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Brunauer, Emmett and Teller's model of multilayer adsorption is a random distribution of molecules on the material surface.

Adsorption is the adhesion of molecules of gas, liquid, or dissolved solids to a surface.[1] This process creates a film of the adsorbate (the molecules or atoms being accumulated) on the surface of the adsorbent. It differs from absorption, in which a fluid permeates or is dissolved by a liquid or solid.[2] The term sorption encompasses both processes, while desorption is the reverse of adsorption.

Similar to surface tension, adsorption is a consequence of surface energy. In a bulk material, all the bonding requirements (be they ionic, covalent, or metallic) of the constituent atoms of the material are filled by other atoms in the material. However, atoms on the surface of the adsorbent are not wholly surrounded by other adsorbent atoms and therefore can attract adsorbates. The exact nature of the bonding depends on the details of the species involved, but the adsorption process is generally classified as physisorption (characteristic of weak van der Waals forces) or chemisorption (characteristic of covalent bonding).

Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as activated charcoal, capturing and using waste heat to provide cold water for air conditioning and other process requirements (adsorption chillers), synthetic resins, increase storage capacity of carbide-derived carbons for tunable nanoporous carbon, and water purification. Adsorption, ion exchange, and chromatography are sorption processes in which certain adsorbates are selectively transferred from the fluid phase to the surface of insoluble, rigid particles suspended in a vessel or packed in a column.



Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (if liquid) at constant temperature. The quantity adsorbed is nearly always normalized by the mass of the adsorbent to allow comparison of different materials.

The first mathematical fit to an isotherm was published by Freundlich and Küster (1894) and is a purely empirical formula for gaseous adsorbates,


where x is the quantity adsorbed, m is the mass of the adsorbent, P is the pressure of adsorbate and k and n are empirical constants for each adsorbent-adsorbate pair at a given temperature. The function has an asymptotic maximum as pressure increases without bound. As the temperature increases, the constants k and n change to reflect the empirical observation that the quantity adsorbed rises more slowly and higher pressures are required to saturate the surface.



In 1916, Irving Langmuir published a new model isotherm for gases adsorbed on solids, which retained his name. It is a semi-empirical isotherm derived from a proposed kinetic mechanism. It is based on four assumptions:

  1. The surface of the adsorbent is uniform, that is, all the adsorption sites are equivalent.
  2. Adsorbed molecules do not interact.
  3. All adsorption occurs through the same mechanism.
  4. At the maximum adsorption, only a monolayer is formed: molecules of adsorbate do not deposit on other, already adsorbed, molecules of adsorbate, only on the free surface of the adsorbent.

These four assumptions are seldom all true: there are always imperfections on the surface, adsorbed molecules are not necessarily inert, and the mechanism is clearly not the same for the very first molecules to adsorb as for the last. The fourth condition is the most troublesome, as frequently more molecules will adsorb on the monolayer; this problem is addressed by the BET isotherm for relatively flat (non-microporous) surfaces. The Langmuir isotherm is nonetheless the first choice for most models of adsorption, and has many applications in surface kinetics (usually called Langmuir-Hinshelwood kinetics) and thermodynamics.

Langmuir suggested that adsorption takes place through this mechanism: A_{g} + S \rightleftharpoons AS, where A is a gas molecule and S is an adsorption site. The direct and inverse rate constants are k and k-1. If we define surface coverage, θ, as the fraction of the adsorption sites occupied, in the equilibrium we have

K=\frac{k}{k_{-1}}=\frac{\theta}{(1-\theta)P} or \theta=\frac{KP}{1+KP}.

Where P is the partial pressure of the gas or the molar concentration of the solution. For very low pressures \theta\approx KP and for high pressures \theta\approx1

θ is difficult to measure experimentally; usually, the adsorbate is a gas and the quantity adsorbed is given in moles, grams, or gas volumes at standard temperature and pressure (STP) per gram of adsorbent. If we call vmon the STP volume of adsorbate required to form a monolayer on the adsorbent (per gram of adsorbent), \theta = \frac{v}{v_\mathrm{mon}} and we obtain an expression for a straight line:


Through its slope and y-intercept we can obtain vmon and K, which are constants for each adsorbent/adsorbate pair at a given temperature. vmon is related to the number of adsorption sites through the ideal gas law. If we assume that the number of sites is just the whole area of the solid divided into the cross section of the adsorbate molecules, we can easily calculate the surface area of the adsorbent. The surface area of an adsorbent depends on its structure; the more pores it has, the greater the area, which has a big influence on reactions on surfaces.

If more than one gas adsorbs on the surface, we define θE as the fraction of empty sites and we have

\theta_E=\frac{1}{\displaystyle 1+\sum_{i=1}^n K_iP_i}


\theta_j=\frac{K_jP_j}{\displaystyle 1+\sum_{i=1}^n K_iP_i}

where i is each one of the gases that adsorb.


Often molecules do form multilayers, that is, some are adsorbed on already adsorbed molecules and the Langmuir isotherm is not valid. In 1938 Stephan Brunauer, Paul Emmett, and Edward Teller developed a model isotherm that takes that possibility into account. Their theory is called BET theory, after the initials in their last names. They modified Langmuir's mechanism as follows:

A(g) + S AS
A(g) + AS A2S
A(g) + A2S A3S and so on
Langmuir isotherm (red) and BET isotherm (green)

The derivation of the formula is more complicated than Langmuir's (see links for complete derivation). We obtain:


x is the pressure divided by the vapor pressure for the adsorbate at that temperature (usually denoted P / P0), v is the STP volume of adsorbed adsorbate, vmon is the STP volume of the amount of adsorbate required to form a monolayer and c is the equilibrium constant K we used in Langmuir isotherm multiplied by the vapor pressure of the adsorbate. The key assumption used in deriving the BET equation that the successive heats of adsorption for all layers except the first are equal to the heat of condensation of the adsorbate.

The Langmuir isotherm is usually better for chemisorption and the BET isotherm works better for physisorption for non-microporous surfaces.


Two adsorbate nitrogen molecules adsorbing onto a tungsten adsorbent from the precursor state around an island of previously adsorbed adsobate (left) and via random adsorption (right)

In other instances, molecular interactions between gas molecules previously adsorbed on a solid surface form significant interactions with gas molecules in the gaseous phase. Hence, adsorption of gas molecules to the surface is more likely to occur around gas molecules that are already present on the solid surface, rendering the Langmuir adsorption isotherm ineffective for the purposes of modelling. This effect was studied in a system where nitrogen was the adsorbate and tungsten was the adsorbent by Paul Kisliuk (b. 1922-d. 2008) in 1957. To compensate for the increased probability of adsorption occurring around molecules present on the substrate surface, Kisliuk developed the precursor state theory, whereby molecules would enter a precursor state at the interface between the solid adsorbent and adsorbate in the gaseous phase. From here, adsorbate molecules would either adsorb to the adsorbant or desorb into the gaseous phase. The probability of adsorption occurring from the precursor state is dependent on the adsorbate’s proximity to other adsorbate molecules that have already been adsorbed. If the adsorbate molecule in the precursor state is in close proximity to an adsorbate molecule which has already formed on the surface, it has a sticking probability reflected by the size of the SE constant and will either be adsorbed from the precursor state at a rate of kEC or will desorb into the gaseous phase at a rate of kES. If an adsorbate molecule enters the precursor state at a location that is remote from any other previously adsorbed adsorbate molecules, the sticking probability is reflected by the size of the SD constant.

These factors were included as part of a single constant termed a "sticking coefficient," kE, described below:


As SD is dictated by factors that are taken into account by the Langmuir model, SD can be assumed to be the adsorption rate constant. However, the rate constant for the Kisliuk model (R’) is different to that of the Langmuir model, as R’ is used to represent the impact of diffusion on monolayer formation and is proportional to the square root of the system’s diffusion coefficient. The Kisliuk adsorption isotherm is written as follows, where Θ(t) is fractional coverage of the adsorbent with adsorbate, and t is immersion time:


Solving for Θ(t) yields:



The Henderson-Kisliuk adsorption equation prediction of normalised impedance as a function of adsorption time, where the first peak corresponds to the formation of an adsorbent surface that is saturated with MPA in its "lying down" structure. The curve then tends to an impedance value that is representative of an adsorbent saturated with "standing up" structure.

This adsorption isotherm was developed for use with the new field of Self Assembling Monolayer (SAM) adsorption. SAM molecules adsorb to the surface of an adsorbent until the surface becomes saturated with the SAM molecules' hydrocarbon chains lying flat against the adsorbate. This is termed "lying down" structure (1st structure). Further adsorption then occurs, causing the hydrocarbon chains to be displaced by thiol groups present on the newly adsorbed SAM molecules. When this adsorption step takes place, electrostatic forces between the newly adsorbed SAM molecules and the ones previously adsorbed, causes a new structure to form, where all of the SAM molecules are occupying a "standing up" orientation (2nd structure). As further adsorption takes place, the entire adsorbent becomes saturated with SAM in a standing up orientation, and no further adsorption takes place.

The SAM adsorbate is usually present in a liquid phase and the adsorbent is normally a solid. Hence, intermolecular interactions are significant and the Kisliuk adsorption isotherm applies. The sequential evolution of "lying down" and "standing up" mercaptopropionic acid (MPA) SAM structures on a gold adsorbent, from a liquid MPA-ethanol adsorbate phase, was studied by Andrew P. Henderson (b. 1982) et al. in 2009. Henderson et al. used electrochemical impedance spectroscopy to quantify adsorption and witnessed that the 1st structure had different impedance properties to the 2nd structure and that both structures evolved sequentially. This allowed four rules to be expressed:

  • That the amount of adsorbate on the adsorbent surface was equal to the sum of the adsorbate occupying 1st structure and 2nd structure.
  • The rate of 1st structure formation is dependent on the availability of potential adsorption sites and intermolecular interactions.
  • The amount of 1st structure is depleted as 2nd structure is formed.
  • The rate of second structure formation is dictated by the amount of adsorbate occupying 1st structure and intermolecular interactions at immersion time, t.

From these statements, Henderson et al. used separate terms to describe rate of fractional adsorption for 1st structure [Θ1(t)] and 2nd structure [Θ2(t)] as a function of immersion time (t). Both of these terms were dictated by the Kisliuk adsorption isotherm, where variables with a subscript of 1 relate to 1st structure formation and a subscript of 2 relates to 2nd structure formation.

These terms were combined in the Henderson adsorption isotherm, which determines the total normalised impedance detection signal strength caused by the adsorbate monolayer (z(t)) as a function of Θ1(t), Θ2(t), φ1 and φ2. Values of φ are weighting constants, which are normalized signal values that would result from an adsorbent covered entirely with either 1st structure or 2nd structure. This isotherm equation is shown below:


Although the Henderson-Kisliuk adsorption isotherm was originally applied to SAM adsorption, Henderson et al. hypothesised that this adsorption isotherm is potentially applicable to many other cases of adsorption and that Θ1(t) and Θ2(t) can be calculated using other adsorption isotherms, in place of the Kisliuk model (such as the Langmuir adsorption isotherm equation).

Adsorption enthalpy

Adsorption constants are equilibrium constants, therefore they obey van 't Hoff's equation:

\left( \frac{\partial \ln K}{\partial \frac{1}{T}} \right)_\theta=-\frac{\Delta H}{R}.

As can be seen in the formula, the variation of K must be isosteric, that is, at constant coverage. If we start from the BET isotherm and assume that the entropy change is the same for liquefaction and adsorption we obtain ΔHads = ΔHliqRTlnc, that is to say, adsorption is more exothermic than liquefaction.


Characteristics and general requirements

Activated carbon is used as an adsorbent

Adsorbents are used usually in the form of spherical pellets, rods, moldings, or monoliths with hydrodynamic diameters between 0.5 and 10 mm. They must have high abrasion resistance, high thermal stability and small pore diameters, which results in higher exposed surface area and hence high surface capacity for adsorption. The adsorbents must also have a distinct pore structure which enables fast transport of the gaseous vapors.

Most industrial adsorbents fall into one of three classes:

  • Oxygen-containing compounds – Are typically hydrophilic and polar, including materials such as silica gel and zeolites.
  • Carbon-based compounds – Are typically hydrophobic and non-polar, including materials such as activated carbon and graphite.
  • Polymer-based compounds - Are polar or non-polar functional groups in a porous polymer matrix.

Silica gel

Silica gel is a chemically inert, nontoxic, polar and dimensionally stable (< 400 °C) amorphous form of SiO2. It is prepared by the reaction between sodium silicate and sulfuric acid, which is followed by a series of after-treatment processes such as aging, pickling, etc. These after treatment methods results in various pore size distributions.

Silica is used for drying of process air (e.g. oxygen, natural gas) and adsorption of heavy (polar) hydrocarbons from natural gas.


Zeolites are natural or synthetic crystalline aluminosilicates which have a repeating pore network and release water at high temperature. Zeolites are polar in nature.

They are manufactured by hydrothermal synthesis of sodium aluminosilicate or another silica source in an autoclave followed by ion exchange with certain cations (Na+, Li+, Ca2+, K+, NH4+). The channel diameter of zeolite cages usually ranges from 2 to 9 Å (200 to 900 pm). The ion exchange process is followed by drying of the crystals, which can be pelletized with a binder to form macroporous pellets.

Zeolites are applied in drying of process air, CO2 removal from natural gas, CO removal from reforming gas, air separation, catalytic cracking, and catalytic synthesis and reforming.

Non-polar (siliceous) zeolites are synthesized from aluminum-free silica sources or by dealumination of aluminum-containing zeolites. The dealumination process is done by treating the zeolite with steam at elevated temperatures, typically greater than 500 °C (900 °F). This high temperature heat treatment breaks the aluminum-oxygen bonds and the aluminum atom is expelled from the zeolite framework.

Activated carbon

Activated carbon is a highly porous, amorphous solid consisting of microcrystallites with a graphite lattice, usually prepared in small pellets or a powder. It is non-polar and cheap. One of its main drawbacks is that it is combustible.

Activated carbon nitrogen isotherm showing a marked microporous type I behavior

Activated carbon can be manufactured from carbonaceous material, including coal (bituminous, subbituminous, and lignite), peat, wood, or nutshells (e.g., coconut). The manufacturing process consists of two phases, carbonization and activation. The carbonization process includes drying and then heating to separate by-products, including tars and other hydrocarbons, from the raw material, as well as to drive off any gases generated. The carbonization process is completed by heating the material at 400–600 °C in an oxygen-deficient atmosphere that cannot support combustion.

The carbonized particles are "activated" by exposing them to an oxidizing agent, usually steam or carbon dioxide at high temperature. This agent burns off the pore blocking structures created during the carbonization phase and so, they develop a porous, three-dimensional graphite lattice structure. The size of the pores developed during activation is a function of the time that they spend in this stage. Longer exposure times result in larger pore sizes. The most popular aqueous phase carbons are bituminous based because of their hardness, abrasion resistance, pore size distribution, and low cost, but their effectiveness needs to be tested in each application to determine the optimal product.

Activated carbon is used for adsorption of organic substances and non-polar adsorbates and it is also usually used for waste gas (and waste water) treatment. It is the most widely used adsorbent. Its usefulness derives mainly from its large micropore and mesopore volumes and the resulting high surface area.

Adsorption chillers

Adsorption chillers are driven by hot water. This hot water may come from any number of industrial sources including waste heat from industrial processes, prime heat from solar thermal installations or from the exhaust or water jacket heat of a piston engine or turbine.

The principle of adsorption is based on the interaction of gases and solids. With adsorption chilling, the molecular interaction between the solid and the gas allow the gas to be adsorbed into the solid. The adsorption chamber of the chiller is filled with solid material, silica gel, eliminating the need for moving parts and eliminating the noise associated with those moving parts. The silica gel creates an extremely low humidity condition that causes the water refrigerant to evaporate at a low temperature. As the water evaporates in the evaporator, it cools the chilled water.

Portal site mediated adsorption

Portal site mediated adsorption is a model for site-selective activated gas adsorption in metallic catalytic systems which contain a variety of different adsorption sites. In such systems, low-coordination "edge and corner" defect-like sites can exhibit significantly lower adsorption enthalpies than high-coordination (basal plane) sites. As a result, these sites can serve as "portals" for very rapid adsorption to the rest of the surface. The phenomenon relies on the common "spillover" effect (described below), where certain adsorbed species exhibit high mobility on some surfaces. The model explains seemingly inconsistent observations of gas adsorption thermodynamics and kinetics in catalytic systems where surfaces can exist in a range of coordination structures, and it has been successfully applied to bimetallic catalytic systems where synergistic activity is observed.

In contrast to pure spillover, portal site adsorption refers to surface diffusion to adjacent adsorption sites, not to non-adsorptive support surfaces.

The model appears to have been first proposed for carbon monoxide on silica-supported platinum by Brandt et al. (1993). A similar, but independent model was developed by King and co-workers (Uner et al. 1997, Narayan et al. 1998, and VanderWiel et al. 1999) to describe hydrogen adsorption on silica-supported alkali promoted ruthenium, silver-ruthenium and copper-ruthenium bimetallic catalysts. The same group applied the model to CO hydrogenation (Fischer-Tropsch synthesis, Uner 1998 ). Zupanc et al. (2002) subsequently confirmed the same model for hydrogen adsorption on magnesia-supported cesium-ruthenium bimetallic catalysts. Trens et al. (2009) have similarly described CO surface diffusion on carbon-supported Pt particles of varying morphology.

Adsorption spillover

In the case catalytic or adsorbant systems where a metal species is dispersed upon a support (or carrier) material (often quasi-inert oxides, such as alumina or silica), it is possible for an adsorptive species to indirectly adsorb onto the support surface under conditions where such adsorption is thermodynamically unfavorable. The presence of the metal serves as a lower-energy pathway for gaseous species to first adsorb on to the metal and then diffuse on to the support surface. This is possible because the adsorbed species attains a lower energy state once it has adsorbed on to the metal center, thus lowering the activation barrier between the gas phase species and the support-adsorbed species.

Hydrogen spillover is the most common example of adsorptive spillover. In the case of hydrogen, adorption is most often accompanied with dissociation of molecular hydrogen (H2) to atomic hydrogen (H), followed by spillover of the hydrogen atoms.

The spillover effect has been used to explain many observations in heterogeneous catalysis and adsorption (see, for example, Rozanov and Krylov 1997), and has been proposed as a means of efficient hydrogen storage.

Adsorption in viruses

Adsorption is the first step in the viral infection cycle. The next steps are penetration, uncoating, synthesis (transcription if needed, and translation), and release. The virus replication cycle, in this respect, is similar for all types of viruses. Factors such as transcription may or may not be needed if the virus is able to integrate its genomic information in the cell's nucleus, or if the virus can replicate itself directly within the cell's cytoplasm.

See also


  1. ^ "Glossary". The Brownfields and Land Revitalization Technology Support Center. Retrieved 2009-12-21.  
  2. ^ "WordNet Search - 3.0". WordNet. Retrieved 2009-12-21.  


  • Brandt, R.K., M.R. Hughes, L.P. Bourget, K. Truszkowska and R.G. Greenler (1993). 'The interpretation of CO adsorbed on Pt/SiO2 of two different particle-size distributions', Surface Science, vol. 286, pp. 15-25.
  • Cussler, E.L. (1997). Diffusion: Mass Transfer in Fluid Systems, 2nd ed., pp. 308-330.
  • Henderson, A.P., L.N. Seetohul, A.K. Dean, P. Russell, S. Pruneanu and Z. Ali (2009). 'A Novel Isotherm, Modelling Self-Assembled Monolayer Adsorption and Structural Changes', Langmuir, vol. 25, no. 2, pp. 931–938.
  • Kisliuk, P. (1957). 'The sticking probabilities of gases chemisorbed on the surfaces of solids', Journal of Physics and Chemistry of Solids, vol. 3, pp. 95–101.
  • Narayan, R.L. and T.S. King (1998). 'Hydrogen adsorption states on silica-supported Ru-Ag and Ru-Cu bimetallic catalysts investigated via microcalorimetry', Thermochimica Acta, vol. 312, nos.1-2, pp. 105-114.
  • Rozanov, V.V., and O.V. Krylov (1997). 'Hydrogen spillover in heterogeneous catalysis', Russ Chem Rev 1997, vol. 66 (2), pp. 107–119.
  • Trens, P., R. Durand, B. Coq, C. Coutanceau, S. Rousseau and C. Lamy (2009). 'Poisoning of Pt/C catalysts by CO and its consequences over the kinetics of hydrogen chemisorption', Applied Catalysis B: Environmental, vol. 92, Issues 3-4, pp. 280-284.
  • Uner, D.O., N. Savargoankar, M. Pruski and T.S. King, (1997). 'The effects of alkali promoters on the dynamics of hydrogen chemisorption and syngas reaction kinetics on Ru/SiO2 catalysts, Studies in Surface Science and Catalysis, vol. 109, pp. 315-324.
  • Uner,D.O. (1998).'A sensible mechanism of alkali promotion in Fischer Tropsch synthesis:Adsorbate mobilities', Industrial and Engineering Chemistry Research, vol. 37, pp. 2239-2245.
  • VanderWiel, D.P., M. Pruski and T.S. King (1999). 'A Kinetic Study of the Adsorption and Reaction of Hydrogen on Silica-Supported Ruthenium and Silver-Ruthenium Bimetallic Catalysts during the Hydrogenation of Carbon Monoxide', Journal of Catalysis, vol. 188, no. 1, pp. 186-202.
  • Zupanc, C., A. Hornung, O. Hinrichsen and M. Muhler (2002). 'The Interaction of Hydrogen with Ru/MgO Catalysts', Journal of Catalysis, vol. 209, pp. 501-514.

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