148
7 Liquid Crystals
7.1.2.3 Columnar Phases
The (uniaxial) nematic phase is common in ensembles of highly anisotropic
molecules, whereas layered smectic phases are characteristic of ensembles of elongated molecules. The counterpart of the latter in ensembles of flat molecules are
columnar phases, though columnar phases made of rod-shaped mesogens are also
known to exist in reality.
Molecules stack on each other to form separate columns, which aggregate in two
dimensions forming a square or triangular (hexagonal) lattice. Many columnar phases
are discriminated based on aggregation modes of columns or inside the columns (e.g.,
titled or normal). For details, the readers are directed to specialized books of liquid
crystal science [1].
7.1.2.4 Cubic Phases
Some liquid crystalline compounds exhibit mesophases having a cubic symmetry.
These are generally called cubic phases. Figure 4.1a shows a basic structure of the
Gyroid phase, which appears most often. The cubic symmetry accompanies a threedimensional periodicity, leading to an understanding of such structures as crystals.
The number of molecules within a unit cell is of the order of 10
3 . They share space
groups with cubic phases in lyotropic liquid crystals and block copolymers, both
of which contain plural “components.” In the case of cubic phases consisting of
small molecules, requisites for their formation are under extensive study. A concise description of cubic phases is unavailable, accordingly. However, the molecular
packing recently revealed (see Fig. 10.8) [6] suggests the molecular shape is essential
for them, as will be discussed in Sect. 10.3.5.
7.1.2.5 Chiral Phases
If a body and its mirror image cannot be exactly superimposed (like your right and
left hands), the body is termed “chiral.” When the body is a molecule, two types
of molecules (right- and left-handed) are equivalent in an isolated state, including
chemical reactivity with an achiral (= “not chiral”) molecule. In contrast, they are
different in interaction with chiral molecules. Such a difference remains even in
macroscopic properties of a macroscopic system unless the system consists of equal
amounts of the two counterparts. Adding a small number of chiral molecules to
the ensemble of achiral molecules also produce a chiral macroscopic system. Such
systems exhibit chiral phases not only for a crystal and isotropic liquid but also for
liquid crystals. Chiral liquid crystalline phases are indicated by adding an asterisk to
the abbreviation of phase (such as N* or SmC*).
The effect of the molecular chirality appears as a local tilt of neighboring
molecules. Note that the local tilt cannot extend over the three-dimensional space.
Some “defects” are necessary. In the chiral nematic (N*) phase, often called also as
7 Liquid Crystals
7.1.2.3 Columnar Phases
The (uniaxial) nematic phase is common in ensembles of highly anisotropic
molecules, whereas layered smectic phases are characteristic of ensembles of elongated molecules. The counterpart of the latter in ensembles of flat molecules are
columnar phases, though columnar phases made of rod-shaped mesogens are also
known to exist in reality.
Molecules stack on each other to form separate columns, which aggregate in two
dimensions forming a square or triangular (hexagonal) lattice. Many columnar phases
are discriminated based on aggregation modes of columns or inside the columns (e.g.,
titled or normal). For details, the readers are directed to specialized books of liquid
crystal science [1].
7.1.2.4 Cubic Phases
Some liquid crystalline compounds exhibit mesophases having a cubic symmetry.
These are generally called cubic phases. Figure 4.1a shows a basic structure of the
Gyroid phase, which appears most often. The cubic symmetry accompanies a threedimensional periodicity, leading to an understanding of such structures as crystals.
The number of molecules within a unit cell is of the order of 10
3 . They share space
groups with cubic phases in lyotropic liquid crystals and block copolymers, both
of which contain plural “components.” In the case of cubic phases consisting of
small molecules, requisites for their formation are under extensive study. A concise description of cubic phases is unavailable, accordingly. However, the molecular
packing recently revealed (see Fig. 10.8) [6] suggests the molecular shape is essential
for them, as will be discussed in Sect. 10.3.5.
7.1.2.5 Chiral Phases
If a body and its mirror image cannot be exactly superimposed (like your right and
left hands), the body is termed “chiral.” When the body is a molecule, two types
of molecules (right- and left-handed) are equivalent in an isolated state, including
chemical reactivity with an achiral (= “not chiral”) molecule. In contrast, they are
different in interaction with chiral molecules. Such a difference remains even in
macroscopic properties of a macroscopic system unless the system consists of equal
amounts of the two counterparts. Adding a small number of chiral molecules to
the ensemble of achiral molecules also produce a chiral macroscopic system. Such
systems exhibit chiral phases not only for a crystal and isotropic liquid but also for
liquid crystals. Chiral liquid crystalline phases are indicated by adding an asterisk to
the abbreviation of phase (such as N* or SmC*).
The effect of the molecular chirality appears as a local tilt of neighboring
molecules. Note that the local tilt cannot extend over the three-dimensional space.
Some “defects” are necessary. In the chiral nematic (N*) phase, often called also as