Academic literature on the topic 'Nernst-Einstein relation'

For the detection of charged particles many detector principles exploit the ionisation in sensing layers and the collection of the generated charges by electrical fields on electrodes, from where the signals can be deduced. In gases and liquids the charge carriers are electrons and ions, in semiconductors they are electrons and holes. To describe the ordered and unordered movement of the charge carriers in electric and magnetic fields the Boltzmann transport equation is introduced and approximate solutions are derived. On the basis of the transport equation drift and diffusion are discussed, first in general and then for applications to gases and semiconductors. It turns out that, at least for the simple approximations, the treatment for both media is very similar, for example also for the description of the movement in magnetic fields (Lorentz angle and Hall effect) or of the critical energy (Nernst-Townsend-Einstein relation).

In the previous chapter, we dealt with the distribution of solutes between gas, liquid and solid phases in the soil at equilibrium; and with the rates of redistribution between these phases within soil pores. In this chapter, we consider movement of the order of 1 –1000 mm from one volume of soil to another. Such movements occur largely by diffusion and mass flow of the soil solution or soil air, and by mass movement of the body of the soil. Major movements that involve the balance and amount of solutes in the whole soil profile, including plant uptake and drainage losses, are treated in chapter 11. The process of diffusion results from the random thermal motion of ions, atoms or molecules. Consider a long column of unit cross-section orientated along the x axis, and containing a mixture of components in a single phase at constant temperature and external pressure. If the concentration of an uncharged component is greater at section A than at section B, then on average more of its molecules will move from A to B than from B to A. The net amount crossing a unit section in unit time, which is the flux, is given by the empirical relation known as Pick’s first law: . . . F = − D dC/dx (4.1) . . . where F is the flux, and dC/dx is the concentration gradient across the section. The minus sign arises because movement is from high to low concentration in the direction of increasing x. The diffusion coefficient, D, is thus defined by the equation as a coefficient between two quantities, F and dC/dx, which can be measured experimentally. It is not necessarily a constant. The diffusion coefficient of the molecules in a phase is directly proportional to their absolute mobility, u, which is the limiting velocity they attain under unit force. Terms D and u are related by the Nernst-Einstein equation: . . . D = ukT (4.2) . . . where k is the Boltzmann constant and T is the temperature on the Kelvin scale. The Nernst-Einstein equation is derived as follows (Atkins 1986, p. 675).

A new constitutive model relating proton conductivity to water content in a polymer electrolyte or membrane is presented. Our constitutive model is based on Faraday’s law and the Nernst-Einstein equation; and it depends on the molar volumes of dry membrane and water but otherwise requires no adjustable parameters. We derive our constitutive model in two different ways. Predictions of proton conductivity as a function of membrane water content computed from our constitutive model are compared with that from a representative correlation and other models as well as experimental data from the literature and those obtained in our laboratory using a 4-point probe.