VIDEOS 1 TO 50

Debye Length

Published: 2016/02/17

Channel: Hagen@Cal Poly

1b Rigorous definition of plasma: Debye length

Published: 2016/02/01

Channel: Plasma Physics and Applications

Debye length

Published: 2015/11/29

Channel: Audiopedia

Debye Length in Doped Semiconductors

Published: 2016/01/15

Channel: Christian Wurm

Mod-01 Lec-01 Introduction to Plasmas

Published: 2013/04/25

Channel: nptelhrd

BASIC PLASMA PARAMETERS.avi

Published: 2012/06/19

Channel: mike hopkins

Debye Length in a Symmetric Electrolyte Solution

Published: 2012/06/04

Channel: wolframmathematica

01B Plasma State Debye Shielding | Introduction to Plasma Physics by J D Callen

Published: 2015/12/23

Channel: Lucius Fox

Debye Length in a Symmetric Electrolyte Solution.3gp

Published: 2013/01/16

Channel: Akshat upadhyay

nanoHUB-U Nanoscale Transistors L2.5: MOS Electrostatics - 2D MOS Electrostatics

Published: 2014/05/20

Channel: nanohubtechtalks

StatMolThermo 11.07 Debye-Hückel Theory 1

Published: 2015/11/02

Channel: Chris Cramer

Debye Screening Length Effects of Nanostructured Materials Springer Tracts in Modern Physics

Published: 2016/10/08

Channel: Trinity Weaver

Download Debye Screening Length Effects of Nanostructured Materials Springer Tracts in Modern Physic

Published: 2016/10/01

Channel: Amedia. C

Chemical Thermodynamics - Debye-Huckel Law (Old Version)

Published: 2014/10/31

Channel: TMP Chem

Chemical Thermodynamics - Debye-Huckel Law

Published: 2016/09/14

Channel: TMP Chem

5d Sheaths and plasma etching: part1

Published: 2015/09/15

Channel: Plasma Physics and Applications

Screening length Meaning

Published: 2015/04/26

Channel: ADictionary

Plasma Physics MOOC - lecture 4a

Published: 2016/05/19

Channel: Marcelo Baquero

nanoHUB-U Nanobiosensors T3.1: Sensitivity - Homework Solution III (Potentiometric)

Published: 2016/03/14

Channel: nanohubtechtalks

Langmuir Double Probe (measurements in a capacitively coupled plasma)

Published: 2011/05/24

Channel: ImpedansTV

Plasma Strikes In A Beautiful Sky

Published: 2012/11/12

Channel: Eternal Love

Large Plasma Device - Video Learning - WizScience.com

Published: 2015/09/09

Channel: Wiz Science™

Powder X-Ray Diffraction (1 out of 2)

Published: 2016/03/30

Channel: NUS Chem Emelyn Tan

nanoHUB-U Fundamentals of AFM L5.4: Dynamic AFM for Biology - Dynamic AFM in Liquids I

Published: 2014/06/02

Channel: nanohubtechtalks

Electronegativity and bonding | Structure and bonding | Organic chemistry | Khan Academy

Published: 2013/10/29

Channel: Khan Academy Organic Chemistry

XRD Peak Analysis

Published: 2011/11/21

Channel: LearnChemE

FWHM determination by Origin

Published: 2015/09/16

Channel: Cuong Nguyen Orvn

√ X-Ray Diffraction Gratings in HSC Physics - From Ideas to Implementation - iitutor

Published: 2013/08/23

Channel: iitutor.com

Electro Chemistry(26- Debye Huckel Onsager equation)

Published: 2016/11/08

Channel: DIGICLASS A

Laue experiment

Published: 2016/07/10

Channel: Physics4students

X ray crystallography basics explained | x ray diffraction

Published: 2016/07/13

Channel: Shomu's Biology

L&S concept activity debye huckel

Published: 2016/08/16

Channel: Fiona Dickinson

Powder X-Ray Diffraction (2 out of 2)

Published: 2016/03/30

Channel: NUS Chem Emelyn Tan

The Debye-Huckel theory of electrolytes

Published: 2016/11/24

Channel: Diego Troya

non linear poisson boltzmann equation and the debye huckel limiting law.wmv

Published: 2011/06/24

Channel: photon2010

ph12c lecture06 Debye

Published: 2016/03/31

Channel: John Preskill

StatMolThermo 11.08 Debye-Hückel Theory 2

Published: 2015/11/02

Channel: Chris Cramer

Peter Debye The chemist & physicist

Published: 2015/02/20

Channel: Hamboy s

debye

Published: 2013/03/07

Channel: Debye Marroquin

PC56 Grundlagen der Debye-Hückel-Theorie - Wie stark wird ein Ion in einem Elektrolyt abgeschirmt?

Published: 2013/04/28

Channel: Physikalische Chemie by SciFox

第13講 Phonon and Debye Theory

Published: 2013/01/11

Channel: NTHUOCW

Debye Interaction

Published: 2016/02/08

Channel: Hagen@Cal Poly

Chemical Thermodynamics - Debye T^3 Law (Old Version)

Published: 2014/09/20

Channel: TMP Chem

Ions in solution simulations in Matlab

Published: 2009/06/21

Channel: mvedenev

debye sears effekt experiment

Published: 2012/03/28

Channel: meGOmbg

1a Plasmas in nature and laboratory

Published: 2015/09/15

Channel: Plasma Physics and Applications

7. Phonon Energy Levels in Crystal and Crystal Structures

Published: 2013/01/16

Channel: MIT OpenCourseWare

Lec 08: Polarization and Dielectrics | 8.02 Electricity and Magnetism, Spring 2002 (Walter Lewin)

Published: 2014/12/10

Channel: For the Allure of Physics

"Introduction to Plasma Physics II: Kinetics" by Matthew Kunz

Published: 2016/07/19

Channel: videosfromIAS

Debye Meaning

Published: 2015/04/20

Channel: SDictionary

From Wikipedia, the free encyclopedia

In plasmas and electrolytes the **Debye length** (also called **Debye radius**), named after the Dutch physicist and physical chemist Peter Debye, is the measure of a charge carrier's net electrostatic effect in solution, and how far those electrostatic effects persist. A **Debye sphere** is a volume whose radius is the Debye length. With each Debye length, charges are increasingly electrically screened. Every Debye‐length, the electric potential will decrease in magnitude by 1/e. The notion of Debye length plays an important role in plasma physics, electrolytes and colloids (DLVO theory).

The Debye length arises naturally in the thermodynamic description of large systems of mobile charges. In a system of different species of charges, the -th species carries charge and has concentration at position . According to the so-called "primitive model", these charges are distributed in a continuous medium that is characterized only by its relative static permittivity, . This distribution of charges within this medium gives rise to an electric potential that satisfies Poisson's equation:

- ,

where , is the electric constant, and is a charge density external (logically, not spatially) to the medium.

The mobile charges not only establish but also move in response to the associated Coulomb force, . If we further assume the system to be in thermodynamic equilibrium with a heat bath at absolute temperature , then the concentrations of discrete charges, , may be considered to be thermodynamic (ensemble) averages and the associated electric potential to be a thermodynamic mean field. With these assumptions, the concentration of the -th charge species is described by the Boltzmann distribution,

- ,

where is Boltzmann's constant and where is the mean concentration of charges of species .

Identifying the instantaneous concentrations and potential in the Poisson equation with their mean-field counterparts in Boltzmann's distribution yields the Poisson–Boltzmann equation:

- .

Solutions to this nonlinear equation are known for some simple systems. Solutions for more general systems may be obtained in the high-temperature (weak coupling) limit, , by Taylor expanding the exponential:

- .

This approximation yields the linearized Poisson-Boltzmann equation

which also is known as the Debye–Hückel equation:^{[1]}^{[2]}^{[3]}^{[4]}^{[5]} The second term on the right-hand side vanishes for systems that are electrically neutral. The term in parentheses divided by , has the units of an inverse length squared and by dimensional analysis leads to the definition of the characteristic length scale

that commonly is referred to as the Debye–Hückel length. As the only characteristic length scale in the Debye–Hückel equation, sets the scale for variations in the potential and in the concentrations of charged species. All charged species contribute to the Debye–Hückel length in the same way, regardless of the sign of their charges. For an electrically neutral system, the Poisson equation becomes

To illustrate Debye screening, the potential produced by an external point charge is

The bare Coulomb potential is exponentially screened by the medium, over a distance of the Debye length.

The Debye–Hückel length may be expressed in terms of the Bjerrum length as

- ,

where is the integer charge number that relates the charge on the -th ionic species to the elementary charge .

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 | Densityn_{e}(m^{−3}) |
Electron temperatureT(K) |
Magnetic fieldB(T) |
Debye lengthλ_{D}(m) |
---|---|---|---|---|

Solar core | 10^{32} |
10^{7} |
-- | 10^{−11} |

Tokamak | 10^{20} |
10^{8} |
10 | 10^{−4} |

Gas discharge | 10^{16} |
10^{4} |
-- | 10^{−4} |

Ionosphere | 10^{12} |
10^{3} |
10^{−5} |
10^{−3} |

Magnetosphere | 10^{7} |
10^{7} |
10^{−8} |
10^{2} |

Solar wind | 10^{6} |
10^{5} |
10^{−9} |
10 |

Interstellar medium | 10^{5} |
10^{4} |
10^{−10} |
10 |

Intergalactic medium | 1 | 10^{6} |
-- | 10^{5} |

Source: Chapter 19: The Particle Kinetics of Plasma |

Hannes Alfvén 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."^{[6]}

In a plasma, the background medium may be treated as the vacuum (), and the Debye length is

where

- λ
_{D}is the Debye length, - ε
_{0}is the permittivity of free space, *k*_{B}is the Boltzmann constant,*q*_{e}is the charge of an electron,*T*and_{e}*T*are the temperatures of the electrons and ions, respectively,_{i}*n*is the density of electrons,_{e}*n*is the density of atomic species_{j}*j*, with positive ionic charge*z*_{j}q_{e}

The ion term is often dropped, giving

although this is only valid when the mobility of ions is negligible compared to the process's timescale.^{[7]}

In an electrolyte or a colloidal suspension, the Debye length^{[8]} for a monovalent electrolyte is usually denoted with symbol *κ*^{−1}

where

*I*is the ionic strength of the electrolyte, and here the unit should be mole/m^{3},- ε
_{0}is the permittivity of free space, - ε
_{r}is the dielectric constant, *k*_{B}is the Boltzmann constant,*T*is the absolute temperature in kelvins,*N*is the Avogadro number._{A}- is the elementary charge,

or, for a symmetric monovalent electrolyte,

where

*R*is the gas constant,*F*is the Faraday constant,*C*_{0}is the molar concentration of the electrolyte.

Alternatively,

where

- is the Bjerrum length of the medium.

For water at room temperature, *λ*_{B} ≈ 0.7 nm.

At room temperature (25 °C), one can consider in water for 1:1 electrolytes the relation:^{[9]}

where

*κ*^{−1}is expressed in nanometers (nm)*I*is the ionic strength expressed in molar (M or mol/L)

The Debye length has become increasingly significant in the modeling of solid state devices as improvements in lithographic technologies have enabled smaller geometries.^{[10]}^{[11]}^{[12]}

The Debye length of semiconductors is given:

where

*ε*is the dielectric constant,*k*_{B}is the Boltzmann's constant,*T*is the absolute temperature in kelvins,*q*is the elementary charge, and*N*is the density of dopants (either donors or acceptors)._{d}

When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants. Instead, a measure of the profile of the doping gradients provides an "effective" profile that better matches the profile of the majority carrier density.

In the context of solids, the Debye length is also called the Thomas–Fermi screening length.

**^**Kirby BJ.*Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices*.**^**Li D (2004).*Electrokinetics in Microfluidics*.**^**PC Clemmow & JP Dougherty (1969).*Electrodynamics of particles and plasmas*. Redwood City CA: Addison-Wesley. pp. § 7.6.7, p. 236 ff. ISBN 0-201-47986-9.**^**RA Robinson &RH Stokes (2002).*Electrolyte solutions*. Mineola, NY: Dover Publications. p. 76. ISBN 0-486-42225-9.**^**See Brydges, David C.; Martin, Ph. A. (1999). "Coulomb Systems at Low Density: A Review".*Journal of Statistical Physics*.**96**(5/6): 1163–1330. arXiv:cond-mat/9904122. Bibcode:1999JSP....96.1163B. doi:10.1023/A:1004600603161.**^**Hannes Alfvèn - Cosmic Plasma vol. 82 (1981) (D. Reidel Publishing Company 2012), II.6. Electric Double Layers, II.6.1. General Properties of Electric Double Layers, p. 29 books.google.ca/books?id=gAnvCAAAQBAJ**^**I. H. Hutchinson*Principles of plasma diagnostics*ISBN 0-521-38583-0**^**Russel, W.B., Saville, D.A. and Schowalter, W. R.*Colloidal Dispersions*, Cambridge University Press, 1989**^**Israelachvili, J.,*Intermolecular and Surface Forces*, Academic Press Inc., 1985, ISBN 0-12-375181-0**^**Stern, Eric; Robin Wagner; Fred J. Sigworth; Ronald Breaker; Tarek M. Fahmy; Mark A. Reed (2007-11-01). "Importance of the Debye Screening Length on Nanowire Field Effect Transistor Sensors".*Nano Letters*.**7**(11): 3405–3409. Bibcode:2007NanoL...7.3405S. doi:10.1021/nl071792z. PMC 2713684. PMID 17914853.**^**Guo, Lingjie; Effendi Leobandung; Stephen Y. Chou (199). "A room-temperature silicon single-electron metal–oxide–semiconductor memory with nanoscale floating-gate and ultranarrow channel".*Applied Physics Letters*.**70**(7): 850. Bibcode:1997ApPhL..70..850G. doi:10.1063/1.118236.**^**Tiwari, Sandip; Farhan Rana; Kevin Chan; Leathen Shi; Hussein Hanafi (1996). "Single charge and confinement effects in nano-crystal memories".*Applied Physics Letters*.**69**(9): 1232. Bibcode:1996ApPhL..69.1232T. doi:10.1063/1.117421.

- Goldston & Rutherford (1997).
*Introduction to Plasma Physics*. Philadelphia: Institute of Physics Publishing. - Lyklema (1993).
*Fundamentals of Interface and Colloid Science*. NY: Academic Press.

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