Langmuir isotherm
/ LANG-mure /
Picture a parking lot with a fixed number of spaces. When the lot is nearly empty, every arriving car finds a spot, so the lot fills fast. As it gets crowded, new cars often find their space taken and have to leave, so filling slows down — and once every space is occupied, no more cars fit no matter how many circle outside. The Langmuir isotherm is the simplest equation that captures exactly this picture for molecules landing on a surface.
More precisely, it describes how much of a surface is covered by adsorbed molecules as the surrounding gas pressure (or solution concentration) rises, at a fixed temperature — that is what "isotherm" means. It rests on a few clean assumptions: the surface has a fixed number of identical sites, each site holds at most one molecule (a single layer), and adsorbed molecules do not interact. The result is a curve that rises steeply at first and then flattens to a plateau as the surface saturates.
This matters because it was the first usable theory of adsorption, earning Irving Langmuir a Nobel Prize, and it still underlies how we describe catalysts, gas sensors, and binding in biology. The honest caveat is that its tidy assumptions often fail: real surfaces have varied sites, molecules can stack into many layers, and they do push on one another — so more elaborate models exist for when the simple picture breaks down.
A carbon monoxide sensor relies on CO molecules sticking to a metal-oxide surface. As CO in the air rises, coverage follows a Langmuir curve — climbing steeply, then levelling off once the surface fills, which sets the sensor's useful range.
Coverage climbs, then plateaus once every surface site is taken.
When adsorbed molecules can pile into more than one layer, the Langmuir model is replaced by the BET isotherm, named for Brunauer, Emmett and Teller, which is the standard way to measure a material's specific surface area.