electrons). In comparison, the high thermal conductivity is due to two factors, the highly ordered crystal structure and the strong atomic bonding that strongly limits the incorporation of impurities into its structure. These two factors severely limit phonon scattering in the crystal lattice.
Figure 4.23 Chart showing the thermal conductivity values for a variety of materials.
In polymers, heat conduction occurs by vibration and rotation of the long chain molecules. Polymers have a low thermal conductivity, although, for a semicrystalline polymer, the conductivity increases with increasing volume fraction of crystalline regions because phonon scattering in the crystalline region is lower than that in an amorphous region of the same composition.
4.7.2 Thermal Expansion Coefficient
The expansion or contraction of a material upon heating or cooling is commonly quantified by its linear coefficient of thermal expansion α defined by the equation
(4.48)
where, Δl is the change in length of a specimen of length lo due to a change in temperature ΔT. The thermal expansion coefficient has the unit °C−1 (or K−1) but is often expressed in units of 10−6 °C−1 because of its low value. The thermal expansion coefficient of one material relative to another is dependent on its interatomic bonding energy versus displacement curve (Section 2.2).
Although α varies slightly, depending on the temperature range of measurement, ceramics and glasses typically have low α values relative to other classes of materials, in the range ~5 × 10−6 to ~15 × 10−6 °C−1 over a temperature range of a few hundred degrees Celsius above room temperature. On the other hand, some glasses, such as fused silica glass, and a few glass‐ceramics have values as low as ~0.5 × 10−6 °C−1. Metals have higher α values, in the range ~10 × 10−6 to ~25 × 10−6 °C−1 but tungsten and a few metal alloys, for example, have values lower than ~5 × 10−6 °C−1. Polymers have the highest values, typically ~100 × 10−6 °C−1 and over.
A difference in thermal expansion coefficient leads to the development of mechanical stresses between two adherent materials upon heating or cooling. If high enough, these stresses can lead to cracking and delamination of one material from the other, such as a coating deposited on a three‐dimensional material. Metal implants, such as Ti6Al4V for example, have been coated with a bioactive material such as hydroxyapatite or bioactive glass, of thickness several tens of microns to a few hundred microns, to improve their bioactivity and osseointegration with host bone. These coatings are often formed on the metal implant at several hundred degrees Celsius. Ti6Al4V, for example, has a thermal expansion coefficient of ~9.5 × 10−6 °C−1. Consequently, coating materials for Ti6Al4V should have a thermal expansion coefficient that is not significantly different from this value to minimize stresses in the coating and reduce the potential for cracking or delamination of the coating during cooling from the fabrication temperature. Bioactive glass‐coated implants have seen little clinical application despite efforts to design glass compositions having thermal expansion coefficients that match those of implants such as titanium or Ti6Al4V (Peddi et al. 2008). In comparison, hydroxyapatite (thermal expansion coefficient of 10.0 × 10−6–10.5 × 10−6 °C−1) has been used for a few decades to coat dental and orthopedic implants, particularly those composed of titanium or Ti6Al4V. While considerable efforts have been devoted to creating adherent hydroxyapatite coatings using a variety of techniques, indications for the capacity of these coatings to enhance the long‐term viability of the implants remain controversial (Le Guéhennec et al. 2007).
4.8 Optical Properties
Optical properties of biomaterials are relevant to their use in applications such as contact lenses and intraoptical lenses, and dental restorations for repairing existing tooth structure, particularly in the anterior of the mouth. Important optical properties for biomaterials are their degree of transparency, refractive index, and color. Light is an electromagnetic wave and, consequently, electrostatic interactions with its electric field component determine the optical properties of a material.
Materials are broadly classified as transparent, translucent, or opaque, depending on their ability to reflect, absorb, or transmit an incident light beam (Figure 4.24). A transparent material is one in which there is little reflection and absorption whereas in an opaque material, there is little or no transmission. In a translucent material, light is scattered within the material and, thus, is transmitted diffusely through the material. If a material is not perfectly transparent, the intensity of light I decreases exponentially with distance x through it, given by Lambert’s law
(4.49)
where, Io is the intensity of the incident light beam and α is the absorption coefficient that can be obtained experimentally by plotting ln I versus x.
Figure 4.24 Reflection, transmission, and absorption of a light beam incident on the surface of a material.
Absorption of light depends on the atomic bonding of the material. Ionic bonded solids such as ceramics show high absorption because of the interaction of their oppositely charged ions with the electric field component of light. Absorption occurs in the region of the electromagnetic radiation spectrum such as the infrared, for example, where these frequencies match the frequencies of the lattice vibrations (phonons). The absorption spectrum of polymers is dominated by absorption by their constituent macromolecules. Light is preferentially absorbed in regions where its frequency excites the various absorption modes in the polymer. Because of the high concentration of nearly free electrons, almost all the incident light over a wide frequency range of the electromagnetic radiation spectrum on a metal is absorbed within ~0.1 μm of its surface and reflected back. Thus, metals of thickness greater than this value are both opaque and reflective.
Refraction (bending) of a light beam occurs when it passes from one medium into another, such as from air into glass. The refractive index n of a material is a measure of the extent to which an incident light beam is bent when it passes from a vacuum into the material. It is defined by
(4.50)
where, c is the velocity of light in a vacuum and v is the velocity of light in the material. As v must be smaller than c, n has values larger than 1. Several glasses, for example have a refractive index of ~1.5. Refraction as well as reflection of light occurs at the interface between two materials (or media) with different refractive index n1 and n2. Assuming that the light is incident normally on the surface, the reflectivity R, defined as the ratio
