Electrical Conductivity and Charge Transport

Ohm s law named after the German scientist Georg Ohm is the most fundamental law describing the measurements of applied voltage and current through simple electric circuits containing various lengths of wire. Its most commonly used form is 

7 is the current in ampere, V is the potential difference across the conductor in volts, and R is the resistance in ohms. Another generalized form of Ohm s law is 

Electrical conductivity ( gi) of a material is its ability to conduct an electric current. It is also defined as the reciprocal of electrical resistivity (Pei) which is a measure of how strongly a material opposes the flow of current  

The SI unit of electrical resistivity is Q-m, and that of electrical conductivity is siemens per meter (S/m). We also can demonstrate the Ohm s law conversion from one form to another as follows. Using equations (6.7) and (6.2) in equation (6.6), we have 

L and A corresponds to the length and area of the conductor/resistor, respectively. The aforementioned Ohm s law formation is valid for solid conductors or resistors. Let us define and discuss the electrical conductivity of a solution. 

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Both are electrically conductive, with charge transport occurring via both positive and negative ions. Both environments can be highly... 

Electrical conduction and heat transport are closely linked, the connection being described by three thermoelectric coefficients, the Seebeck coefficient (or thermopower), the Peltier coefficient and the Thomson coefficient, all of which have relevance to thermoelectric power generation and refrigeration. In perovskites, the most reported values are for the Seebeck coefficient. The magnitude and sign (+ or -) of the Seebeck coefficient are related to the concentration and type of mobile charge carriers present. For band-like perovskites, the magnitude of the Seebeck coefficient is proportional to the density of states, either in the conduction band, for electron transport, or the valence band for hole transport. 

The diffusion process in general may be viewed as the model for specific well-defined transport problems. In particle diffusion, one is concerned with the transport of particles through systems of particles in a direction perpendicular to surfaces of constant concentration in a viscous fluid flow, with the transport of momentum by particles in a direction perpendicular to the flow and in electrical conductivity, with the transport of charges by particles in a direction perpendicular to equal-potential surfaces. 

The Lorenz number as derived from thermal conductivity and electrical resistivity has small values just above Tc indicating different scattering mechanisms being important in the heat and charge transport for YNi2B2C, LuNi2B2C, and HoNi2B2C (Sera et al., 1996 Boaknin et al., 2000 Schneider, 2005). The shape of a typical minimum in the temperature dependence of the Lorenz number at about 40 K seems to be connected with the residual resistivity of the crystals (Boaknin et al., 2000). 

During mass and charge transport in a PEVD system, the solid electrolyte serves as an ion-pass filter and the external electric circuit as an electron-pass filter. Consequently, two kinds of conducting passes are separated in the system as shown in Figure 3. One is the ionic conduction path from location (I) through the bulk of the solid electrolyte (E) to location (II), then across the bulk of the PEVD deposit (D) to location (III). The other is the electronic conduction path from location (I) through the source electrode (C), the external electric circuit, and the sink electrode (W) to location (II), then across the bulk of the PEVD deposit (D) to location (III). 

We start our discussion with simple concepts from the band theory for solids, discuss what can break the symmetry of one-dimensional systems, introduce electrical conductivity and superconductivity, present the Mulliken charge transfer theory for solution complexes and its extension to solids, then discuss briefly the simple tt electron theory for long polyenes. Other articles in this volume review the detailed interplay between structure and electronic properties of conductors and superconductors [206], and electrical transport in conducting polymers [207],... 

About the turn of the century cuid shortly thereafter, certain developments in mathematical physics and in physical chemistry were realized which were to prove important in the theory of mass and charge transport in solids, later. Einsteinand Smoluchowski( ) initiated the modern theory of Brownian motion by idealizing it as a problem in random flights. Then some seventeen years or so later, Joffee A proposed that interstitial defects could form inside the lattice of ionic crystals and play a role in electrical conductivity. The first tenable model for ionic conductivity was proposed by Frenkel, who recognized that vaccin-cies and interstitials could form internally to account for ion movement. 

The plasma transport properties of various charged species are usually described by drift velodty and drift mobility in tlw electric fiekl. Correspondingly the electrical conductivity and diffusion coefficients are introdiK d. 

Conductivity in conjugated polymers was discovered several decades ago [1]. Since then, there has been major advances in the synthesis, characterization and applicability of conjugated polymers for different device applications. They all have in common a conjugated bond structure that allows for electron delocalization and charge transport along the polymer backbone resulting in unique electrical, optical and magnetic properties. Molecular structures for some commonly used CPs are shown in Fig. 7.1. 

The kinetic motion of molecules may cause them to change their spatial distribution through successive random movements. This is the process of diffusion, which is a transport property. Other transport properties include viscosity, electrical conductivity, and thermal conductivity. While diffusion is concerned with the transport of matter, these are associated with the transport of momentum, electrical charge, and heat energy, respectively. Transport is driven in each case by a gradient in the respective property. Thus, the diffusion rate of species A is given by Pick s law. 

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