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Numerous medical applications have been developed for siloxane polymers. Prostheses, artificial organs, objects for facial reconstruction, vitreous substitutes in the eyes, tubing and catheters, for example, take advantage of the inertness, stability, and pliability of polysiloxanes. Artificial skin, contact lenses, and drug delivery systems utilize their high permeability as well. Such biomedical applications have led to extensive biocompatability studies, particularly on the interactions of polysiloxanes with proteins. There has been considerable interest in modifying these materials to improve their suitability for biomedical applications in general. Advances seem to be coming particularly rapidly in the area of high-tech drug-delivery systems. Figure 10.1 shows the range of diameters of Silastic medical-grade siloxane tubing available for medical applications. The smallest tubing has an internal diameter of only 0.012 inches (0.031 cm) and an outer diameter of only 0.025 inches (0.064 cm). Such materials must first be extensively tested (sensitization of skin, tissue cell culture compatibility, implant compatibility). There has been considerable controversy, for example, over the safety of using polysiloxanes in breast implants. The major concern was “bleeding” of low molecular polysiloxanes out of the gels into the chest cavity, followed by transport to other parts of the body. The extent to which “bleeding” occurred and its possible systemic effects on the body were argued vigorously in the media and in the courts, and led to restrictions on the use of polysiloxanes. In the case of controlled drug-delivery systems, the goal is to have the drug released at a relatively constant rate (zero-order kinetics) at a concentration within the therapeutic range. It is obviously important to minimize the amount of time the concentration is in the low, ineffective range, and to eliminate completely the time it is in the high, toxic range (figure 10.2). Figure 10.3 illustrates the use of polysiloxanes in such drug-delivery systems. The goal mentioned is approached by placing the drug inside a siloxane elastomeric capsule, which is then implanted in an appropriate location in the body. The drug within the capsule can be in the free state, in a fluid suspension, or mixed or dissolved into an elastomeric matrix.

The dielectric constant K is a measure of a material’s ability to store electric charge. In scalar form the defining relations are as follows: . . . D = εE, . . . where D is the electric displacement measured in C/m2, ε is the electric permittivity in F/m, and E is electric field in V/m. The dielectric constant K is the relative permittivity: . . . K = ε/ε0, . . . where ε0 = 8.85 × 10−12 F/m is the permittivity of free space. The electric displacement D is equal to the sum of the charges stored on the electrode plus those originating from the polarization, P [C/m2] . . . D = ε0 E + P. . . . In this chapter we discuss the tensor nature of the dielectric constant, how it is represented geometrically, and some typical structure–property relationships. Dielectric constants range over about four orders of magnitude in insulator materials. Because of their low density, gases have dielectric constants only slightly larger than one. At one atmosphere, the dielectric constant of air is 1.0006. Most common ceramics and polymers have dielectric constants in the range between 2 and 10. Polyethylene is 2.3 and silica glass is 3.8. These are low-density dielectrics with substantially covalent bonding. More ionic materials like NaCl and Al2O3 have slightly higher K values in the 6–10 range. High K materials like water (K ∽ 80) and BaTiO3 (K∽1000) have special polarization mechanisms involving rotating dipoles or ferroelectric phase transformations. A schematic view of the principal types of polarization mechanisms is illustrated in Fig. 9.1. The electronic component of polarization arising from field-induced changes in the electron cloud around each atom is found in all matter. The ionic contribution is also common and is associated with the relative motions of cations and anions in an electric field. Orientational polarizability arises from the rotation of molecular dipoles in the field. These motions are common in organic substances. Many materials also contain mobile charge carriers in the form of ions or electrons that can migrate under applied fields.

The physical properties discussed thus far are linear relationships between two measured quantities. This is only an approximation to the truth, and often not a very good approximation, especially for materials near a phase transformation. A more accurate description can be obtained by introducing higher order coefficients. To illustrate nonlinearity we discuss electrostriction, magnetostriction, and higher order elastic, and dielectric effects. These phenomena are described in terms of fourth and sixth rank tensors. Many of the recent innovations in the field of electroceramics have exploited the nonlinearities of material properties with factors such as electric field, mechanical stress, temperature, or frequency. The nonlinear dielectric behavior of ferroelectric ceramics (Fig. 15.1), for example, has opened up new markets in electronics and communications. In these materials the electric polarization saturates under high fields. Electric displacement Di varies with applied electric field Ej as … Di = εijEj + εijkEjEk + εijklEjEkEl +· · ·, … where εij is the dielectric permittivity and εijk and εijkl are higher order terms. The data in Fig. 15.1 were collected for a relaxor ferroelectric in its paraelectric state above Tc where the symmetry is centrosymmetric. Therefore the third rank tensor εijk is zero, and the shape of the curve is largely controlled by the first and third terms. For cubic crystals, the fourth rank tensor εijkl is similar in form to the elastic constants discussed in Chapter 13. Tunable microwave devices utilize nonlinear dielectrics in which the polarization saturates as in Fig. 15.1. By applying a DC bias the dielectric constant can be adjusted over a wide range.

“Umklapp collisions and thermal conductivity” deals with heat conduction in a dielectric solid. Collisions of phonons are divided into Umklapp and normal according as a reciprocal lattice vector is or is not involved in the phonon momentum balance. A local temperature is defined by appeal to local thermodynamic equilibrium. An equilibrium phonon distribution can be off-centred, yet non-decaying, if the only collisions are “normal”, conserving the total phonon momentum. Then heat flow does not decay, even if a representative collision reverses the phonon group velocity. Conversely, in an Umklapp collision it is the non-conservation of phonon momentum that causes heat flow to decay.

Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac equation (having zero mass in this case). Its device-friendly properties of high electron mobility and excellent sensitivity as a sensor have attracted a huge world-wide research effort since its discovery about ten years ago. Here, the associated retarded Graphene Green’s function is treated and the dynamic, non-local dielectric function is discussed in the degenerate limit. The effects of a quantizing magnetic field on the Green’s function of a Graphene sheet and on its energy spectrum are derived in detail: Also the magnetic-field Green’s function and energy spectrum of a Graphene sheet with a quantum dot (modelled by a 2D Dirac delta-function potential) are thoroughly examined. Furthermore, Chapter 12 similarly addresses the problem of a Graphene anti-dot lattice in a magnetic field, discussing the Green’s function for propagation along the lattice axis, with a formulation of the associated eigen-energy dispersion relation. Finally, magnetic Landau quantization effects on the statistical thermodynamics of Graphene, including its Free Energy and magnetic moment, are also treated in Chapter 12 and are seen to exhibit magnetic oscillatory features.

Numerous medical applications have been developed for siloxane polymers. Prostheses, artificial organs, objects for facial reconstruction, vitreous substitutes in the eyes, tubing and catheters, for example, take advantage of the inertness, stability, and pliability of polysiloxanes. Artificial skin, contact lenses, and drug delivery systems utilize their high permeability as well. Such biomedical applications have led to extensive biocompatability studies, particularly on the interactions of polysiloxanes with proteins. There has been considerable interest in modifying these materials to improve their suitability for biomedical applications in general. Advances seem to be coming particularly rapidly in the area of high-tech drug-delivery systems. Figure 10.1 shows the range of diameters of Silastic medical-grade siloxane tubing available for medical applications. The smallest tubing has an internal diameter of only 0.012 inches (0.031 cm) and an outer diameter of only 0.025 inches (0.064 cm). Such materials must first be extensively tested (sensitization of skin, tissue cell culture compatibility, implant compatibility). There has been considerable controversy, for example, over the safety of using polysiloxanes in breast implants. The major concern was “bleeding” of low molecular polysiloxanes out of the gels into the chest cavity, followed by transport to other parts of the body. The extent to which “bleeding” occurred and its possible systemic effects on the body were argued vigorously in the media and in the courts, and led to restrictions on the use of polysiloxanes. In the case of controlled drug-delivery systems, the goal is to have the drug released at a relatively constant rate (zero-order kinetics) at a concentration within the therapeutic range. It is obviously important to minimize the amount of time the concentration is in the low, ineffective range, and to eliminate completely the time it is in the high, toxic range (figure 10.2). Figure 10.3 illustrates the use of polysiloxanes in such drug-delivery systems. The goal mentioned is approached by placing the drug inside a siloxane elastomeric capsule, which is then implanted in an appropriate location in the body. The drug within the capsule can be in the free state, in a fluid suspension, or mixed or dissolved into an elastomeric matrix.