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Einstein relation (kinetic theory)
Additional recommended knowledge
linking D, the Diffusion constant, and μp, the mobility of the particles; where kB is Boltzmann's constant, and T is the absolute temperature.
The mobility μp is the ratio of the particle's terminal drift velocity to an applied force, μp = vd / F.
This equation is an early example of a fluctuation-dissipation relation.
Diffusion of particles
where η is the viscosity of the medium. Thus the Einstein relation becomes
This equation is also known as the Stokes-Einstein Relation. We can use this to estimate the Diffusion coefficient of a globular protein in aqueous solution: For a 100 kDalton protein, we obtain D ~10-10 m² s-1, assuming a "standard" protein density of ~1.2 103 kg m-3.
When applied to electrical conduction, it is normal to divide through by the charge q of the charge carriers, defining electron mobility (or hole mobility)
where E is the applied electric field; so the Einstein relation becomes
where η is the chemical potential and p the particle number
|This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Einstein_relation_(kinetic_theory)". A list of authors is available in Wikipedia.|