people_outline
Imaginary Contact Angles: Characterizing Highly Wettable Surfaces DataPhysics Instruments Logo

Imaginary Contact Angles: Characterizing Highly Wettable Surfaces

Figure 1: Especially for highly hydrophilic and rough surfaces, such as those found in dental implants, imaginary contact angles allow a differentiated characterization of wettability.

Figure 1: Especially for highly hydrophilic and rough surfaces, such as those found in dental implants, imaginary contact angles allow a differentiated characterization of wettability.

Contact angles provide information about the wettability of solid samples. Dynamic contact angles can be determined using a force-based tensiometer and the Wilhelmy equation. Imaginary contact angles are mathematical solutions to the Wilhelmy equation, which are particularly important for highly wettable and rough surfaces.

Fundamentals: The contact angle at the three-phase contact line

Before we turn our attention to imaginary contact angles, we need to clarify a few basic concepts. The contact angle θ is one of the most important parameters for describing the situation at the interface between different materials. The contact angle can be measured by placing a drop of liquid on a solid surface. Three different phases – solid, liquid and gas – now meet at the three-phase contact line.

When the system is at rest, there is a balance of tangential forces at the three-phase contact line. In this state, the static contact angle θC forms at the three-phase contact line. When the system is in motion, for example when the solid surface is tilted, the dynamic contact angles θAdv and θRec can be determined.

Contact angles provide information about the wetting of the solid material

Measuring the contact angle of a liquid on a solid provides information about the wetting behavior of this combination. The desired wetting behavior depends on the specific application.

At a contact angle of 180°, the drop lies on the surface in a spherical shape and touches the solid only at one point. In this case, we speak of complete wetting. At a contact angle of 0°, the drop is completely spread out or spread across the solid surface. The drop forms a thin film of liquid on the solid surface. In this case, we refer to complete wetting. However, with exceptionally wettable samples, it is possible to achieve better wetting than with a contact angle of 0°. This is referred to as imaginary contact angles.

What are dynamic contact angles?

The static contact angle describes the state of equilibrium, i.e. at rest. In addition to the static contact angle, dynamic contact angles can also be determined. They describe a state in which the three-phase contact line is in motion.

There are two types of dynamic contact angles. The advancing contact angle θAdv describes how a liquid wets a solid. Specifically, it provides insights into how a dry solid is wetted by a liquid. The receding contact angle θRec describes how the liquid detaches from the solid. The receding contact angle therefore characterizes how the liquid detaches from a wet solid.

Measurement of dynamic contact angles

A force-based tensiometer, such as the models in the DCAT series from DataPhysics Instruments, can perform force-based investigations of interface parameters and phenomena. This includes measuring the dynamic contact angle using the Wilhelmy plate method. It is particularly useful for investigating highly wettable samples. When optical contour analysis reaches its limits, the DCAT's precise weighing system still delivers reliable results when measuring dynamic contact angles.

To measure dynamic contact angles, the solid sample is attached to the device's balance using a holder and then immersed in a test liquid with a known surface tension and withdrawn again. This allows the advancing and receding contact angles for immersion and withdrawal to be measured.

The calculation is based on the Wilhelmy equation:

cos⁡(θ) = FG / (Lσ)


θ: contact angle to be determined
FG: measured weight force of the liquid lamella
L: length of the contact line
σ: known surface tension

Calculate imaginary contact angles

For a real contact angle between 0° and 180°, the value of cos(θ) can only be between -1 and 1. In practice, however, measurements of very hydrophilic, i.e. highly wettable, surfaces yield values greater than 1, especially in the case of rough surfaces. In these cases, an additional force is generated during wetting due to the capillarity of a porous surface. In his two articles, Contact angle measurement on dental implants and Hydrophilic rough surfaces and imaginary contact angles, H. P. Jennisen defined a method for calculating such contact angles. He calls this method the determination of imaginary contact angles.

Instead of assigning the same contact angle of 0° to all surfaces in these cases, the tensiometer software from DataPhysics Instruments calculates the imaginary contact angle, i.e. the complex number iθ, for which cos(iθ) yields values greater than 1 and thus satisfies the Wilhelmy equation for the measured values. This opens up the possibility of continuing to distinguish between highly hydrophilic materials and investigating surface treatment techniques such as UV or plasma treatment of dental implants, for example.