9.4 Conformational Disordering of Alkyl Groups
193
The nano-segregated structure thus revealed has a layered structure characteristic
to smectics, and seems reasonable concerning its formation mechanism. The structure
is also consistent with the excellent carrier mobility reported for SmE compounds
[80] because the electron transfer is possible even in the dynamically disordered state
[4, 5].
The fact that the SmE phase is the closest to the ordered crystal again plays essential importance here. The above description has not relied on any specific properties
of compounds under discussion beyond the possession of an alkyl chain attached
to the core moiety. The supposed mechanism to stabilize such a segregated structure should apply equally to a wide variety of real mesogens. In this respect, the
nano-segregated structure should be a fundamental structure of any smectic phases.
Although the nano-segregation may compete with two-dimensional fluidity, which
is deeply involved in the formation mechanism of the smectic phase of rigid rodlike
molecules [47, 48], its entropic gain would be smaller than the chain entropy in real
mesogens with an alkyl chain(s). It is noteworthy that the molecular aggregation
in smectic phases may be significantly different between asymmetric (chain–core)
mesogens and seemingly symmetric (chain–core–chain) mesogens, in which the
two-dimensional fluidity can play a substantial role in its stabilization.
9.4.4.4 Alkyl Chains in Smectics: Revisit
The layer spacing (d in Fig. 9.10) is significantly larger than the length of nCB
molecules with the fully extended alkyl chain, in contrast to the “ideal” SmA phase
naïvely expected for a system of hard rodlike objects [47, 48]. Thus, the structure
of the SmA phase in nCB was the object of extensive studies. The assumption of
interdigitated bilayers [83, 84] finally resolved this discrepancy. The resultant model
of the smectic phase is denoted as the SmA d phase. This understanding mainly
concerns the cores. The information concerning the aggregation structures of the
alkyl chains, on average, lies in the systematic dependence of the layer spacing
on the chain length, as noticed in Sect. 9.4.2. The discussion here concerns only
orthogonal phases, properties of which are isotropic around the layer normal [93].
Since the polarizability of the core part dominates, the cores are widely believed to
be normal to the smectic layers.
When the alkyl chain is in the so-called all-trans conformation shown in Fig. 9.11,
the length of the chain increases with the rate of a sin
θ
2
per methylene.
4 Here, a is
the C–C bond length (ca. 1.5 Å), and θ is the bond angle, which is ideally equal
to 2 cos
−1
√
1/3 ≈ 109.5
◦ . Using these typical values, we obtain an estimate as
a
√
2/3 ≈ 1.2 Å(CH 2 )
−1 . However, we know that the alkyl chains in liquid crystalline phases, including the SmE phase, are mostly molten. The assumption of the
all-trans conformation is inapplicable accordingly. Since the estimation needs the
magnitude appropriately averaged, the logical deduction is not only complicated but
also impractical.
4 Hereafter, “per methylene” is indicated by (CH 2 ) −1 in numerical expressions.
193
The nano-segregated structure thus revealed has a layered structure characteristic
to smectics, and seems reasonable concerning its formation mechanism. The structure
is also consistent with the excellent carrier mobility reported for SmE compounds
[80] because the electron transfer is possible even in the dynamically disordered state
[4, 5].
The fact that the SmE phase is the closest to the ordered crystal again plays essential importance here. The above description has not relied on any specific properties
of compounds under discussion beyond the possession of an alkyl chain attached
to the core moiety. The supposed mechanism to stabilize such a segregated structure should apply equally to a wide variety of real mesogens. In this respect, the
nano-segregated structure should be a fundamental structure of any smectic phases.
Although the nano-segregation may compete with two-dimensional fluidity, which
is deeply involved in the formation mechanism of the smectic phase of rigid rodlike
molecules [47, 48], its entropic gain would be smaller than the chain entropy in real
mesogens with an alkyl chain(s). It is noteworthy that the molecular aggregation
in smectic phases may be significantly different between asymmetric (chain–core)
mesogens and seemingly symmetric (chain–core–chain) mesogens, in which the
two-dimensional fluidity can play a substantial role in its stabilization.
9.4.4.4 Alkyl Chains in Smectics: Revisit
The layer spacing (d in Fig. 9.10) is significantly larger than the length of nCB
molecules with the fully extended alkyl chain, in contrast to the “ideal” SmA phase
naïvely expected for a system of hard rodlike objects [47, 48]. Thus, the structure
of the SmA phase in nCB was the object of extensive studies. The assumption of
interdigitated bilayers [83, 84] finally resolved this discrepancy. The resultant model
of the smectic phase is denoted as the SmA d phase. This understanding mainly
concerns the cores. The information concerning the aggregation structures of the
alkyl chains, on average, lies in the systematic dependence of the layer spacing
on the chain length, as noticed in Sect. 9.4.2. The discussion here concerns only
orthogonal phases, properties of which are isotropic around the layer normal [93].
Since the polarizability of the core part dominates, the cores are widely believed to
be normal to the smectic layers.
When the alkyl chain is in the so-called all-trans conformation shown in Fig. 9.11,
the length of the chain increases with the rate of a sin
θ
2
per methylene.
4 Here, a is
the C–C bond length (ca. 1.5 Å), and θ is the bond angle, which is ideally equal
to 2 cos
−1
√
1/3 ≈ 109.5
◦ . Using these typical values, we obtain an estimate as
a
√
2/3 ≈ 1.2 Å(CH 2 )
−1 . However, we know that the alkyl chains in liquid crystalline phases, including the SmE phase, are mostly molten. The assumption of the
all-trans conformation is inapplicable accordingly. Since the estimation needs the
magnitude appropriately averaged, the logical deduction is not only complicated but
also impractical.
4 Hereafter, “per methylene” is indicated by (CH 2 ) −1 in numerical expressions.