critical micelle concentration
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Add soap to water a little at a time. At first nothing dramatic happens — the soap molecules wander as singles and crowd onto the water's surface. But keep adding, and at one sharp point the water suddenly starts forming micelles and its cleaning power jumps. That tipping point — the concentration at which micelles first appear — is the critical micelle concentration, or CMC.
More precisely, the critical micelle concentration is the surfactant concentration above which added surfactant molecules stop floating as singles and instead bunch together into micelles. Below the CMC, the surface fills up and the rest of the surfactant drifts as lone molecules. Once the surface is saturated and the CMC is reached, any further surfactant has nowhere to go but into micelles, so micelles form and multiply from that point on.
The CMC matters because it marks the concentration where a detergent truly starts to work — below it, there are no micelles to trap grease. It also shows up as a kink in many measured properties: surface tension drops steadily, then levels off right at the CMC. The caveat is that the CMC is not one fixed number for a surfactant; it shifts with temperature, with added salt, and with the exact mix of molecules present.
Adding more dish soap helps clean a greasy sink — but only up to a point. Once you pass the CMC, extra soap just forms more micelles and barely improves things, which is why drowning the dishes in soap wastes it.
Below the CMC: lone molecules. Above it: micelles, and full cleaning power.
You can spot the CMC experimentally because many properties bend sharply at it: surface tension stops falling, while light scattering, electrical conductivity per molecule, and the solubility of greasy substances all change course right at that concentration.