Materials for Biomedical Engineering. Mohamed N. Rahaman

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, I_o 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 of the intensity of the reflected light I_R to the intensity of the incident light I_o, is given by

      (4.51)

      Light that has entered a material can be reflected out due to scattering inside the material. If the amount of scattering is not too excessive, the material can appear translucent. Even the transmitted light can be scattered as it passes through the material, giving a transmitted beam that will spread out and appear blurred. Scattering occurs at the grain boundaries of polycrystalline materials, at fine pores within a material and at the interface between two phases of different refractive index. A dense homogeneous pore‐free glass lacks these microstructural features and, thus, suffers from little scattering.

      Small changes in composition can lead to large changes in the color of a material as, for example, the formation of glasses with a variety of colors by the addition of less than ~1% by weight of a transition metal oxide to a composition that would normally form a transparent glass. Changes in the electronic energy levels of the transition metal ions give rise to selective absorption of light at certain frequency ranges in the visible region of the electromagnetic spectrum, and, thus, to different colors.

      Lithium disilicate glass‐ceramics have become one of the most commonly used materials for dental restorations such as crowns and bridges (Chapter 7). The microstructure of these glass‐ceramics consists of fine lithium disilicate crystals within a glass matrix (Figure d). In addition to an attractive combination of mechanical properties, thermal conductivity, and chemical stability in the oral environment, lithium disilicate glass‐ceramic compositions have been designed to provide desirable optical properties such as color and fluorescence to match those of the existing tooth structure. This is achieved by adding small quantities of various transition metal oxides to the glass composition during its manufacturing process. In this way, the refractive index of the glass phase is made approximately equal to that of the crystals to reduce scattering of light at the enormous number of interfaces between the fine crystals and the glass matrix. A few of these metal ions and, if required, the use of additional metal ions, provide an additional benefit of esthetic appearance. They lead to the production of a wide range of desirable colors and fluorescence to match the existing tooth structure.

4.9 Concluding Remarks

      In this chapter, we discussed how a three‐dimensional material responds to an applied physical stimulus such as a mechanical stress, an electric field, a magnetic field or an electromagnetic field (light). Overall, the response