The relationship between the specific surface free energy (SSFE) and the contact angle of a liquid is shown by Young’s equation [1] :

where is the SSFE of the solid, is the interfacial tension between the solid and the liquid, and is the surface tension of the liquid. Because there are two unknown parameters and in Equation (1), we

cannot introduce from a single contact angle, , only. In order to evaluate the SSFE from the contact angle of liquid, several models are proposed [2] - [6] . For example, Fowkes [5] proposed that the surface tension could be described as a sum of the dispersion component and the polar component as,

where and are dispersion and polar component of the surface tension of the liquid, respectively. The values of can be obtained from as

Three kinds of synthetic alkali halide single crystals, NaCl, KCl, and KBr from Furu-Uchi Chemicals were used as sample crystals. Each alkali halide crystal was cleaved using sharp edge of a knife and (100) surface was prepared. Droplet of formamide or ethylene glycol was dropped on the cleaved face of each crystal using micropipette. The droplets sized ~0.1 mm³ were observed using digital camera with a magnifying lens. We took more than 40 photographs for each crystal face and used the photographs in which the boundary between the liquid and solid was clearly recognized the contact angles of the droplets were measured manually using printed photographs.

Average and standard deviation of contact angles of ethylene glycol and formamide on NaCl, KCl, and KBr are summarized in Table 1.

The contact angles of liquids on alkali halide crystal are much smaller than those on inorganic oxide crystals [10] . The values of dispersion and polar component of the SSFE can be calculated from the contact angle of liquids using Equation (4). The dispersion and polar components of ethylene glycol are 30.1 and 17.6 mN∙m⁻¹, and those of formamide are 39.5 and 18.7 mN∙m⁻¹ [2] .

Calculated SSFE of NaCl, KCl, and KBr and dispersion and polar components of them are summarized in Table 2. In our previous research, we did not discuss the dispersion and polar component separately, but we discussed summed SSFE only [7] - [9] .

Here we re-calculated and for CaCO₃, Ba₅Cl(PO₄)₃, SiO₂, and Al₂O₃ using former data. For inorganic oxide materials, the value of dispersion and polar component is close. On the other hand, dispersion component for alkali halides is much larger than the polar component of the SSFE. The ratio of and is almost even for inorganic oxides, but of alkali halide is very large and is very small.

Polar component of SSFE is caused by the potential energy of interaction between two permanent dipoles. On the other hand, the dispersion component results from interaction between two induced dipoles. On (100) face of these alkali halide crystals, same number of anion and cation arrange alternately, which compose neutral surface as shown in Figure 1(a). Therefore, interaction between induced-dipoles is dominant and the dipole-dipole interaction should be subordinate.

The relationship between dispersion component of SSFE and lattice enthalpy was compared as shown in Figure 2, and the polar components of SSFE are also compared with lattice enthalpy as shown in Figure 3. The lattice enthalpy for NaCl, KCl, and KBr is 787, 717, and 689 kJ∙mol⁻¹, respectively [11] .

The larger lattice enthalpy causes the smaller dispersion component of SSFE. The larger enthalpy causes the larger value of polar component of the SSFE of each alkali halide crystal. Though the potential energy for each ion in the alkali halide crystal is symmetric, the potential for the surface ions is asymmetric. The ions are attracted inside of the crystal, which caused the rumpling of the crystal surface. The structure of crystal surface of NaCl, KCl, and KBr is studied by Vogt and Weiss using LEED, and reported that the rumpling of the first layer (Δ) are 0.007, 0.003, and 0.002 nm for NaCl, KCl, and KBr, respectively [12] [13] . The crystal with the larger lattice enthalpy has the larger rumpling. As shown in Figure 1(b), the surface of alkali halide is neutral, but the rumpling of the crystal face decreases the neutrality, and the surface became a little polar. NaCl crystal has the largest lattice enthalpy and the largest rumpling. Therefore, NaCl has the largest ratio of polar component and the smallest dispersion component. On the other hand, KBr has the smallest lattice enthalpy and the smallest rumpling, and KBr has the smallest rate of polar component and largest dispersion component.

Although contact angle of liquid on crystal surface is macroscopic value as we can see by our naked eye, the contact angle of liquid includes microscopic information such as atomic scale roughness of the crystal surface.