Application Note DataPhysics Determination of the Work of Adhesion

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Optical Contact Angle OCA20 with multiple dosing unit

DataPhysics Application Note 14 Figure 1

DataPhysics Application Note 14 Figure 2

Application note 14 - Determination of the maximum work of adhesion of certain liquids

Task

Liquids (e.g. inks, glues or varnishes) perform work of adhesion to their solid base. In many cases it is necessary to know the optimum work of adhesion of a liquid, if a certain solid surface has to be wetted and the adhesion force has to be maximized. In the given example, inks with different colour pigments (red, yellow and blue) have to wet a foil so that the work of adhesion has a maximum in order to imprint the foil permanently.

In the present case, the surface free energy of the film is 40 mN/m with a polar contribution of 10 mN/m. The inks have the following surface tensions (determined by measurements of the interfacial tension):

Red ink = 47.5 mN/m; polar 10.5 mN/m

Yellow ink = 40.0 mN/m; polar 5.0 mN/m

Blue ink = 39.0 mN/m; polar 9.5 mN/m

Method

The method follows the calculation according to Owens-Wendt-Rabel-Kälble (OWRK). (Symbols explained at end of text):

W_A = σ₁(1 + cosΘ)        (1)

The work of adhesion according to OWRK is described by the following equation:

W_A = 2(√(σ₁^d·σ_s^d) + √(σ₁^p·σ_s^p))             (2)

The surface properties are divided into:

σ₁ = σ₁^d + σ₁^p                 (3)

From (2) and (3) we get the work of adhesion:

W_A = 2(√(σ₁ -  σ₁^p ·σ_s^d)+√σ₁^p·σ_s^p)            (4)

For certain surfaces, σ_s^p and σ_s^d are constant; for a constant work of adhesion, a function σ₁ (σ₁^p) if σ₁^p> 0 results

σ₁(σ₁^p) = ((W_A/2) - √(σ_s^p·σ₁^p) + (σ_s^d·σ₁^p))/ σ_s^d          (5)

This function yields the so called isograms of a defined work of adhesion for a certain surface. Fig. 1 shows that these isograms have a minimum. This minimum describes the lowest surface tension of a liquid with a defined polarity. A liquid with these parameters will exert the maximum adhesion force on the surface.

Fig. 1: Isograms for the values given in the example

If in the derivative (5) is set = 0, the polarity of the minimum can be calculated. For σ₁^p

min the following is valid:

σ_1min^p = (W_A√σ_s^p/2·(σ_s^p+σ_s^d))²              (6)

For each value of the work of adhesion, the optimum polarity of the liquid with reference to its surface tension can be calculated. The solution is a straight line (Fig. 2), which defines by corresponding factors a zone within the liquid even adheres.

Fig. 2: Diagram of the isograms (blue) of the adhesion work with the wetting envelope (red) and the corridor for optimum adhesion (green), as well as the values for the three sample inks.

Legend

R: Red ink

B: Blue ink

Y: Yellow ink

W_A : Adhesion work

σ_s : Solid surface free energy

σ_s^d : Surface free energy; dispersive contribution

σ_s^p : Surface free energy; polar contribution

σ₁ : Liquid surface tension

σ₁^d : Surface tension; dispersive contribution

σ₁^p : Surface tension; polar contribution

Θ : Contact angle

Results

The result shows that the blue ink has good adhesive properties, because it is closest to the optimum straight line with excellent spreading behaviour due to low surface tension. The red ink is also close to the optimum straight line, but the liquid has, because of the high surface tension, a limited spreading behaviour. The yellow ink will have in comparison to the red ink a better spreading behaviour, because of the low amount of polar parts the ink will have bad adhesion on the solid surface.

Summary

This method allows a unique opportunity to solve problems concerning adhesion of liquids on solids in a quick and cost-effective way. It allows an easy screening of liquids and solids and to predict adhesion properties e.g. for printing or gluing processes. To optimize the work of adhesion there are two possibilities: On the one hand to modify the liquid by addition of polar respectively non-polar substances. On the other hand, there is a possibility to treat the surface, e.g. increase polarity of solid surface by plasma treatment.

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