J. Phys. Chem. B 1998, 102, 507-513
507
Shear Orientation of Lyotropic Hexagonal Phases Gudrun Schmidt, Stefan Mu1 ller, Peter Lindner,† Claudia Schmidt,* and Walter Richtering* Institut fu¨ r Makromolekulare Chemie, Albert-Ludwigs-UniVersita¨ t Freiburg, Stefan-Meier Strasse 31, D-79104 Freiburg, Germany, and Institut Laue-LangeVin, BP156, F-38042 Grenoble, France ReceiVed: August 7, 1997X
The shear orientation of the hexagonal liquid crystal phase of nonionic surfactant/water mixtures was investigated by means of different techniques, namely, microscopy, small-angle light and neutron scattering, (SALS, SANS), birefringence, and nuclear magnetic resonance (NMR). On a microscopic length scale probed by NMR, SANS, and birefringence, the shear flow results in an alignment of rodlike micelles along the flow direction. The 10 plane was parallel to the shear plane. On a mesoscopic length scale, studied by microscopy and SALS, a stripe texture was observed. This is due to an undulation of the director which is on average aligned in flow direction. The corresponding SALS pattern shows a better orientation correlation perpendicular to the flow direction.
Introduction Surfactants are known to form lyotropic liquid crystalline mesophases in concentrated aqueous mixtures, and phase diagrams of many different systems have been reported in the literature.1,2 Often a hexagonal phase is observed that consists of a hexagonal packing of rodlike micelles. In liquid crystalline phases, a long range orientational order of anisotropic species exists which can be characterized by a director orientation. Samples of macroscopic size, however, are usually not uniformly aligned, and a polydomain structure is present. This polydomain structure gives rise to characteristic textures that can be observed by polarizing microscopy. The structure of liquid crystalline materials can be strongly affected by shear deformation. Often complicated flow properties are found and different behavior as shear alignment or director tumbling can occur.3-6 Shear-induced structural changes in complex fluids of anisotropic species are a very general problem encountered not only in surfactant mesophases but also in liquid crystalline solutions of stiff macromolecules,4 thermotropic liquid crystals,5 and block copolymer melts.6-9 Different experimental techniques as, for example, flow birefringence, small-angle scattering, and nuclear magnetic resonance (NMR) from samples under shear have been developed in order to monitor such shear-induced structural changes. Since shear flow can influence both the texture and the orientation of the underlying anisotropic species, it is very helpful to combine different techniques in order to obtain information on different length scales. Previous investigations of hexagonal lyomesophases gave somewhat ambiguous results. NMR experiments showed that the rodlike micelles get aligned along the flow direction.10,11 With light scattering, two different orientations were observed which are characterized by enhanced scattering intensity, one along and one perpendicular to the flow direction.12,13 The objective of this contribution is therefore to investigate the influence of shear on the structure of micellar hexagonal phases * To whom correspondence should be sent. E-mail:
[email protected]. † Institut Laue-Langevin. X Abstract published in AdVance ACS Abstracts, December 15, 1997.
and especially to compare results obtained from different methods. The hexagonal phase of two surfactants was studied and the samples were investigated with the following techniques: (i) NMR, (ii) small-angle neutron scattering (SANS), (iii) birefringence, (iv) microscopy, and (v) small-angle light scattering (SALS). Experimental Section The first system chosen was the hexagonal phase of the nonionic surfactant H3C(CH2)13OCH[CH2O(CH2CH2O)4CH3]2 abbreviated as C14G(E4M)2. The amphiphile was synthesized as described by Kratzat and Finkelmann.14 Solutions of 58% (w/w) and 52% (w/w) C14G(E4M)2 in D2O were prepared which had an isotropic to hexagonal transition at 29 and 28 °C, respectively. The solution of 52% (w/w) C14G(E4M)2 had a hexagonal to cubic phase transition at ca. 8 °C. The second system was the common C12E6 surfactant (hexaethyleneglycol monododecyl ether) at a concentration of 40%. For all the different types of measurements, the shear cells were loaded with the sample being in the isotropic phase, and then the material was cooled into the hexagonal phase. All experiments described below were started with a polydomain sample. The deuterium NMR measurements were performed with a Bruker MSL spectrometer at a resonance of 46.07 MHz using a cone-and-plate shear cell which is integrated into an NMR probe for a superconducting magnet.15 The axis of the shear cell is aligned along the external magnetic field. Thus, the velocity gradient is parallel to the magnetic field, whereas both the velocity and the vorticity axis are perpendicular to the magnetic field. The cone-and-plate tool has a diameter of 15 mm and a gap angle of 5°. The sample was sheared at a rate of 8 × 10-3 s-1. Spectra were recorded as a function of shear strain. For one spectrum, 64 scans were accumulated, using the quadrupole echo pulse sequence 90°x - τ - 90°y - τ acquisition with τ ) 100 µs. The duration of a 90 pulse was 18 µs with the 18 mm saddle coil surrounding the shear cell. A Leitz Ortholux II Pol-Bk microscope with crossed polarizers was used to study textures, and the sample was sheared by pressing it through microslides of 4.8 mm × 50 mm (rectangular capillaries) with a thickness of 0.4 mm. Here the
S1089-5647(97)02574-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/15/1998
508 J. Phys. Chem. B, Vol. 102, No. 3, 1998
Schmidt et al.
Ires(Θ,δmeas) ) I0A(1 + cos(2Θ - δmeas))
(2)
where A is the scaling factor which takes into account an absorption of light. The phase angle δmeas (retardation) is measured as follows: using a plate with two 90° chopper segments the rotating analyzer interrupts a light barrier two times on each rotation. Thus one obtains the phase angle δ from the cos(2Θ - δ) of the measured intensity and the chopper signal at Θ ) 0, 90, 180, 270°, etc., from the rotating analyzer. The retardation of the probe is given as multiples of 2π
δ ) δmeas + 2πN Figure 1. Couette shear cell and the cooling system (striped parts) used for SANS measurements. The inner cylinder containing the cooling system is the stator (46-mm diameter), and the outer cylinder rotates (48-mm diameter).
flow velocity cannot be controlled, but at low velocities wellaligned samples can be obtained. SANS measurements were performed with the instrument D11 at the Institute Laue-Langevin using 4.5 Å wavelength neutrons. The shear cell used has couette geometry with a gap size of 1 mm (see Figure 1).16 In the standard configuration, the incident beam is oriented parallel to the shear gradient axis called the “radial-beam“ geometry. A second configuration is the “tangential-beam“, where the beam enters the couette cell tangentially, i.e., along the flow direction. The design of the temperature control is due to the fact that the neutron beam must not pass through the liquid of the temperature control bath. The q-range was 0.06 < q < 1.8 nm-1, with q the magnitude of the scattering vector given as q ) 4π/λ sin θ/2. λ and θ are the radiation wavelength and scattering angle, respectively. Scattering intensities in the “radial-beam“ configuration were corrected for sample thickness and transmission and were reduced to absolute units. SALS and birefringence experiments were performed with a homemade device consisting of a Bohlin stress rheometer with either integrated light-scattering or birefringence setup. It is equipped with a 4 cm (diameter)/3° cone-and-plate shear geometry. The incident beam was parallel to the velocity gradient, and the sample thickness probed by the laser beam was 0.78 mm. Both polarized and depolarized scattering can be detected. Here only results from depolarized scattering (Hv) will be discussed. The largest accessible scattering vector was 3 µm-1. The determination of flow birefringence is based on a method described by K. C. Lim and J. T. Ho.17 The light beam was parallel to the direction of the velocity gradient. It is useful to define the retardation δ when the birefringence ∆n is detected by means of the different velocities of the light along the two orthogonal axes for the refractive indices n1 and n2 (∆n ) n1 - n2). Then the electric vector of the incoming light has to point into the direction of both axes, and this can be realized by linear polarized light, with a direction of polarization at 45° to both axes. The retardation δ is the phase difference of both beams after passing through a material of the thickness d and is defined by the equation
δ ) 2π
d∆n λ
(1)
The effect of the optical elements and the retardation of the sample on the measured intensity I(Θ) (with Θ being the rotation angle between the analyzer and polarizer) can be calculated with Stokes vectors and Mu¨ller matrixes.18,19 The resulting intensity Ires(Θ,δ) is
(3)
and the number of orders has to be taken into account in order to calculate the correct value of birefringence. Since the sample thickness in the cone-and-plate shear geometry is much smaller as compared to that of concentric cylinders, the number of orders is only a problem when strongly birefringent samples are investigated. A further advantage of the cone-and-plate setup as compared to using a couette cell is the smaller inertia of the cone that allows to perform dynamic-mechanical experiments within a broad frequency range.20 Results and Discussion Experiments were performed with two surfactants: C14G(E4M)2 described in the experimental section and the more common C12E6 surfactant. Various concentrations were used. Observations regarding shear orientation were independent of the type of surfactant and its concentration, and therefore, we will focus only on the main results obtained by the different techniques from the 58% C14G(E4M)2/D2O system at 25 °C. (i) Nuclear Magnetic Resonance. In deuterium NMR spectroscopy,21 the orientation dependence of the electric interaction between the quadrupole moment of the deuterium nucleus (spin I ) 1) and the electric field gradient at the site of the nucleus is used to probe molecular orientations. In uniaxial phases, like the hexagonal phase, averaging of the electric quadrupole interaction over fast molecular reorientations gives rise to a residual quadrupole splitting
∆ν ) 3/4d(3 cos2 β - 1)
(4)
where β is the angle between the external magnetic field and the averaged electric field gradient, which is parallel to the phase axis (director). The averaged quadrupole coupling constant d ) e2qQ/h is about 1 kHz for D2O in surfactant mesophases, a value which is about 2 orders of magnitude smaller than that for immobile D2O. According to eq 4, deuterium NMR line shapes of surfactant/D2O liquid crystals yield information about the orientational distribution of the director in the sample. Figure 2 shows deuterium NMR spectra of a sheared sample at different values of shear strain. The initial spectrum obtained at rest before any shear was applied to the sample has the shape of the powder pattern (Pake spectrum) characteristic of polydomain samples with an isotropic director distribution. The peaks correspond to director orientations at an angle of 90° with respect to the magnetic field and the edges with twice the splitting of the peaks to a director orientation of 0°. A slightly enhanced intensity at the edges of the spectrum at rest indicates a small partial alignment of the sample, which probably occurred while cooling the sample from the isotropic phase in the presence of the magnetic field. Extended annealing at the phase transition can result in samples with the director uniformly aligned parallel to the magnetic field.11 The spectra in Figure 2 show how the polydomain sample transforms into a uniformly
Lyotropic Hexagonal Phases
Figure 2. Deuterium NMR spectra of a 58 wt % surfactant/D2O mixture at 25 °C as a function of shear strain. The strain is given by the numbers to the right of each spectrum. The shear rate was 8 × 10-3 s-1.
aligned sample with increasing shear strain. At first, the intensity at the edges decreases indicating that orientations close to 0° disappear. With increasing shear strain, the intensity in the center of the spectrum resulting from orientations close to the magic angle of 54.7° vanishes, until finally only the doublet corresponding to the 90° orientation remains. By combining the results from NMR measurements using the cone-and-plate cell with NMR data obtained in a Couette cell, it has been shown for the hexagonal phase of other nonionic surfactants that shear causes the director to align parallel to the velocity.8,9 Furthermore, NMR experiments in the cone-and-plate cell starting from uniformly oriented samples (β ) 0) have shown that the director becomes slowly tilted at an angle β due to the shear strain γ according to the relationship β ) arctan γ.11 (ii) Small-Angle Neutron Scattering. SANS can also provide information on the micellar orientation. The length scale probed by SANS is given by the magnitude of the scattering vector q ) (4π/λ)sin(θ/2), with λ the wavelength of the neutrons and the scattering angle. The results obtained from the hexagonal phase in the “radial” beam configuration are summarized in Figure 3. A Bragg peak caused by the local order of the rodlike micelles was observed on the twodimensional multidetector at qmax ) 1.4 nm-1. X-ray-scattering experiments at a similar concentration gave reflections at q ) 1.38, 2.21, 2.80 nm-1 (i.e., a 1: 30.5: 2 sequence typical of hexagonal structures).22 The comparison allows us to assign the observed SANS peak to the 10 reflection and the intermicellar distance is calculated to 5.2 nm. The two-dimensional scattering pattern was radially symmetric when the sample was in the quiescent state. A symmetric intensity distribution is typical of a polydomain sample where all spatial orientations of domains of rodlike micelles are present. A strongly anisotropic scattering pattern was found with the sample under shear and also after cessation of shear. The Bragg peak was only observed perpendicular to the flow direction, showing that the rodlike micelles were aligned along the flow direction. The same behavior was observed recently by Fairhurst et al. with a different surfactant23 and also from lyotropic block copolymers.24,25
J. Phys. Chem. B, Vol. 102, No. 3, 1998 509
Figure 3. Top: Two-dimensional-SANS profiles obtained in the “radial” beam (a) at rest after filling, γ ) 0; (b) at a strain of γ ) 4; and (c) γ ) 49, respectively. The q-range: 0.3 < q < 1.8 nm-1 Bottom: Integrated scattering intensity from 30°: sectors perpendicular to (circle) and along (square) the flow direction plotted vs strain.
Figure 4. Azimuthal SANS intensity distribution in the “radial” configuration at qmax after strains of γ ) 4 (square), 12 (triangle), and 49 (circle).
To get more information on the evolution of shear orientation, the sample was sheared at constant rate for certain time intervals. Scattering patterns were recorded immediately after cessation of shear, and the integrated scattering intensity was determined from 30°-sectors perpendicular to and along the flow direction. In Figure 3 (bottom) these intensities are plotted vs strain. Apparently a constant degree of orientation within the resolution given by the sector width of 30° was reached after ca. 10 strain units. Figure 4 displays the azimuthal intensity distribution on the two-dimensional multidetector after strains of 4, 12, and 49, respectively, showing that the intensity at qmax increased and the half-width decreased with strain (i.e., the degree of order increased with strain). This can be compared with the NMR results. The NMR line shape measured for four strain units (last spectrum of Figure 2) at first glance suggests a much higher degree of orientation than measured by neutron scattering. It must be pointed out,
510 J. Phys. Chem. B, Vol. 102, No. 3, 1998
Schmidt et al.
Figure 5. SANS patterns obtained in the “tangential” beam configuration. (a) Sample cooled into the hexagonal phase; at rest prior to shear. (b) Scattering pattern from the sheared sample at a strain of γ ) 49. (c) Relaxation pattern 320 s after cessation of shear. Figure 7. Real space orientation of sheared micelles in the couette cell.
Figure 6. Azimuthal intensity distribution from the patterns shown in Figure 5. (a) At rest after filling, (b) γ ) 49; (c) Relaxation pattern after 320 s.
however, that by NMR small degrees of orientations appear overemphasized because of the nonlinearity in the relationship between orientation and quadrupole splitting (eq 4). The peak width of the spectrum at γ ) 4 and the still considerable intensity in the center show that the director distribution is far from perfect alignment. As was shown earlier,11 only prolonged shear up to strains of a few hundreds or thousands leads to nearly perfect alignment characterized by a sharp doublet with much narrower line width. SANS data of the same q-range but obtained in the “tangential” beam are shown in Figure 5. Surprisingly a scattering pattern with 6-fold symmetry was observed with the sample cooled from the isotropic to the hexagonal phase. The scattering pattern indicates the presence of a highly oriented sample, and a reason for this high degree of order will be discussed below. The position of qmax is identical with that determined with the “radial-beam” setup. The 6-fold symmetry was lost under shear and the scattering pattern changed significantly. Strong scattering intensity was observed in the neutral direction only. After cessation of shear, the six peaks appeared again. The behavior under shear is different from nematic solutions of wormlike micelles. There a shear induced hexagonal structure was observed in plane couette flow.26 Apparently the rotational component of the flow field disturbed the single-crystal structure and caused the dissappearance of the hexagonal symmetry similar to block copolymer melts.6 The azimuthal intensity distribution at qmax is shown in Figure 6. The peaks in the direction of the shear gradient (0 and 180°) were broader compared to the other peaks. Thus a smaller degree of order was found along the gradient direction, which is due to the rotational component of the flow field. The position of the six peaks corresponds to a real space orientation of the micelles as shown in Figure 7. The 10 plane was parallel
to the plane given by the neutral and the flow direction (shear plane) (i.e., the 10 plane was aligned parallel to the walls of the couette cells). The same orientation was found in block copolymer melts.5,25,27-29 However, the orientation was not perfect as can be seen from the azimuthal intensity in Figure 6c. The observation of the first-order peak in the “radial beam“ configuration also indicates the nonperfect orientation.24,27 A possible explanation for the astonishing monodomain formation in the couette cell without shear is the special design of this cell (see Figure 1). The material in the gap between stator and rotor will be cooled or heated faster in the “tangential“ parts of the shear cell compared to the “radial“ parts of the cell. This design of the temperature control was chosen because of the requirement that the neutron beam must not pass through the liquid of the temperature control bath. The transition from the isotropic to hexagonal phase is accompanied by a small volume change and a tremendous increase of viscosity. These changes will occur first within the “tangential” parts of the couette cell and will cause a material flow from the “radial” position to the “tangential” position. Apparently this flow gives rise to a well-aligned sample. The situation is different for the material in the “radial” zone. A homogeneous flow from the other parts is not possible, because the “tangential” zone is already in the viscous hexagonal state. Consequently, a powder spectrum typical of a polydomain sample was observed in Figure 3. The SANS data obtained at high q show that the rodlike micelles are always aligned along the flow direction. Different behavior was observed at smaller q in the radial beam. The q-dependence of the absolute scattering intensity for small q is shown in Figure 8. The intensity was averaged within 30° sectors perpendicular to and along the flow direction and one can see that the small angle scattering is enhanced along the direction of flow. Such scattering patterns have been reported before30 and were also obtained from nematic polymer solutions.31 The scattering pattern in Figure 8.a) is similar to that observed in SALS (see below), but the q-range is much higher. (iii) Birefringence. Birefringence was measured with the method of a rotating analyzer using a single wavelength, and the retardance was obtained.17,32 Because the retardance can pass through multiple orders, it is difficult to calculate the absolute value of birefringence from the observed retardance. Consequently, the birefringence of a polydomain sample could not be determined. The retardance became constant when the sample was sheared, indicating a shear-induced orientation. The oriented sample was then slowly heated into the isotropic phase, and the retardance was measured while keeping track of the
Lyotropic Hexagonal Phases
J. Phys. Chem. B, Vol. 102, No. 3, 1998 511
Figure 8. q-Dependence of absolute SANS scattering intensity in the hexagonal phase along flow (square) and neutral direction (circle). Insets a and b show two-dimensional scattering patterns at (a) 0.006-0.033 nm-1 and (b) 0.033-0.18 Å-1.
number of orders. With this procedure it was possible to determine the absolute value of the birefringence of a shearaligned sample. In general the birefringence can have two contributions: one corresponding to the intrinsic birefringence of the molecules and a second corresponding to a form birefringence. The form birefringence of a rodlike object aligned in flow direction is always positive.33 The intrinsic birefringence, however, depends on the molecular orientation and polarizability.33-35 The maximum thickness of rodlike micelles is given by the chain dimension in the extended conformation. Usually the diameter is only sligthly smaller (i.e., the surfactant molecules are rather extended). The orientation of the surfactant molecules is perpendicular to the long axis of a rodlike micelle, and therefore, for surfactants with aliphatic tail group, the intrinsic birefringence will be negative.33 The NMR and SANS data discussed above show that shear flow leads to an alignment of rodlike micelles along the flow direction. This observation is in perfect agreement with the observation of a negative birefringence. Apparently the positive form birefringence of rodlike micelles does not contribute significantly to the total birefringence. Birefringence can be measured with a better time resolution than NMR and SANS experiments. Therefore oscillatory shear deformation as well as creep experiments can be monitored by birefringence measurements. Oscillatory shear flow with simultaneously detected birefringence showed that the average orientation is not changed but improved when the direction of flow is reversed. These oscillatory experiments will be described in detail elsewere. Here we will only discuss results from creep experiments. Figure 9a displays the compliance J(t) ) γ(t)/σ in a creep experiment at a shear stress of σ ) 100 Pa and Figure 9 b the evolution of the retardance δmeas for two identical measurements. Due to the small sample volume probed by the laser beam in these experiments, averaging of many domains could not be achieved.36 Therefore the δmeas-value at the beginning has no meaning. During the creep experiments, δ changed and a plateau was reached at δmeas ) 0 or 2π. These values are indistinguishable in the experiment. By heating the oriented sample into the nonbirefringent isotropic phase, a value of ∆n ) -(0.86 ( 0.07) × 10-3 was calculated for the aligned hexagonal phase. A variation of the sample thickness in a plate/ plate shear geometry gave consistent values of ∆n confirming that absolute ∆n values were obtained for the shear aligned samples by the procedure used. According to the NMR and SANS results, the sheared sample was still far away from a monodomain structure. This bire-
Figure 9. (a) Creep compliance vs time at a stress of 100 Pa. Strain dependence of retardance. Circles (full and open) correspond to two creep experiments. Since the creep curves were identical, only one curve is shown in Figure 9a.
fringence plateau, as well as the plateau obtained from scattering intensity in SANS experiments, therefore corresponds to a limited degree of orientation of the sample. Figure 9a shows that a jump in the creep compliance occurred (at 850-900 s) when the retardance plateau was reached (γ ≈ 10). The SALS pattern changed during this jump of J(t), indicating that the sample became shear aligned on a larger length scale.12 In SANS a constant degree of orientation was also reached after ca. 10 strain units. (see Figure 3). (iv) Polarization Microscopy. A typical fanlike texture under crossed polarizers was observed from the hexagonal phase at rest (see Figure 10a). Striations of fanlike textures such as this have been discussed recently by Oswald and co-workers.37 They are due to a thermomechanical undulation of the columns.38-40 Under shear, the pattern changed to a stripe texture with stripes perpendicular to the flow direction, see Figure 10b). It is due to an undulation of the director which, on average, is aligned along the flow direction. Such undulations, either in shear-aligned or magnetically aligned samples, can be analyzed by polarizing microscopy.11 For magnetically aligned samples, the analysis of the NMR line shape as a function of the orientation of the sample with respect to the magnetic field shows a significant deviation of the local director from its average orientation confirming the undulation.11 The undulation of the director causes a spatially periodic change of the alignment of the indicatrix when moving along a line parallel to the flow direction, and consequently, stripes are observed perpendicular to the flow direction. In other words, due to the undulation of the director, the orientation correlation in flow direction is smaller than perpendicular to the flow direction. At higher deformation obtained by stronger shear this stripe texture can be disrupted as shown in Figure 10c,d. To correlate the micrographs with the other techniques, the birefringence of samples sheared in microslides was also determined. A value of ∆n ) -(1.1 ( 0.1) × 10-3 was obtained for both the stripe texture and the partly disrupted textures. Obviously, the large scale structure which is observed in optical microscopy does not influence the birefringence. The disrupture of the stripe texture may be caused by inhomogeneities of the shear field in the microslides used here
512 J. Phys. Chem. B, Vol. 102, No. 3, 1998
Schmidt et al.
Figure 10. Optical micrographs of hexagonal texture viewed under crossed polarizers: (a) at rest, and (b-d) with increasing shear deformation.
structure, not shown here, was not as sharp as that of the perfect stripe texture and showed some scattering intensity perpendicular to flow direction. Obviously one has to distinguish between the orientation of a rodlike micelle and the orientation correlation of an ensemble of micelles. Conclusions
Figure 11. Two-dimensional Hv-SALS scattering pattern of a sheared hexagonal phase.
for microscopy. Previously reported NMR experiments on pentaethylene glycol monododecyl ether (C12E5) with the coneand-plate cell have shown that the degree of the shear-induced orientation improves for high-shear strains.11 However, SALS and SANS experiments revealed secondary flows at higher shear rates caused by normal forces.30 (v) Small-Angle Light Scattering. Finally, results obtained from SALS will be discussed. Depolarized light scattering is mainly determined by orientation fluctuations and probes the structure on a length scale of a few micrometers. The scattering pattern observed in depolarized SALS from the hexagonal phase under shear is shown in Figure 11. Scattering was obtained along the flow direction. Light-scattering probes dimensions in reciprocal space and an elongated object aligned perpendicular to the flow direction will give rise to enhanced scattering intensity along the flow direction. The light-scattering pattern can be correlated to the texture observed in optical microscopy. This stripe texture corresponds to a better orientation correlation of the micelles perpendicular to the flow direction, that is less fluctuations and therefore less scattering perpendicular to the flow direction. A light-scattering pattern of the partly disrupted
The results presented above provide clear information on the shear orientation of the micellar hexagonal phase. On the microscopic length scale, the rodlike micelles were aligned along the flow direction. This can be observed by NMR spectroscopy, SANS in the q-range of the Bragg peak and birefringence. SANS with the “tangential“ beam showed that the 10 plane of the H1phase was aligned parallel to the shear plane. The 6-fold symmetry was lost under shear but recovered after cessation of shear. The larger length scale can be probed by SANS, SALS, and optical microscopy. Here a better orientation correlation was found perpendicular to the flow direction. The SALS and SANS patterns have been interpreted before in terms of a log-rolling model.13,30 A log-rolling state was predicted theoretically for systems of high elasticity which can cause a perpendicular orientation of the director. All the experiments reported here, however, show that the director is always aligned in flow direction. The observed orientation correlation perpendicular to the flow direction exists on a much longer length scale than the diameter of a micelle. Light scattering along the flow direction can be explained by an undulation of the director with a period of several µm. The fact that the director is always aligned along the flow direction also explains why the hexagonal phase can be aligned both in simple shear flow as well as in large amplitude oscillatory shear flow. Identical light-scattering patterns and birefringence values were obtained in both types of experi-
Lyotropic Hexagonal Phases
Figure 12. Proposed model describing density fluctuations along the flow direction.
ments.13 Although the director undulates along the flow direction, its average orientation is not changed when the direction of flow is reversed. However, there is still an open question concerning the SANS data at low q. Figure 8 a shows that enhanced scattering was observed along the flow direction, indicating larger density fluctuations along the flow direction than in the neutral direction.30 This scattering pattern is similar to that observed in SALS, but the q-range in SANS is much higher. Thus the SANS pattern cannot be related to the macroscopic undulation of the director. At least two models can be discussed to describe density fluctuations along the flow direction. Figure 12 illustrates these models: (i) a bending of the rod like micelles41 or (ii) a constricted or cut like micellar form. Fluctuations of the type (ii) might eventually lead to a transition to spherical micelles and were also discussed in the context of block copolymers.7,42,43 We might note that the anisotropic SANS pattern of C14G(E4M)2 at low q was best observed at low concentrations. Here a phase transition to the body centered cubic phase occurs at ca. 8 °C. However, more SANS experiments at low q have to be performed to obtain more information on this intermediate length scale. Acknowledgment. Support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. References and Notes (1) Tiddy, G. J. T. Phys. Rep. 1989, 57, 1. (2) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (3) Chandrasekhar, S. Liquid Crystals, 2nd ed.; Cambridge University Press: Cambridge, 1992. (4) Marruci, G.; Greco, F. AdV. Chem. Phys. 1993, 86. (5) Jamieson, A. M.; Gu, D. F.; Chen, F. L.; Smith, S. Prog. Polym. Sci. 1996, 21, 981. (6) Nakatani, A. I.; Morrison, F. A.; Jackson, C. L.; Douglas, J. F.; Mays, J. W.; Muthukumar, M.; Han, C. C. J. Macromol. Sci., Phys. 1996, B35, 489.
J. Phys. Chem. B, Vol. 102, No. 3, 1998 513 (7) Bates, F. S.; Koppi, K. A.; Tirrel, M.; Almdal, K.; Mortensen, K. Macromolecules 1994, 27, 5934. (8) Hadziioannou, G.; Mathis, A.; Skoulios, A. Colloid Polym. Sci. 1979, 257, 136. (9) Fredrickson, G. H.; Bates, F. S. Annu. ReV. Mater. Sci. 1996, 26, 501. (10) Lukaschek, M.; Grabowski, D. A.; Schmidt, C. Langmuir 1995, 11, 3590. (11) Mu¨ller, S.; Fischer, P.; Schmidt, C. J. Phys. II(France) 1997, 7, 421. (12) Richtering, W.; La¨uger, J.; Linemann, R. Langmuir 1994, 10, 4374. (13) Linemann, R.; La¨uger, J.; Schmidt, G.; Kratzat, K.; Richtering, W. Rheol. Acta. 1995, 440. (14) Kratzat, K.; Finkelmann, H.; Liq. Cryst. 1993, 13 (5), 691. (15) Grabowski, D. A.; Schmidt, C. Macromolecules 1994, 27, 2632. (16) Lindner, P.; Oberthu¨r, R. C. ReV. Phys. Appl. 1984, 19, 759. (17) Lim, K. C.; Ho, J. T. Mol. Cryst. Liq. Cryst. 1978, 47, 173. (18) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; North Holland Publishing Co.: Amsterdam, 1987. (19) Fuller, G. G. Optical Rheometry of Complex Fluids; Oxford University Press: New York, 1995. (20) Schmidt, J.; Weigel, R.; Richtering, W.; Burchard, W. Macromol. Symp. 1997, 120, 247. (21) Hoatson, G. L.; Vold, R. L. NMR-Basic principles and Progress, Springer-Verlag: Berlin, 1994; Vol. 32, p 1. (22) Berend, K. Diploma thesis, Freiburg, 1991. (23) Fairhurst, C. E.; Holmes, M. C.; Leaver, M. S. Langmuir 1996, 12, 6336. (24) Mortensen, K. J. Phys.: Condens. Matter 1996, 8, A103. (25) Schmidt, G.; Richtering, W.; Lindner, P.; Alexandridis, P. Macromolecules. Submitted for publication. (26) Hamilton, W. A.; Butler, P. D.; Baker, S. M.; Smith, G. S.; Hayter, J. B.; Magid, L. J.; Pynn, R. Phys. ReV. Lett. 1994, 72, 2219. (27) Winter, H. H.; Scott, D. B.; Gronski, W.; Okamoto, S.; Hashimoto, T. Macromolecules 1993, 26, 7236. (28) Almdal, K.; Bates, F. S.; Mortensen, K. J. Chem. Phys. 1992, 96, 9122. (29) Tepe, T.; Schulz, M. F.; Zhao, J.; Tirrell, M.; Bates, F. S.; Mortensen, K.; Almdal, K. Macromolecules 1995, 28, 3008. (30) Richtering, W.; Schmidt, G.; Lindner, P. Colloid Polym. Sci. 1996, 274, 85. (31) Dadmun, M. D.; Han, C. C.; Macromolecules. 1994, 27, 7522. (32) Abetz, V.; Fuller, G. G. Rheol. Acta. 1990, 29, 11. (33) Wheeler, E. K.; Izu, P.; Fuller, G. G. Rheol. Acta 1996, 35, 139. (34) Janeschitz-Kriegl, H. Flow birefringence of elastico-viscous polymer systems. Fortschr. Hochpolym.-Forsch. 1969, 6, 170. (35) Tsvetkov, V. N. Flow birefringence in Newer Methods of Polymer Characterization; Bacon, K., Ed.; Interscience: New York, 1964. (36) Hongladarom, K.; Ugaz, V. M.; Cinader, D. K.; Burghard, W. R.; Quintana, J. P.; Hsiao, B. S.; Dadmun, M. D.; Hamilton, W. A.; Butler P. D. Macromolecules 1996, 29, 5346. (37) Oswald, P.; Geminard, J. C.; Lejcek, L.; Sallen, L. J. Phys. II (France) 1996, 6, 281. (38) Bouligand, Y. J. Phys. (France) 1980, 41, 1297. (39) Livolant, F.; Bouligand, Y. J. Phys. (France) 1986, 47, 1986. (40) Oswald, P.; Kleman, M. J. Phys. (France) 1981, 42, 1461. (41) Penfold, J.; Staples, E.; Khan Lhodi, A.; Tucker, I. Int. J. Thermophys. 1995, 16, 1109. (42) Almdal, K.; Mortensen, K.; Koppi, K. A.; Tirrel, M.; Bates, F. S. J. Phys. II (France) 1996, 6, 617. (43) Koppi, K. A.; Tirrel, M.; Bates, F. S.; Almdal, K.; Mortensen, K. J. Rheol. 1994, 38, 999.
