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).

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,

$\frac{x}{m}=kP^{\frac{1}{n}}$

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.

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.

 At the air/liquid interface: And the solid/liquid interface: Lowers the surface tension. Stabilizes dispersions.

## Culinary applications

• Mayonnaise is a classic example of an emulsion of an oil in water. Howard McGee gives an extensive discussion of how to prepare this well-known condiment:
• The surface tension of water makes it highly-favorable for the water and oil to exist in distinct phases. Energy, in the form of vigorous mixing, needs to be added to the mixture to create a dispersion of oil droplets in water. As an order of magnitude estimate, 15 ml of oil can separate into 30 billion drops in the final product! Enthusiastic mixing by hand can achieve droplets on the order of 3 micron, but industrial-grade homogenizers can produce drops less than one micron in size.
• As described in the previous section, this process of dispersing the droplets can be made easier with the presence of surfactants, also known as emulsifiers. In mayonnaise, the phospholipid lecithin in the eggs serves this purpose. The proteins in the egg yolks contain separate hydrophobic and hydrophillic regions, which is also effective. Warm, raw eggs yolks are traditionally used since they are more flexible and can flow more easily than their refrigerated or cooked counterparts. The casein in milk and cream are also sometimes used in emulsions.
• However, it is not enough to simply create the droplets: something is needed to keep them from coalescing into larger drops. In mayonnaise, the polymers in mustard seeds do the job.
• Chocolate is an emulsion of cocoa particles in cocoa butter. Starting in the 1930's, lecithin was used to replace some of the cocoa butter. One part lecithin can lubricate as many cocoa particles as 10 parts cocoa butter. Due to this efficiency, chocolate typically contains only 0.3 to 0.5% lecithin my weight.
• Whisky may often be served "on the rocks" to enhance the flavor of the beverage, rather than just to dilute the alcohol. As the ice melts and the liquid becomes more polar, long chain esters and alcohols form micelles, which "masks" their flavor. On the other hand, ethanol becomes more soluble in water as the liquid cools, which causes it to break up existing micelles of flavor molecules. For more information, see the blog post on khymos.org.

## Foam

Surfactants lower interfacial tension. This promotes finer dispersions. But they also keep dispersed droplets from coalescing. Surfactant coated surfaces repel each other, and merging of droplets would also require the surfactants to reorganize on the surface. "Thus, it is that two adjacent surfactant-coated droplets can coalesce only on the timescale of years." Thus, emulsions such as mayo or cold cream can have a long shelf life.

Foam is just a dispersion where the solute is air. Foams can be made either by stirring or by lowering the pressure of a gas-saturated solution. The solution becomes supersaturated with gas and begins to bubble. This is what happens with shaving cream or with beer bottles when they are opened. (Witten p. 197)

Great Experiment: Put some dry ice in soapy water, and you will get soap bubbles rising from the surface!

A derivation by Gibbs gives a relation between the chemical potential of a solute in solution, the surface tension of an interface and the excess concentration the solute at that interface. The interface is considered to be wide compared to the concentration gradients; the excess number of moles associated with that interface is calculated and is expressed as a surface concentration, moles per area:

Morrison. Fig. 15.1
 The differential of the total energy: $dU=TdS-pdV+\sigma dA+\sum{\mu _{i}dn_{i}}$ Integrating to get the total energy: $U=TS-pV+\sigma A+\sum{\mu _{i}n_{i}}$ Taking the differential gives the Gibbs-Duhem relation $SdT-Vdp+Ad\sigma +\sum{n_{i}d\mu _{i}}=0$ Defining that relation for both bulk phases: $S^{\alpha }dT-V^{\alpha }dp+\sum{n_{i}^{\alpha }}d\mu _{i}^{\alpha }=0$ $S^{\beta }dT-V^{\beta }dp+\sum{n_{i}^{\beta }}d\mu _{i}^{\beta }=0$ Chemical potentials are constant: $d\mu _{i}=d\mu _{i}^{\alpha }=d\mu _{i}^{\beta }$ Subtracting the phases from the total: $\left( S-S^{\alpha }-S^{\beta } \right)dT-\left( V-V^{\alpha }-V^{\beta } \right)dp+Ad\sigma +\sum{\left( n_{i}-n_{i}^{\alpha }-n_{i}^{\beta } \right)}d\mu _{i}=0$ Defining the excess quantities: $S^{\sigma }=S-S^{\alpha }-S^{\beta }$ $S^{\sigma }=S-S^{\alpha }-S^{\beta }$ $S^{\sigma }=S-S^{\alpha }-S^{\beta }$ Substitution and subtraction gives: $Ad\sigma +S^{\sigma }dT-V^{\sigma }dp+\sum{n_{i}^{\sigma }d\mu _{i}}$

Finally:

 Gibbs adsorption isotherm: $-d\sigma =\sum{\frac{n_{i}^{\sigma }}{A}}d\mu _{i}=\sum{\Gamma _{i}}d\mu _{i}$ The surface excess: $\Gamma _{i}=\frac{n_{i}^{\sigma }}{A}\text{ mol m}^{\text{-2}}$ For a 2-component system: $-d\sigma =\Gamma _{2}d\mu _{2}\simeq kT\Gamma _{2}d\ln c_{2}$

 Air-water surface Air-oil surface Oil-water interface Strong adsorption, substantial lowering of surface tension. Little adsorption, little lowering of surface tension. Strong adsorption, substantial lowering of interfacial tension.

Ratio of the observed velocity of ascent of a bubble to the calculated Stokes’ velocity in solutions of various concentrations of

• (a) polydimethylsiloxane in trimethylolpropane–heptanoate;
• (b) polydimethylsiloxane in mineral oil;
• (c) N-phenyl–1–1napthylamine in trimethylolpropane–heptanoate.

Each figure shows the transition from the Hadamard to the Stokes regime.

Suzin and Ross, 1985

Suzin, Y.; Ross, S. Retardation of the ascent of gas bubbles by surface-active solutes in nonaqueous solutions, J. Colloid Interface Sci. 1985, 103, 578 – 585.

## Adsorption by a solid surface

The surfactant must be soluble in the liquid !

 Solid-water interface Solid-oil interface The adsorption is driven by both strong tail/solid interaction and entropy – the hydrophobic effect. The adsorption is driven by strong head group/solid interaction.
What would happen to this configuration if the water and oil were alternated at the surface? Would the molecules at the surface just keep flipping?


Adsorbents most commonly exist as spherical rods, pellets or monoliths with hydrodynamic diameters at the order 1 to 10 mm. The properties that characterize them are high abrasion resistance, high thermal stability, as well as small pore diameters. All these characteristics make the exposed surface area greater therefore enable higher surface capacity for adsorption. In addition, adsorbents must also have a specific structure which enables fast transport of the vapors.

Adsorbents in industry are usually classified in three categories:

- Oxygen-containing compounds – hydrophilic and polar (silica gel, zeolites).
- Carbon-based compounds – hydrophobic and non-polar (activated carbon, graphite).
- Polymer-based compounds - could be polar or non-polar.


## Industrial Application: Cryosorption Pumping

The phenomenon of adsorption is very important in vacuum science, and is the physics behind a very important class of vacuum pump. A cryosorption pump (sometimes called simply a cryopump) uses cooled surfaces covered with a material that adsorbs a certain vapor. Because they have no moving parts and require no oil (only a cold surface), cryopumps are a clean, effective, and simple way to achieve a very high high vacuum.

While a flat, smooth surface will cryopump most gases, helium requires a very porous material to be cryopumped. Modern cryopumps use materials with very high surface areas and internals mircopores; common materials are activated charcoal (usually made from coconut, but also made from wood, petroleum byproducts, or bone), porous metals such as copper, or solid argon.

A well-constructed cryopump, cooled down to a few Kelvin, can pump several liters of helium per second per square centimeter, and has a capacity of several Torr-liters per square centimeter. In other words, the adsorbing materials can contain a few hundred times their own volume!

Coconut-charcoal based cryopumps are a common tool in cryogenics labs, and are the vacuum pumps of choice in fusion reactors because of their huge pumping speeds and low contamination.