Einstein relation (kinetic theory)

The Einstein - Smoluchowski relation, also called Einstein 's equation is a relationship in the field of kinetic gas theory, which was first proposed by Albert Einstein (1905 ) and then by Marian Smoluchowski (1906 ) revealed in their writings on Brownian motion. You verknüpftden diffusion coefficient D with the mobility μ of the particles:

And mentions the

It is an early example of a fluctuation-dissipation relation.

Diffusion of particles

In low Reynolds number, the mobility of the reciprocal value of the flow coefficient:

The Stokes equation gives for spherical particles with radius r:

Wherein η refers to the viscosity of the medium.

This allows the Einstein equation in transform:

This form is called the Stokes -Einstein equation.

You can for example be used to determine the diffusion coefficient of a globular protein in aqueous solution: if we assume a density of ~ 1.2 × 103 kg/m3, we obtain for a protein of 100 kDa: D ~ 10 - 10 m2 / s

Electrical conductivity

Based on the electrical conductivity is defined first the electron mobility:

In which

  • E is the electric field acting and
  • The drift velocity.

For a semiconductor with an arbitrary density of states are divided usually the right part of the equation by the charge q of the charge carrier. Then is the Einstein equation

With

  • The chemical potential and
  • The number of particles p.

This relationship also applies to the movement of ions. Thus, the Einstein equation for the " Nernst - Einstein relation " is:

With

  • Charge of the particles,
  • The Boltzmann constant,
  • Is the absolute temperature,
  • Diffusion coefficient of the particles in the medium
  • Statistical Physics
  • Physical chemistry
Thermodynamic temperature Electrical mobility
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