observed in BCP-directed inorganic nanostructures [14]. Thus, the importance of
these structures cannot be overemphasized. However, alignment of crystallographic
axes of 1D and 2D BCP structures is typically required for potential applications
that make use of the nanostructures rather than scalar polymer properties.
3.2 Three-Dimensional Cubic Structures
A variety of 3D structures have been observed in BCP SA. The majority of them are
cubic and bicontinuous structures, where all polymer blocks are continuous in all
three directions. Since cubic structures are isotropic, thus exhibiting isotropic
physical properties in any orientation, they can be very useful for applications
such as photonics [15, 16], phononics, batteries [17], and membranes. These
applications are discussed in Sect. 6.
Discontinuous 3D cubic structures commonly observed in BCP SA are spherical
morphologies as shown in Fig. 2. In this case, the minority block of the BCP forms
spheres and the spatial arrangement of the spheres varies from body-centered cubic
(Im3 m, Q229 space group) to closed packed spheres as the volume fraction of the
minority block and/or the product χN decrease [18]. Furthermore, the so-called A15
phase with Pm3 n symmetry was observed in amphiphilic di-BCPs containing a
linear block and a dendron block [17].
A variety of 3D cubic bicontinuous morphologies such as double gyroid, double
diamond, and plumber’s nightmare have been observed in BCP SA. The gyroid
has been observed not only in self-assembled BCPs but also in nature [19, 20],
intermetallic materials [21], and surfactants [22]. The gyroid network has chiral
helices along various crystallographic directions and thus is characterized by a lack
of mirror planes. Gyroid structures usually consist of two minority networks related
by an inversion. If these networks are composed of the same material, the structure
is a double gyroid with Ia3 d symmetry and space group Q230. Since inversion
symmetry exists, the double gyroid structure is achiral, where respective screw axes
with opposite handedness cancel local chirality. The alternating gyroid is composed
of two networks from different materials, thus disallowing an inversion center and
resulting in a chiral structure. The alternating gyroid, has I4 l 32 symmetry with
Q214 space group (see Fig. 2)
A plumber’s nightmare structure (Im3 m, Q229 space group) was observed in
BCP/oxide hybrid materials [11, 23]. The structure has two intertwining networks,
where both networks have the same structure but one of them is shifted along half
the diagonal as shown in Fig. 2. Due to structural similarity, a uniaxial contraction
of a double gyroid along the axis perpendicular to the [210] plane exhibits similar
real (transmission electron microscope, TEM) and reciprocal (small angle X-ray
scattering) space images [23].
Recently, the bicontinuous double diamond structure (Pn3 m, Q224 space group)
has been experimentally observed in a BCP system [24]. It is believed to be
Design and Applications of Multiscale Organic–Inorganic Hybrid Materials. . .
267
these structures cannot be overemphasized. However, alignment of crystallographic
axes of 1D and 2D BCP structures is typically required for potential applications
that make use of the nanostructures rather than scalar polymer properties.
3.2 Three-Dimensional Cubic Structures
A variety of 3D structures have been observed in BCP SA. The majority of them are
cubic and bicontinuous structures, where all polymer blocks are continuous in all
three directions. Since cubic structures are isotropic, thus exhibiting isotropic
physical properties in any orientation, they can be very useful for applications
such as photonics [15, 16], phononics, batteries [17], and membranes. These
applications are discussed in Sect. 6.
Discontinuous 3D cubic structures commonly observed in BCP SA are spherical
morphologies as shown in Fig. 2. In this case, the minority block of the BCP forms
spheres and the spatial arrangement of the spheres varies from body-centered cubic
(Im3 m, Q229 space group) to closed packed spheres as the volume fraction of the
minority block and/or the product χN decrease [18]. Furthermore, the so-called A15
phase with Pm3 n symmetry was observed in amphiphilic di-BCPs containing a
linear block and a dendron block [17].
A variety of 3D cubic bicontinuous morphologies such as double gyroid, double
diamond, and plumber’s nightmare have been observed in BCP SA. The gyroid
has been observed not only in self-assembled BCPs but also in nature [19, 20],
intermetallic materials [21], and surfactants [22]. The gyroid network has chiral
helices along various crystallographic directions and thus is characterized by a lack
of mirror planes. Gyroid structures usually consist of two minority networks related
by an inversion. If these networks are composed of the same material, the structure
is a double gyroid with Ia3 d symmetry and space group Q230. Since inversion
symmetry exists, the double gyroid structure is achiral, where respective screw axes
with opposite handedness cancel local chirality. The alternating gyroid is composed
of two networks from different materials, thus disallowing an inversion center and
resulting in a chiral structure. The alternating gyroid, has I4 l 32 symmetry with
Q214 space group (see Fig. 2)
A plumber’s nightmare structure (Im3 m, Q229 space group) was observed in
BCP/oxide hybrid materials [11, 23]. The structure has two intertwining networks,
where both networks have the same structure but one of them is shifted along half
the diagonal as shown in Fig. 2. Due to structural similarity, a uniaxial contraction
of a double gyroid along the axis perpendicular to the [210] plane exhibits similar
real (transmission electron microscope, TEM) and reciprocal (small angle X-ray
scattering) space images [23].
Recently, the bicontinuous double diamond structure (Pn3 m, Q224 space group)
has been experimentally observed in a BCP system [24]. It is believed to be
Design and Applications of Multiscale Organic–Inorganic Hybrid Materials. . .
267