SIZE DEPENDENT INTERFACE ENERGY - Energy Research Developments: Tidal Energy, Energy Efficiency and Solar Energy - page 200

γ sl0 (T m ) for Organic Crystals
As shown in table 2, for 15 different organic molecular crystals, the predictions in terms
of Eq. (2.13) partly correspond to the latest experimental results [13,47-49] but are smaller
than the early experimental results [12,50-52].
Organic crystals as molecular crystals differ from metallic and ionic ones, whose
chemical bonds are covalent within molecules but consist of van der Waals forces or
hydrogen bonds among molecules. The former being responsible for stability of individual
molecules, are much stronger than the latter, being primarily responsible for bulk properties
of matter, such as γ sl0 . Because bond strengths of van der Waals forces or hydrogen bonds are
weaker than those of metallic or ionic bonds, γ sl0 values of organic crystals are also smaller
than those of metallic and ionic crystals, such as Pb with γ sl0 ≈ 40±7 mJ/m 2 [γ sl0 value of Pb in
fact is one of the smallest γ sl0 values among metallic or ionic crystals because its S m and H m
values are small, which leads to a small γ sl0 value of Pb in terms of Eq. (2.13)] [12].
Moreover, γ sl0 values of compounds composed of full hydrogen bonds, such as H 2 O with γ sl0
≈ 25~45 mJ/m 2 , should also be larger than those of organic crystals since molecules of
organic crystals have only partly hydrogen bonds while the other is van der Waals force [12].
Thus, γ sl0 values for organic crystals could be not more than 30~40 mJ/m 2 .
It is known that organic molecules mostly consist of C-H bonds with intermolecular
dispersion forces caused by relative movement between electrons and the atomic nucleus.
Their relative movements change electron density within the molecule. Generally, the larger
the number of electrons and the more diffuse the electron cloud in the molecule, the greater
its dispersion forces. However, the forces hardly affect the net attraction applied to a unit area
of interface, the size difference of γ sl0 values for organic molecules thus is smaller than those
of metallic and ionic crystals (for other three kinds of intermolecular forces, orientation forces
and induced forces, a similar discussion may be carried out).
Although measured γ sl0 values of organic crystals composed of chain molecules are much
larger than the above limits shown in table 2 [50-52], their real values should be similar to
those composed of spherical molecules since γ sl0 denotes excess energy of unit area where
molecular weight has negligible effect on it. Even if chain molecules may contain one or
more hydrogen bonds, γ sl0 values still vary little since most bonds of the molecules are van
der Waals forces. This result also implies that anisotropy of γ sl0 of organic crystals is small,
although this issue up to now is still debated [11-12,32].
Moreover, for a typical fcc crystal, the coordinate number ( CN ) or bond number decrease
of molecules on a solid-liquid interface is usually 1~2 while that on a liquid-vapor interface is
3~4. If this bond number is proportional to the corresponding interface energy, with the note
that the bond strength difference of molecules between solid and liquid states is only several
percent, γ sl0 value must be lower than γ lv0 value, which is easy to measure with better
measuring accuracy. Thus, γ lv0 value of the same substance is good reference as an upper
limit on γ sl0 [25]. For organic crystals, the γ sl0 value may be around half γ lv0 as a rough
estimation. Since γ lv0 ≈ 20~40 mJ/m 2 shown in table 2, γ sl0 < 20 mJ/m 2 , which is also smaller
than the above-stated limits in terms of considerations of the bond strength of metallic, ionic,
and hydrogen bonds.