Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 166

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 V_l = 18.0 cm³, and V_s = 83.4 cm³. Substituting in Eq. (5.5), we get Φ = 0.94. Then, substituting the values for Φ, γ_lv, and θ in Eq. (5.6) gives γ_sv = 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 γ_lv, that is

(5.7)

where a and b are constants. Eq. (5.7) can be expressed in the form

(5.8)

where c is a constant and γ_cr is a characteristic property of the material called the critical surface tension. The significance of γ_cr is that a liquid of surface tension less than or equal to γ_cr 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 γ_lv (Figure 5.5). For many polymers, it is found that γ_cr is approximately equal to γ_sv, 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.