Current understanding of static and dynamic contact angles 87

Theory of surface wetting has significantly advanced since Thomas Young first wrote about interfacial surface tension in 1805.141 While the concept of wetting may initially seem rather facile, its mechanism has proven complicated and a thorough understanding is still not available. Nevertheless, previous studies have provided valuable insight into wetting behaviour and recent technology advances have allowed fabrication of micropatterned arrays which has substantially advanced understanding of the mechanisms behind advancing and receding contact angles. Wetting is a function of the contact line as shown by Extrand260 and Gao and McCarthy;261 therefore, the mechanism for static and advancing/receding contact angle will be analyzed based only on the contact line and not contact area (see Figure 24 on page 99).

Advancing or receding contact angle can not be evaluated unless a static drop is first placed on the sample. Therefore, analysis of wetting begins with phenomena of the static water drop followed by the advancing then receding water drop. The sample surface is initially unwet (dry). When the water drop is placed onto the surface, the water will contact both surface and

defects indiscriminately. The water has no choice but to interact with both the surface and defects. This situation will look like Figure 20a. The experimentally observed WCA can now be defined as the thermodynamic equilibrium of water, defects, and substrate along the contact line.251, 253, 262

Adding liquid to the water drop will cause WCA to increase while maintaining a constant diameter. This is due to pinning of the contact line as shown in in Figure 20b. For the case of graphite, the graphite surface restricts water from advancing further onto the hydrophobic surface. As liquid is continually added to the drop, a critical point will be reached where advancing onto the hydrophobic surface is more energetically favorable than further increasing WCA. At this advancing critical point, the drop is at quasi-equilibrium where further adding liquid will cause the drop to reconfigure. This point is taken as θa, the WCA immediately before

drop diameter increases. This situation is depicted in Figure 20c.

For a hydrophobic surface with hydrophilic defects, Raj et al. showed that advancing WCA is not a function of defect density up to the defect packing limit.251 _{This is consistent with}

the aforementioned mechanism since water maximizes its interaction with hydrophilic defects and minimizes its interaction with the hydrophobic surface. Increasing defect density – up to its packing limit – will not cause WCAa to change because the advancing motion is restricted by the

Figure 20. Advancing contact angle mechanism. The upper figures are a side view and the lower figures are an overhead view. The colored lines represent the water contact line. The black

area represents the hydrophobic surface and the circles represent hydrophilic defects. (a) Static water drop placed on the sample surface. The contact line interacts with both surface and defects. (b) Intermediate state: the drop begins to advance onto the defects as liquid is added. The contact line becomes pinned and contact angle increases. (c) Advancing contact angle: the

contact line remains pinned by the hydrophobic surface and does not advance as water is added to the drop. The drop advances onto the unwet surface once the advancing critical point is

reached.

Receding contact angle is exactly the opposite mechanism of advancing contact angle. Removing liquid from the water drop will cause the WCA to first decrease while maintaining a constant diameter. This is due to pinning of the contact line by defect sites as shown in Figure 21b. For the case of graphite, hydrophilic defects restrict water from receding onto the hydrophobic graphite. As liquid is continually removed from the drop, a critical point will be reached where receding onto the hydrophobic surface is more energetically favorable than further decreasing WCA. At this receding critical point, the drop is at quasi-equilibrium where further removing liquid will cause the drop to reconfigure. This point is taken as θr, the WCA

immediately before drop diameter decreases. This situation is depicted in Figure 21c.

For a hydrophobic surface with hydrophilic defects, Raj et al. shows that receding WCA is a strong function of defect density up to the defect packing limit.251 This is consistent with the aforementioned theory since water maximizes its interaction with hydrophilic defects and minimizes its interaction with the hydrophobic surface. Increasing defect density – up to its packing limit – will cause WCAr to asymptotically decrease because the receding motion is

restricted by the hydrophilic defects. Therefore, WCAr represents the defect wettability when

defects are at or above their packing limit (which is not the case for fresh graphite).

Figure 21. Receding contact angle mechanism. The upper figures are a side view and the lower figures are an overhead view. The colored lines represent the water contact line. The black area represents the hydrophobic surface and the circles represent hydrophilic defects. (a) Static water

drop placed on the sample surface. (b) Intermediate state: the drop begins to recede towards the defects as liquid is withdrawn. The contact line becomes pinned and contact angle decreases. (c) Receding contact angle: the contact line remains pinned by hydrophilic defects and does not recede as water is withdrawn from the drop. Pinning causes the tortuous contact line. The drop

recedes onto the wet surface once the receding critical point is reached.

The aforementioned dynamic contact angle mechanisms allow for the wettability of sp2- hybridized carbon to be evaluated based on the advancing WCA and the wettability of defects to be estimated based on the receding WCA. Because defect density is very low (below its packing limit) for both ZYA and PG, the advancing WCA corresponds to WCA of the sample surface (i.e., sp2 carbon sans defects); whereas the receding WCA corresponds to the WCA of defects at the present defect density. Increasing defect density (up to its packing limit) will asymptotically decrease receding WCA and reflect wettability of the defects as shown in Figure 19.