Adsorption

Adsorption is a process that takes place when a liquid or, most commonly, a gas (adsorbate) accumulates on the surface of a solid (adsorbent), forming a molecular or atomic film.

Note: Do not confuse with absorption, which is different in that rather than adhering to the surface, substance A, when absorbed, will diffuse into the substance B, but when adsorbed will form, as stated above, a thin film at the surface of B.

Adsorption, similar to surface tension, is a consequence of surface energy: consider a clean surface exposed to a gaseous atmosphere. In the bulk material, all the bonding requirements (be they ionic, covalent or metallic) of the constituent atoms of the material are filled. However, atoms on the surface experience a bond deficiency, because they are not wholly surrounded by other atoms. It is, then, energetically favourable for these dangling bonds to react with whatever happens to be available. The exact nature of the bonding depends on the details of the species involved, but the adsorbed material is generally classed as exhibiting physisorption or chemisorption.

Adsorption isotherms

Adsorption is usually described through isotherms, that is, functions which connect the amount of adsorbate on the adsorbent, with its pressure (if gas) or concentration (if liquid).

The first isotherm is due to Freundlich and Küster (1894) and it is a purely empirical formula valid for gases as adsorbates: ${\frac {x}{m}}=kP^{\frac {1}{n}}$, where x is the adsorbed quantity, m is the mass of adsorbent, P is the pressure of adsorbate and k and n are empirical constants for each adsorbant/adsorbate pair at each temperature. The function has an asymtotic maximum and, as the temperature increases, the adsorbed quantity rises more slowly and the required pressure for the maximum is greater.

Langmuir isotherm

In 1916, Irving Langmuir published a new isotherm for gases adsorbed on solids, which retained his name. It is an empirical isotherm derived from a proposed kinetic mechanism. It is based on four hypotheses: 1) The surface of the adsorbent is uniform, that is, all the adsorption sites are equal. 2) Adsorbed molecules do not interact. 3) All adsorption takes place 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.

As usual, these four points are seldom true: there are always imperfections on the surface, adsorbed molecules are not necessarily inert, the mechanism is clearly not the same for the very first molecules as for the last to adsorb. The fourth condition is the most troublesome, as often, more molecules can adsorb on the monolayer, but this problem is solved by another isotherm.

Langmuir suggests that adsorption takes place through this mechanism: A_(g) + S ⇌ 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, $\theta$, as the fraction of the adsorption sites which are occupied, in the equilibrium we have

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

For very low pressures $\theta \approx KP$ and for high pressures $\theta \approx 1$

$\theta$ is difficult to measure experimentally; usually, the adsorbate is a gas and the adsorbed quantity is given in STP (standard temperature and pressure) volume per gram of adsorbent. Therefore, if we call v_mon the STP volume of adsorbate required to form a monolayer on the adsorbant (per gram of adsorbent too), $\theta ={\frac {v}{v_{\mathrm {mon} }}}$ and we obtain an expression for a straight line:

${\frac {1}{v}}={\frac {1}{Kv_{\mathrm {mon} }}}{\frac {1}{P}}+{\frac {1}{v_{\mathrm {mon} }}}.$

Through its slope and y-intercept we can obtain v_mon and K, which are constants for each adsorbent/adsorbate pair at a given temperature. v_mon 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. Surface area of adsorbents depends on their structure, the more pores they have, the greater the area, which has a big influence on reactions on surfaces.

If more than one gas adsorbs on the surface, we call $\theta _{E}$ the fraction of empty sites and we have

$\theta _{E}={\frac {1}{1+\sum _{i=1}^{n}K_{i}P_{i}}}$

and

$\theta _{j}={\frac {K_{j}P_{j}}{1+\sum _{i=1}^{n}K_{i}P_{i}}}$

where i is each one of the gases that adsorb.

Frumkin isotherm

Frumkin isotherm is an extension of Langmuir isotherm. It states that adsorbed molecule do iteract and affect further adsorption by either repulsion or attraction of molecules.

$\delta G_{Frumkin}=\delta G_{Langmuir}-2g\Gamma _{i}$

BET isotherm

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 an isotherm that takes into account that possibility. The proposed mechanism is now:

A_(g) + S ⇌ AS

A_(g) + AS ⇌ A₂S

A_(g) + A₂S ⇌ A₃S and so on

File:Adsorption Isotherms (Langmuir red & BET green.JPG

Langmuir isotherm red and BET green)

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

${\frac {x}{v(1-x)}}={\frac {1}{v_{\mathrm {mon} }c}}+{\frac {x(c-1)}{v_{\mathrm {mon} }c}}.$

x is the pressure divided into the vapour pressure for the adsorbate at that temperature, v is the STP volume of adsorbed adsorbate, v_mon 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 vapour pressure of the adsorbate. The biggest step in BET isotherm is to consider that the successive equilibria for all the layers except for the first are equal to the liquefaction of the adsorbate.

Langmuir isotherm is usually better for chemisorption and BET isotherm works better for physisorption.

Adsorption enthalpy

Adsorption is an exothermic process because energy is liberated, therefore enthalpy is always negative. Adsorption constants are equilibrium constants, therefore they obey van't Hoff 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 BET isotherm and assume that the entropy change is the same for liquefaction and adsorption we obtain $\Delta H_{\mathrm {ads} }=\Delta H_{\mathrm {liq} }-RT\ln c$, that is to say, adsorption is more exothermic than liquefaction.

Examples of adsorption

• Activated carbon
• Heterogeneous catalysis, the most commonly encountered form of chemisorption in industry, occurs when a solid catalyst interacts with a gaseous feedstock, the reactant/s. The adsorption of reactant/s to the catalyst surface creates a chemical bond, altering the electron density around the reactant molecule and allowing it to undergo reactions that would not normally be available to it.

Adsorption in viruses

Adsorption is the first step in the viral infection cycle. The next steps are penetration, uncoating, synthesise (transcription if needed, and translation), and release. The virus replication cycle is similar if not the same 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

• Langmuir equation
• BET theory
• Absorption
• Reactions on surfaces
• http://www.jhu.edu/~chem/fairbr/derive.html Derivation of Langmuir and BET isotherms
• Freundlich equation