Contact Angle

The wetting of a solid surface is characterised by the contact angle, this is the angle between the water/air and water/solid interface and is controlled both by the surface energy and the geometric micro-structuring of the substrate. Manipulation of the contact angle is commonplace in chemistry and has already been mentioned in the previous section on template formation. Here, cysteamine was used to alter the surface energy and reduce the contact angle of the gold, forming a long meniscus tail in the solution of micro-spheres. While the effect of surface energy on the contact angle is well understood, the effect of altering the surface geometry on the micro- and nano-scales has been less thoroughly explored. Again nature has been utilising this effect for many millions of years, the butterfly Papilio Ulysses, shown at the beginning of chapter 2 (figure 2.1), uses the nano-structuring of its wings not only to produce the vibrant blue colour but also to help water droplets slip off with ease. The droplets carry with them dust and so the structuring provides a mechanism for self-cleaning as well as protection against becoming waterlogged. With a similar structure to the butterfly wings, the samples detailed here are ideal for testing the effect of changing contact angle with structural geometry. In these experiments 5µl droplets of water are placed on a sample at different thicknesses, photographs were then taken and analysed to find the contact angles of the droplets for the different geometries, figure 4.18a, b.

Figure 4.18: Images of 5µl droplets of water on samples of thickness (a) ¯t= 0.1, and

(b) ¯t = 0.6. (c) Graph showing contact angle vs. normalised sample thickness, solid line shows theory predicted by the Cassie-Baxter model.

On smooth gold the contact angle is measured to be 70o _{as expected, while on the} structured surfaces contact angles up to 130o are recorded, showing the surfaces have become significantly more hydrophobic. There are also clear variations in how proud of the surface each droplet stands between the images. Since the material and pitch of the structures are constant this effect comes purely from surface geometry[87]. A plot of contact angle vs.thicknesses is presented in figure4.18c. This shows that the maximum

contact angle occurs when ¯t = 0.5, corresponding to sharp features separated by large air spacings.

There are two well-established contact angle modelling techniques, these are based on different assumptions, as shown schematically in figure4.19.

Figure 4.19: (a) Schematic of Wenzel model. (b) Schematic of Cassie-Baxter model.

(c) Plot of contact angle against normalised sample thickness using both models.

The first model, attributed to Wenzel[88], assumes that liquid fills a nano-structured surface completely, fig4.19a. The apparent contact angle, θ∗, of the liquid is given by:

cosθ∗=r.cosθ (4.2)

whereris the roughness factor of the surface, equal to the ratio of the total surface area to the area projected in the horizontal plane. This model effectively considers the ratio of the surface tensions between the solid/liquid interface and the solid/air interface. An increase in surface area gives rise to an increased importance of the solid/liquid surface tension. Since the smooth gold surface wets, the increased surface area thus leads to a further increase in wetability, and a reduction in the contact angle.

The second model, attributed to Cassie and Baxter[89], assumes that air is trapped below the contact line within the structures, fig 4.19b. The apparent contact angle in this case is given by:

cosθ∗ =f1cosθ−f2 (4.3)

wheref1 andf2 are the fractions of surface made up of solid material and air filled voids

respectively. This model is solely dependent on the topology of the top surface and so follows a parabolic relationship with film thickness due to spherical nature of the voids. Figure 4.19c plots the apparent contact angle according to both models between ¯t = 0 to 1. The Cassie-Baxter model predicts a maximum contact angle at ¯t = 0.5 due to

the minimisation of the solid surface. The Wenzel model on the other hand predicts a continuous reduction in contact angle due to the continuous increase in surface area. Figure4.18c shows the experimentally recorded contact angle over a fully graded sample. Also presented on the image is the theory given by the Cassie-Baxter approach. A clear correlation between the Cassie-Baxter model and the experimental data strongly indicate that water does not enter the cavities for the majority of the surface geometries, instead sitting on a cushion of air trapped within the voids.

A further interesting feature of the data is that at ¯t < 0.1 where the contact angle drops below 90o; this means the surface turns from hydrophobic to hydrophilic. This change from wetting to non-wetting implies that the dishes should become filled with liquid for these geometries and change to the Wenzel modelled scenario. Unfortunately, the possible step in contact angle is close to the experimental errors so may be hard to observe and so this conclusion currently remains unresolved. A similar change from hydrophobic to hydrophilic is also observed above ¯t= 0.9. In this case the change corre- sponds to water wetting the top metal surface, not penetrating the almost encapsulated voids. Understanding the wettability of these nano-structured surfaces is important to understand how liquids act on the nano-scale, a topic of particular importance if the surfaces are to be used in sensor applications.