122
6 Melting of Molecular Crystals
the orientational melting depends on molecular anisotropy. The internal molecular
flexibility might contribute further in the case of trans-azobenzene.
Since the crystals of rare gas elements have only the positional order to be lost
upon their melting, the accompanied change in entropy of fusion is expected to be
minimum. However, this is not the case. In Table 6.1, crystals of some substances
melt with a smaller entropy of transition than rare gas crystals. We can interpret the
smaller entropy of transition as a symptom of severe orientational disorder in the
crystal because we expect a similar entropy of fusion while assuming the complete
disorder in both translational and orientational degrees of freedom in the isotropic
liquid. Timmermans [25], thus, defined “plastic crystals” as crystals that melt with
a smaller entropy of fusion than those of crystals of rare gas elements. According to
this definition, crystals at a respective triple point among gas, liquid, and solid are
plastic crystal phases for nitrogen, oxygen, fluorine, ethane, and CCl 4 in the table.
As described above, the melting behavior of molecular crystals is qualitatively
rationalized. However, there exists a difficulty in interpreting its magnitude in terms
of microscopic view. For example, recent molecular dynamical simulation of the
Lennard-Jones particles mimicking argon [26] indicates that the entropy of fusion
under constant volume is ca. 0.5N k B in contrast to the experimental one under constant pressure 1.7N k B shown in Table 6.1. However, the heat capacity under constant
volume c V exhibits excessive contribution in the premelting region below the temperature of fusion due to the activation of diffusion. The entropy increment involved
in this excess heat capacity is ca. 0.5N k B . The difference between entropies of transition under constant pressure and at constant volume is thus calculated as ca. 0.7N k B ,
which is larger than the entropy increment of the ideal gas N k B ln(V liq /V crystal )
(≈0.1N k B ). The larger increment indicates that the entropy of liquid has a stronger
dependence on volume than gasses.
Although the melting occurs as a result of an accidental coincidence of the molar
Gibbs energies of a liquid and a crystal (Sect. 2.1.1),
2 physical properties often exhibit
anomalies in the close vicinity below the melting temperature, even in an ideal measurement. These are called premelting behavior. The apparent premelting anomaly
consists of two contributions. One comes from the effect of impurities, which cause
the so-called melting point depression. By this effect, the sample starts to melt below
the true melting point. After suitably correcting this effect, however, the anomalous
increase in heat capacity survives. This excess is due to the formation of some defects
in the crystalline lattice.
3 By assuming the equilibrium between normal molecules
(on the lattice) M norm and defects D,
M norm D,
2 Here, the word “accidental” indicates that two phases are stable in both sides of the coexistence
border and that the locating the transition point requires their comparison, in contrast to an ideal
second-order transition with a diverging susceptibility at the critical point.
3 Observations for bulk samples implies that the tail is mainly not a surface effect but a bulk effect.
6 Melting of Molecular Crystals
the orientational melting depends on molecular anisotropy. The internal molecular
flexibility might contribute further in the case of trans-azobenzene.
Since the crystals of rare gas elements have only the positional order to be lost
upon their melting, the accompanied change in entropy of fusion is expected to be
minimum. However, this is not the case. In Table 6.1, crystals of some substances
melt with a smaller entropy of transition than rare gas crystals. We can interpret the
smaller entropy of transition as a symptom of severe orientational disorder in the
crystal because we expect a similar entropy of fusion while assuming the complete
disorder in both translational and orientational degrees of freedom in the isotropic
liquid. Timmermans [25], thus, defined “plastic crystals” as crystals that melt with
a smaller entropy of fusion than those of crystals of rare gas elements. According to
this definition, crystals at a respective triple point among gas, liquid, and solid are
plastic crystal phases for nitrogen, oxygen, fluorine, ethane, and CCl 4 in the table.
As described above, the melting behavior of molecular crystals is qualitatively
rationalized. However, there exists a difficulty in interpreting its magnitude in terms
of microscopic view. For example, recent molecular dynamical simulation of the
Lennard-Jones particles mimicking argon [26] indicates that the entropy of fusion
under constant volume is ca. 0.5N k B in contrast to the experimental one under constant pressure 1.7N k B shown in Table 6.1. However, the heat capacity under constant
volume c V exhibits excessive contribution in the premelting region below the temperature of fusion due to the activation of diffusion. The entropy increment involved
in this excess heat capacity is ca. 0.5N k B . The difference between entropies of transition under constant pressure and at constant volume is thus calculated as ca. 0.7N k B ,
which is larger than the entropy increment of the ideal gas N k B ln(V liq /V crystal )
(≈0.1N k B ). The larger increment indicates that the entropy of liquid has a stronger
dependence on volume than gasses.
Although the melting occurs as a result of an accidental coincidence of the molar
Gibbs energies of a liquid and a crystal (Sect. 2.1.1),
2 physical properties often exhibit
anomalies in the close vicinity below the melting temperature, even in an ideal measurement. These are called premelting behavior. The apparent premelting anomaly
consists of two contributions. One comes from the effect of impurities, which cause
the so-called melting point depression. By this effect, the sample starts to melt below
the true melting point. After suitably correcting this effect, however, the anomalous
increase in heat capacity survives. This excess is due to the formation of some defects
in the crystalline lattice.
3 By assuming the equilibrium between normal molecules
(on the lattice) M norm and defects D,
M norm D,
2 Here, the word “accidental” indicates that two phases are stable in both sides of the coexistence
border and that the locating the transition point requires their comparison, in contrast to an ideal
second-order transition with a diverging susceptibility at the critical point.
3 Observations for bulk samples implies that the tail is mainly not a surface effect but a bulk effect.