J. Phys. Chem. B 1997, 101, 8169-8179
8169
Measurement of the Compressibility Modulus in a Lyotropic Lamellar Phase Stabilized by Undulation Forces David A. Antelmi*,† and Patrick Ke´ kicheff‡ Department of Applied Mathematics, Research School of Physical Sciences and Engineering, Australian National UniVersity, Canberra ACT 0200, Australia, and Institut Charles Sadron, Centre Nationalla de Recherche Scientifique, 6 rue Boussingault, 67083 Strasbourg Cedex, France ReceiVed: May 7, 1997X
Lamellar mesophases of the anionic double-chain surfactant AOT in brine were oriented homeotropically between two smooth silica surfaces of a surface force apparatus (SFA). The force-distance profile was measured at different membrane volume fractions (Φ )0.09-0.18) all close to the sponge/lamellar phase boundary in the phase diagram. Oscillatory profiles were consistently observed with the same characteristic features. The periodicity of the oscillations was twice the reticular spacing of the bulk lamellar phase, indicating that the lamellar stack responds to the applied strains by creating edge dislocations of Burgers vector 2. Such a defect is topologically equivalent to a handle joining two membranes and arises naturally from the topology of the neighboring sponge phase. The compressibility modulus at constant chemical potential, B h , was extracted from the parabolic shape of the force oscillations and was found to be consistent with an intermembrane interaction dominated by undulation forces.
Introduction Of the large variety of self-assembled surfactant structures, membrane phases are among the most studied. One reason for this is that surfactant membranes provide a well-defined system for the study of the physical properties of biological membranes. Much emphasis has been placed on characterization of the elastic properties of the membranes which play a major role in determining the intermembrane interactions and the overall topology assumed by the membrane.1-10 From this it follows that the elastic properties of the membranes greatly influence the overall bulk structure of a membrane phase. One notable example which has received considerable attention recently is the sponge/lamellar system. Both the sponge phase (L3) and lamellar phase (LR) are membrane phases with similar local structures but different global organizations.1,11 The membranes that make up the lamellar phase remain flat on average and are stacked in one dimension with a smectic order. In the sponge phase the membranes are curved and interconnected, forming local saddle-like shapes giving an overall random bicontinuous structure with many pores or passages.1,11 In practice the topological transformation between the sponge and the lamellar phase may be brought about by variations in the components of the system, adjusting the salt or cosurfactant composition in particular, or by adjusting the temperature, as evidenced in the many phase diagrams now available in the literature (for example refs 6, 12-16). The geometry in which the sponge phase exists is also important, and experiments have shown that the sponge to lamellar transition can be induced upon confining a pure sponge phase between rigid walls.17-19 This phenomenon is an example of a surface-induced phase transition where the lamellar phase is the preferred wetting phase. Using the surface force apparatus (SFA),20,21 the sponge/lamellar transition was quantified for the system AOT/brine and shown * Corresponding author. Present address: CEA Saclay, Equipe Mixte CEA-Rhoˆne Poulenc, Service de Chimie Mole´culaire, Baˆt 125, 91191 Gif Sur Yvette, France. Email:
[email protected]. † Australian National University. ‡ Institut Charles Sadron. X Abstract published in AdVance ACS Abstracts, September 1, 1997.
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to be first order in nature, analogous to the capillary condensation of simple liquids in narrow pores.18 The sponge phase was found to exist in such a confined geometry until the separation between the walls was reduced to a threshold separation D*in.18 At this point the structure of the fluid confined between the walls transformed to the lamellar structure. This induced lamellar phase was stable until the two walls were separated beyond another threshold separation D*out (D*in < D*out), at which point the sponge structure was recovered. In the regime of lamellar phase stability, certain elastic properties of the induced lamellar phase were measured.18 The compressibility modulus was found to be consistent with that expected for a stack of lamellae stabilized by undulation forces. Furthermore, edge dislocations within the induced lamellar phase were always observed to have a Burgers vector of magnitude equal to 2. Such a defect can be seen as a handle joining two neighboring membranes arising naturally from the topology of the sponge phase from which the lamellar phase condensed.18 In this article we present complimentary measurements using the SFA on samples in the pure lamellar phase of the same surfactant system and compare these results to those measured previously on the lamellar phase induced from the sponge phase.18 The SFA technique used in this study gives a measure of the compressibility modulus directly from the force-distance profile, and the data obtained can also be compared to similar measurements in systems where a neighboring sponge phase was absent.22-24 To begin, a brief description of the relevant parameters characterizing a lamellar phase will be given followed by a description of the way the SFA can be used to directly measure some of these parameters. For a lamellar phase to be stable, there must be a repulsive interaction between the membranes to prevent the collapse of the smectic ordering under the influence of attractive van der Waals forces. At short range (
