Contact angle

2.1 The ZISMAN method

In the ZISMAN method the surface energy of the solid is determined by using the critical surface tension (explained below) of the liquid. This method is based on a revised version of the ANTONOW method , it is implemented in the DSA1 program primarily for historical reasons and should not be used for routine measurements.

The method is based on the following consideration:
A liquid wets a solid completely when the work of cohesion for the formation of a liquid surface $W_{ll}$ is smaller than the work of cohesion for the formation of the interface boundary $W_{sl}$ .

The difference between these two quantities is known as the spreading pressure $S_{l \mid s}$ :

$S_{l \mid s} = W_{sl} - W_{ll}$ (Equation 14)

The solid will be wetted completely when the spreading pressure is positive; at a negative spreading pressure the solid will not be wetted completely.

In addition, the following relationship exists between the work of cohesion $W_{sl}$ , the contact angle $\theta$ and the surface tension of the liquid (see also 1.3.2):

$W_{sl} = \sigma_l (\cos\theta + 1)$ (Equation 15)

As the work of cohesion $W_{ll}$ is defined as $2\cdot \sigma_l$ according to DUPRÉ then, for a contact angle of 0° ( $\cos\theta = 1$ ) the work of cohesion will be the same as the work of adhesion; this results in a spreading pressure of 0. This means that the contact angle of 0° can be called the limiting angle for spreading (=complete wetting). Theoretically, a positive spreading pressure corresponds with negative contact angles which cannot be measured in practice.

The method according to ZISMAN uses this relationship by plotting cos Θ against the surface tension for various liquids and extrapolating the compensation curve to $\cos\theta = 1$ . The corresponding value for the surface tension is known as the critical surface tension $\sigma_{krit}$ .

: Fig. 2: Determining the critical surface tension according to ZISMAN

ZISMAN equates this value with the surface energy of the solid $\sigma_s$ .

Setting up a linear relationship between $\cos\theta$ and the surface tension σl is based on the now outdated assumption of ANTONOW that the interfacial tension is determined by the difference between the surface tensions. In fact this linear relationship only applies when the relationship between the disperse and polar interactions is the same between the solid and the liquid. This practically only occurs when a purely disperse interactive solid and liquid are involved; i.e. only under exceptional circumstances. This means that other methods should normally be used for determining the surface energy.

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