adsorption is the phenomenon of one chemical substance (adsorbate) adhering to another substance (the adsorbent), whether because the physical environment near the adsorbent is more favorable (lower energy) - physical adsorption; or because the adsorbent molecules react chemically with the adsorbed molecules - chemisorption. Adsorption is an aspect of sorption
A common example of simple physical adsorption is partly- or sparingly-soluble organic molecules in water being removed by activated carbon. Within the pores of activated carbon, the abundant surfaces of atomic carbon are locations where partially soluble organic molecules can find lower energy by being only partly surrounded by polar water molecules instead of being fully surrounded as in the bulk liquid.
An intermediate example between physical adsorption and chemisorption is the adhesion of carbon dioxide molecules to amine polymers. Amine nitrogens have a pair of electrons not involved in chemical bonding, and these electrons are attractive to the central, relatively positive carbon atom in carbon dioxide molecules.
A case of chemisorption is the reaction between carbon dioxide and monoethanolamine (MEA) to form 2-hydroxyethyl-carbamate or MEA-bicarbonate.
Because adsorption occurs at a surface - at a phase boundary - it is often beneficial for the sorbent to be finely divided or have a highly porous surface to increase the adsorption capacity. Alternatively, the adsorption surface can be renewed if the adsorbent can absorb the adsorbed substance into the bulk phase. The absorption process can be diffusion-limited if the adsorbent is fixed as solid or thin-film or droplets.
The reverse of adsorption is desorption. The tendency of adsorbed molecules to adhere can be disrupted by changing the chemical environment - raising the temperature, lowering the pressure, or changing the humidity may each promote desorption.
Technicalities
The adsorption of adsorbate (say carbon dioxide gas) depends on the partial pressure of the carbon dioxide and the properties of the adsorbent. A graphical analysis of the appropriately chosen variables is linear and the slope and vertical-axis intercept are characteristic of the adsorbate-adsorbent system being studied. Appropriate variables are log (x/m) where x/m is the adsorbate/adsorbent mass ratio, and log (P) where P is the partial pressure of the adsorbate. A graph of log (x/m) vs log (P) has slope 1/n, and intercept log(K), so the equation x/m = k P ^ (1/n) is the Freundlich isotherm of the sorbent system.
It is called an isotherm because it is valid for a particular temperature. The process of physical adsorption is always exothermic, so it always decreases with increasing temperature. Chemical adsorption is more complex, and the degree of chemical adsorption often has a “hump” of higher adsorption at higher temperature before the trend of decrease with increasing temperature ultimately prevails.
In ideal gases, the total pressure is simply the sum of the partial pressures of the individual gases in a mixture, and each gas occupies a portion of the total volume that is proportional to the mole fraction of the gas. So for air at one atmosphere, where nitrogen is 78.08% of the mixture, the partial pressure of nitrogen is 78.08% x 1 atm = 0.7808 atm.
In the same air, where carbon dioxide is 420 ppm, the partial pressure of carbon dioxide is 420 x 1E-6 x 1 atm = 0.00042 atm
Real gases do not always behave ideally. When a gas departs from ideal behavior, particularly at high pressures or low temperatures (where intermolecular forces and molecule size can start to affect the measured properties of the gas), the mole fraction of the gas no longer serves to predict the partial pressure - an additional factor is required. This added term is called the fugacity. It is the product of the mole fraction and the fugacity that is proportional to the partial pressure.
Fortunately, for CO2 at atmospheric pressure and ambient temperature, the fugacity is very close to 1, and the partial pressure of CO2 is only about 1% less than would be expected based on its mole fraction.
References
https://knowledgeburrow.com/how-does-amine-absorb-co2/
CDR Horizons E06 - metal-organic frame engineered adsorbent media
More references on this topic may be found at the article on Direct Air Capture.