View source for Adsorption

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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 $T$ and on the pressure $p$, 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 $\phi=p/p_s$ of the adsorbent and the relative concentration $\theta=c/c_s$, where the index $s$ 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

$$\phi=\frac{\theta}{k(1-\theta)},$$

where $k$ 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:

$$\frac1\theta=A\ln\phi+1,$$

where $A$ 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>