VOLUME 62, NUMBER 3 PHYSICAL REVIEW LETTERS Dynamic Light Scattering Study of Dilute Lamellar Phases 16 JANUARY 1989 F. Nallet, ' D. Roux, ' and J. Prost ' Centre de Recherche Paul-Pascal, Domaine Universitaire, 33405 Talence CEDEX, France Ecole Superieure de Physique et de Chimie Industrielles, l0 rue Vauquelin, 75231 Paris CEDE 05, France (Received 22 August 1988) Dynamic light scattering measurements on oriented samples of lyotropic smectics have been per- formed. The layer compressibility modulus B is extracted from the anisotropic dispersion relation of the so-called slip mode, which arises from the coupling between concentration and layer displacement Auc- tuations. The samples are diluted with three different solvents (repeat distances 50 to 800 A): The be- havior of B suggests either undulation or electrostatic repulsions between membranes, depending on the swelling solvent. PACS numbers: 61.30. — v, 62.90.+k, 82. 70.Dd A lot of interest is currently focused on the under- standing of the physics of fluctuating surfaces. ' In the absence of surface tension, deformation of surfaces is governed by elastic bending energy. Thermal fluctua- tions leading to undulations of the membrane may have important consequences when the bending modulus is of the order of kaT. Dilute lamellar phases are particularly interesting systems for the study of fluctuating surfaces. Indeed, in some favorable cases, multimembrane lyotrop- ic smectics with repeat distances of hundreds and even thousands of angstroms can be prepared with addition of suitable solvents. It has been recently demonstrated that in many cases these extreme dilutions result from the existence of a universal repulsive interaction due to the steric hindrance to thermal fluctuations. ' This purely entropically driven interaction first proposed by Helfrich is long range and keeps the layers apart even for such large distances. These dilute lamellar phases are also a unique example of colloidal smectics. The very large repeat distances one can obtain are responsi- ble for very low elastic constants. The layer compressi- bility modulus 8 may vary continuously over about 6 or- ders of magnitude along the dilution range and the layer bending modulus over 2 orders of magnitude. We have carried out a dynamic light scattering study of lamellar samples derived from a unique basic system but located on three distinct dilution paths. The system consists of a concentrated lyotropic smectic (repeat dis- tance about 40 A) of water-pentanol-SDS (sodium dode- cyl sulfate). It has been swollen by (1) a mixture of dodecane and pentanol ("oil dilution" ), (2) a 0.4M sodi- um chloride solution in water (" brine dilution" ), and (3) pure water ("water dilution" ). The limiting repeat dis- tances that can be obtained are 460, 800, and 80 A, re- spectively. These three dilution paths have been previ- ously investigated by a high-resolution x-ray tech- nique. ' However, because of experimental limitations, x-ray experiments have been restricted to repeat dis- tances smaller than 200 A. Here, our light scattering method allowed us to get data through the whole dilution range. We recall the theoretical basis of the hydrodynamics of a two-component smectic-3 liquid crystal, due to Bro- chard and de Gennes. In addition to the classical six modes of an ordinary (one-component) smectic A, an ad- ditional mode (called the slip mode in Ref. 8) comes into existence for lyotropic systems, arising from the coupling between concentration (a conserved quantity) and layer displacement (a broken symmetry variable). These seven modes may be sorted into two groups: a "high- frequency, " four-mode group which comprises sound, a thermal wave, and a shear wave; a "low-frequency, " group of three modes, the slip mode and second sound, with highly anisotropic properties (the second sound de- generates into an undulation mode and a shear wave when the wave vector q is parallel to the layers, or into a permeation mode and a shear wave when q is normal to the layers). In the high-frequency group there is essen- tially no coupling to layer displacement nor to concentra- tion fluctuations and thus little scatter of light. On the other hand, all three modes of the low-frequency group may, in principle, be studied by light scattering. Whereas the second sound is propagative (when q is ob lique), the slip mode is always diff'usive; its anisotropic dispersion relation has two simple limiting expressions. (i) When q is parallel to the layers, the relaxation fre- quency co is given by co=pD33q, where p is a dissipa- tive coefficient, D33 is the inverse of the osmotic compressibility, and q is the modulus of the wave vector. In this limit, concentration and layer displacement Auc- tuations get uncoupled and the slip mode degenerates into the usual mutual diA'usion mode of a two-component system. The slip mode has been experimentally observed in this geometry by Chan and Pershan. (ii) When q is oblique with respect to the layers, co = p =q &, where q & is the modulus of the projection of q along the layers, and:- is a reactive coefficient which reduces to B, the layer compressibility modulus at con- stant chemical potential, in the limit B/D33«1. The spectral analysis of the light scattered by the slip mode 276 1989 The American Physical Society