Adsorption

# Overview
Adsorption is a process that occurs when a  gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a film of molecules or atoms (the adsorbate).  It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution. The term sorption encompasses both processes, while desorption is the reverse process.
Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as activated charcoal, synthetic resins, 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.
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).

# Isotherms
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 Kuster (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.

## Langmuir
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:
- The surface of the adsorbent is uniform, that is, all the adsorption sites are equivalent.
- Adsorbed molecules do not interact.
- All adsorption occurs through the same mechanism.
- 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 Template:Unicode 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 occupied, in the equilibrium we have
Where P is the partial pressure (gas) or the molar concentration of the solution (liquid)
For very low pressures \theta\approx KP and for high pressures \theta\approx1
\theta 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 \theta_E as the fraction of empty sites and we have
and
where i is each one of the gases that adsorb.

## BET
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:
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/P^0), 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.

## Adsorption enthalpy
Adsorption constants are equilibrium constants, therefore they obey van 't Hoff's equation:
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 
\Delta H_\mathrm{ads}=\Delta H_\mathrm{liq}-RT\ln c, that is to say, adsorption is more exothermic than liquefaction.

# Adsorbents

## Characteristics and general requirements
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
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 A (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 (1000 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 can be manufactured from carbonaceous material, including coal (bituminous, subbituminous, and lignite), peat, wood, or nutshells (i.e., 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 400600 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 treated 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.

# 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 phenomena relies on the common "spillover" effect, 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.
The original model was developed by King and co-workers (Narayan et al. 1998 and VanderWiel et al. 1999) to describe hydrogen adsorption on silica-supported silver-ruthenium and copper-ruthenium bimetallic catalysts.  The same group applied the model to CO hydrogenation (Fischer-Tropsch synthesis).  Zupanc et al. (2002) subsequently confirmed the same model on magnesia-supported cesium-ruthenium bimetallic catalysts.

# 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 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.