View source for Adsorption

"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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109201.png" /> and on the pressure <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109202.png" />, 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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109203.png" /> of the adsorbent and the relative concentration <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109204.png" />, where the index <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109205.png" /> 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

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109206.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109207.png" /> is the equilibrium constant which roughly describes the interaction between the adsorbent and the adsorbate.

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

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

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109208.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109209.png" /> is a coefficient which varies with the temperature and with the structure of the adsorbent.

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



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

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  S. Brunauer,   P.H. Emmett,   E. Teller,   ''J. Amer. Chem. Soc.'' , '''60'''  (1938)  pp. 309</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  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</TD></TR></table>