Richardson equation

The kinetic energy of charge earners in a solid increases with increasing temperature and therefore the probability that a charge carrier passes a given potential barrier also increases. The thermally induced current flow of the charge earners from a metal contact into a polymer film can be derived from the Richardson equation, which describes the temperature-induced emission of hot charge carriers from a metal surface... 

For electrostatically or sterically interacting drops, emulsion viscosity will be higher when droplets are smaller. The viscosity will also be higher when the droplet sizes are relatively homogeneous, that is, when the drop size distribution is narrow rather than wide. The nature of the emulsifier can influence not just emulsion stability but also the size distribution, mean droplet size, and therefore the viscosity. To describe the effect of emulsifiers on emulsion viscosity Sherman [215] has suggested a modification of the Richardson Equation to the following form ... 

Formula (3.7) is of the familiar form, often called a Richardson equation. We notice in it that 6 does not represent the latent heat at the absolute zero but a slightly different quantity without theoretical significance, since the expression (3.5) is merely a convenient approximation for a small temperature range. And A is not the value of Eq. (3.4) but has the additional factor eP. This factor is of the order of magnitude of... 

Here A is a universal constant, is the work function of the surface, and R is the average reflection coefficient for electrons in the range of energies of interest. The experimental situation to which the Richardson equation applies is difficult to realize. Oily recently has it been possible to work under experimental conditions sufficiently controlled to allow an unambiguous determination of all the parameters appearing in it (15). At last it is now clear that the Richardson equation truly... 

So far only one specific characteristic of computed surface potentials seems to have an important effect on experimental results. For thermionic emission of surfaces subject to an electric field, the Richardson equation must be modified in two ways. First the potential barrier is lowered by the electric field to give a new work function. In addition the reflection coefficient is altered. The relative current )/ 0 as a function of applied field E becomes... 

It can be shown, either from thermodynamic considerations or from the application of statistical mechanics in connection with the quantum mechanics of electrons in metals, that the current density J of electrons emitted from a uniform surface of a pure metal of absolute temperature T can be expressed by the Richardson equation. 

Richardson equation (Rlchardson-Dushman equation) SeexHERMioNic emission. 

The application of these reactor models is quite straightforward. For example, let us consider again the hydrogen production in a membrane reactor applied for methane steam reforming. Suppose that the membrane used is a dense defect free Pd-based membrane which obeys the Richardson equation (10.9). The reactions taking place in the reactor are ... 

Suppose that the membrane used is a dense defect-free Pd-based membrane that obeys to the Richardson equation. 

A few comparable studies have been made upon the per-meabihties of metals to oxygen and hydrogen. Smithells and Ransley(76) observed that at pressures of 112 atm. the permeation rate-pressure isotherm obeyed accurately the Richardson equation ... 

Note that Rep is calculated at Ut. At this value of Reynolds number, the flow is intermediate between viscous and inertial, and so we must use the correlation of Khan and Richardson [Equation (3.25)1 to determine the exponent n in Equation (7.21) ... 

Accounting for the momenta of the electrons traveling in the direction of the surface, the thermionic current is given by the Richardson equation. 

According to the Dushman-Richardson equation, the electron current upon heating a substrate of work function O is given by... 

The temperature dependence of the hydrogen permeability can be expressed by the well-known Arrhenius expression P exp( - )], formally similar to the self-diffusivity coefficient mentioned in Section 15.3. However, in this case, the activation energy for diffusion, E , is referred to the jumps of the hydrogen atoms in the bulk of the Pd-aUoy (the rate-determining step is the H diffusion according to the Richardson equation). Considering that 0 depends on the partial pressure of the carbon monoxide, in addition to the temperature of the mixture, that is 0 (T, ), the scaling factor g(T,p ) can... 

---