**3. Contact angle method**

The contact angle θ is the angle between the liquid surface and the outline of the contact surface at an interface between a liquid and a solid. The external stress of a liquid is defined by the imbalance of molecules within the liquid and at the liquid boundary (interface between liquid and gas). This intermolecular force that contacts the surface is called surface tension. A drop is formed due to the surface tension of a liquid. In addition, external influences such as gravity play a role shaping the drop. The contact angle of a drop occurs at the contact surface of the drop on a solid and also depends on the shape of the drop. The contact angle can provide information about the wettability of a solid with a liquid. The contact angle of a drop of water placed on a component surface can be

**Figure 4.** *Contact angle measurement with the tangent method, P. Körber.*

measured macroscopically or microscopically. Water is well suited for carrying out a contact angle measurement, as it is characterized by a relatively high surface tension (=0.072 n/m). The principle of the contact angle measurement is illustrated in the **Figure 4**. The static contact angle is measured by applying a tangent to the point where the water droplet touches the solid surface and the ambient phase (here it is air). The contact angle decreases with increasing wettability of the solid (building material surface). The contact angle θ is defined as an angle at the phase boundary of the gaseous, liquid and solid phases of liquids on a solid surface surrounded by gas [21, 22]. This relationship was already defined in 1805 by Thomas Young.

Eq. (1): Interfacial tension between solid and gaseous:

$$\boldsymbol{\gamma}\_{\rm SG} = \boldsymbol{\gamma}\_{\rm SL} + \boldsymbol{\gamma}\_{\rm LG} \cos \theta \tag{1}$$

In Young's equation, the solid-gas interfacial tension is calculated by adding the solid-liquid interfacial tension to the liquid-gas interfacial tension and multiplying it by the contact angle. The equation below is used to calculate the Young's contact angle.

Eq. (2): Young's equation for calculating the contact angle:

$$\cos \theta = \frac{\sigma\_{\text{S}} - \sigma\_{\text{LS}}}{\sigma\_{\text{L}}} \tag{2}$$

Surface and interfacial tension defines the 'work' required to increase the interface area. Within the liquid, the molecules interact in all directions (cohesion), while at the interface there is no interaction of the liquid molecules with the outside (adhesion). Young's equation describes the balance of these forces. This is viewed at the three-phase contact line and exists when the contact line is balanced and at rest. Then the horizontal forces acting on the contact line exactly cancel each other out. The interfacial tension is temperature-dependent, so the contact angles also depend on the temperature and, for most substances, decrease with increasing temperature. However, because there are other forces acting on the contact line in addition to surface tension, the Young's contact angle cannot be measured per se. If there are movements of the contact line, one speaks of 'dynamic contact angles'. When the drop volume increases, one speaks of 'advancing contact angles', while when liquids evaporate, one speaks of 'receding contact angles'. In this context, it can be assumed that the advancing contact angle is always greater than the receding contact angle. The difference between these two contact angles is called 'contact angle hysteresis'.

The hydrophilic or hydrophobic properties of substances can be precisely determined using the 'Drop Shape Analysis System'. In this method, a droplet illuminated from behind is observed with a camera and displayed on a monitor. With this method a static contact angle is measured by assuming, for the sake of simplicity, that static conditions are present for the contact angle measurement. In fact, this is not the case, because contact angles determined in this way are also subject to certain, very small, changes during the measurement. However, this inaccuracy is included in the tolerance to be estimated and can therefore remain irrelevant for the purposes considered here.

The static contact angle can be measured using the tangent method, as shown above. The results of the contact angle measurements on building materials are differentiated using the 90° limit in A) hydrophobic > 90° and B) hydrophilic < 90°. In addition to this 90° angle definition, the angle measurements also provide information about the gradual water absorption capacity of the substance being examined. If a dynamic condensation/evaporation process is present, static contact angles can only be measured when the dynamic equilibrium between condensation and evaporation

*Investigation on Building Materials with the SEM in the ESEM Mode to Demonstrate… DOI: http://dx.doi.org/10.5772/intechopen.104292*

is reached. The contact angle method described here for determining the capillarity of a building material can also be applied macroscopically. In the present case, however, this method is applied microscopically in the ESEM. A reliable optical method for drop shape measurement can be carried out on the drops measured in the ESEM: The Drop Shape Analysis (DSA).

In the Drop Shape Analysis (DSA), images are taken of the droplets that are formed and then examined by using computer software. The contact angle is determined by the use of an image. The software can sharpen the captured image and recognize the contour of the drop. The measurement is computer-aided utilizing a geometric model. In the next step, the surface tension can be calculated applying the 'Young-Laplace-Fit' if the density difference and thus the imaging scale between the droplet phase and the surrounding phase are known. Accuracies of ±0.2° can be achieved here.

The optically measured drop contour can be calculated using a conic section equation =>Conic Section Method. The conic section method is based on the assumption that the contour of the drop to be measured describes an arc of an ellipse.
