10.2 Molecular Crystals as Tunable Model System
209
DPTZ molecule prefers the planar form. Considering that the twist transition vanishes
in difluorobiphenyl (DFBP), the single-particle potential of which still has the hump
at the planar form in the isolated state, DPTZ is effectively an impurity without the
tendency to the twist. We thus expect that the inclusion of DPTZ corresponds to the
disappearance of the relevant degree with a minimum perturbation on the crystal
lattice.
The investigation of solid TP samples doped with 2 and 5% DPTZ indicated
a lower temperature of the twist transition and the reduction in the excess heat
capacity due to the transition [62]. The lowering is proportional to the concentration
(x) of doped DPTZ. That is, ΔT trs ≈
2
3
xT trs . The reduction in the excess entropy
Δ(ΔS) is compatible with Δ(ΔS)/x = N k B ln 2. These results are consistent with
that expected for the so-called mean-field treatment of the Ising model, except for
the more modest decrease than ΔT trs = xT trs .
This investigation offered a valuable byproduct, the experimental identification
of the entity that behaves like the “spin.” The reduction in the entropy of transition
by the doping is proportional to the net entropy involved in this transition. It is
noteworthy that an operational baseline is arbitrary for this purpose as long as it is
common for other doping levels. The deduced net entropy is k B ln 2 per TP molecule.
This magnitude asserts that a TP molecule carries only a single degree of freedom
for disordering. The situation is possible only when the two conformations of the
alternate twist are allowed, but the other twist modes are prohibited. Namely, the
motional correlation, discussed in Sect. 10.1, is almost perfect inside a molecule.
In contrast to a rather trivial (and anticipated) result in the case of the orderdisorder transition, the study of the displacive transition revealed marked effects
depending on the nature of impurity [63]. The compounds chosen as impurities
are naphthalene (NA) and DFBP. A molecule of DFBP is twisted in the isolated
state but planar in crystal down to low temperatures without the twist transition
[49, 55], as described above. The twisting is possible with a low frequency in the
crystal accordingly. On the other hand, NA is a condensed aromatic with a planar
conformation. The characteristic frequency of the “twisting” vibration should be
much higher than those of BP and DFBP.
Since the transition temperature of the pure biphenyl crystal is rather low (40.4
K), the heat capacity calorimetry was used to monitor the effects of impurities. While
the heat capacity anomaly scarcely exhibited the effect (without the change in the
transition temperature) in the 1% NA-doped BP, that disappeared in the DFBP-doped
BP with the same concentration. A negligible effect on the transition temperature in
the NA-doped BP is remarkably different from the order-disorder transition of TP
crystal. Also, the survival and the disappearance of the twist transition are counterintuitive because the NA molecule has effectively no twisting degree, whereas the
DFBP molecule has.
The counterintuitive behaviors resemble the impurity effect on lattice vibrations
[64, 65]. When an atom that has a significantly different mass exists in a crystal lattice,
a single vibrational mode localizes on the atom. In contrast, the mild difference in
mass causes a weak localization of vibrational modes with a large localization radius.
Although the variable parameter in the case of the BP crystal is not the mass but the
209
DPTZ molecule prefers the planar form. Considering that the twist transition vanishes
in difluorobiphenyl (DFBP), the single-particle potential of which still has the hump
at the planar form in the isolated state, DPTZ is effectively an impurity without the
tendency to the twist. We thus expect that the inclusion of DPTZ corresponds to the
disappearance of the relevant degree with a minimum perturbation on the crystal
lattice.
The investigation of solid TP samples doped with 2 and 5% DPTZ indicated
a lower temperature of the twist transition and the reduction in the excess heat
capacity due to the transition [62]. The lowering is proportional to the concentration
(x) of doped DPTZ. That is, ΔT trs ≈
2
3
xT trs . The reduction in the excess entropy
Δ(ΔS) is compatible with Δ(ΔS)/x = N k B ln 2. These results are consistent with
that expected for the so-called mean-field treatment of the Ising model, except for
the more modest decrease than ΔT trs = xT trs .
This investigation offered a valuable byproduct, the experimental identification
of the entity that behaves like the “spin.” The reduction in the entropy of transition
by the doping is proportional to the net entropy involved in this transition. It is
noteworthy that an operational baseline is arbitrary for this purpose as long as it is
common for other doping levels. The deduced net entropy is k B ln 2 per TP molecule.
This magnitude asserts that a TP molecule carries only a single degree of freedom
for disordering. The situation is possible only when the two conformations of the
alternate twist are allowed, but the other twist modes are prohibited. Namely, the
motional correlation, discussed in Sect. 10.1, is almost perfect inside a molecule.
In contrast to a rather trivial (and anticipated) result in the case of the orderdisorder transition, the study of the displacive transition revealed marked effects
depending on the nature of impurity [63]. The compounds chosen as impurities
are naphthalene (NA) and DFBP. A molecule of DFBP is twisted in the isolated
state but planar in crystal down to low temperatures without the twist transition
[49, 55], as described above. The twisting is possible with a low frequency in the
crystal accordingly. On the other hand, NA is a condensed aromatic with a planar
conformation. The characteristic frequency of the “twisting” vibration should be
much higher than those of BP and DFBP.
Since the transition temperature of the pure biphenyl crystal is rather low (40.4
K), the heat capacity calorimetry was used to monitor the effects of impurities. While
the heat capacity anomaly scarcely exhibited the effect (without the change in the
transition temperature) in the 1% NA-doped BP, that disappeared in the DFBP-doped
BP with the same concentration. A negligible effect on the transition temperature in
the NA-doped BP is remarkably different from the order-disorder transition of TP
crystal. Also, the survival and the disappearance of the twist transition are counterintuitive because the NA molecule has effectively no twisting degree, whereas the
DFBP molecule has.
The counterintuitive behaviors resemble the impurity effect on lattice vibrations
[64, 65]. When an atom that has a significantly different mass exists in a crystal lattice,
a single vibrational mode localizes on the atom. In contrast, the mild difference in
mass causes a weak localization of vibrational modes with a large localization radius.
Although the variable parameter in the case of the BP crystal is not the mass but the