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"Consumption" of matter from a gas or from an opening of the interface between them (or from the surface of a solid body). In other words, adsorption is the "consumption" by an adsorbate from a volume of gas on the surface of the adsorbent. Adsorption is a particular case of sorption.

The molecules of the adsorbate falling on the surface of the adsorbent are retained by the surface force for a period of time, which depends on the natures of the adsorbent and adsorbate, on the temperature and on the pressure , after which they leave the surface (are desorbed). Under conditions of thermodynamic and molecular equilibrium, the rates of adsorption and desorption are equal. The relation between the relative pressure of the adsorbent and the relative concentration , where the index stands for the limit value at a constant temperature, is known as the adsorption isotherm.

Langmuir's equation of mono-molecular adsorption has the form

where is the equilibrium constant which roughly describes the interaction between the adsorbent and the adsorbate.

Brunauer's equation [1] is commonly used in the case of a homogeneous surface of the adsorbent and poly-molecular adsorption.

Posnov's formula [2], which is empirical, is widely employed for capillary bodies:

where is a coefficient which varies with the temperature and with the structure of the adsorbent.


[1] S. Brunauer, "Adsorption of gases and vapors" , Princeton Univ. Press (1943)
[2] V.A. Posnov, Zh. Tekhn. Fiz. : 23 (1953) pp. 865
[3] B.V. Il'in, "The nature of adsorption forces" , Moscow-Leningrad (1952) (In Russian)
[4] J.H. de Boer, "The dynamical character of adsorption" , Clarendon Press (1968)


The Brunauer–Emmett–Teller equation, or BET-equation, [a1] generalizes the Langmuir equation. It assumes multi-molecular adsorption for which each layer obeys a Langmuir equation. There are several modifications, cf. [a2].


[a1] S. Brunauer, P.H. Emmett, E. Teller, J. Amer. Chem. Soc. , 60 (1938) pp. 309
[a2] S. Brunauer, L.E. Copeland, "Surface tension, adsorption" E.U. Condon (ed.) H. Odishaw (ed.) , Handbook of physics , 2 , McGraw-Hill (1967) pp. Chapt. 7
How to Cite This Entry:
Adsorption. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Lykov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article