276 15 Liquid Crystals and Other Anisotropic Fluids
years, the research dealing with blue phases was considered as a rather exotic topic.
This changed in 2005 when substances with a wide temperature range of blue-phase
liquid crystalline state were found [75]. In the meantime, a blue phase LC display
has been developed.
Colloidal particles are localized at the defects of liquid crystals and they may form
periodic structures [76]. Colloidal particles immersed in a blue phase liquid crystal
stabilize the blue phase [77]. The resulting 3D periodic structure has the optical
properties of ordinary colloidal crystals [78] but is mechanically more stable.
15.1.2 Smectic Phases.
Smectic liquid crystals possess a partial positional ordering, in addition to an ori-
entational order. The different phases are labelled by the lettersA,B,C,...in
the order they were originally identified as distinct thermodynamic phases, before
the underlying microscopic structure was identified. The most prominent cases
are thesmectic Aandsmectic Cphases, where the centers of mass of the mole-
cules are preferentially located in planes.
In theA-phase, the director specifying the average direction of the long axes of
the molecules is perpendicular to the planes, in theC-phase, it is tilted with respect to
the planes. A cartoon of the orientation of ‘particles’ in the smectic A and C phases
is shown in Fig.15.3. The tilt angleθwhich distinguishes the C from the A phase
can be used as an order parameter, e.g. see [67]. Alternatively, cf. [79], the transition
A→Ccan be looked upon as a spontaneous shear displacementu(r)of the centers
of mass of the molecules whereuand its gradient are parallel and perpendicular,
respectively, to the directorn. Withuinx-direction and its gradient iny-direction,
the deformation∂ux/∂yis equal to tanθ.Intheferro-electricsmecticC∗liquid
crystals, the electric polarization is proportional to the axial vector associated with
the antisymmetric part of the deformation tensor∇μuν, [79].
Thesmectic Bphase is similar to theA-phase but with an additional hexago-
nal short range order of neighbor molecules within a plane. Thesmectic Dphase
has a 3D cubic order, rather than the layered structure typical for smectics. For
chiral and ferro-electric smectics, as well as columnar phases, andbanana phases
see, e.g. [67–69].
Fig. 15.3Cartoon of the
orientation of molecules in
the smectic A (left)and
smectic C (right) phases, as
shown in [74]