How to calculate the polar and dispersive surface tension components of a liquid?
by JikanGroup
There are two methods for calculating the polar and dispersive surface tension components of a liquid:
- pendant drop method (preferred).
- sessile drop method.
1. The pendant drop method for measuring the surface tension components of a liquid
Using the OWRK (Owens-Wendt-Rabel-Kaelble) or geometric mean method, the surface tension between test and reference liquids (also known as the interfacial tension) is calculated as:
|
(1) |
where γ_lr is the interfacial (surface) tension between test and reference liquids, γ_l and γ_r are the surface tensions of test and reference liquids, accordingly, p and d superscripts show the polar and dispersive surface tension components.
For a strictly dispersive reference liquid, i.e. γr=γrd, Eq. 1 becomes:
|
(2) |
And γlp can be found using Eq. 3.
|
(3) |
If using the OWRK method, the value of γlp was found negative, Wu method (harmonic mean) should be used as follows:
|
(4) |
For a strictly dispersive reference, i.e. γr=γrd, Eq. 4 becomes:
|
(5) |
And γlp can be found using Eq. 3.
The reference liquid shall be:
- immiscible and be able to form a meniscus.
- chemically homogenous.
- strictly dispersive (and free from polar contaminations)
- colourless with a melting point lower than 20°C.
Suggested reference liquids:
Preferably use liquid hydrocarbons (e.g. n-decane, n-dodecane, n-tetradecane and n-hexadecane) but if the test liquid is soluble to hydrocarbon, use perfluorohydrocarbons (e.g. n-perfluorohexane and n-perfluorooctane).
Cleaning of reference liquids:
Hydrocarbon:
- distillation
- chromatography columns with a minimum length of 60 cm filled with silica gel (e.g. particle size mesh 60). The silica gel with polar surfaces absorbs the polar contaminations (e.g. ketones).
Perfluorohydrocarbon:
- does not need cleaning.
After cleaning, for the hydrocarbon and perfluorohydrocarbon, the measurable interfacial tension compared to water shall be at least 52 mN/m and 54 mN/m at 23°C, accordingly.
Storage of reference liquids:
The cleaned n-alkanes shall be stored in light-proof glass bottles in the refrigerator at a maximum temperature of 4°C.
2. The sessile drop method for measuring the surface tension components of liquids
Using the OWRK method (geometric mean), on a pure dispersive solid surface, the relation between contact angle (θ) and surface tension components of the test liquid is:
|
(6) |
Using the Wu method (harmonic mean), on a pure dispersive solid surface, the relation between contact angle and surface tension components of the test liquid is:
|
(7) |
The polar component of the test liquid surface tension is found using Eq. 3.
Note: For γs > 20 mN/m use Eq. 6 otherwise use Eq.7:
The reference solid shall be:
- Sufficiently, chemically and topologically homogenous.
- Dispersive, e.g. made of paraffin (25.5 ± 0.5 mN/m) or PTFE (18.5 ± 0.5 mN/m).
- Where γsp < 0.5 mN/m
- Mean roughness value Ra < 0.3 μm