A R T I C L E S
Bellomo et al.
typical of lyotropic nematic phases. The X-ray pattern became
isotropic in less than an hour as the sample relaxed in the
absence of the magnetic field, similar to our optical microscopy
observations.
Due to our inability to record structural information in situ
during magnetic field alignment, a Couette cell setup was used
to shear the liquid-crystalline samples and allow simultaneous
recording of their X-ray scattering patterns. Application of a
shear flow is a very powerful way of aligning viscous meso-
phases and has been successfully applied to liquid-crystal phases
of PBLG in m-cresol.20 For similar alignment of our samples,
a small Couette shear cell was built that can be placed in the
X-ray apparatus and that requires sample volumes of only ca.
80 µL.12 The outer cylinder rotates with a controlled angular
speed with respect to the fixed inner cylinder. Two classical
scattering geometries were used.21,22 In the radial configuration,
the beam goes through the center of the cell and the velocity/
vorticity plane is explored. In the tangential configuration, the
X-ray beam is sent through the gap and the velocity gradient/
vorticity plane is explored. Comparison of data from these two
planes usually allows a full understanding of reciprocal space.
Figure 7. Radial (I versus q) X-ray scattering pattern of a 55 mol % L-1
sample (>70 wt % in deionized water) showing hexagonal symmetry of
mesophase of 1 with diffraction lines in the ratio 1, 31/2, 2, 71/2 (labeled as
the 10, 11, 20, and 21 reflections, respectively). DH ) diffuse halo of
scattering from ethylene glycol side-chains.
found to orient along the velocity direction like the hexagonal
mesophases of other compounds.23-26
Discussion
The phase behavior of concentrated aqueous solutions of L-1,
D-1, and L-1 + D-1 mixtures was found to be that predicted
by both the Onsager model of the isotropic/nematic phase
transition and the numerical simulations on rodlike particles.27,28
Qualitatively, the Onsager model and derived theories predict
a strongly first-order isotropic/nematic phase transition, with
phase coexistence and a large jump of nematic order parameter.
These predictions are valid for very long rodlike particles that
only interact through purely steric excluded-volume effects.
Cholesteric ordering is usually considered as only a small
perturbation to the nematic order, so this model should describe
the isotropic/cholesteric transition as well. The series of test
tubes showing phase coexistence (Figure 2), together with the
large value of the nematic order parameter derived from the
SAXS patterns, are evidence that the isotropic/cholesteric
transition of L-1, D-1, and L-1 + D-1 mixtures can be explained
by the Onsager model. Moreover, we believe that electrostatic
interactions are negligible in this system because similar
properties were observed when samples were prepared in NaCl
solutions (100 mM) where any electrostatic interactions were
screened. An additional prediction of the Onsager model is that
temperature should have no influence on the phase transition.
However, this prediction could not be tested here because all
liquid-crystalline samples became turbid upon heating. This
observation is likely related to the complex miscibility of PEG
with water as a function of temperature.10
In contrast to the magnetic field studies, all samples that were
sheared in the Couette cell did show some degree of alignment.
However, the cholesteric phase of the pure enantiomers was
found to be too viscoelastic to be completely aligned even at a
shear rate of 400 s-1 (Figure 5B). Weak cholesterics (L-1 +
D-1 mixtures) showed the best shear orientation, yet their
alignment became markedly more difficult as optical purity was
increased. The best alignment was seen immediately after the
cessation of shear using a weak cholesteric sample (55 mol %
L-1) (Figure 5C). The scattering pattern in the radial geometry
displayed two symmetrical diffuse spots, whereas the pattern
in the tangential geometry showed no anisotropy. The nematic
order parameter measured from this scattering pattern (S ) 0.88
( 0.05, Figure 6A,B) is comparable to that measured above
using magnetic field alignment. The diffuse spots in Figure 5C
represent the intersection with the Ewald sphere of a diffuse
torus, perpendicular to the nematic director, due to interparticle
interferences. This proves that the rodlike molecules align
parallel to the shear flow, as was intuitively expected.
At very high volume fractions of polypeptide (ca. >70 wt
%), reached by water evaporation from samples in the unsealed
Couette cell, a sharp diffraction line appeared, superimposed
over the diffuse spots. This diffraction line was due to the onset
of some positional long-range order typical of another meso-
phase. Its symmetry was determined by recording additional
diffraction lines on a different X-ray diffraction setup.12 Dif-
fraction lines in a ratio 1, 31/2, 2, 71/2 were observed (Figure 7),
which identified the symmetry of this mesophase as hexagonal.
This is not surprising because suspensions of rodlike particles
often form lyotropic hexagonal mesophases. Upon shearing in
the Couette cell, the hexagonal phase became partially aligned
as shown by the rather small mosaic spread of the reflection
(∼20° fwhm). The R-helices, and therefore the C6 axis, were
To analyze this system more quantitatively, the Onsager
model predicts the volume fractions Φn and Φi of the nematic
and isotropic phases at the transition: Φn ) 4.2 D/L and Φi )
3.3 D/L. For a short L-1 (Mw ) 62 kDa; L ) 32.3 nm and D
) 2.2 nm), we obtained Φn ) 29% and Φi ) 23%. These results
are in fair agreement with the experimental values of 47% and
38%, respectively, all the more because the Onsager model only
gives quantitative predictions for very long rods (L/D > 100).
It is also likely that the experimental values are higher than
predicted because the R-helix does have some finite flexibility,
(23) Impe´ror-Clerc, M.; Davidson, P. Eur. Phys. J. B 1999, 9, 93-104.
(24) Ramos, L.; Molino, F.; Porte, G. Langmuir 2000, 16, 5846-5848.
(25) Hamley, I. W. The Physics of Block-Copolymers; Oxford University
Press: New York, 1998.
(26) Camerel, F.; Gabriel, J. C. G.; Batail, P.; Davidson, P.; Lemaire, B. J.;
Schmutz, M.; Gulik-Krzywicki, T.; Bourgaux, C. Nano Lett. 2002, 2, 403-
407.
(27) Onsager, L. Ann. N.Y. Acad. Sci. 1949, 51, 627-659.
(28) Vroege, G. J.; Lekkerkerker, H. N. W. Rep. Prog. Phys. 1992, 55, 1241-
1309.
(20) Ugaz, V. M.; Cinader, D. K., Jr.; Burghardt, W. R. J. Rheol. 1997, 42,
379-394.
(21) Molino, F. R.; Berret, J. F.; Porte, G.; Diat, O.; Lindner, P. Eur. Phys. J.
B 1998, 3, 59-72.
(22) Hamley, I. W.; Pople, J. A.; Fairclough, J. P. A.; Terrilli, N. J.; Ryan, A.
J.; Booth, C.; Yu, G. E.; Diat, O.; Almdal, K.; Mortensen, K.; Vilgid, M.
J. Chem. Phys. 1998, 108, 6929-6936.
9
9104 J. AM. CHEM. SOC. VOL. 126, NO. 29, 2004