## Theoretical background

Wetting is the process of making contact between a solid and a liquid. Controlling the wettability of solid materials is a classical and key issue in surface engineering. Typical examples for wetting-dependent processes in daily life, biology and industry include adhesion, printing, cleaning, painting, lubrication, and many more.

Most processes that involve liquids deal with situations where the free surface of the liquid meets a solid boundary, thus forming the so-called three-phase-contact line - solid-liquid-gas. The contact line can move along the solid surface, leading to "wetting" or "dewetting". The interaction between a liquid and a solid involves three interfaces; the solid-liquid interface, the liquid-vapor interface and the solid-vapor interface. Each of these interfaces has an associated surface tension, γ, which represents the energy required to create a unit area of that particular interface. A different approach is to regard γ as a force acting on the drop. This approach is shown in Figure 1, where γ appears as an arrow. At equilibrium, force equilibrium along the X axis provides a reltion between the angle, θ, and the surface tensions of the three interfaces. This is called Young's equation:

 γSG = γSL + γLGcos(θ) (1)

Where γSG, γSL and γLG are the surface tensions of interfaces solid/gas, solid/liquid and liquid/gas respectively. θ is the angle between a liquid drop and a solid surface, called the contact angle.

The magnitude of Young's contact angle is the result of energy minimization. If the liquid-gas surface tension is smaller than the solid-gas surface tension (γLG < γSG), the liquid-solid interface will increase to minimize energy. As the drop wets the surface, the contact angle approaches zero, leading to complete wetting. Other ratios of γLG and γSG will lead to the formation of drops of different shapes as shown in Figure 1. A hydrophilic surface is defined as a surface where 0o < θ < 90o, and hydrophobic surface is a surface where θ≥90o. The surface tensions of different substances in contact with the gas phase vary over a wide range is shown in Figure 2.

Figure 1: Different shapes of drops on a solid.

Figure 2: Comparison of surface tension of different materials in contact with their vapor

### Interaction between surfaces and liquids

In order to understand why different surfaces and liquids form different contact angle, we must consider the interaction between the liquid and the surface and between the liquid molecules themselves. The adhesive force between the surface and the liquid causes the drop to spread and wet the surface, and the cohesive force within the liquid drop causes it to ball up and avoid contact with the surface. For example, let's consider the contact angle water and three types of surfaces - polymer, metal and oxide.

1. Some polymers, such as PVC and Teflon, form mainly Van-Der-Waals bonds with a water drop placed on them. These bonds are weak relative to the hydrogen bonds within the drop, so that the water prefers to bond with itself and not with the surface. The result is a bead shaped drop that almost doesn't wet the surface. These are hydrophobic surfaces.
2. Oxide surfaces can form hydrogen bonds with the water in the drop. These are strong bonds, and so the water prefers to wet the surface rather than ball into a bead. These are hydrophilic surfaces.
3. Metal surfaces don't form strong hydrogen bonds with water, however their polarity is greater than that of PVC or Teflon, so their affinity to water is greater, the result is that their contact angle is usually between that of the previous surfaces.
The same consideration can be used to predict the contact angle of an organic liquid such as oil on different surfaces.

### Controlling the contact angle

The surface tension and contact angle can be controlled through different methods.

1. Temperature: generally, surface tension decreases as the temperature increases. The dependence of surface tension on temperature is usually approximately linear reaching zero at the critical temperature, as in Figure 3.

Figure 3: Surface Tension of water and benzene at different temperature

2. Surface roughness: if the surface is rough and water penetrates into the roughness, whatever trend the flat surface showed will be enhanced: a hydrophobic surface will become even more hydrophobic and a hydrophilic surface will become more hydrophilic. This is Wenzel's model. According to Cassie and Baxter's model, the water drop doesn't penetrate into the surface grooves and instead lies on top of them, so that air bubbles are trapped inside. The trapped air increases the contact angle and the surface becomes superhydrophobic. Both models are shown in Figure 4.

3. Figure 4: the effect of surface roughness on the contact angle

4. Electro-wetting: when a potential difference is applied between the liquid and the solid surface, the electric force at the corners of the drop pulls it down onto the surface, lowering the contact angle.
5. Chemical modifications: chemical modification of the surface can lead to a change in its surface tension. For example, adding polar, hydrophilic groups to the surface will lead to a lower contact angle. The next section gives two concrete examples of such a modification.

### Surface modifications

A metal surface is usually hydrophilic, especially if it is oxidized. Pure metal surface exhibits a strong interaction with the oxygen of water molecules (Figure 7a), whereas oxidized surface creates H-bonds with water (Figure 7b).

 a b

Figure 5: Schematic view of (a) metal/water interface and (b) oxide/water interface.

The most common way to make a surface hydrophobic consists in the use of sulfur-containing alkyls with more than six repeating units ((-CH2)n) in the chain. The interaction of these substances with a copper surface can be described as follows:

 (A) (B) (C) (D)

As a result of these reactions the metal surface is blocked from interacting with solvent molecules by alkyl-chains, replacing strong metal-water interactions by weak interactions of water with saturated alkyl chains. If, instead of HS - R or (S - R)2, one uses substances like HS - R - X or (S - R - X)2, where X can form H-bonds (e.g. NH, NH2, SO2 etc.), then the modified surface will be hydrophilic.

 a b c

Figure 6: (a) disulfide and (b) thiol groups. (c) shows the metal/alkyl/water interface

### Surfactant and surface tension of water

The surfactant molecules accumulate preferentially at the liquid-vapor interface with the polar groups oriented toward the aqueous phase (Figure 6i). This positive adsorption of surfactant molecules lowers the liquid-vapor interfacial energy, and consequently the surface tension decreases. The surface tension continues to fall as the surfactant concentration increases until the critical micelle concentration is attained. At this stage the adsorbed molecules are closely packed, forming an oriented monomolecular layer (monolayer) (Figure 6ii). Above this concentration, additional surfactant molecules aggregate to form micelles in the bulk. This cooperative association process continues in the bulk with further increase of surfactant concentration, while at the surface of the solution the molecules remain in a highly condensed state. The concentration of free surfactant is essentially constant as the micelle concentration increases (Figure 6iii); free surfactant and micelles exist in dynamic equilibrium. The surface tension remains approximately constant for the systems studied since it depends only on the liquid-vapor interfacial structure. The same type of behavior is found for the magnitude of the contact angle; that is, as the surfactant concentration increases, the contact angle decreases until a constant value is attained. For higher concentrations the contact angle remains approximately constant.

Figure 9: Schematic arrangement of surfactant molecules in aqueous solutions: (i) at low concentrations - the surfactant molecules adsorb preferentially at the air-water interface; (ii) at at some higher concentration a monolayer is formed at the air-solution interface; (iii) increase of concentration does not change the state of surface, all additional surfactant molecules aggregate as micelles.

### Zisman plot

The surface tension at a solid/gas interface can be determined from a Zisman Plot, which measures variation in contact angle as a function of the known surface tension, γLG, for a series of liquids. The experimentally obtained dependence of cos(θ) on γLG is often linear. The value for which cos(θ) extrapolates to 1 is termed the surface tension, γSG , of the solid/gas interface. A typical Zisman Plot is shown in Figure 5.

Figure 8: Zisman Plot for a polyethylene surface with a series of liquid.

The idea of this approach is as follows: a liquid with a surface tension less than or equal to the surface tension of a particular material will wet that surface, i.e. the contact angle will be 0o. However, this widely-used approach can be applied only under proper conditions.
The Young equation at θ = 0 gives:

 γSG = γSL + γLG (1.2)

But not γSG = γLG as obtained from the Zisman approach. In other words, the liquid and solid studied must have an interface with γSL≈0. This is approximated in the case of organic polymer solids and liquid saturated hydrocarbons or aqueous solutions of saturated alcohols at sufficiently high concentrations (>20%). This is the reason why the surface tension obtained from a Zisman plot is often referred to in the literature as the critical surface tension of wetting but not the surface tension of a solid/gas interface.