Double-twist cylinders in liquid crystalline cholesteric blue phases observed by transmission electron microscopy

Cholesteric blue phases are liquid crystalline phases in which the constituent rod-like molecules spontaneously form three-dimensional, helical structures. Despite theoretical predictions that they are composed of cylindrical substructures within which the liquid crystal molecules are doubly twisted, real space observation of the arrangement of such structures had not been performed. Through transmission electron microscopy of photopolymerized blue phases with controlled lattice plane orientations, we report real space observation and comparison of the lattice structures of blue phases I and II. The two systems show distinctly different contrasts, reflecting the theoretically predicted, body centred and simple cubic arrangement of the double-twist cylinders. Transmission electron microscopy also reveals different tendencies of the two blue phases to align on unidirectionally rubbed surfaces. We thus show that TEM observation of alignment-controlled, photopolymerized liquid crystals can be a powerful tool to investigate complex liquid crystalline order.


Refractive index dispersion of quenched BP I and BP II sample.
The refractive indices of the photopolymerizable BP films were evaluated by means of spectroscopic ellipsometry (J.A. Woollam, M-2000). Because the films have no absorption resonances in the visible region, Cauchy model was employed to describe the wavelength dispersion. Figure S1 shows the wavelength dependence of the refractive index for BPs I and II. At 387 nm and 455 nm where Bragg reflection is observed for BPs I and II, respectively, the corresponding refractive indices are 1.64 and 1.61. The refractive indices for  = 420 nm, at which the Kossel diagrams were observed, are 1.63 and 1.62.

Microtoming-induced compression in a photopolymerized liquid crystal.
Compression of the specimen along the cut direction is an artifact often encountered in soft materials 1 . Figure S2 shows a TEM image of BP I where a knife mark is visible in the field of view. The knife edge is sharp, but not perfectly sharp, thus causing deformation close to the surface of the sample section. Knife marks are artificial furrows caused by places where the knife edge is damaged. The image is compressed in the direction of the knife mark, thereby supporting that distortion of the image is caused by the microtoming process.

TEM contrast in a long-pitch cholesteric liquid crystal film.
A long-pitch cholesteric liquid crystal was prepared by adjusting the concentration of the chiral dopant to 0.2 wt%. The cholesteric pitch was first determined optically by the Grandjean-Cano-method 2 , using a glass sandwich cell with a wedge-angle of 0.31 °. As seen in the POM image of Fig. S3a, a discontinuous change in the number of half-pitches along the wedge direction causes a periodic array of disclination lines to be observed. The pitch of the cholesteric helix, p, can be evaluated from the spacing of the disclination line, , and the wedge angle, , according to the equation tanp/2. The periodicity of the disclination lines is 1070 µm (average measured at 10 points), which yields a pitch length of approximately 12 µm.
After photopolymerizing the sample, its cross-section was observed in the TEM. The sample was embedded in epoxy resin following the procedure described in text, but the cut direction was adjusted for cross-sectional observation. Figure S3b

Cross-sectional structures of disclinations
The unit cell of BPs I and II not only contain DTCs, but also regions of disorder where the orientation of the LC director cannot be defined unanimously (disclinations) 3 .
Considering that such regions typically have reduced molecular order 4 and thus can be considered to have lower densities than the bulk 5 , disclinations may also affect the image contrast. We show that this possibility is ruled out by showing that the observed contrast of disclinations would be different from that observed in experiment if the disclinations were the source of the image contrast. Figure S4a and c show cross sectional structures of disclinations shaded in green in Fig. 3a and d of the manuscript. Figure S4b   Inset shows the FFT image. Scale bars, 300 nm.

Wide-field TEM observation of BPs I and II
TEM observations were performed at different locations from those in Fig. 5 of the manuscript. Figure S5 shows TEM images of BPs I and II at two different locations, clearly representing the polydomain nature of BP I, and monodomain nature of BP II.   FFT image in the inset shows that the lattice is compressed in the direction of the knifemark. Arrow indicates a cutting knife direction trace. Scale bar 5 µm. Figure S7 shows the histograms of the domain size and azimuthal orientation angle for BP I.
As described in the main text, the domain size was measured at 58 domains and the orientation angle was measured at 98 domains. The domain size had a log-normal distribution with a mode of 6.7 µm 2 and logarithmic standard deviation of 0.97. The azimuthal orientation of the lattice indicated only a weak tendency to orient along the rubbing direction, agreeing with the quasi-isotropic FFT pattern observed.