phys. 1994, 101, 4260. (6) Thomas, W. T. L. K. Philos. Mag. 1871, 42, 448.

wall/fluid interfacial tension and wetting properties. When two interfaces are present at finite separation, a second contribution to the free energy arises due to the surface excess pressure. The latter, known as the solvation force,7 arises from intermolecular forces between the wall-fluid and fluid-fluid molecules and vanishes as the wall separation becomes infinite. Thus the separation between two confining walls can act as an additional field variable with the solvation force as its conjugate density.8 The phase equilibria of a confined fluid, defined by the minimum in the free energy density, will therefore be governed not only by the interplay of the usual thermodynamic parameters operating for a bulk system (temperature, chemical potential, etc.) but also by these two additional surface terms. Many examples of surface-induced transitions may be found in the literature, particularly for confined liquid crystals. Some general trends have been shown to exist in the behavior of isotropic or nematic fluids confined between ordering walls while approaching the ordered phase domain.9 If the bulk phase transition is secondorder, the thickness of the preordered film wetting the walls grows continuously and diverges at the bulk transition (critical wetting10). On the other hand, when the transition is first-order the preordering at the solid/ fluid interface is lost upon reaching some threshold separation, D*, at which time the whole fluid becomes ordered over its remaining thickness1,2 (first-order wetting10). A surface that is rough on a scale that tends to disorder the neighboring fluid will allow the disordered (7) Israelachvili, J. N. Intermolecular and Surface Forces; 2nd ed.; Academic Press: London, 1994. (8) Evans, R.; Marini Bettolo Marconi, U. J. Chem. Phys. 1987, 86, 7138. (9) Miyano, K. Phys. Rev. Lett. 1979, 43, 51. Als-Nielsen, J.; Christensen, F.; Pershan, P. S. Phys. Rev. Lett. 1982, 48, 1107. Pershan, P. S.; Als-Nielsen, J. Phys. Rev. Lett. 1984, 52, 759. Ocko, B. M.; Braslau, A.; Pershan, P. S.; Als-Nielsen, J.; Deutsch, M. Phys. Rev. Lett. 1986, 57, 94. Iannacchione, G. S.; Finotello, D. Phys. Rev. Lett. 1992, 69, 2094. Shi, Y.; Cull, B.; Kumar, S. Phys. Rev. Lett. 1993, 71, 2773. (10) Schick, M. In Liquids at Interfaces; Charvolin, J., Joanny, J. F., Zinn-Justin, J., Eds.; North-Holland: Amsterdam, 1990; p 415.

10.1021/la9903191 CCC: $18.00 © 1999 American Chemical Society Published on Web 09/08/1999

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structure to persist where bulk conditions would otherwise favor an ordered structure and the transition in the confined medium is then delayed.11 Control of fluid structure at interfaces in this way is used in many applications such as liquid crystal displays. Most of the above-mentioned experimental studies have paid attention to the ordering, dynamics, and electrooptical properties of confined liquid crystals, while the interactions between the confining walls or the forces between objects immersed in these fluids have been left aside. Some theoretical studies have, however, explored the pretransitional effect on the interactions between the confining walls. Generally, two identical walls imposing a contact ordering potential (of zero range) on an intervening fluid will be attracted to each other, since the thinner the confined film the more the film approaches a uniform state which is thermodynamically favored. The range of the attraction is related to the correlation length of the order parameter of the induced phase. A theoretical analysis of this effect in the Landau-Ginzburg formalism was first performed by Marcˇelja and Radic´12 for a second-order process and recently extended to a smectic transition by de Gennes.13 The case of a first-order transition has been considered by Poniewierski and Sluckin.11 To our knowledge, only a few experimental studies have dealt with the measurement of the force between walls confining complex fluids near a phase transition. Horn et al. measured interactions between mica surfaces immersed in a thermotropic liquid crystal.14 They studied both the first-order isotropic-smectic transition and the second-order nematic-smectic transition. An extension to this study on a different (lyotropic) nematic system that included an extensive analysis of the effect of temperature quantified the effect of the enhancement of the surface-induced order in terms of the smectic order parameter.15 An overall attractive interaction between the confining interfaces that decayed exponentially with separation was observed in both the isotropic phase and the nematic phase. By configuring the experiment so that the fluid was confined between one ordering surface and an opposing disordering surface, it was confirmed that an overall repulsive interaction occurs when the surfaces impose an asymmetric distribution of the order parameter.16 The present work completes the latter study as it investigates the effect of confinement on an isotropic fluid near its first-order phase transition to an ordered phase. The sponge (L3) phase of a lyotropic surfactant system was considered a good system for this study given that it displays a first-order transition to a lamellar phase. The sponge phase was perhaps first evidenced by Fontell,17 and its structure was elucidated in detail some years later with the advent of small-angle scattering techniques.18-22 The phase is made up of surfactant bilayers which are locally flat but randomly oriented on a global scale, giving (11) Poniewierski, A.; Slucklin, T. J. Liq. Cryst. 1987, 2, 281. (12) Marcˇelja, S.; Radic´, N. Chem. Phys. Lett. 1976, 42, 129. (13) de Gennes, P. G. Langmuir 1990, 6, 1448. (14) Horn, R. G.; Israelachvili, J. N.; Perez, E. J. Phys. 1981, 42, 38. (15) Moreau, L.; Richetti, P.; Barois, P. Phys. Rev. Lett. 1994, 73, 3556. (16) Richetti, P.; Moreau, L.; Barois, P.; Ke´kicheff, P. Phys. Rev. E 1996, 54, 1749. (17) Fontell, K. In Colloid Dispersions and Micellar Behaviour; American Chemical Society: Washington DC, 1975; p 270. (18) Porte, G.; Marignan, J.; Bassereau, P.; May, R. J. Phys. Fr. 1988, 49, 511. (19) Cates, M. E.; Roux, D.; Andelman, D.; Milner, S. T.; Safran, S. A. Europhys. Lett. 1988, 5, 733. (20) Gazeau, D.; Bellocq, A. M.; Roux, D.; Zemb, T. Europhys. Lett. 1989, 9, 447. (21) Strey, R.; Winkler, J.; Magid, L. J. Phys. Chem. 1991, 95, 19. (22) Pieruschka, P.; Marcˇelja, S. Langmuir 1994, 10, 345.

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rise to multiple connections in three dimensions. As a result, the intervening solvent is partitioned into two equivalent, but separate, subvolumes resulting in the bicontinuous nature of the phase. A characteristic length scale (pore size), ξ, is present in the structure which scales as the inverse of the membrane volume fraction. The sponge phase is therefore closely related to the lamellar (LR) phase in which the surfactant membranes remain flat on average and stack up in one dimension separated by solvent layers (with the surfactant chains in a liquidlike state23,24). The LR structure is periodic along the normal direction with a reticular distance, d, defining the thickness of the solvent layer and surfactant bilayer. Sponge and lamellar phases are always located adjacent to each other in phase diagrams. Transformation between the two phases can be effected by a change in any of the usual parameters defining the thermodynamic equilibrium of bulk phases such as the membrane volume fraction, salinity, or temperature. Other external fields can also induce the transformation such as imposing a shear stress25 or a confining field, as has been shown for the system sodium bis(2-ethylhexyl)sulfosuccinate (AOT) and brine.26,27 The aims of this work were to characterize the state of the sponge phase, near its first-order bulk transition to the lamellar phase, when confined between rigid walls and measure the interactions between the two confining walls. The measurements were performed with surface force apparatus (SFA)7 that allowed precise variation of the separation between the two macroscopic surfaces used to confine the sponge fluid. Structural changes in the confined fluid film as a function of separation could therefore be seen by monitoring the interaction between the two walls. Under certain conditions, either phase can be favored by the surfaces allowing insights on the structural characteristics of the two phases to be extracted from the force-distance profiles. The chosen system also showed some thermotropic behavior, making it possible to use temperature as an additional fine-tuning parameter and adjust proximity of the fluid to the bulk phase transition. Moreover, since the condensed droplet of LR phase coexists with the surrounding bulk L3 phase, the force-distance profile further yields the interfacial surface tension between the two phases. This is an important consequence of measuring such a transition in an SFA since very few techniques provide a means to measure ultralow interfacial tensions between two closely related mesophases. Experimental Section System Studied. All of the work presented here was performed using the system comprised of sodium bis(2-ethylhexyl)sulfosuccinate (AOT), sodium nitrate (NaNO3), and water. This system is analogous to the AOT/NaCl/H2O system studied in detail by Fontell17 and by Miller and Ghosh,28,29 but the Clion has been replaced with the NO3- ion to avoid degradation of the silver layers used to make the optical cavity in the SFA.30-32 (23) Luzzati, V. Biological Membranes; Academic Press: New York, 1968; p 71. (24) Laughlin, R. G. The Aqueous Phase Behaviour of Surfactants; 1st ed.; Academic Press: London, 1994. (25) Mahjoub, H. F.; Bourgaux, C.; Segot, P.; Kle´man, M. Phys. Rev. Lett. 1998, 81, 2076. (26) Antelmi, D. A.; Ke´kicheff, P.; Richetti, P. J. Phys. II Fr. 1995, 5, 103. (27) Petrov, P.; Miklavic, S.; Olsson, U.; Wennerstro¨m, H. Langmuir 1995, 11, 3928. (28) Miller, C. A.; Ghosh, O. Langmuir 1986, 2, 321. (29) Ghosh, O.; Miller, C. A. J. Phys. Chem. 1987, 91, 4528. (30) Ke´kicheff, P.; Marcˇelja, S.; Senden, T. J.; Shubin, V. E. J. Chem. Phys. 1993, 99, 6098.

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Table 1. Summary of the Lr Reticular Distance (d) and the Characteristic Size of the Sponge (ξ) Measured from Small-Angle X-ray Scatteringa LR Samples Φ

dmeasured (nm)

dideal (nm)

dln (nm)

0.091 0.134 0.181

26.0 15.6 11.7

21.0 14.2 10.6

25.0 16.5 12.0

L3 Samples Φ

ξmeasured (nm)

ξideal (nm)

ξln (nm)

0.091 0.137 0.188

35.0 21.0 16.5

31.0 20.5 14.9

37.0 24.2 17.6

a The values predicted by the classical scaling law, d ideal ) δ/Φ and ξideal ) Rδ/Φ, are shown (with δ ) 1.91 nm, and R ) 1.47 from ref 33), together with predicted values using the logarithmic correction, dln, and ξln.66

Nevertheless, the resulting phase diagram is not significantly altered with respect to the chloride system. The LR and L3 phases are found quasi-parallel to the AOT/H2O axis, and a transition between the two can be initiated by adjusting the salt concentration. The system also shows thermotropic behavior where the LR to L3 transition can be induced upon decreasing the temperature.33 Small-Angle X-ray Scattering (SAXS). Several previous scattering studies have characterized the structure of both the LR and L3 phases of the AOT/NaCl/H2O system.34,33 These studies have shown that the thickness of the membrane, δ, remains constant (1.9 nm) in both phases over the complete range of Φ. In this study we performed scattering on several samples to check that the presence of the NaNO3 did not significantly alter the characteristic spacing with respect to the NaCl system. The measurements were performed using the SAXS facility at the Service de Chimie Mole´culaire (SCM, Saclay, France) and are summarized in Table 1. Sample Preparation. Three different sample compositions were studied with membrane volume fractions Φ ) 0.182, 0.135, and 0.090, or approximately 20, 15, and 10 wt %, respectively. The sponge samples were prepared simply by weighing each component (NaNO3, H2O, then AOT) separately into a flask which was then sealed. The samples were shaken on a vortex mixer and equilibrated at a constant temperature of 25 °C in a water bath. Typically, equilibrium was obtained after 2 or 3 days with frequent shaking. Once the samples were equilibrated, they were filtered through a 0.8 µm filter to ensure that no foreign particles were present. The samples were once again left to equilibrate for another 2 days at 25 °C. A small aliquot of the sample was placed in a rectangular capillary (400 µm path length, Vitrodynamics Inc.), and the L3/LR transition temperature, TLR, was determined to (0.5 °C via crossed polarizing microscopy. A Mettler hot stage was used to increase the temperature in small steps until the first focal conics appeared as shown in Figure 1. The focal conics appeared first on the upper and lower surfaces of the capillary as judged by the position of the focal planes. SFA Experiments. The Mark IV surface force apparatus, described extensively elsewhere,35,36 was used for the force measurements. To eliminate nonlinearity and hysteresis in the adjustment of the surface separation, the magnetic positioning system developed by Stewart and Christenson was used in (31) Shubin, V. E.; Ke´kicheff, P. J. Colloid Interface Sci. 1993, 155, 108. (32) Antelmi, D. A.; Ke´kicheff, P. J. Phys. Chem. B 1997, 101, 8169. (33) Strey, R.; Jahn, W.; Skouri, M.; Porte, G.; Marignan, J.; Olsson, U. In Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution; Chen, S., Huang, J. S., Tartaglia, P., Eds.; Kluwer Academic Publishers: Dordrecht, 1992; p 351. (34) Skouri, M.; Marignan, J.; May, R. Colloid Polym. Sci. 1991, 269, 929. (35) Israelachvili, J. N.; Adams, G. E. Nature 1976, 262, 774. (36) Parker, J. L.; Christenson, H. K.; Ninham, B. W. Rev. Sci. Instrum. 1989, 60, 3135.

Figure 1. Appearance of birefringent spherulites of lamellar phase upon reaching the LR/L3 bulk transition temperature, TLR. preference to the conventional piezoelectric device.37 The working surfaces of the SFA were produced from pure synthetic silica (Heraeus Suprasil T-21) following the method of Horn et al.38 Silica, back-coated with silver, proved to give a robust substrate capable of retaining its integrity for days in contact with the sponge samples. Immediately prior to installing the surfaces into the SFA, the silica surfaces were treated with water plasma (125 kHz, at a power of 10 W for 1 min with PH2O ) 0.065 Torr and PAr ) 0.022 Torr) to remove any surface contaminants and to render them hydrophilic. Calculation of the surface separation was carried out using the complete analysis for the asymmetric interferometer outlined by Horn et al.39 Temperature Variation. Since the measurements were performed as a function of temperature, it was useful to define a control parameter, ∆T, as the difference between the actual temperature and the bulk sponge to lamellar transition temperature, that is, ∆T ) T - TLR.26 Generally, samples were injected into the apparatus at a temperature well below the bulk transition temperature (∆T ) -8 to -10 °C). Starting at this temperature, and then incrementing the temperature in steps of around 2 °C, force-distance profiles were measured upon approach and separation of the surfaces. The effect of temperature was studied by adjusting the temperature of the enclosure surrounding the SFA. Equilibration times of 12-18 h were allowed after each change in the temperature. The temperature was stable to (0.03 °C by separately controlling the experimental room temperature and the enclosure surrounding the SFA using PID temperature controllers. Control of the temperature to this extent eliminated much of the drift that can occur due to thermal expansion and contraction of the SFA. It should be emphasized that the bulk phase inside the SFA chamber remained in the sponge state at all times since the temperature was never allowed to reach TLR. If bulk phase separation does occur, then reequilibration back to the pure sponge phase is difficult as the sample cannot be conveniently mixed while inside the SFA chamber. The highest temperature used in the experiments for any sample was therefore around ∆T ) -2 °C. After taking measurements at ∆T ) -2 °C, the temperature was decreased, in steps of about 2 °C down to ∆T ) -8 or -10 °C, to check the reversibility of the system. Contact Position. The duration of an experiment was typically 1 or, at most, 2 weeks. To obtain reproducible results over this long period of time, it was important to avoid applying excessive loads to the surfaces that could damage the contact position. For all of the samples studied, comparison of the contact position in equilibrium surfactant solutions with that of bare silica in dry nitrogen indicated that both silica surfaces were coated with a weakly compressible layer. This is a wetting layer that most likely consists of a bilayer of surfactant separated (37) Stewart, A. M.; Christenson, H. K. Meas. Sci. Technol. 1990, 1, 1301. (38) Horn, R. G.; Smith, D. T.; Haller, W. Chem. Phys. Lett. 1989, 162, 404. (39) Horn, R. G.; Smith, D. T. Appl. Opt. 1991, 30, 59.

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Figure 2. Forces, F (normalized by the radius of curvature, R), as a function of the separation between two silica surfaces, D, immersed in pure sponge phases. Measurements for three different sample compositions are shown: (a) Φ ) 0.182, (b) Φ ) 0.135, and (c) Φ ) 0.090. The curves were measured upon approach (b) and upon separation (O, 0) of the surfaces at a temperature far from the respective LR/ L3 bulk transition. In (a) the minima of the L3 oscillations were measured using a separate approach/ separation cycle (0). The minima of the oscillations are superimposed on an exponentially attractive background (dashed line) with an order correlation length ξΨ (eq 1). Some parameters measured from the curves are summarized in Table 2. from the silica wall by a solvent layer in a structure similar to that which AOT forms on mica surfaces.40 The structure gave rise to a steep force barrier at separations of about 10-20 nm and could only be disrupted under high applied loads. Applying a large load to the surfaces and disrupting these layers was avoided until the very end of the experiment where the contact (40) Parker, J. L.; Richetti, P.; Ke´kicheff, P.; Sarman, S. Phys. Rev. Lett. 1992, 68, 1955.

wavelengths were remeasured. A damaged contact position was easily recognized by the observation of a large repulsive barrier, >1 mN/m, at variable surface separations independent of temperature. Presumably, this was due to resulting surface roughness and its effects on the neighboring surfactant solution, but no systematic study of this effect was performed. When a contact position became damaged, a new position had to be found by translating the surfaces with respect to one another and allowing time for reequilibration (around 12 h). Similar observa-

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tions concerning the state of the contact region were also noted by Horn et al. during their study on thermotropic liquid crystals14 and also by Moreau et al.15 The data presented below for each of the sponge samples were obtained using the same contact position over the whole temperature range studied. Materials. The AOT used throughout this work was obtained from Fluka (AG purum) and further purified using a method described in ref 32. Water was passed through a Krystal Klear reverse osmosis system, distilled once, and finally passed through a four-cartridge Milli Q-plus purification unit. The sodium nitrate (BDH, AnalaR grade) was dried in vacuo at 120 °C and stored in a desiccator prior to use.

Results L3 Regime. The results presented in Figure 2 were measured at a temperature far from the respective bulk phase transitions for the three membrane volume fractions studied. In Figure 2a,b spatially decaying oscillatory forces superimposed on a weakly attractive background are observed down to the steep force barrier near contact. The magnitude of the oscillations was always weak ( D*in at this temperature (∆T ) -4.5 °C). The force-distance profile shown in Figure 4c, measured at ∆T ) -2.5 °C, shows that the LR regime persists to very large surface separations (D*out . D*in). Here, the oscillatory profile of the LR regime can be traced using a single separation of the surfaces as no large jumps occur. However, some of these oscillations appear to be jumped over, but can be recovered using separate approach/separation cycles. Note also that the minima of the oscillations characteristic of the LR regime are superimposed on a background which is approximately linear with surface separation. This point will be discussed later (see Discussion). The trend D*out . D*in and the fact that the difference in these locations increases as ∆T increases both indicate that there is a hysteresis in the phase transformation signifying a firstorder phase transition induced by confinement. Similar trends with temperature were observed for the sample of volume fraction Φ ) 0.135 (Figure 5). The location of D*out was more distinct at this volume fraction as regions of spring instability were much reduced in magnitude. Once again, it was observed that both D*in and D*out moved to larger separations with increasing temperature. The hysteresis between D*in and D*out was again observed and increased with increasing temperature. Note that in Figure 5a, the surfaces were not pushed far beyond the position of the barrier at D*in. At a temperature closer to the phase transition (Figure 5c), the persistence of the LR regime at large separations was still observed even though the surfaces were separated just after penetrating the barrier at D*in. Hence, it was not necessary to reduce the surface separation all the way to the steep wall near contact to observe the regimes delimited by D*in and D*out; it was only necessary to initiate the LR by reducing the surface separation to D*in. Thus D*in marked the point of a transition which was reversed only when the surfaces were separated beyond D*out. The force-distance profiles measured for the most dilute sample (Φ ) 0.090) as shown in Figure 6 reveal trends similar to those previously observed. The oscillations of the L3 regime cannot be distinguished at this volume fraction (as in Figure 2c at lower temperature), but the position of D*in can be identified. In concordance with the more concentrated samples, D*in was seen to increase as the temperature approached TLR. Some difficulty was encountered in identifying the position of D*out as the LR oscillations were also quite weak. However, in Figure 6c when the temperature is close to TLR, the persistence of the LR regime quite obviously extends out to large surface separations. The structure of the LR regime only becomes apparent at around 120 nm and is then seen to propagate to large separations. However, the background force is quite low in contrast to the more concentrated samples (compare Figure 6c with Figures 4c and 5c). At this volume fraction the profiles measured upon separation did not

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Figure 7. Plot of ∆T versus 1/D*in where ∆T ) (T - TLR). The surface separation at which the LR regime is first observed upon approach of the two surfaces is denoted D*in and estimated at the position of the oscillation minimum in Figures 4-6 for each volume fraction: (b) Φ ) 0.182, (9) Φ ) 0.135, and (]) Φ ) 0.090.

superimpose very well with those measured on approach, at any of the measured temperatures. The estimated values of D*in are summarized in Figure 7 as a plot of ∆T versus 1/D*in for all of the membrane volume fractions studied. Lr Regime. For each of the samples studied, the LR regime was found to disappear only when the surfaces were separated beyond D*out. Thus if the LR regime is induced by reducing the separation below D*in, then its characteristic oscillations were observed regardless of the direction of movement of the surfaces, until the surface separation exceeded D*out. After separation of the surfaces beyond D*out, a subsequent force-distance profile measured on approach displayed the L3 regime up to D*in once again. Note that the same type of behavior has been observed in SFA experiments upon capillary condensation of a pure liquid from its vapor.41-43 At temperatures close to the bulk transition where the LR regime persists to large separations and many oscillations are seen, further characterization of the shape of the oscillation around the minima is possible. Analysis of the shape of the oscillations yields two parameters.44 First, the minima of each oscillation can be located and the periodicity of the LR regime is then given by the distance between consecutive minima. Alternatively, the position of each oscillation minimum can be plotted against the rank of each oscillation revealing dLR as slope of the lines shown in Figure 8. The minima of the characteristic LR oscillations for the samples at Φ ) 0.135 and Φ ) 0.090 were taken directly from Figure 5c and Figure 6c, respectively. Since, in both cases, not every minima from zero separation was measured, the absolute rank plotted in Figure 8 was estimated. However, the slope is not affected by the choice of the absolute rank since the rank for consecutive minima is always unambiguous. The most concentrated sample, Φ ) 0.182, required several approach/separation cycles to obtain the shape of each of the oscillations since some of the oscillations were often jumped over during a single separation cycle as seen in Figure 4c. About 10 of the oscillations were measured in this way, the minima of which have been plotted in Figure 8. For each volume fraction, the periodicity of the LR regime was constant as indicated by the straight line obtained and the results are summarized in Table 3. (41) Fisher, L. R.; Israelachvilli, J. N. J. Colloid Interface Sci. 1981, 80, 528. (42) Christenson, H. K. Phys. Rev. Lett. 1994, 73, 1821. (43) Crassous, J.; Charlaix, E.; Loubet, J.-L. Europhys. Lett. 1994, 28, 37. (44) Richetti, P.; Ke´kicheff, P.; Parker, J. L.; Ninham, B. W. Nature 1990, 346, 252.

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Figure 8. Location of the oscillation minima of the induced lamellar phase ranked from zero separation. The periodicity given by the slope is 19 ( 2, 25 ( 2, and 40 ( 3 nm, for Φ ) 0.182, 0.135, and 0.090, respectively. It is proposed that this periodicity arises from edge dislocations within the induced lamellar phase of Burgers vector, b ) 2.

The shape of the oscillations around their minima was found to be parabolic. However, there was a slight deviation from a parabola as the strain on the confined film increased during compression. This effect was also noted during measurements in the pure lamellar phase and has been discussed in ref 32. Following the analysis developed by Richetti and co-workers, the compressibility modulus B h for a lamellar phase can be obtained from the force-distance profile using the following relation;44

D2n(F - F2n) )B h (D2n - D)2 πR

(2)

Because the oscillations were superimposed on an attractive background, the fit is applied to the difference (F - F2n)/R, where F2n is the nonzero force at the minimum D2n. Data from each oscillation lie on a straight line of slope B h as shown in Figure 9. A complete description of this procedure has been given in ref 45. The value of B h is taken from the average of the slopes for each oscillation, and the uncertainty is the largest deviation from the mean value. The measured values of B h increase as the membrane volume fraction increases as shown in Figure 10. Also plotted in Figure 10 is the expected behavior of B h for a lamellar phase stabilized by undulation forces46 (see also Table 3). The theoretical curves in Figure 10 were calculated using the following equation assuming a range of different values for the membrane bending constant, κ:47

B h )

2 9π2 (kBT) d 64κ (d - δ)4

(3)

Discussion The SFA data presented have shown the presence of two different force regimes, the extent of each was dependent upon temperature and surface separation, in a single homogeneous fluid. This suggests that the thin film between the confining surfaces undergoes structural changes depending on the surface separation and the proximity of the temperature to the bulk transition temperature. Fluid Structure Near the Rigid Walls. A large force barrier was always observed at small surface separation, indicating that a weakly compressible structure had (45) Richetti, P.; Ke´kicheff, P.; Barois, P. J. Phys. II Fr. 1995, 5, 1129. (46) Helfrich, W. Z. Naturforsch. 1978, 33a, 305. (47) Roux, D.; Safinya, C. R. J. Phys. Fr. 1988, 49, 307.

formed on the surfaces. As already mentioned, this is most likely due to the presence of a surfactant bilayer structure that forms regardless of the temperature and state of the confined fluid. Note that AOT should not directly adsorb onto the negatively charged and hydrophilic silica interface (the pH of the sponge phase was around 6). The AOT bilayer should therefore be separated from the silica interface by a layer of the brine solvent. A similar surface structure has been invoked in other SFA studies using (negatively charged) mica surfaces40,48 on aqueous AOT solutions. For example, Parker et al. observed a large force barrier at small separation during a study of a dilute AOT micellar solution and explained it as the self-assembly of a surfactant bilayer near the surfaces separated by a solvent layer.40 In this study, the surfactant bilayers are already present in the bulk sample of sponge phase in random orientations. When the silica surfaces are immersed in the sample, the bulk sponge symmetry is broken at each silica wall, which can be considered quite flat since R . ξ. Rigid walls have a screening effect on the membrane undulations,49,50 and a bilayer would be expected to flatten out to contour each surface. In this picture, the adsorbed AOT bilayer and solvent layer are a surface wetting phenomenon rather than an effect of the confinement and would be present at all surface separations. Several features of the force-distance profiles lend support to this structure close to each silica wall. First, the location of oscillations observed in the L3 regime, as indicated by the minima, was commensurate with the location of the large force barriers at small separation rather than with the zero of separation (silica-silica contact). In other words, the structure responsible for the L3 oscillations extends from the wetting layers rather than from the bare silica walls. Furthermore, the large force barrier at small separations was always located at around the same surface separation for each AOT volume fraction as indicated by the constant negative y-intercept in Figure 3. Note that in many systems the refractive index can be used to estimate the thickness of layers adsorbed on the SFA surfaces as in the study by Parker et al.40 Unfortunately a similar measurement is not possible for the experiments presented here as there is virtually no difference in refractive index between the bulk sponge phase and the lamellar structure. However, we have recently performed independent scanning angle reflectometry measurements around the Brewster angle on sponge samples of similar composition in contact with a single macroscopic silica wall. The results, to be published elsewhere, were consistent with a layered surfactant structure on the wall.51 The L3 Regime. The L3 regime was characterized by a weak oscillatory force superimposed upon an attractive background. These characteristic features were most clearly seen at temperatures far from TLR, where the L3 regime was observed over the whole force-distance profile down to the steep force barrier near contact. Nevertheless the range of the attraction, the position of the oscillation minima, and their periodicity were observed to be independent of temperature. The fact that periodic oscillations were seen for a disordered isotropic fluid with only shortrange order indicates that the rigid walls break the bulk symmetry of the phase in the confined film and induce a (48) Chen, Y.-L.; Xu, Z.; Israelachvili, J. Langmuir 1992, 8, 2966. (49) Ke´kicheff, P.; Christenson, H. K. Phys. Rev. Lett. 1989, 63, 2823. Ke´kicheff, P.; Richetti P., Christenson, H. K. Langmuir 1991, 7, 1874. (50) Janke, W.; Kleinert, H.; Meinhart, M. Phys. Lett. B. 1989, 217, 525. (51) Ngankam, P.; Mann, E.; Ke´kicheff, P.; Antelmi, D. A.; Schaaf, P. To be published.

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Table 3. Characteristics of the Lr Regime for Each Sample Measured at a Temperature Close to the Bulk Transition Temperature, TLra Φ

TLR ((0.5 °C)

∆T (°C)

dLR (nm)

dideal (nm)

B h (J/m3) × 103

B h H (J/m3) × 103

0.182 0.135 0.090

28.5 28.0 29.0

-2.5 -2.0 -3.0

19 ( 2 25 ( 2 40 ( 3

10.5 14.2 21.2

17 ( 3 4.3 ( 0.8 1.7 ( 0.6

11 3.6 0.87

a The period of the oscillations, d , measured in the SFA (see Figure 8) is compared with the reticular spacing of the lamellar phase, LR dideal. The measured elastic compressibility modulus B h is compared to the prediction from the Helfrich formula, B h H, assuming κ ) 1kBT in eq 3 and neglecting any change in volume fraction when the induced lamellar phase appears.

local ordering which penetrates into the fluid film. The penetration length is expected to be related to the bulk correlation length of the sponge phase, ξ. Upon compression of the film, the oscillations arise due to the preordered fluid’s response to the strain imposed by the surfaces. The relation of the measured force-distance profiles, including the background force and the oscillations, to the known properties of the sponge phase will now be discussed. The Attractive Background Force. The attractive force upon which the L3 oscillations are superimposed can be understood by noting that the silica walls break the symmetry of the bulk sponge phase. A wetting layer of smectic structure forms and membrane fluctuations are reduced near the wall constituting an enhanced ordering of the sponge fluid. The degree of enhanced order decays back to the bulk order at some distance away from the silica surface. When the two identical silica surfaces oppose each other separated by some distance D, the profile of the order parameter (Ψ) will therefore be symmetric, with a maximum at the rigid boundaries and minimum at the midplane. A related situation has been previously analyzed by Marcˇelja and Radic´ for the ordering of water molecules at opposing lecithin bilayers.12 In that case the orientation of the water molecules gives an antisymmetric distribution of the order parameter and it was shown that an exponentially repulsive free energy profile between the interfaces resulted, with a decay length reflecting the decay of the order parameter. Similarly, in the present work the decay length, ξΨ, extracted from the fits of Figure 2a-c is an order parameter correlation length indicating how the enhanced order in the confined sponge film decays away from the surfaces back to the bulk value. However, the order parameter distribution is symmetric and the interaction is attractive for the sponge system presented here. The same effect has been observed in several other SFA studies on simple and complex fluids confined between rigid symmetric boundaries.14,15,52 Conversely, an overall repulsive interaction has been observed when asymmetric boundary conditions were imposed.16 The physical origin of the order parameter Ψ in the present system seems straightforward to define. A smectic order parameter is tempting given that ultimately the confined film transforms to a lamellar structure. However, the periodicity of the L3 regime seems to be related to the sponge structure, observed as approximately 2ξ, rather than the lamellar structure. Nevertheless the induced ordering at the interfaces may still be thought of as a prelamellar order where the sponge cells are positioned perpendicular to the silica surfaces. At this point the sponge cells have not yet melted together to form the lamellar phase. The force-distance profiles generated by such an induced one-dimensional ordering have been addressed by de Gennes13 and measured by Horn et al.14 and Moreau et al.15,16 Note that the order parameter decay length measured here is the same order as the correlation length describing the fluctuations of the inside and outside (52) Horn, R. G.; Israelachvili, J. N. Chem. Phys. Lett. 1981, 75, 1400.

subvolumes of the bulk sponge phase measured in light scattering experiments. This length measures the spatial correlation between the sponge cells.53-55 The Periodicity of the L3 Regime. The oscillations of the L3 regime can be interpreted as the elastic response of a preordered film of sponge fluid to the strain imposed by the two approaching rigid surfaces. The induced ordering is a positional ordering which implies that a finite number of layers, having an equilibrium thickness, make up the confined fluid film. When the surface separation is not commensurate with the equilibrium thickness of the ordered film, the layers are in either a compressed or stretched state. However, the confined fluid film is in equilibrium with a reservoir of bulk sponge fluid, allowing layers to be expelled from, or incorporated into, the gap between the surfaces. In so doing the elastic stress due to the distortion is relieved. The number of layers therefore changes according to the surface separation and each oscillation corresponds to an integral number of ordered layers. The energy minimum of each oscillation indicates the surface separation at which all the confined layers are undistorted. Changing the surface separation then increases the free energy to the point where a relaxation mechanism causes material to be removed or introduced in the confined region. The elastic stress and the relaxation mechanism together define the amplitude, periodicity, and shape of the oscillations. The literature is rich with similar examples of oscillatory force-distance profiles arising from surface-induced preordered fluid films. The phenomenon has been observed with simple liquids,52 colloidal solutions,56 polyelectrolyte solutions, and liquid crystals.14,15 In contrast, the oscillations of the L3 regime described here exhibit two unusual features. First, the periodicity is twice the characteristic size of the bulk sponge phase, and second, the oscillations occur at overall negative values of F/R. That is, the elastic stress is not enough to compensate the attractive background due to the symmetric distribution of the induced order. That dL3 was twice the characteristic size of the sponge possibly originates from the symmetric nature of the bicontinuous sponge structure. No symmetric/asymmetric transition has been identified in the AOT/brine system, and it is assumed that all the sponge samples studied here were symmetric. The symmetric nature of the sponge requires that the volume fractions of the inside and outside subvolumes remain equal. Therefore, during approach of the SFA surfaces, the free energy would be minimal only when the surface separation is an integral multiple of 2(nξ + ts), where n is the number of sponge cell pairs confined between the surfaces and ts is the thickness of the membrane/solvent wetting layer adjacent to each silica surface. As the surfaces approach each other from large (53) Roux, D.; Cates, M. E.; Olsson, U.; Ball, R. C.; Nallet, F.; Bellocq, A. M. Europhys. Lett. 1990, 11, 229. (54) Coulon, C.; Roux, D.; Bellocq, A. M. Phys. Rev. Lett. 1991, 66, 1709. (55) Vinches, C.; Coulon, C.; Roux, D. J. Phys. II Fr. 1994, 4, 1165. (56) Richetti, P.; Ke´kicheff, P. Phys. Rev. Lett. 1992, 68, 1951.

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Figure 9. The compressibility modulus of the induced lamellar stack may be extracted from the slope of (F - F2n)D2n/πR vs (D2n - D)2 using the Derjaguin approximation, where F(D)/2πR is the elastic energy density of the nth parabola centered at (D2n, F2n/2πR) (2n bilayers at zero stress confined in the gap). The measurements are made during dilation of the surfaces when the temperature is close to the bulk transition temperature as in Figures 4c, 5c, and 6c (i.e., D*out is located at large surface separations). (a) Φ ) 0.182, (b) Φ ) 0.135, and (c) Φ ) 0.090.

separation, the free energy increases as soon as D < 2(nξ + ts). The strain is eventually released by moving a pair of cells maintaining the overall inside/outside symmetry. This process repeats until all the sponge cells are removed from the confined film, giving the observed oscillatory force-distance profile. The precise mechanism by which the sponge cells are expelled from (or introduced into) the confined region,

during the relaxation mechanism, is not understood, and a model to account for the magnitude of the L3 oscillations has not been attempted. However, the magnitude of the oscillations should be related to the interaction between the preordered sponge cells and the results show that the magnitude of this interaction decreases as the sponge phase becomes more dilute. This is in agreement with scattering studies where an increase in small-angle

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Figure 10. Measured compressibility modulus, B h , of the induced lamellar phase (extracted from Figure 9) plotted against dLR/2, i.e., the measured reticular distance. The behavior expected from the Helfrich approximation is compared where the value of κ in eq 3 is 0.5kBT (dotted line), 1kBT (solid line), and 3kBT (dashed line).

scattering upon dilution indicates an increase in the compressibility of the sponge. Theoretical models show that the increase in the compressibility of the sponge phase scales as Φ-3.19,57 The L3 to Lr Phase Transition. The link between the force-distance profiles and the state of the confined fluid film is summarized in Figure 11 (for ∆T > -8 °C). After the transition at D*in, the induced lamellar phase exists in a central droplet surrounded by the bulk sponge phase and is directly analogous to the capillary condensation of simple liquids from their vapors.41-43 Similar capillary condensates of lamellar structure have also been observed in bicontinuous microemulsions58,59 and micellar phases.60 In all cases, including the sponge system presented here, a linear attractive profile is observed as soon as the condensation takes place (at D*in). This attractive interaction is controlled by the interfacial tension of the sponge/ lamellar interface, γ|, and the energy of condensing a finite volume, V, of lamellar phase from the bulk phase. Before the L3/LR transition, the adsorbed surfactant layers that wet the silica surfaces share an interface with the L3 phase, which fills the remainder of the gap. During the transition a finite area, A, of this interface is annihilated, constituting the gain in free energy γ|A. However, a volume V of sponge phase is transformed to the lamellar phase constituting the loss of free energy µV, where µ is the difference in chemical potential between the two phases. As derived by several authors, the resulting interaction between the two crossed cylinders can be written:58-60

(

)

D - 2ts F ) -4πγ| 1 R 2RK

(4)

where the range of the interaction is RK ) γ/µ, otherwise referred to as the Kelvin radius. The parameter ts is the thickness of smectic layer wetting each surface before capillary condensation. (57) Porte, G.; Delsanti, M.; Billard, I. J. Phys. II Fr. 1991, 1, 1101. (58) Petrov, P.; Olsson, U.; Wennerstro¨m, H. Langmuir 1997, 13, 3331. (59) Moreau, L.; Barois, P.; Richetti, P. In Supramolecular Structure in Confined Geometries; ACS Symposium Series 436; Manne, S., Warr, G. G., Eds.; Oxford University Press: London, 1999; Chapter 4. (60) Freyssingeas, E.; Antelmi, D. A.; Ke´kicheff, P.; Richetti, P.; Bellocq, A. M. JEPB 1999, 9, 123.

Figure 11. Schematic diagram showing the confinementinduced L3 to LR transition and corresponding force-distance profile at constant temperature (T < TLR). Beginning at large D, the sponge phase exists between the surfaces giving rise to the L3 regime upon approach of the surfaces. The shaded region represents the LR phase which is the preferred wetting phase. The confined fluid film transforms to the lamellar phase at a well-defined separation, D*in, and exists in a central droplet surrounded by the sponge phase. The lamellar droplet reverts to the sponge state only after separating the surfaces beyond D*out. Two distinctive oscillatory force profiles are observed depending on the state of the fluid film allowing the transition to be seen.

A second contribution to the free energy must be taken into account since the induced phase is a lamellar phase. As discussed in ref 45, the stack of induced layers experiences an elastic stress in order to match the imposed surface separation. The resulting force between the crossed cylinders is

(D - D2n)2 F ) πB h R D2n

(5)

and the overall interaction between the macroscopic surfaces confining the droplet of induced lamellar phase is59,60

(

)

D - 2ts (D - D2n)2 F ) -4πγ| 1 + πB h R 2RK D2n

(6)

Equation 6 indicates that the force-distance profile for a confined droplet of lamellar phase surrounded by a bulk phase is a set of regularly spaced parabolic oscillations whose minima fall on a linear attractive background. Note that strict linearity is not valid for separations D ∼ 2RK, as evidenced in Figure 4c, since the droplet curvature becomes small in this limit. At D ) 2RK the capillary condensate is metastable, and at larger separations (D > 2RK), it is no longer thermodynamically favorable for the lamellar droplet to exist. The first-order nature of the transition is clearly evidenced in the force-distance profiles. First, the onset of the LR regime is abrupt, and second, significant hysteresis is seen between D*in and D*out. The plot of ∆T versus 1/D*in in Figure 7 shows a fairly linear trend as

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Table 4. Characteristics of the Background Attraction of the Lr Regime for the Sponge Sample at Φ ) 0.182 for Different Temperaturesa ∆T (°C)

F/R intercept (mN‚m-1)

γ| (mN‚m-1)

2RK (nm)

-2.5 -4.5 -6.5

-0.36 -0.33 -0.32

0.026 0.022 0.020

220 110 75

a The interfacial tension γ and maximum stability range 2R | K are given by eq 6 using 2ts ) 20 nm. Values are measured from Figure 4.

expected for a first-order surface-induced transition.6,11,61 Recall that D*in is restricted to values that can accommodate an integral number of smectic layers. Moreover, the observation of Burgers vectors of 2 in the LR regime suggests that the smallest allowed increase in D*in should be 2n smectic layers. Equation 6 is of further significance since it allows an estimation of the interfacial tension of the LR/L3 interface from overall linear attractive background observed in for the LR regime. A linear fit according to eq 6 has been performed for the sponge sample at Φ ) 0.182, and an example is shown by the dashed line in Figure 4c. The results for three different temperatures are summarized in Table 4. Unfortunately the surface tension at the lower volume fractions could not be made with any certainty since the LR regime was less well defined due to the sensitivity of the technique. The results in Table 4 indicate that the surface tension is essentially constant over the temperature range studied. The Kelvin radius RK, however, increases significantly as the temperature approaches the bulk phase transition temperature TLR as expected since µ decreases as the bulk transition is approached. The L3/LR interfacial tension measured in this work is comparable to the interfacial tension of the microemulsion/ LR58,59 and L1/LR phases60 measured using SFA forcedistance profiles. Only a few other techniques have been able to measure such low interfacial surface tensions (for example, ref 62-64). Of particular note is the study of Quilliet et al. in which the L3/LR interfacial tension was measured using optical microscopy.63,64 A value of 10-4 mN‚m-1 was found for the component of the surface tension where the lamellae meet the L3/LR interface obliquely (the angle measured was 75° rather than 90°, which is thought to arise from epitaxy at the interface64). Hence their value is 2 orders of magnitude lower than the value presented here, but in our SFA experiment, the perpendicular component of the interfacial tension, γ⊥, is negligible and the resulting measured interfacial tension is primarily that of the interface where the lamellae of the induced LR phase are essentially parallel to the L3/LR interface contouring the silica surfaces. The two results indicate that γ⊥ , γ| as expected. Finally, we point out that the transformation of the confined fluid film does not affect the optical measurement of the surface separation. The lamellar phase is induced between the surfaces homeotropically and is aligned throughout its whole thickness. In the SFA used here, the light passes through these aligned layers normally, or parallel to the director of the membranes, and hence the bulk anisotropy of the lamellar phase does not interfere (61) Milner, S. T.; Morse, D. C. Phys. Rev. E 1996, 54, 3793. (62) Aveyard, R.; Binks, B. P.; Lawless, T. A.; Mead, J. Can. J. Chem. 1988, 66, 3031. (63) Quilliet, C.; Kle´man, M.; Benillouche, M.; Kalb, F. C. R. Acad. Sci. Paris 1994, 319, 1469. (64) Quilliet, C.; Blanc, C.; Kle´man, M. Phys. Rev. Lett. 1996, 77, 522.

with the interferometry. Furthermore, the refractive indices of the sponge phase and the lamellar phase do not differ significantly. The ordinary refractive index for the aligned lamellar phase can be calculated from the refractive index of the membranes and their volume fraction using the procedure detailed in ref 49. Following this approach, an induced lamellar phase of volume fraction of Φ ) 0.135 will have a refractive index of around 1.35 (taking the refractive index for AOT membranes as 1.48, known from light scattering studies65). The refractive index of the bulk sponge phase, measured with an Abbe-type refractometer, was found to be 1.3552 at Φ ) 0.135. Since the two refractive indices are similar, no discontinuities in the FECO are seen. By contrast, strong FECO discontinuities are seen upon the condensation of liquids from their vapor phase in the SFA, which can be useful in estimating the curvature radius of the capillary condensate.41 The Lr Regime. The oscillations of the LR regime appeared at locations roughly independent of the temperature, and it was concluded that their increasing number with temperature was the signature of a thickening film of fluid with LR structure. The relation of these oscillations to the LR structure is further supported by the parabolic shape of the oscillations around the minima, which is the expected profile for the elastic response of a stack of interacting layers aligned homeotropically between two rigid walls.44,45 In addition, the measured compressibility modulus B h agreed well with the value predicted by the Helfrich approximation for a lamellar phase stabilized by undulation forces, eq 3. In Figure 10, eq 3 gave the best fit for the data when the value of the membrane bending constant κ was around 1kBT. However, scattering studies on the AOT/brine system, using various theoretical models for the lamellar phase, have given higher values for κ. Skouri et al. and Daicic et al. have both reported values of around 3kBT.34,65 Given that only three membrane volume fractions were measured in this study, it is not possible to fit the curve shown in Figure 10 to obtain a conclusive value for κ. However, these results, which are a direct measure of B h , are consistent with low values for the membrane elastic constant, κ, as expected for a system stabilized by undulation forces. Note that the periodicity of the oscillations in the LR regime, dLR, was approximately twice the reticular spacing, dideal, for a lamellar sample of the same membrane volume fraction. This suggests that the stack of membranes responds to the applied strain by removing (or adding) two smectic layers. The corresponding defect is an edge dislocation with Burgers vector of magnitude equal to 2. This defect can be seen as a handle joining two membranes and therefore arises naturally from the topology of the neighboring sponge phase. Note that dLR is not exactly 2dideal but about 5-10% lower, that is, between 1.8 and 1.9d. The slightly lower value measured for dLR, compared to 2dideal, probably arises since the oscillations are superimposed on a strong background attraction, and hence, the minima of the oscillation does not strictly represent the unstressed equilibrium spacing of the lamellar stack. At small surface separations screening of the membrane undulations by the two rigid surfaces would also tend to reduce the average intermembrane spacing. This has been previously predicted50 and observed experimentally in other lamellar systems using a SFA49 but is only significant for the first one or two oscillations next (65) Daicic, J.; Olsson, U.; Wennerstro¨m, H.; Jerke, G.; Schurtenberger, P. Phys. Rev. E 1995, 52, 3266. (66) Roux, D.; Nallet, F.; Freyssingeas, E.; Porte, G.; Bassereau, P.; Skouri, M.; Marignan, J. Europhys. Lett. 1992, 17, 575.

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to the silica walls. Alternatively, the reduction in dLR may be explained if the volume fraction of the induced LR phase is slightly lower than that of the bulk L3 phase. In other words, this situation would correspond to a tie line between the L3 phase and the induced LR phase that is not completely vertical, with respect to membrane volume fraction, in the corresponding phase diagram. Such a phenomenon is reasonable as the chemical potential is constant at the phase transition, but not necessarily the membrane volume fraction between the two phases. Conclusions The data presented in this work showed that confinement of a sponge phase between two rigid macroscopic walls can lead to a first-order phase transition to the lamellar phase. These conclusions were based upon the observation of two distinct force regimes in the forcedistance profile, called the L3 regime and the LR regime. Performing the measurement over a range of temperatures showed that the extent of each regime is dependent on the surface separation and on the proximity of the temperature to the LR/L3 bulk transition temperature. The first-order nature of the transition was established by the observation that the LR regime occurs at well-defined surface separations; that is, the force profile transits discontinuously from the L3 regime to the LR regime. Furthermore, the data showed a lag in the transformation from the LR phase back to the L3 isotropic phase upon separating the surfaces. The first-order nature of the transition is further emphasized by the increases in the hysteresis between D*in and D*out as the temperature approaches the bulk transition temperature. The periodicity of the oscillations observed in the L3 regime were about twice the characterisitic cell size expected for the bulk sponge phase. It was suggested that

Antelmi et al.

this occurs to maintain the bicontinuous symmetry of the phase by moving pairs of basic sponge units when a strain is applied to the system by the confining walls. Likewise, the oscillations observed in the LR regime result from edge defects of Burgers vector equal to 2 within the induced lamellar phase. This observation suggests that the defects in the lamellar phase are strongly linked with the topology of the neighboring sponge phase since such a defect is essentially a handle joining two membranes. Further characterization of the induced lamellar phase allowed its elastic compressibility modulus to be measured, which showed good agreement with Helfrich theory and with measurements on bulk pure lamellar phase at the same volume fractions.32 The results suggested that the value of the bending constant κ is around 1kBT for the induced lamellar phase, a slightly lower value than that inferred in scattering studies. Finally, the capillary condensation of the lamellar phase upon confinement gave rise to a linear attactive force between the surfaces that was used to extract the L3/LR interfacial tension. The value found was comparable to that of lamellar phase and microemulsion interfaces or lamellar and micellar interfaces. The force-distance profile due to the confinement-induced phase transitions therefore provides a powerful method to evaluate the interfacial tension between two closely related mesophases. Acknowledgment. The authors thank Thomas Zemb for allowing us to use the SAXS facility of the Service de Chimie Moleculaire, CEN Saclay. We also thank Eric Freyssingeas and Stephen Hyde for many fruitful discussions. LA9903191