an unstable phase due to energetically unfavorable chain stretching in the nodes of
the minority networks. Local packing of short-range ordered segments, energetically more favorable than random packing, can compensate the free energy penalty
from the frustration, resulting in stable bicontinuous double diamond structures.
Although a few 3D isotropic cubic network phases have already been observed,
other cubic network phases have stayed elusive in BCP SA, such as the I-WP [25],
Neovius [26], K surface [27], and Lidinoid [28] structures (see Fig. 2). Packing
frustration of polymer chains in the network nodes of these structures is a primary
hurdle for formation of these phases. However, as shown in the cases of the
plumber’s nightmare and double diamond structures, BCP co-assembly with additive molecules or ordered local packing of monomer units may open new routes
to such cubic structures.
3.3 Three-Dimensional Noncubic Structures
A perforated lamellar structure (P6 3 /mmc, 194 space group) has been frequently
observed in BCP SA. The structure is believed to be a metastable phase in di-BCPs
since it is energetically less stable than a competing phase, the double gyroid
morphology. Thus, the perforated lamellar structure observed experimentally may
be a kinetically trapped state that lasts for a reasonably long time period. The
structure has layered lamellar sheets that are connected through cylindrical
channels. The channels arrange hexagonally and perpendicular to the lamellar
planes (see Fig. 2).
A woodpile structure, a similar layered structure with an unidentified space group
similar to the O70 space group (Fddd), was observed in a BCP/aluminosilicate
assembly [9]. In contrast to the perforated lamellar structure, zig-zag cylinders are
stacked layer-by-layer (see Fig. 2). Although a zig-zag cylinder is usually energetically less stable than a parallel cylinder due to larger interfacial energy, the relaxed
chain conformation of polymer chains, leading to a reduced entropic penalty, may
allow the zig-zag cylinder formation.
Most of the noncubic structures are not continuous in all three directions.
However, one of the O70 structures (Fddd, O70 space group) is bicontinuous, as
shown in Fig. 2. Its structural characteristics are quite similar to the gyroid
morphologies [29], where triple nodes are connected in all three directions.
Non-frustrated ABC triblock terpolymers, where interactions between terminal
blocks are most repulsive, generate the bicontinuous structure [29, 30]. Later, it
was shown that the structure exists in di-BCP phase space both theoretically and
experimentally [5, 31]. Interestingly, it appears in a very narrow regime of di-BCP
phase space but occupies quite a wide phase space in non-frustrated triblock
terpolymer SA [5, 30].
Despite the nonchiral nature of monomer units, BCPs can generate chiral
morphologies such as in the alternating gyroid. Due to the identical free energy
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the minority networks. Local packing of short-range ordered segments, energetically more favorable than random packing, can compensate the free energy penalty
from the frustration, resulting in stable bicontinuous double diamond structures.
Although a few 3D isotropic cubic network phases have already been observed,
other cubic network phases have stayed elusive in BCP SA, such as the I-WP [25],
Neovius [26], K surface [27], and Lidinoid [28] structures (see Fig. 2). Packing
frustration of polymer chains in the network nodes of these structures is a primary
hurdle for formation of these phases. However, as shown in the cases of the
plumber’s nightmare and double diamond structures, BCP co-assembly with additive molecules or ordered local packing of monomer units may open new routes
to such cubic structures.
3.3 Three-Dimensional Noncubic Structures
A perforated lamellar structure (P6 3 /mmc, 194 space group) has been frequently
observed in BCP SA. The structure is believed to be a metastable phase in di-BCPs
since it is energetically less stable than a competing phase, the double gyroid
morphology. Thus, the perforated lamellar structure observed experimentally may
be a kinetically trapped state that lasts for a reasonably long time period. The
structure has layered lamellar sheets that are connected through cylindrical
channels. The channels arrange hexagonally and perpendicular to the lamellar
planes (see Fig. 2).
A woodpile structure, a similar layered structure with an unidentified space group
similar to the O70 space group (Fddd), was observed in a BCP/aluminosilicate
assembly [9]. In contrast to the perforated lamellar structure, zig-zag cylinders are
stacked layer-by-layer (see Fig. 2). Although a zig-zag cylinder is usually energetically less stable than a parallel cylinder due to larger interfacial energy, the relaxed
chain conformation of polymer chains, leading to a reduced entropic penalty, may
allow the zig-zag cylinder formation.
Most of the noncubic structures are not continuous in all three directions.
However, one of the O70 structures (Fddd, O70 space group) is bicontinuous, as
shown in Fig. 2. Its structural characteristics are quite similar to the gyroid
morphologies [29], where triple nodes are connected in all three directions.
Non-frustrated ABC triblock terpolymers, where interactions between terminal
blocks are most repulsive, generate the bicontinuous structure [29, 30]. Later, it
was shown that the structure exists in di-BCP phase space both theoretically and
experimentally [5, 31]. Interestingly, it appears in a very narrow regime of di-BCP
phase space but occupies quite a wide phase space in non-frustrated triblock
terpolymer SA [5, 30].
Despite the nonchiral nature of monomer units, BCPs can generate chiral
morphologies such as in the alternating gyroid. Due to the identical free energy
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K. Hur and U. Wiesner