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For a polymer, the repeating unit in the polymer chain can be taken to approximate the molecular segment. Using Eqs. (5.3) and (5.4), we get
Example 5.1
The measured contact angle of a water droplet on polymethyl methacrylate (PMMA) is 70°. Determine the surface energy of PMMA, given that the densities of PMMA and water are 1.2 and 1.0 g/cm3, respectively, and the surface tension of water is 73.0 mN/m.
Solution:
The molecular weight of water is 18.0 g/mol and the molecular weight of the repeating unit in PMMA is 100.1 g/mol, giving Vl = 18.0 cm3, and Vs = 83.4 cm3. Substituting in Eq. (5.5), we get Φ = 0.94. Then, substituting the values for Φ, γlv, and θ in Eq. (5.6) gives γsv = 37 mJ/m2.
Another method applicable to materials of low surface energy, such as polymers, is referred to as the Zisman method. Fox and Zisman (1950, 1952) found that cos θ for a variety of polymers was approximately a monotonic function of γlv, that is
where a and b are constants. Eq. (5.7) can be expressed in the form
(5.8)
where c is a constant and γcr is a characteristic property of the material called the critical surface tension. The significance of γcr is that a liquid of surface tension less than or equal to γcr will wet and spread over the material. This follows from the limiting condition for spreading is θ = 0° and the fact that the contact angle cannot be less than 0°. The Zisman method involves measuring the contact angle θ for several liquids of known surface tension on a given polymer and plotting cos θ versus γlv (Figure 5.5). For many polymers, it is found that γcr is approximately equal to γsv, as exemplified by the data for PMMA in Figure 5.5. However, because of the time‐consuming nature of the experiments and the less than rigorous theoretical justification, the Zisman method has found only limited application in recent years.
Figure 5.5 Zisman plot for polymethyl methacrylate (PMMA) using various liquids.
5.2.2 Measurement of Contact Angle
While a variety of methods can be used to measure the contact angle of a liquid on a solid (Ratner 2013), the sessile drop technique is easy to perform and, thus, finds considerable use. In this technique, a drop of the appropriate liquid, for example deionized water, is placed on a flat surface of the material according to a standard procedure and the contact angle is determined from images of the drop using automated equipment (Figure 5.3). The surface tension γlv of liquids used in contact angle measurements to determine γcr or to estimate γsv of a material (Eq. (5.6)) can be measured using simple techniques such as capillary rise of a liquid. However, this is often not necessary because the surface tension values of pure liquids at an appropriate experimental temperature such as room temperature are given in reference tables.
For a given liquid, the contact angle and, thus, the wettability of a material depends mainly on its surface chemistry but they can depend on the surface topography as well. Most metals and ceramics are typically more hydrophilic to varying extent due to the lower coordinated bonds at their surface whereas most polymers are more hydrophobic due to their organic surface groups. A rough surface that is wetted without any trapped air between a liquid droplet and the solid (Figure 5.6), referred to as homogeneous wetting, has an apparent contact angle θW given by (Marmur 2003):
where θ is the contact angle for a smooth surface of the same composition and Ρ is the roughness ratio defined as the true area of the rough surface relative to its nominal cross sectional area. In comparison, when wetting of the rough surface is inhomogeneous, that is, when air is trapped between the drop and the rough surface, the apparent contact angle θCB is given by
where f is the fraction of the projected area of the solid surface that is wetted by the liquid and Ρf is the roughness ratio of the wet area. Equations (5.9) and (5.10) are valid when the drop is sufficiently large relative to the roughness scale of the surface. The significance of these equations is that they predict how the roughness of a surface influences its contact angle with a liquid drop.
Figure 5.6 Homogeneous wetting (a) and heterogeneous wetting (b) of a rough surface illustrated for a hydrophobic liquid.
For homogeneous wetting, Eq. (5.9) predicts that a rough surface will decrease the contact angle of a hydrophilic material ( θ < 90°), that is, the hydrophilicity of the material will increase. In comparison, the contact angle of a hydrophobic material ( θ > 90°) will increase with surface roughness, that is, the hydrophobicity of the material will increase. For a greater amount of air trapped between the liquid and the rough surface, f decreases and, consequently, the apparent contact angle is higher. Subsequently, if the liquid slowly infiltrates the areas of trapped air, the contact angle is predicted to decrease with time, eventually becoming smaller than the contact angle of a smooth
