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The notion of Debye length plays an important role in plasma physics, electrolytes and colloids (DLVO theory). A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ...
An electrolyte is a substance which dissociates free ions when dissolved (or molten), to produce an electrically conductive medium. ...
A colloid or colloidal dispersion, is a form of matter intermediate between a true solution and a mixture (suspension). ...
The DLVO theory is named after Derjaguin, Landau, Verwey and Overbeek who developed it in the 1940s. ...
In plasma physics, the Debye length, named after the Dutch physical chemist Peter Debye, is the scale over which mobile charge carriers (e.g. electrons) screen out electric fields in plasmas and other conductors. In other words, the Debye length is the distance over which significant charge separation can occur. A Debye sphere is a volume whose radius is the Debye length, in which there is a sphere of influence, and outside of which charges are screened. A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ...
Petrus Josephus Wilhelmus Debije (March 24, 1884 – November 2, 1966) was a Dutch physical chemist. ...
Screening is the damping of electric fields caused by the presence of mobile charge carriers. ...
A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ...
In space plasmas where the electron density is relatively low, the Debye length may reach macroscopic values, such as in the magnetosphere, solar wind, interstellar medium and intergalactic medium (see table):
| Plasma | Density
ne(m-3) | Electron temperature
T(K) | Magnetic field
B(T) | Debye length
λD(m) | | Gas discharge | 1016 | 104 | -- | 10−4 | | Tokamak | 1020 | 108 | 10 | 10−4 | | Ionosphere | 1012 | 103 | 10−5 | 10−3 | | Magnetosphere | 107 | 107 | 10−8 | 102 | | Solar core | 1032 | 107 | -- | 10−11 | | Solar wind | 106 | 105 | 10−9 | 10 | | Interstellar medium | 105 | 104 | 10−10 | 10 | | Intergalactic medium | 1 | 106 | -- | 105 | Source: Chapter 19: The Particle Kinetics of Plasma
http://www.pma.caltech.edu/Courses/ph136/yr2002/ Hannes Alfven pointed out that: "In a low density plasma, localized space charge regions may build up large potential drops over distances of the order of some tens of the Debye lengths. Such regions have been called electric double layers. An electric double layer is the simplest space charge distribution that gives a potential drop in the layer and a vanishing electric field on each side of the layer. In the laboratory, double layers have been studied for half a century, but their importance in cosmic plasmas has not been generally recognized.". Hannes Olof Gösta Alfvén (May 30, 1908; Norrköping, Sweden - April 2, 1995; Djursholm, Sweden) was a Swedish electrical power engineer. ...
Debye length in a plasma
In a plasma, the Debye length is  where - λD is the Debye length,
- ε0 is the permittivity of free space,
- k is Boltzmann's constant,
- qe is the charge on an electron,
- Te and Ti are the temperatures of the electrons and ions, respectively,
- ne is the density of electrons,
- nij'is the density of atomic species i, with positive ionic charge jqe
The ion term is often dropped, giving This article is in need of attention. ...
The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...
This article is about the electrically charged particle. ...
 although this is only valid when the ions are much colder than the electrons.
Debye length in an electrolyte In an electrolyte or a colloidal dispersion, the Debye length is usually denoted with symbol κ−1 An electrolyte is any substance containing free ions that behaves as an electrically conductive medium. ...
A colloid or colloidal dispersion, is a form of matter intermediate between a true solution and a mixture (suspension). ...
 where - I is the ionic strength of the electrolyte,
- ε0 is the permittivity of free space,
- εr is the dielectric constant,
- k is the Boltzmann's constant,
- T is the absolute temperature in kelvins,
- NA is Avogadro's number.
- e is the elementary charge,
or, for a symmetric monovalent electrolyte, The ionic strength of a solution is a function of the concentration of all ions present in a solution. ...
This article is in need of attention. ...
The relative dielectric constant of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. ...
The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...
For other uses, see Kelvin (disambiguation). ...
Avogadros number, also called Avogadros constant (NA), named after Amedeo Avogadro, is formally defined to be the number of carbon-12 atoms in 12 grams (0. ...
The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ...
 where - R is the gas constant,
- F is the Faraday constant,
- C0 is the molar concentration of the electrolyte.
Alternatively, The gas constant (also known as the molar, universal, or ideal gas constant, usually denoted by symbol R) is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. ...
I am the man. ...
 where - λB is the Bjerrum length of the medium.
For water at room temperature, λB ≈ 0.7 nm. The Bjerrum length refers to the approximate distance within which electrostatic interactions dominate thermal motions for two charges, usually with the value of 0. ...
References - Goldston & Rutherford (1997). Introduction to Plasma Physics. Institute of Physics Publishing, Philadelphia.
- Lyklema (1993). Fundamentals of Interface and Colloid Science. Academic Press, NY.
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