Conductivity and dielectric function

The response of a crystal to an external electric field E is described in terms of the conductivity a through the relation J = tE, where J is the induced current (for details see Appendix A). Thus, the conductivity is the appropriate response function which relates the intrinsic properties of the solid to the effect of the external perturbation that the electromagnetic field represents. The conductivity is actually inferred from experimental measurements of the dielectric function. Accordingly, our first task is to establish the relationship between these two quantities. Before we do this, we discuss briefly how the dielectric function is measured experimentally. 

The fraction R of reflected power for normally incident radiation on a solid with dielectric constant s is given by the classical theory of electrodynamics 

The real and imaginary parts of the dielectric function s = ei+ are related by 

We next derive the relation between the dielectric function and the conductivity. Using the plane wave expressions for the charge and current densities and the electric field, 

With the use of this relation, the continuity equation connecting the current J to the induced charge gives 

---

Optical Conductivity Optical Dielectric Function Discussion of Conductivity and Dielectric Functions Microwave Frequency Dielectric Constant Pseudoprotonic Add Doping of Polyanihne Comparison of Doped Aniline Tetramers, Aniline Octamers, and Polyanihne Chiral Metalhc-Doped Polyanihne... 

The quantitative difference between the Op and t estimated from IR and microwave transport measurements may be a reflection of the inhomogendty of the percolating network [105]. From the discussion of the optical conductivity and dielectric functions, a distribution of scattering times for the conduction electrons is likely involved in the transport. Therefore, at the lowest frequencies, the carriers that are the most delocalized (with the longest scattering times, t 10 s) may dominate the transport, fip appears smaller because a smaller fraction of the charge carriers have such a long mean free time (t 10 s). 

Having estabUshed the connection between conductivity and dielectric function, we will next express the conductivity in terms of microscopic properties of the solid (the electronic wavefunctions and their energies and occupation numbers) as a final step, we will use the eonnection between conductivity and dielectric function to obtain an expression of the latter in terms of the microscopic properties of the solid. This will provide the direct link between the electronic structure at the microscopic level and the experimentally measured dielectric function, which captures the macroscopic response of the solid to an external electromagnetic field. 

Polymer thick films also perform conductor, resistor, and dielectric functions, but here the polymeric resias remain an iategral part after cuting. Owiag to the relatively low (120—165°C) processiag temperatures, both plastic and ceramic substrates can be used, lea ding to overall low costs ia materials and fabrication. A common conductive composition for flexible membrane switches ia touch keyboards uses fine silver particles ia a thermoplastic or thermoset polymeric biader. 

In chapter 7, several aspects of conductivity and dielectric relaxation were discussed. Various other properties such as shear modulus, viscosity, refractive index, volume, enthalpy etc. also exhibit relaxational behaviour particularly in the glass transition region. In this chapter, few further aspects of relaxation are discussed. Relaxation of generalized stress or perturbation whether electrical, mechanical or any other form is typically non-exponential in nature. The associated property is a function of time. A variety of empirical functions, (/) t), have been used to describe the relaxation. Some of them have already been discussed in chapters 6 and 7. The most widely used function is the Kohlraush-Williams-Watts (KWW) function (Kohlraush, 1847 Williams and Watts, 1970 Williams et al., 1971). It is more commonly referred to as the stretched exponential function. The decay or relaxation of the quantity is given by,... 

The measurements of conductivities and dielectric constants furnish data for the computation of concentrations of the diflFerent types of defects as a function of solute concentration and of temperature, as well as interpretations in terms of lattice position, thermodynamics, and kinetics of these defects (77, 79). The quantitative evaluation of these measurements depends critically on the determination of the proton mobility, ion concentration, and dissociation constant in pure ice (Table IV) made by Eigen and coworkers (46, 47). 

Fig. 4.4. Threshold voltage Uc as a function of the frequency / calculated using Phase 5 material parameters and for different values of the flexoelectric strength Circles and bullets represent the experimental data for conductive and dielectric EC, respectively.

Thermal breakdown is caused by the fact that d.c. conductivity results in Joule heating. Under an a.c. field, there is additional energy dissipation, with heat being generated in the dielectric materials faster than it can be dissipated to the surroundings. The subsequent rise in temperature will lead to an increase in conductivity and dielectric loss, which eventually culminates in a runaway situation and thermal breakdown. The breakdown voltage, Ub. is proportional to the thermal conductivity of the materials, X, the function

flat disc and the heat transfer coefficient), and is inversely proportional to the angular frequency of the a.c. field to, the temperature coefficient of the loss factor T, the dielectric permittivily e, and the loss factor tan 5 ... 

---