Butterfly patterns in a sheared lamellar-system

P. Lindner (ILL), J. Zipfel and W. Richtering (Univ. Freiburg).

A technologically important extension of "classical" scattering techniques is to investigate soft-matter systems under non-equilibrium conditions. Shear flow is known to have a profound influence on the structure and orientation of complex fluids like thermotropic or lyotropic liquid-crystals, colloidal and polymeric solutions. There is a fundamental interest in understanding the microscopic structure and dynamics of such complex fluids as the macroscopic material properties might change with the application of an external perturbation like shear. The following example illustrates a recent study of the influence of shear on the structure of a lyotropic lamellar phase. Results using a cone-and-plate and the ILL Couette type shear-cell were obtained by rheo-small-angle light scattering (rheo-SALS) and small-angle neutron scattering (SANS) at D11. Because of the broad range of momentum transfer Q available at D11 a characteristic butterfly-pattern(*) with a scattering peak revealing both the structure and the supramolecular structure of the system could be detected at very low Q.

The influence of shear on the structure of lyotropic lamellar phases was studied with aqueous mixtures of the non-ionic surfactant C12E4 (tetraethyleneglycol dodecylether) with 33.6% C12E4 in D2O by weight. At low shear-rates, a four lobe pattern was observed in depolarised rheo-SALS indicating the existence of vesicles on the length scale of a few micrometers. SANS experiments at relatively high Q (³ 0.01 Å-1) using the ILL Couette type shear-cell with a 1 mm gap at the instrument D11 revealed a lamellar spacing of 80 Å (d1 in Fig. 3). The scattering intensity was higher perpendicular to the flow direction as compared to along the flow direction. From these results we concluded that the vesicles are elongated under flow.

At high shear-rates, a characteristic butterfly pattern was found in rheo-SALS. The SANS measurements at high Q (³ 0.01 Å-1 ), however, revealed no obvious changes at high shear-rates. Thus the local structure was not significantly altered at higher shear-rates. Therefore additional SANS experiments at very low Q were performed, in order to investigate the structure under shear on a greater length-scale.

With the D11 detector at 35.7 m (0.0011 £ Q [Å-1 ] £ 0.0063) a butterfly pattern has been observed at shear-rates of about 1200 s-1 (see Fig. 1). It disappeared immediately after cessation of flow (Fig. 2). This butterfly pattern was accompanied by a scattering peak at 0.0048 Å-1 perpendicular to the flow direction.

After cessation of flow the diffraction pattern showed a ring at the same Q but with an intensity maximum still perpendicular to the direction of flow.

This corresponds to a structure with a preferential distance of approximately 1300 Å (d2 in Fig. 3) between individual vesicles. Fig. 3 displays the angular dependence of the absolute scattering intensity for both higher and very low Q experiments combined.

The data are averaged over 30°-sectors parallel and perpendicular to the flow direction. Also shown in the figure is a model for the structure in real space in the quiescent state (left side) and under shear (right side).

At low Q one can see in Fig. 3 (a) the enhanced scattering intensity along the direction of flow, (b) the scattering peak perpendicular to the flow direction.

Figure 1 (left): Butterfly pattern at a shear gradient of 1200 s-1 (sample-to-detector distance 35.7 m, wavelength l = 10 Å).
Figure 2 (right): Pattern after cessation of flow.

At high Q, the scattering peak due to the distance between surfactant double layers (d1) can be observed both perpendicular and along the flow direction.

The butterfly pattern indicates the formation of flow-enhanced concentration fluctuations along the flow direction and is known from semi-dilute polymer solutions and polymer networks. The length scale of the concentration fluctuations along the flow direction is of the order of approximately 7000 Å. In the quiescent state the scattering ring (1300 Å) indicates that the vesicles have a random dense packing. Under shear the vesicles are elongated and the ordered structure is perturbed along the flow direction but prevails perpendicular to the flow direction where no enhancement of scattering was observed at small angles, thus explaining both the butterfly pattern and the diffraction peak.

It is also possible to control the size of the relatively monodisperse vesicles by means of the shear-rate. For example, when the shear-rate was reduced to 80 s-1, the butterfly pattern was still observed but at smaller momentum transfers Q. Again a ring was found after cessation of shear and the scattering peak was now at 0.0021 Å-1 corresponding to a vesicle distance of 3000 Å.

This work describes a new structure of a lyotropic lamellar phase at high shear-rates, in addition to the previously reported aligned defect free lamellar phase and the hexagonal assembly of vesicles.

Figure 3: Absolute scattering intensity averaged over 30°-sectors along (a) and perpendicular (b) to flow direction. Model for the structure at rest (left side) and under shear (right side) in real space. d1 corresponds to the distance of the double layers, d2 to the preferential distance between individual vesicles.