Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 163

The outermost atoms at the surface of a material have a higher energy when compared to atoms in the interior due to their lower coordination and disrupted bonding (Figure 5.2). This excess energy is referred to as the surface energy, defined as the work required to create a unit area of surface. Surface energy (J/m²) and surface tension (N/m) have different units but they are numerically equal. These two terms are often used interchangeably but, largely, surface energy has been more commonly associated with a solid whereas surface tension has been associated with a liquid. The difference in units stems from the way in which the terms are defined. Surface tension is defined mechanically in terms of a pressure difference Δp across a curved surface by the Laplace equation

(5.1)

where γ_s is the surface tension, and r₁ and r₂ are the principal radii of curvature of the surface. According to Eq. (5.1), the units of γ_s are N/m. On the other hand, surface energy γ_s is defined thermodynamically as the surface energy per unit area, giving units of J/m².

Figure 5.2 Illustration of lower coordination and disrupted bonding of outermost atoms at the surface of a crystalline material that gives rise to a surface energy.

Unless a material is in an ideal vacuum, its surface will be in contact with another medium such as a vapor (gas) phase or a liquid phase, which will influence the bonding at the solid surface and, thus, its surface energy. Consequently, the surface energy γ_s of a solid commonly refers to the energy of the solid–vapor interface, that is, the solid surface in contact with the appropriate vapor (gas) phase such as air. It is often designated γ_sv to signify this, where the subscript sv refers to the solid–vapor interface. Similarly, the surface energy (surface tension) of a liquid is the interfacial energy of the liquid–vapor interface, designated γ_lv. At room temperature, γ_sv of many synthetic polymers are in the range ~20–50 mJ/m². In comparison, many metals and ceramics show much higher γ_sv values, in the range ~0.2–2 J/m², while a few metals show γ_sv values higher than 2 J/m². The low γ_sv for polymers is related to their weak van der Waals intermolecular bonds whereas the higher γ_sv for metals and ceramics is related to their strong interatomic bonding.

Surface energy has a significant influence on reactions that take place at the surface of a material. As there is a thermodynamical driving force to lower its energy, a material with a high surface energy will tend to encourage adsorption of substances from its surroundings if this will lead to a reduction in energy. In this sense, the surface energy of a solid has often been discussed in terms of the degree of contact between a drop of liquid and the solid surface (Figure 5.3). The change in the Gibbs free energy dG when the area A of the drop in contact with the solid increases by an infinitesimal amount dA is given by

(5.2)

where γ_sv, γ_sl, and γ_lv are the specific energies (energy per unit area) of the solid–vapor, solid–liquid, and liquid–vapor interfaces, respectively, and θ is the contact angle between the liquid and the solid (the angle between the tangent to the liquid–vapor interface at the contact point with the solid surface). At equilibrium, dG/dA = 0 and Eq. (5.2) gives

(5.3)

Figure 5.3 Contributions to the Gibbs free energy change due to change in area dA of a liquid drop on a solid.

Equation (5.3), sometimes referred to as the Young and Dupré equation, is what we would obtain by taking the horizontal components of the interfacial tensions in Figure 5.3. Roughly, good wetting of a solid by a liquid is said to be characterized by a low contact angle ( θ < 90°) and poor wetting by a high contact angle ( θ > 90°). Complete wetting and spreading of a liquid occurs when θ = 0° (Figure 5.4).

Figure 5.4 Wetting behavior between a liquid and a solid showing (a) good wetting, (b) poor wetting, and (c) complete wetting for a liquid of contact angle θ .

As the physiological fluid is aqueous in nature, the extent to which water will wet a biomaterial and spread over it has significant consequences for its interaction with the aqueous medium in vivo. A material that shows good wetting and spreading by water (low θ ) is referred to as hydrophilic (literally, water‐loving). If the solid has a higher surface energy than water, there is a thermodynamic driving force for wetting and spreading of the liquid in order to reduce the energy of the system. In comparison, a material that shows poor wetting by water (high θ ) is referred to as hydrophobic (literally, water‐hating). In this case, the material has a lower surface energy than water and, thus, wetting is thermodynamically unfavorable because it will lead to an increase in the energy of the system.