Einstein relation (kinetic theory)

Einstein relation (kinetic theory)

In physics (namely, in kinetic theory) the Einstein relation (also known as Einstein–Smoluchowski relation) is a previously unexpected connection revealed independently by Albert Einstein in 1905 and by Marian Smoluchowski (1906) in their papers on Brownian motion:

: D = {mu_p , k_B T}

linking "D", the diffusion constant, and "μp", the mobility of the particles; where "k_B" 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. It is frequently used in the electrodiffusion phenomena.

Diffusion of particles

In the limit of low Reynolds number, the mobility "μ" is the inverse of the drag coefficient "γ".For spherical particles of radius "r", Stokes' law gives

: gamma = 6 pi , eta , r,

where "η" is the viscosity of the medium. Thus the Einstein relation becomes

: D=frac{k_B T}{6pi,eta,r}

This equation is also known as the Stokes–Einstein Relation or Stokes–Einstein–Sutherland equation [http://www.physics.emory.edu/~weeks/lab/papers/sendai2007.pdf] . It can be used 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" proteindensity of ~1.2 103 kg m-3.

Electrical conduction

When applied to electrical conduction, it is normal to define an electrical mobility by multiplying the mechanical mobility mu_p by the charge of the particle "q" of the charge carriers:

: mu_q = q*{mu_p}

or alternatively formulated:

: mu_q = v_d}over{E

where "E" is the applied electric field; so the Einstein relation becomes

: D = mu_q , k_B T}over{q

In a semiconductor with an arbitrary density of states the Einstein relation is

: D = mu_q , p}over{q d , p}over{d eta

where eta is the chemical potential and p the particle number.


*"Fluctuation-Dissipation: Response Theory in Statistical Physics" by Umberto Marini Bettolo Marconi, Andrea Puglisi, Lamberto Rondoni, Angelo Vulpiani, [http://arxiv.org/abs/0803.0719]

Wikimedia Foundation. 2010.

См. также в других словарях:

  • Kinetic theory — [ temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move. In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure.… …   Wikipedia

  • Kinetic energy — The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity . Having gained this energy during its acceleration …   Wikipedia

  • List of things named after Albert Einstein — This is a list of things named after Albert Einstein. Scientific and mathematical concepts * Higher dimensional Einstein gravity * Einstein solid * Einstein force * Einstein s constant * Einstein relation (kinetic theory) * Stark Einstein law *… …   Wikipedia

  • probability theory — Math., Statistics. the theory of analyzing and making statements concerning the probability of the occurrence of uncertain events. Cf. probability (def. 4). [1830 40] * * * Branch of mathematics that deals with analysis of random events.… …   Universalium

  • Le Sage's theory of gravitation — is the most common name for the kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton s gravitational force in terms… …   Wikipedia

  • String theory — This article is about the branch of theoretical physics. For other uses, see String theory (disambiguation). String theory …   Wikipedia

  • History of gravitational theory — In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times.AntiquityIn the 4th century BC, the Greek philosopher… …   Wikipedia

  • Introduction to gauge theory — This article is an accessible, non technical introduction to the subject. For the main encyclopedia article, see Gauge theory. Quantum field theory …   Wikipedia

  • Dynamo theory — In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can… …   Wikipedia

  • Green's function (many-body theory) — In many body theory, the term Green s function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators of field operators or creation and annihilation operators.The name comes from… …   Wikipedia

Поделиться ссылкой на выделенное

Прямая ссылка:
Нажмите правой клавишей мыши и выберите «Копировать ссылку»