10.3 Molecular Crystals as Stage for Novelties
217
gyration along the direction of the rod of a jungle gym. The gyration angle is cos
−1 1
3
from a junction to the neighboring junction. These results are compatible with the
following model of molecular aggregation. In essence, the molecules locally form a
single layer (short-chain cases) or doubled layers (long-chain), the normal of which
coincides with a body diagonal, and the long axes of molecules continuously twist
from a junction to neighboring junctions along a rod of the jungle gym. It is crucially
important that the model is free from the packing frustration at junctions. It is also
interesting to note that the formation of doubled core layers brings the recovery of
the volume fraction of core parts, possibly resulting in the reentrance to the Gyroid
phase [88, 100] in the phase diagrams of BABH(n) [91, 101] and ANBC(n) [102].
Having revealed the average core arrangements in the Gyroid phase, it is in order to
consider the packing of alkyl chains [100]. Since molecules locally form layers with
normal coinciding the body diagonal of the unit cell, the chain-length dependence
of the body diagonal should give useful information as in orthogonal smectic phases
discussed in Sect. 9.4.4.4. The analysis yields a smaller increment for long-chain
BABH(n) than those discussed there. The increment is compatible with the normal
orientation to the layer on average. The smaller increment implies that the chain
layer is not bilayer-like but monolayer-like. That is, the single chain-layer consists
of chains from both sides.
The molecular description enables us to discuss the formation mechanism of the
Gyroid phases, which is ubiquitous in the materials world. The sense of the gyration
of molecular arrangements on jungle gyms is opposing in two subspaces, following
the chirality of two subspaces divided by the G surface. Some mechanisms, which
are mostly independent and do not interfere with one another, have been suggested to
rationalize the formation of the Gyroid phase [84, 103–109]. If we once accept such
mechanisms, it is possible to imagine a virtual lattice structure on jungle gyms. The
linear segregation of domains with opposing local chirality with equal volumes is an
essential feature of the Gyroid phase. It plausibly originates in the anti-spindle shape
of molecules assuming some next-nearest-neighbor interaction, as naïvely and widely
assumed [101]. Since constituting molecules are seemingly achiral in real systems,
molecules should have the same volume for opposing twists. The Gyroid phase
guarantees the volumetric equivalence of two spaces. The equal preference for the
two handedness of twisted molecular arrangement is, therefore, another microscopic
factor that brings the superior stability of the Gyroid phase, in addition to the factors
previously identified by existing treatments [84, 103–109].
The simulations assuming the preference for the twist between neighboring
molecules [89] do not give a symptom of a phase exhibiting net chirality (Sect. 7.3).
However, the nano segregation of local chirality may emerge. These facts suggest
that the chirality of a molecule itself is necessary for such chiral phases. Recently,
chiral phases made of seemingly and dynamically achiral molecules were reported
[110–114]. The results described suggest that the flexibility of molecules (twisting
degrees of freedom around single bonds) and a resulting adaptive chirality responding to the environment play important roles in the formation of such chiral phases,
as naïvely assumed without reasoning by the authors of previous reports [112–114].
217
gyration along the direction of the rod of a jungle gym. The gyration angle is cos
−1 1
3
from a junction to the neighboring junction. These results are compatible with the
following model of molecular aggregation. In essence, the molecules locally form a
single layer (short-chain cases) or doubled layers (long-chain), the normal of which
coincides with a body diagonal, and the long axes of molecules continuously twist
from a junction to neighboring junctions along a rod of the jungle gym. It is crucially
important that the model is free from the packing frustration at junctions. It is also
interesting to note that the formation of doubled core layers brings the recovery of
the volume fraction of core parts, possibly resulting in the reentrance to the Gyroid
phase [88, 100] in the phase diagrams of BABH(n) [91, 101] and ANBC(n) [102].
Having revealed the average core arrangements in the Gyroid phase, it is in order to
consider the packing of alkyl chains [100]. Since molecules locally form layers with
normal coinciding the body diagonal of the unit cell, the chain-length dependence
of the body diagonal should give useful information as in orthogonal smectic phases
discussed in Sect. 9.4.4.4. The analysis yields a smaller increment for long-chain
BABH(n) than those discussed there. The increment is compatible with the normal
orientation to the layer on average. The smaller increment implies that the chain
layer is not bilayer-like but monolayer-like. That is, the single chain-layer consists
of chains from both sides.
The molecular description enables us to discuss the formation mechanism of the
Gyroid phases, which is ubiquitous in the materials world. The sense of the gyration
of molecular arrangements on jungle gyms is opposing in two subspaces, following
the chirality of two subspaces divided by the G surface. Some mechanisms, which
are mostly independent and do not interfere with one another, have been suggested to
rationalize the formation of the Gyroid phase [84, 103–109]. If we once accept such
mechanisms, it is possible to imagine a virtual lattice structure on jungle gyms. The
linear segregation of domains with opposing local chirality with equal volumes is an
essential feature of the Gyroid phase. It plausibly originates in the anti-spindle shape
of molecules assuming some next-nearest-neighbor interaction, as naïvely and widely
assumed [101]. Since constituting molecules are seemingly achiral in real systems,
molecules should have the same volume for opposing twists. The Gyroid phase
guarantees the volumetric equivalence of two spaces. The equal preference for the
two handedness of twisted molecular arrangement is, therefore, another microscopic
factor that brings the superior stability of the Gyroid phase, in addition to the factors
previously identified by existing treatments [84, 103–109].
The simulations assuming the preference for the twist between neighboring
molecules [89] do not give a symptom of a phase exhibiting net chirality (Sect. 7.3).
However, the nano segregation of local chirality may emerge. These facts suggest
that the chirality of a molecule itself is necessary for such chiral phases. Recently,
chiral phases made of seemingly and dynamically achiral molecules were reported
[110–114]. The results described suggest that the flexibility of molecules (twisting
degrees of freedom around single bonds) and a resulting adaptive chirality responding to the environment play important roles in the formation of such chiral phases,
as naïvely assumed without reasoning by the authors of previous reports [112–114].