Figure 6. Typical texture of the onion phase observed using an optical microscope between crossed polarisers.
The characteristic size is easily detectable using a laser beam and a screen placed at a few centimetres from the sample [Zl]. Figure 7 presents the small angle patterns obtained when sending a laser beam through the onion texture onto an observation screen [20, 211.
This technique allows the measurement of sizes from 1pm to more than 50pm [20, 21, 301. Below the micron size scale, a more specialised set-up must be used allowing the experimentalist to access to larger scattering angles.
Figure 7. Small-angle light scattering patterns observed in the onion texture b y increasing the shear rate (from left to right). The ring of scattering is directly related to the onion size which obeys D
-
?-'I2. (see Reference 21 and Figure 8.)Equilibrium and flow properties of surfactants in solution 193 The narrow ring of scattering observed on the screen shows the presence of a single characteristic length scale. Since the sample is birefringent, it is most probably a modu- lation of the orientation of the layers which is responsible for the contrast, with the index of refraction varying from its ordinary value to its extraordinary one as one traverses the characteristic length. The ring is obtained only if circularly polarised light is sent through the sample. Otherwise, using a linearly polarised beam and crossed analyser, a pattern of four blobs is observed because of the coupling between the polarisation of the incident light and the birefringence of the phase.
The position of the ring in reciprocal space is related to the characteristic size of the modulation. It corresponds directly to the onions diameter D through the classical Debye relation:
where n is the index of refraction of the phase (the average one), X is the light wavelength and 0 the scattering angle. The width of the peak is an indication of the uniformity of the size: the narrower it is, the narrower is the size distribution. For the main cases which have been studied, the size within a given sample does not vary more than 20% in radius [21]. The fact that the ring intensity is uniform in all directions is an indication that the onions are disordered. Indeed, they adopt a kind of amorphous arrangement (liquid-like). Because the position of the ring varies with the shear rate, it is possible to measure how the onion size evolves with the shear. Figure 8 represents such an evolution for a liquid-like structure. The size is inversely proportional to the square root of the shear rate : D N ?-'I2. This is an easy way to control experimentally the onion size.
Depending upon the formulation (the surfactant choice) and the shear rate, sizes ranging from 0.2pm to more than 50pm have been found.
n
E
W
a Q
Figure 8.
system, as a function of the inverse of the square root of the shear rate [21].
Evolution of the size of the onions for the SDS-dodecane-water-pentanol
194 Didier Roux
Figure 9. Evolution of the small angle light scattering patterns as a function of the shear rate. (a)
+
= lOs-l, the ring is isotropic and corresponds to an ensemble of monodisperse multilayered vesicles with no long-range order. (b)+
= OS-', the ring of scattering is replaced b y six dots. The organisation now exhibits a long range order. (c)9
= 2OOs-l, small angle pattern after the transition of size. The characteristic size of the vesicles is now much bigger and several orders of scattering can be easily seen. (d)+
= Os-l, same as ( c ) but after a rapid arrest of the shear. The long range order is kept and even more pronounced. (e) = Os-', same as (d) but after a few oscillations of small amplatude (made by hand). The long range order is even better, more than 5 orders of diflraction can be seen.3.3 Ordered structure of the onion phase under shear
An interesting system made of SDS, octanol and brine exhibits a more complex be- haviour [30]. In addition to the steady states previously described, this system exhibits several new transitions. First, a transition between the disordered state described above and an ordered state can be observed. Second, a transition between two states of ordered multilayered vesicles, differentiated by the size of the vesicles, has been found. The tran- sition between these two states is observed as a jump from small to big vesicles when either the shear rate or the temperature is increased. This transition, which is in general discontinuous (the size jumps abruptly), becomes continuous (smooth size evolution) at a critical temperature.
The system studied is a quaternary lyotropic lamellar phase whose phase diagram has been published [31]. A single sample is studied under shear (85.6% of brine at 20g/l of NaC1, 6.5% of SDS, 7.9% of octanol, in weight). This system is studied both as a function of temperature and shear rate. Let us first described what is observed in reciprocal space using small angle light scattering. Above
q
w ls-l, an isotropic ring of scattering(Figure 9a) appears characteristic of the multilayered vesicle state. This ring corresponds to the characteristic size of the close packed vesicles. Its radius increases with increasing
q,
indicating that the vesicle size decreases with the shear rate. The isotropy of the ring is the signature of no long-range order in the positions of the vesicles. Above a well-defined shear rate of lOs-l, a modulation in the radial intensity of the ring appears, leading to a well-defined pattern of six spots above 50s-' (Figure 9b). This is the so-called layering transition which corresponds to the ordering of the multilayered vesicles in planes exhibiting an hexagonal order (in-plane). This transition does not affect the onion size since the dots appear on the ring: the size of the onions before and after the transition is practically the same and is around 3-4pm at the transition. After the transition, the size evolves very slowly with the shear rate, still decreasing when the shear rate increases [30].Equilibrium and Aow properties of surfactants in solution 195
-2-
When a shear rate of 200s-' is reached, a new phenomenon is observed. The previous pattern of six dots evolves toward two rings of scattering: one at the previous position and a new ring appears at smaller angles. With time, the former ring of scattering disappears and a clear new set of dots is seen at a much smaller angle than the previous one. After some time (typically from 20 minutes to two hours), the pattern shown on Figure 9c is observed under shear. This new pattern corresponds to an ordered structure of onions similar to the state previously described, but constituted of much bigger onions (around 10pm at T x 24°C). Moreover, even under shear, several orders of diffraction can be observed (up to 3-4). In contrast to the previous ordered state, this pattern persists once the shear is stopped (Figure 9d). The quality of the long range order can even be improved significantly by applying small amplitude oscillations to the shear cell (Figure se). We have been able to keep this ordered structure after the shear has been stopped for several days. The exact nature of the structure of this phase has recently been studied in more detail and consists of a so-called random stacking structure [32] (see Section 4).
The transition between small and big vesicles can be mapped in the (?,T) plane.
Figure 10 shows the shear diagram obtained from these measurements. The two regions of ordered vesicles (small and big) are separated by a line corresponding to a discontinuous transition. This line ends on a critical point at x OS-', T x 26°C. The decrease of the small angle position of the ring or the Bragg peaks is the signature of the large increase in size of the onions. Direct space imaging can also be observed, confirming that the transition does involve a change in the onion size [30].
t
\ e Jump of size
Continuous .
\
Figure 10. Shear diagram of the jump-of-size transition. The full circles are the ex- perimental points, the dotted lane is a guide for the eye and the circle around the dot is the location of critical point above which the discontinuous transition is replaced b y a continuous evolution.