Cassie-Baxter State surfaces

Before proceeding further we note that the problem of drops on top of rough surfaces with pillars or protrusions is different from the one in which rough surfaces have cavities. In case of rough substrates (made of hydrophilic materials) with pillars, a Cassie-Baxter state will typically transition to a Wenzel state by simply displacing the air which is part of the ambient, thus trapping of air is not possible. 

When a drop is deposited on a surface with cavities, it will be assumed that the air is trapped in the cavities under the drop by a liquid-air interface at top of the cavities. This state will be termed the Cassie-Baxter state as shown in Fig. 1. The interface at the top of the cavities will have a curvature equal to that of the drop itself. However, compared to the length scale of the cavities, the radius of curvature of this interface is large — it will be assumed to be flat. As such the pressure in the drop will be approximated to be equal to Fo as far as computing the equilibrium inside the cavities is concerned. This assumption is no different from the flat interface assumption in case of surfaces with pillars or bumps [14,29, 30]. In the Cassie-Baxter state the air in the cavity will be assumed at pressure Pq and temperature To — same as the ambient. 

Note that the summation in (8) is only for the cavities below the drop. The remaining cavities give zero contribution. In equation (8), R T = Pq Vcav has been used by assuming that the amount of air trapped in the cavities under the drop is determined by the Cassie-Baxter state. In the Cassie-Baxter state, the air is at pressure Pq and volume Vcav- An ideal gas law is used. AUy. denotes the change in the surface energy in cavity i as the liquid-air interface moves into the cavity. 

Note that is the change in energy corresponding to the transition from the Cassie-Baxter state to the Wenzel state. Since all air in both the Cassie-Baxter and Wenzel states is at the ambient conditions, there is no contribution to from the pressure terms in equation (14). The only contribution comes from the surface energy change. 

For the first two structure distances of 30 and 45 pm, the final structure forms are close and interconnected enough to produce a kind of capillary effect which forces the water to fill the cavities, leading to very high hysteresis values (Fig. 4). This interconnection between the pillars leads, especially for the 30 pm distance, to an area more fikely made of holes than free-standing pillars. For the next distances of 60, 75 and 90 pm, both Wenzel and Cassie-Baxter states are observable depending on how carefully the drop is placed on the surface (Fig. 6). For the last dimension of 30/120 pm we could not achieve a Cassie-Baxter state because of the large distance between the pillars. 

Figure 1. Behavior of a droplet on a perfectly flat surface (a), on a rough surface according to the Wenzel state (h) and on a rough surface according to the Cassie-Baxter state (c).

Surfaces of certain plants — such as the leaf of the Lotus plant — have a surface topography with two scales of roughness in the form of a base profile with peak-to-peak distances of the order of several micrometers and a superposed fine structure with peak-to-peak distances significantly below one micrometer [7-11]. Given this, the Lotus leaf follows the Cassie-Baxter state as sketched in Fig. Ic. Surfaces with... 

Figure 9 a) A drop of water on a lotus-leaf surface, b) Cassie Baxter state of a droplet on a hydrophobic, rough surface. Note the air enclosed under the drop. Pictures courtesy of Doris Spori, ETH Zurich. 

In addition to its influence on surface reactivity, surface structure is also seen to affect wettability on the micrometer scale, as is best illustrated by the lotus effect (see Chapter 3b). The lotus leaf is superhydrophobic, i.e. has a water contact angle of about 160°, thanks to the combination of the waxes on the surface with a characteristic dual micrometer- and nanometer-scale surface topography. Without the structure, the wax chemistry would only impart mild hydrophobicity to the surface. Superhydrophobicity comes about only when a water droplet is in contact with a rough surface with a substantial enclosure of air beneath the drop (Figure 9). This is the so-called Cassie-Baxter state, named after the authors of the work that described the contact angle of water droplets in this state by means of the equation ... 

For the nanoparticle surfaces, a similar mixed wetting state as described above is assumed [11, 17]. Only on silica sphere arrays decorated by gold nanoparticles we observe CA > 150°, reduced hysteresis and SA < 5°, which are characteristic for superhydrophobic substrates. Although a detailed characterization of the wetting mechanism on these hierarchical surfaces lies outside the scope of this work, we assume that the droplets on the substrates with hierarchical roughness are neither in the Wenzel nor Cassie-Baxter state. Most likely they reside in a mixed state as presented by... 

Figure 9.1 (a) Cassie-Baxter state that promotes liquid repellenqr. (b) Wenzel state where the liquid penetrates in the rough asperities of the surface, increasing the surface-liquid adhesion, (c) SLIPS type of surface where the lubricant covers the surface features, (d)... 

In general, most superhydrophobic, superoleophobic, and superomniphobic surfaces are very fragile (i.e. they will lose liquid repellency if touched or rubbed by human hands) and are not suitable for commercial uses. This mechanical fragility of the surface texture can cause surface defects which leads to collapse of the Cassie-Baxter state. As a result, a subsequent... 

If the liquid, on the other hand, sits on top of the surface features without penetrating the valleys , air will be enclosed between the droplet and the substrate and the liquid/air interface increases (cf [4,5]). In this Cassie-Baxter state , the solid/liquid interface approaches a minimum. The further increase of surface area (i.e. spreading of the droplet) is hindered for energetic reasons [5]. The apparent contact angle observed xmder these conditions is usually described by the simplified equation... 

A schematic of a drop partially wetting a solid surface in the case of a solid in the Young, Wenzel, and Cassie-Baxter states is shown in Figs. 10.1a, 10.1b, and 10.1c, respectively. 

Behavior of a liquid drop on a rough surface. Left, liquid penetrates into the spikes (Wenzel state) right liquid suspends on the spikes (Cassie-Baxter state) [72],... 

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