484
Bull. Chem. Soc. Jpn. Vol. 85, No. 4 (2012)
Crystalline Phase Transition of Adamantane Derivative
For the fusion transition, the translational motions also take
place. So the sums of the entropy of fusion are:
7.16
7.14
7.12
7.10
7.08
7.06
7.04
7.02
7.00
6.98
α = 4.9 x10-3
X
X
X
ꢀfusSm0
¼
ꢀvSm0 þ
ꢀ
ꢀ
int:rot:Sm0
X
X
þ
orient:Sm0 þ
ꢀ
tra:Sm0
ð2Þ
P
where
ꢀ
tra:Sm0 denotes the contribution of translational
motion. Formula (1) applies to solid to plastic crystal transition
T = 177.8°C
of neopentane.
α = 3.5 x10-3
P
Why is
ꢀfusSm0 of tetrakis(1-adamantanecarboxymethyl)-
methane significantly larger than Timmermans’ criterion of
plastic crystal, and is it a plastic crystal or only a highly
disordered crystalline phase? The former question might
be explained based on the two formulas above. From the
comparison of the structures between neopentane and tetra-
kis(1-adamantanecarboxymethyl)methane we know that: 1)
The four arms of tetrakis(1-adamantanecarboxymethyl)methane
are much longer than the arms of neopentane, so there is more
space for the moving of the arms. 2) Good flexibility of the ester
bond makes the arms rotate more easily. 3) Timmermans’
criterion of plastic crystal is about the molar entropy change
of the fusion, and the additive property of entropy makes
the entropy change of tetrakis(1-adamantanecarboxymethyl)-
methane larger for the randomness probability of tetrakis(1-
adamantanecarboxymethyl)methane itself is larger than neopen-
tane. Since there is already isotropic reorientation of tetrakis(1-
adamantanecarboxymethyl)methane in phase I, its fusion en-
tropy (¦Sfus = 70.07 J mol¹1 K¹1) is smaller than structurally
similar compounds forming “rigid” crystal, even smaller
than the transition entropy of phase II ¼ I (¦Strs = 110.55
J mol¹1 K¹1). Combine this with the following two facts:
a) The fusion entropy (¦Sfus = 70.07 J mol¹1 K¹1) of tetra-
kis(1-adamantanecarboxymethyl)methane is much larger than
Timmermans’ criterion; b) The crystal system of tetrakis(1-
adamantanecarboxymethyl)methane in phase I is not highly
symmetric. This suggests that phase I of tetrakis(1-adamantane-
carboxymethyl)methane is not a plastic crystalline phase but a
highly disordered crystalline phase.
150 155 160 165 170 175 180 185 190 195
T/°C
Figure 5. Temperature evolution of cell volume in low-
and high-temperature phases. The cross-point temperature
is the solid-solid transition temperature.
lent positions can be assumed. With increasing temperature, the
whole tetrakis(1-adamantanecarboxymethyl)methane molecule
extended and distributed more uniformly in the three-dimen-
sional space. So we can image a picture that there is one
tetrakis(1-adamantanecarboxymethyl)methane molecule in each
tetragonal lattice, and tetrakis(1-adamantanecarboxymethyl)-
methane molecules can constantly spin on their own or oscillate
in their own lattice, that is to say, entropy change of 110.55
J mol¹1 K¹1 corresponds to isotropic reorientation of tetrakis(1-
adamantanecarboxymethyl)methane molecules. Thus, the struc-
ture must be highly disordered in the short range in phase I.
Volumes in low- and high-temperature phases at different
temperatures obtained from XRD are shown in Figure 5, and
they were fitted by a linear fit method. It is clear from this
figure that a break in the temperature evolution of the cell
volume occurs and the cross-point temperature of these two
straight-line segments is 177.8 °C, which is close to the
solid-solid transition temperature shown in DSC. The change
of slope results in an increment of the thermal expansion
coefficient by about 40%, which suggests that structure change
exists.
Conclusion
Entropy Changes of Transformations. Entropy, from a
statistical point of view, is a measurement of molecule disorder
or molecule randomness. Even in the solid state, the molecules
of a substance continually oscillate, creating an uncertainty in
position.39 The ways to increase the entropy include: 1) Adding
particles; 2) adding energy; 3) increasing the volume; 4)
decomposing molecules; 5) letting a linear polymer curl up.40
As for tetrakis(1-adamantanecarboxymethyl)methane, if
variations in vibration frequencies in crystal lattice and mole-
cules, changes of the concentration of positional defects and so
on, are ignored, the thermodynamic parameters corresponding
to the solid-solid transition can be represented as the following
sums:41
Tetrakis(1-adamantanecarboxymethyl)methane, which is
composed of pentaerythritol core and adamantane arms, was
prepared through esterification and its chemical structure
was confirmed by FT-IR, 1H NMR, and elemental analysis.
DSC and XRD were used to demonstrate tetrakis(1-adaman-
tanecarboxymethyl)methane is a novel compound with a
highly disordered crystalline phase. DSC characterization
displayed that tetrakis(1-adamantanecarboxymethyl)methane
goes through two phase transitions at 177.6 and 278.8 °C,
respectively, and entropy ratio of these two peaks: ¦Strs/
¦Sfus = 1.58 > 1. Further research by XRD confirmed that
there is a solid-solid transition before melting, and solving of
the XRD powder diffractions showed that in high-temperature
phase, tetrakis(1-adamantanecarboxymethyl)methane adopts te-
tragonal unit cell. The P4/mmm space group and the structure
of tetrakis(1-adamantanecarboxymethyl)methane suggests that
the high-temperature phase is a highly disordered crystalline
phase. The XRD also indicates an abrupt decrease of density
(approximately by 14%) at the solid-solid phase transition.
X
X
X
X
ꢀtrsSm0
¼
ꢀvSm0 þ
ꢀ
int:rot:Sm0 þ
ꢀ
orient:Sm0 ð1Þ
P
where
ꢀvSm0 denotes the contribution of volume changes
P
P
to the values of
internal rotation of the tops,
orientational motion.
ꢀtrsSm0 ,
ꢀ
int:rot:Sm0 the contribution of
P
ꢀ
orient:Sm0 the contribution of