Diffusion Coefficients in a Lamellar Lyotropic Phase: Evidence for Defects Connecting the Surfactant Structure

Abstract

We measure diffusion coefficients in the lamellar phase of the nonionic binary system C12EO6/H2O using fluorescence recovery after photobleaching (FRAP). The diffusion coefficient across the lamellae shows an abrupt increase upon approaching the lamellar-isotropic phase transition. We interpret this feature in terms of defects connecting the surfactant structure. An estimation of the defect density and of the variation in defect energy close to the transition is given in terms of a simple model. PACS numbers: 61.30.Jf, 64.70.Md, 66.30.Jt Topological defects are very important in condensed matter. In solids, most of the defects are out of equilibrium and form during growth or plastic deformation. In soft matter, like liquid crystals, defects sometimes nucleate spontaneously in great number. In this case, they often announce the transition towards a phase of higher symmetry.Defective lamellar phases of lyotropic systems belong to this category. They contain structural defects that can be point-like or linear (dislocations). Unlike textural defects (e. g. focal conics), they are not visible in optical microscopy but they can be investigated using techniques such as FFEM (freeze-fracture electron microscopy) [1][2][3][4][5] For instance, in lamellar phases, three elementary point defects are possible: "pores", "necks", and "passages" [13]. Necks connect the non-polar medium (surfactant structure) ( fig.1a), pores (fig.1b) connect the polar medium (water), whereas passages join both media ( fig.1c). Screw dislocations are also frequent because their energy is low [14]. These defects also connect both media and their core may be filled with the polar or the non-polar medium.In this Letter we present a method of determining the topology of defects by monitoring the variation of the diffusion coefficients parallel D and perpendicularly D ⊥ to the director (normal to the layers) of fluorescent probes that are dissolved either in the polar medium or in the non-polar one.The system chosen is the lamellar phase of the lyotropic mixture of the non ionic surfactant C 12 EO 6 with water. Spin-labeling measurements [7] have shown the existence of highly curved defects, the density of which abruptly increases a few degrees before melting. Dislocation loops perpendicular to the layers have been observed in FFEM [1, 2] ,but they can only account for a small fraction of the total defect density. In the following we present experimental results showing the existence of point defects. We confirm the existence of pores [7], and we also show that necks appear close to the lamellarisotropic transition. We have first investigated the evolution of the diffusion coefficients for a fluorescent and hydrophobic dye. If D ⊥ (parallel to the layers) must not be significantly affected by the defects, D (across the layers), which is very small for a perfect structure (the molecule has to cross a water barrier), should dramatically increase if the defects connect the surfactant structure. We performed these measures on planar domains (director ...

Tracer Diffusion in a Dislocated Lamellar System

“…(12) in a lamellar phase of a lyotropic surfactant can be estimated by taking D ϳ 10 210 m 2 ͞s and d ϳ 50 Å from Ref. [18] to obtain fractions of a microsecond. In diblock copolymer systems, this prefactor is about 1000 times larger.…”

Connectivity of the Hexagonal, Cubic, and Isotropic Phases of the C12EO6/H2O Lyotropic Mixture Investigated by Tracer Diffusion and X-ray Scattering

“…Indeed, it is reasonable to assume (as demonstrated by the experimental results below) that the tracer is confined to the surfactant cylinders and spends very little time in water. Hence, its diffusion must give valuable structural information about the surfactant aggregates, as we have shown in a recent investigation of the lamellar phase in the C 12 EO 6 /H 2 O system [17]. Two transitions were investigated : the H α → I at the azeotropic point of the hexagonal phase (50.0 % C 12 EO 6 weight concentration) and the V 1 → I (concentration 59.0 %).…”

Effects of Electric Fields on Block Copolymer Nanostructures

“…Such bridges allow chain transport in the direction orthogonal to the PS-PMMA interface without crossing it. This kind of point defect was observed in the lyotropic lamellar liquid crystal phase [38,39], and very recently in cylinderforming block copolymer films with sufficient chain mobility [37]. After further annealing, the bridges between ordered lamella are annihilated (Fig.…”