Polar and Dispersive Surface Tension Calculation

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:

  1.  pendant drop method (preferred).
  2.  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:

    \[  {\gamma }_{lr}={\gamma }_l+{\gamma }_r-2\sqrt{{\gamma }^p_l{\gamma }^p_r}-2\sqrt{{\gamma }^d_l{\gamma }^d_r} \]

(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. γrrd, Eq. 1 becomes:

    \[  {\gamma }^d_l=\frac{{\left({\gamma }_l+{\gamma }_r-{\gamma }_{lr}\right)}^2}{4{\gamma }_r} \]

(2)

And γlp can be found using Eq. 3.

    \[  {\gamma }^p_l={\gamma }_l-{\gamma }^d_l} \]

(3)

If using the OWRK method, the value of γlp was found negative, Wu method (harmonic mean) should be used as follows:

    \[  {\gamma }_{lr}={\gamma }_l+{\gamma }_r-4\frac{{\gamma }^p_l{\gamma }^p_r}{{\gamma }^p_l+{\gamma }^p_r}-4\frac{{\gamma }^d_l{\gamma }^d_r}{{\gamma }^d_l+{\gamma }^d_r} \]

(4)

For a strictly dispersive reference, i.e. γrrd, Eq. 4 becomes:

    \[  {\gamma }^d_l=\frac{{\gamma }_r\left({\gamma }_l+{\gamma }_r-{\gamma }_{lr}\right)}{3{\gamma }_r-{\gamma }_l+{\gamma }_{lr}} \]

(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:

  1. distillation
  2. 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:

    \[  {\gamma }^d_l=\frac{{\gamma }^2_l{\left(1+{\mathrm{cos} \theta \ }\right)}^2}{4{\gamma }_s} \]

(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:

    \[  {\gamma }^d_l=\frac{{\gamma }_l{\gamma }_s\left(1+{\mathrm{cos} \theta \ }\right)}{4{\gamma }_s-{\gamma }_l\left(1+{\mathrm{cos} \theta \ }\right)} \]

(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
Polar and Dispersive Surface Tension Calculation

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