**adsorption isotherm**(rus. изотерма адсорбции) — dependence of the amount of adsorbed substance (adsorption value) on the partial pressure of the gaseous substance (or solution concentration) at constant temperature.

### Description

Experimental adsorption isotherms are the most common way of describing adsorption phenomena. Methods for obtaining the adsorption data for the adsorption isotherms are based on measuring the amount of gas (liquid) removed from the gas (liquid) phase during adsorption, and on various ways of determining the amount of the adsorbed substance (adsorbate) on the surface of the adsorbing substance (adsorbent); for example, volumetric method, gravimetric method, etc.

There are six main types of adsorption isotherms (see Fig.). Type I is characteristic of microporous solids with a relatively small proportion of the outer surface. Type II refers to polymolecular adsorption in nonporous or macroporous adsorbents. Type III is characteristic of non-porous sorbents with low energy of adsorbent-adsorbate interaction. Types IV and V are similar to types II and III, but refer to porous adsorbents. Type VI isotherms are characteristic of non-porous adsorbents with homogeneous surface.

Adsorption isotherms are used to calculate the specific surface area of materials, mean pore size or mean size of deposited particles, as well as pore size or particle size distribution.

There are several methods of mathematically representing adsorption isotherms, with different models used to describe the adsorption process. At low surface coverage by the adsorbate the adsorption isotherm equation for a uniform surface is given by Henry’s equation: a = Kp, where a is the adsorption value, p is the gas pressure, K is a constant. At medium coverage Freundlich’s empirical equation can be applied: a = kp

A rigorous adsorption isotherm theory was proposed by I. Langmuir for the model of monolayer adsorption on a uniform surface, in which the attraction between adsorbate molecules and their mobility along the surface can be ignored. Langmuir’s isotherm equation has the form: a = a

Further development of the theory consisted in the exclusion of one of the assumptions used by Langmuir. Thus, S. Brunauer, P. Emmett and E. Teller proposed a theory of polymolecular adsorption (BET method); T. Hill and J. de Boer developed a theory that takes into account the interaction between the adsorbed molecules (Hill-de Boer isotherm), etc.

There are six main types of adsorption isotherms (see Fig.). Type I is characteristic of microporous solids with a relatively small proportion of the outer surface. Type II refers to polymolecular adsorption in nonporous or macroporous adsorbents. Type III is characteristic of non-porous sorbents with low energy of adsorbent-adsorbate interaction. Types IV and V are similar to types II and III, but refer to porous adsorbents. Type VI isotherms are characteristic of non-porous adsorbents with homogeneous surface.

Adsorption isotherms are used to calculate the specific surface area of materials, mean pore size or mean size of deposited particles, as well as pore size or particle size distribution.

There are several methods of mathematically representing adsorption isotherms, with different models used to describe the adsorption process. At low surface coverage by the adsorbate the adsorption isotherm equation for a uniform surface is given by Henry’s equation: a = Kp, where a is the adsorption value, p is the gas pressure, K is a constant. At medium coverage Freundlich’s empirical equation can be applied: a = kp

^{n}, where k and n are constants.A rigorous adsorption isotherm theory was proposed by I. Langmuir for the model of monolayer adsorption on a uniform surface, in which the attraction between adsorbate molecules and their mobility along the surface can be ignored. Langmuir’s isotherm equation has the form: a = a

_{m}bp / (1 + bp), where b is the adsorption coefficient, which depends on the adsorption energy and temperature; a_{m}is the monolayer capacity.Further development of the theory consisted in the exclusion of one of the assumptions used by Langmuir. Thus, S. Brunauer, P. Emmett and E. Teller proposed a theory of polymolecular adsorption (BET method); T. Hill and J. de Boer developed a theory that takes into account the interaction between the adsorbed molecules (Hill-de Boer isotherm), etc.

### Illustrations

#### Authors

- Smirnov Andrey V.
- Tolkachev Nikolay N.

#### Sources

- Poltorak O.M. Thermodynamics in Physical Chemistry (in Russian). — Moscow: Vysshaja shkola, 1991. — 319 pp.
- Sing K. S.W. et al. Reporting physisorption data for gas/solid systems with special reference to the determination of surface area and porosity (recommendations) // Pure Appl. Chem. 1985. V. 57, №4. P. 603–619.
- Karnaukhov A.P. Adsorption: Texture of Dispersed and Porous Materials (in Russian). — Novosibirsk: Nauka, 1999. — 470 pp.