186
9 Molecular Flexibility and Material Properties
The entropy transfer phenomenon has also been recognized in a series of inorganic complexes (MMX complexes) [41–44], which have been studied mainly from
interests on their variety in electronic states arising from its one-dimensional nature.
The entropy transfer between the alkyl chain and other moieties in ligands upon
phase transition demonstrates the universal importance of the role of alkyl chains as
the entropy reserver.
The entropy “capacity” of alkyl chains amounts to ca. 10 J K
−1 (mol of CH 2 )
−1
as revealed in the case of fusion of n-alkanes (Fig. 6.6). Only two methylene groups
suffice to surmount the entropy increment expected for the positional melting. In
terms of the free energy, its contribution (T ΔS) at room temperature amounts to a
quarter of the hydrogen bond, which is the strongest interaction between molecules
(Sect. 1.2.6.1).
Finally, a comment is in order concerning the thermodynamic implication of the
entropy transfer. The transfer seemingly accompanies the decrease in entropy. At a
glance, the decrease contradicts the fundamental property of entropy: The entropy
is a monotonic non-decreasing function of temperature.
2 The entropy transfer and
the associated decrease in entropy are, however, compatible with thermodynamics
because the considered system is inseparable into “component” systems.
9.4.4 Chains in Liquid Crystals
Real thermotropic mesogens most often have long and flexible alkyl group(s) at
its end(s). Even for such mesogens, the excluded volume effect is, not explicitly
but implicitly, assumed as a driving force to form the smectic and nematic phases
[45, 46], because the assembly of hard rods undoubtedly exhibits these liquid crystalline phases besides the isotropic liquid [47, 48]. A theory by McMillan [49]
assumes that the chain elongates the molecular length. There is no doubt concerning
this point. In the context of the melting of molecular crystals described in Chap. 6,
however, some questions arise for the alkyl chains: When and how does the chain
melt during the process? Is there any active role played by the alkyl chains in liquid
crystals? Although some roles played by alkyl chains were theoretically suggested
in the 1980s [50–57], little efforts have been paid experimentally to this subject.
9.4.4.1 Chain Melting and Entropic Stabilization
It is trivially unnecessary to seek for the particular role(s) in the liquid crystal formation for the alkyl chains if they remain rigid and ordered in the liquid state because
the molecules behave as (semi)rigid rods. However, the chain-length dependence
of the cumulative entropies of transitions up to the isotropic liquid (Fig. 6.6) indi2 C p = T (∂ S/∂ T ) p ≥ C v > 0. The last inequality is a condition of the thermodynamic stability of
the system.
9 Molecular Flexibility and Material Properties
The entropy transfer phenomenon has also been recognized in a series of inorganic complexes (MMX complexes) [41–44], which have been studied mainly from
interests on their variety in electronic states arising from its one-dimensional nature.
The entropy transfer between the alkyl chain and other moieties in ligands upon
phase transition demonstrates the universal importance of the role of alkyl chains as
the entropy reserver.
The entropy “capacity” of alkyl chains amounts to ca. 10 J K
−1 (mol of CH 2 )
−1
as revealed in the case of fusion of n-alkanes (Fig. 6.6). Only two methylene groups
suffice to surmount the entropy increment expected for the positional melting. In
terms of the free energy, its contribution (T ΔS) at room temperature amounts to a
quarter of the hydrogen bond, which is the strongest interaction between molecules
(Sect. 1.2.6.1).
Finally, a comment is in order concerning the thermodynamic implication of the
entropy transfer. The transfer seemingly accompanies the decrease in entropy. At a
glance, the decrease contradicts the fundamental property of entropy: The entropy
is a monotonic non-decreasing function of temperature.
2 The entropy transfer and
the associated decrease in entropy are, however, compatible with thermodynamics
because the considered system is inseparable into “component” systems.
9.4.4 Chains in Liquid Crystals
Real thermotropic mesogens most often have long and flexible alkyl group(s) at
its end(s). Even for such mesogens, the excluded volume effect is, not explicitly
but implicitly, assumed as a driving force to form the smectic and nematic phases
[45, 46], because the assembly of hard rods undoubtedly exhibits these liquid crystalline phases besides the isotropic liquid [47, 48]. A theory by McMillan [49]
assumes that the chain elongates the molecular length. There is no doubt concerning
this point. In the context of the melting of molecular crystals described in Chap. 6,
however, some questions arise for the alkyl chains: When and how does the chain
melt during the process? Is there any active role played by the alkyl chains in liquid
crystals? Although some roles played by alkyl chains were theoretically suggested
in the 1980s [50–57], little efforts have been paid experimentally to this subject.
9.4.4.1 Chain Melting and Entropic Stabilization
It is trivially unnecessary to seek for the particular role(s) in the liquid crystal formation for the alkyl chains if they remain rigid and ordered in the liquid state because
the molecules behave as (semi)rigid rods. However, the chain-length dependence
of the cumulative entropies of transitions up to the isotropic liquid (Fig. 6.6) indi2 C p = T (∂ S/∂ T ) p ≥ C v > 0. The last inequality is a condition of the thermodynamic stability of
the system.