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
where γs 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 γs are N/m. On the other hand, surface energy γs 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 γs 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 γsv 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 γlv. At room temperature, γsv of many synthetic polymers are in the range ~20–50 mJ/m2. In comparison, many metals and ceramics show much higher γsv values, in the range ~0.2–2 J/m2, while a few metals show γsv values higher than 2 J/m2. The low γsv for polymers is related to their weak van der Waals intermolecular bonds whereas the higher γsv 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
where γsv, γsl, and γlv 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
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.
5.2.1 Determination of Surface Energy of Materials
According to Eq. (5.3), the surface energy γsv is related to the surface energy of the liquid γlv, the solid–liquid interfacial energy γsl and the contact angle θ . Whereas γlv and θ can be easily measured, γsv and γsl cannot. Consequently, methods for estimating γsv often involve a combination of measuring γlv and θ, and estimating γsl using theoretical analyses, some of which can be fairly complex. While a variety of methods have been proposed, a useful method for polymers, based on its simplicity and accuracy, involves measuring θ for a single liquid of known surface energy (surface tension) γlv and using a theoretical expression for γsl (Girifalco and Good 1957):
where Φ is expressed in terms of Vs and Vl, the molar volume (molecular weight divided by the density) of the molecules or molecular segments of the solid and the liquid, respectively, given by
