Effect of shear on lyotropic lamellar phases

Some years ago, in studying the effect of shear on lyotropic lamellar phases, a new hydro- dynamic instability was described [20-241 .This instability leads to a phase of multilamellar vesicles compactly packed in space (the so-called onion tezture). Evidence for the struc- ture of this metastable phase and some dynamics properties such as the viscoelasticity are described in what follows. In the current section, we will briefly describe the basic experimental facts leading to the formation of the onion texture. Then, we will give some details of its viscoelastic behaviour (Section 4) and develop the theoretical description of the lamellar-to-onion transition (Section 5).

As discussed above, a lyotropic lamellar phase is made of surfactant and water (Fig-

190 Didier Roux

ure 2), and sometimes contains an additional hydrophobic component (oil). It is a very common phase, most often found for relatively high concentration of the surfactant [l], while in certain special cases, very dilute lamellar phases can be prepared due to long range repulsive interactions between membranes [25]. The symmetry of the phase is that of a ‘smectic A’ in the nomenclature of the liquid crystalline phases. When present, the hydrophobic compound swells the bilayers. In all the cases, the lamellar phase behaves macroscopically as a viscous liquid whose viscosity varies tremendously depending upon the formulation, and also (because of uncontrolled defects in the packing) on the Sam- ple preparation [23, 261. Upon dilution with extra water, two main behaviours can be described [25]. The dilution of the lamellar phase is limited either by a phase transition to an isotropic liquid phase (micellar phase or sponge phase) or by a phase transition to another liquid crystalline phase. In a limited number of interesting cases the lamellar phase reaches a maximum uptake of water and subsequently phase coexists with excess (virtually pure) water. This arises whenever phospholipids are used as the surfactant.

3.1 Shear diagrams

To understand the effect of flow on such phases, we have studied using rheophysics meth- ods the structure of lyotropic smectic A phases submitted to a simple shear (Figure 3).

Using a number of structural probes under shear, such as scattering techniques (light scattering ^[21], neutron [22], X-ray [27]; see Pine, this volume) or dielectric measure- ments [28], it was possible to show that the effect of shear can be described using a shear diagram. This diagram, which can be considered as a generalisation of the phase diagram for out-of-equilibrium systems, describes the effect of shear as a succession of station- ary states of orientation separated by dynamic transitions. Indeed, while always staying thermodynamically within the stable lamellar phase, the sample experiences a series of transitions modifying the orientation of the lamellae with respect of the direction of the shear. These different orientations correspond to differing spatial organisations and den- sities of the topological defects that are anyway present in most smectic samples. Each transition thus brings a modification of what is named the texture of the phase. Conse- quently, it is not a traditional phase transition but has to be viewed as an instability. It is different, however, from the classical hydrodynamic instabilities observed when a fluid is submitted to shear (convection rolls, etc.) because the resulting texture involves no length scale directly related to the size of the shear apparatus. Instead, structure forms on some microscopic (micron) length scale related to the intrinsic properties of the fluid.

Shear gradient

Velocity Vorticity

Figure 3. Characterisation of the g e o m e t y of a simple shearflow. The orientations that the membranes of a lamellar phase adopt under shear are described using this geometry.

Equilibrium and flow properties of surfactants in solution 191

Figure 4. Representation of the shear diagram of a typical lamellar phase (made of water, dodecane, pentanol, sodium dodecyl sulphate). T h e horizontal axis represents the concentration of dodecane (the bilayers are swollen upon addition of dodecane), which f i e s the characteristic distance d between the lamellae, and the vertical axis represents

the shear rate.

Figure ⁴ is a schematic representation of the shear diagram obtained in the case of a lamellar phase made of water, dodecane, pentanol and sodium dodecyl sulfate (SDS) [21].

At very low shear rate, the phase is more-or-less oriented with the membranes parallel to the velocity direction. Defects however remain in the velocity direction as well as in the vorticity direction. At high shear rate, the orientation is basically very similar but the defects in the velocity direction have disappeared. In the intermediate regime, a new and interesting orientation appears. The membranes are broken into pieces by the flow and the phase organises itself into a phase of multilamellar vesicles all of the same size. We called these vesicles onions because of their multilamellar structure. Figure 5 presents freeze fracture picture of the phase after shearing it [24]. This picture reveals that onions are truly discrete entities and also shows that they adopt a polyhedral shape. While not

‘universal’, such a phenomenology is quite general and has been encountered in many systems [29, 301.

Figure 5. Electron-microscopic picture of freeze fracture sample obtained after shearing a lamellar phase. T h e size of the onions i s typically f p m [2.4].

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3.2

Several techniques can be used to demonstrate the existence of the onion texture besides the sophisticated electronic microscopy technique. Direct observation of the texture using a regular optical microscope equipped with crossed polarisers is certainly the easiest one.

Figure 6 shows a typical texture of a sheared lamellar phase in the onion state [21].

One easily observes a regular modulation of white and black, with a characteristic length corresponding to the size of the onions. This characteristic length varies with the shear rate until it reaches very small scales below the optical resolution (typically lpm). A uniform grey colour is then observed.