Materials for Biomedical Engineering. Mohamed N. Rahaman

polymers have attracted interest for use in biomedical applications such as biosensors, neural probes, tissue engineering, and drug delivery.

      4.5.1 Electrical Conductivity of Materials

      The ability of a material to transmit an electric current is quantified by its electrical conductivity or, less commonly, by its electrical resistivity which is the inverse of the electrical conductivity. The resistivity ρ of a material is independent of its geometry but, for a wire of length l and uniform cross sectional area A, it is related to the measured electrical resistance R by the equation

(4.39)

      As the unit of R is ohm (Ω), the unit of ρ is ohm‐meter (Ω m), and the electrical conductivity, equal to 1/ ρ, has the unit (Ω m)⁻¹, commonly written S/m, where S, the inverse of Ω, is the unit Siemens.

The electrical conductivity of materials covers an enormous range of ~28 orders of magnitude. Metals are good conductors, with a conductivity in the range ~10⁴–0⁸ S/m, whereas most ceramics and polymers are insulators with conductivity in the range ~10⁻²⁰–10⁻¹⁰ S/m. Materials with intermediate conductivity, ~10⁻⁶–10⁴ S/m, are called semiconductors (Figure 4.16).

Figure 4.16 Bar chart showing the range of electrical conductivity for different types of materials at room temperature.

      Transmission of an electric current results from the motion of electrically charged particles in response to forces that act on them from an externally applied electric field. The high electrical conductivity of metals arises from the ease with which the sea of nearly free electrons that surround the metal cations move through the material (Chapter 2). Thus, metals are said to show electronic conductivity because electrons are essentially responsible for their ability to conduct an electric current. In comparison, a few ionic‐bonded ceramics can show a limited capacity to conduct an electric current, which arises from the migration of ions, referred to as ionic conductivity, plus any contribution from electronic conductivity. While the total electrical conductivity due to the electronic and ionic contributions increases with temperature, ceramics are essentially insulators at temperatures relevant to biomedical applications.

      Platinum alloys (conductivity ~10⁷ S/m) are commonly used in cardiac pacemakers while silver alloys with a higher conductivity (~10⁸ S/m) find use in some implantable defibrillators. On the other hand, polyurethane (conductivity ~10⁻¹² S/m), is often used as a coating to isolate or insulate sensitive electronic devices from surrounding tissues and fluids.

      4.5.2 Electrical Conductivity of Conducting Polymers

      Conducting polymers have attracted considerable interest in recent years because they can show an electrical conductivity as high as some metals (Figure 4.16). In addition to a high electrical conductivity, conducting polymers have an attractive combination of properties that make them suitable for use as biomaterials in applications such as biosensors, neural probes, tissue engineering and drug delivery (Guimard et al. 2007). These properties include ease of synthesis, flexibility of forming into desirable shapes, which are characteristic of polymers in general, and the potential for functionalizing their surface with appropriate molecules.

      Polyacetylene has shown one of the highest electrical conductivities, up to ~10⁷ S/m, whereas polypyrrole is the most widely studied conducting polymer. These and other conducting polymers typically show a characteristic structure composed of alternating single and double bonds in the polymer chain (Chapter 3). While conducting polymers can show an electrical conductivity as high as some metals, the source of their electrical conductivity is not the sea of almost free electrons that surround the cations in a metal. Instead, their high conductivity arises from a combination of factors that depend on the atomic bonding and structure of the polymer.

A key factor is the alternating single and double bonds in the polymer chain backbone, allowing the π electrons of the double bond to be more easily delocalized and move more freely between the atoms of the chain (Figure a). However, this type of atomic bonding alone is not sufficient to endow the polymers with a high conductivity. Another key factor is the ability of these polymers to be doped with appropriate molecules that introduce a charge carrier into the system by removing electrons from, or adding electrons to, the polymer chain. While the mechanism is more complex, Figure 4.17 illustrates a simplified explanation of the electrical conductivity (Balint et al. 2014).

Figure 4.17 Simplified explanation of the electrical conductivity of conducting polymers. (a) A dopant D removes or adds an electron from/to the polymer chain, creating a delocalized charge. (b) It is energetically favorable to localize this charge and surround it with a local distortion of the crystal lattice. (c) A charge surrounded by a distortion is known as a polaron P (a radical ion associated with a lattice distortion). (d) The polaron can travel along the polymer chain, allowing it to conduct electricity.

      Source: From Balint et al. (2014).

4.6 Magnetic Properties

      Magnetic properties have not traditionally played an important role in the development of biomaterials but the interesting and improved properties observed for nanoparticles and nanostructured materials have generated considerable interest in the use of magnetic nanoparticles for biomedical applications. Magnetic nanoparticles are being considered for a variety of biomedical applications such as drug delivery, hyperthermia treatment of tumors and contrast agents for magnetic resonance imaging (Pankhurst et al. 2003).

      Magnetism is commonly viewed as an attraction or repulsion between two materials. Whereas all materials are magnetic to some extent, the magnetism that we know from daily experience, such as iron filings or nails attracted to a bar magnet, is an important but special type of magnetic behavior called ferromagnetism. This type of magnetism is relevant to biomedical applications of magnetic nanoparticles and to engineering applications as well but there are weaker forms of magnetism called paramagnetism and diamagnetism. These different types of magnetism have their origins in the atomic structure of the constituent atoms or ions of the material. It is useful to understand how they arise in order to control or improve the magnetic properties of materials used as biomaterials.

      4.6.1 Origins of Magnetic Response in Materials

The magnetic response of a material depends on its atomic structure and, in the case of some materials, on its temperature, although the effect of temperature is not normally relevant to the application of biomaterials. We can view a magnet as a dipole with a certain magnetic moment in much the same way as we view an electric dipole with an electric dipole moment (Chapter 2). The magnetic response of a material has its origins in the tiny magnetic