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2014-11-09T17:13:10Z

Changed # of load instructions in the calculation from 4 to 5, changed the result

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2014-02-01T22:46:47Z

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The '''langmuir''' (symbol: '''L''') is a unit of exposure (or dosage) to a [[surface]] (''e.g.'' of a [[crystal]]) and is used in [[ultra-high vacuum]] (UHV) [[surface physics]] to study the [[adsorption]] of [[gas]]es. It is a practical unit, and is not [[Dimensional analysis|dimensionally homogeneous]], and so is only used in this one field. It is named after American physicist [[Irving Langmuir]].

== Definition ==
The langmuir is defined by multiplying the [[pressure]] of the gas by the time of exposure. One langmuir corresponds to an exposure of 10−6 [[torr]] during one [[second]].<ref>{{GreenBookRef|page=65}}</ref> For example, exposing a surface to a gas pressure of 10−8 torr for 100 seconds corresponds to 1 L.
Similarly, keeping the pressure of oxygen gas at 2.5 10−6 [[Bar (unit)|torr]] for 40 seconds will give a dose of 100 L.

== Derivation ==
Exposure of a surface in surface physics is a type of [[fluence]], that is the integral of number flux (''JN'') with respect to exposed time (''t'') to give a number of particles per unit area (''Φ''):

:<math>\Phi = \int{J_N} \, {\rm d}t</math>

The number flux for an ideal gas, that is the number of gas molecules passing through (in a single direction) a surface of unit area in unit time, can be derived from [[kinetic theory]]:<ref>http://www.chem.arizona.edu/~salzmanr/480a/480ants/collsurf/collsurf.html</ref>

:<math>J_N = \frac{C\bar u}{4}</math>

where ''C'' is the [[number density]] of the gas and ''u'' is the mean speed of the molecules (''not'' the root mean square speed, although the two are related). The number density of an ideal gas depends the [[thermodynamic temperature]] (''T'') and the pressure (''p''):
:<math>C = \frac{N}{V} = \frac{p}{kT}</math>
The mean speed of the gas molecules can also be derived from kinetic theory:<ref>http://www.chem.arizona.edu/~salzmanr/480a/480ants/kmt3dpdf/kmt3dpdf.html</ref>

:<math>\bar u = \sqrt{\frac{8kT}{\pi m}}</math>

where ''m'' is the mass of a gas molecule. Hence

:<math>J_N = \frac{C\bar u}{4} = p\sqrt{\frac{1}{2\pi kTm}}</math>

The [[Proportionality (mathematics)|proportionality]] between number flux and pressure is only strictly valid for a given temperature and a given [[molecular mass]] of adsorbing gas. However, the dependence is only on the square roots of ''m'' and ''T''. Gas adsorption experiments typically operate around ambient temperature with light gases, and so the langmuir remains useful as a practical unit.

== Usage ==
Assuming that every gas [[molecule]] which hits the surface sticks to it (that is, the [[sticking coefficient]] is 1.00), one langmuir (1 L) leads to a coverage of about one [[monolayer]] of the adsorbed gas molecules on the surface. In general, the [[sticking coefficient]] varies depending on the [[reactivity (chemistry)|reactivity]] of the surface and the molecules, so that the langmuir gives a lower limit of the time it needs to completely cover a surface.

This also illustrates why ultra-high vacuum must be used to study [[Solid-state physics|solid-state]] surfaces, [[nanostructure]]s or even single molecules. The typical time to perform [[physical experiment]]s on sample surfaces is in the range of one to several hours. In order to keep the surface free of [[contamination]]s, the pressure of the residual gas in a UHV chamber should be below 10−10 torr.

==References==
*{{citation | author = Lueth, H. | year = 1997 | title = Surfaces and Interfaces of Solid Materials | edition = 3rd | publisher = Springer}}.
{{reflist}}

[[Category:Gases]]
[[Category:Units of amount of substance]]

Cycles per instruction - Revision history

198.168.152.20: Changed # of load instructions in the calculation from 4 to 5, changed the result

71.17.148.9: Apparently there's a latex error using medium spaces for non-mathjax or something? Formulas fail when logged out.