What quantities does Einstein relate to?

The equation which relates the mobility µ (of electrons or holes) and the diffusion coefficient (of electrons Dn or holes Dp) is known as Einstein Relationship.

What is the relationship between diffusion coefficient and mobility?

The relationship between the mobility and the diffusion coefficient has been derived from the Langevin equation which takes into account the random electric field resulting from the randomly located and the randomly oriented electric dipoles.

How is the Nernst-Einstein equation for an anomalous diffusion obtained?

The Nernst–Einstein correlation for anomalous diffusion at short scales was obtained. We propose a fractional diffusion equation for anomalous transport at short spatial scales, where the anomalous diffusion can be observed due to non-Markovian process of scattering.

How is the Nernst-Einstein equation used in science?

The Nernst–Einstein equation establishes a correlation between a diffusion coefficient D and a mobility of a particle in an external electrical field E. In the simplest case it can be obtained as follows. Let us consider two types of fluxes: the diffusion flux (1) and the convection one (2) where is the electrostatic potential.

How is the Stokes-Einstein equation related to the Einstein relation?

D = k B T 6 π η r {\\displaystyle D= {\\frac {k_ {\ext {B}}T} {6\\pi \\,\\eta \\,r}}} ( Stokes–Einstein equation, for diffusion of spherical particles through a liquid with low Reynolds number) Here. q is the electrical charge of a particle; μq is the electrical mobility of the charged particle; η is the dynamic viscosity;

Is the Nernst-Einstein equation valid for molar limiting conductivities?

The Nernst-Einstein equation is restricted and valid only for molar limiting conductivities Λ0 m,i Λ m, i 0. In contrast, the EC of real aqueous solutions rest upon molar conductivities Λm,i Λ m, i: