Critical micelle concentration

In colloidal and surface chemistry, the critical micelle concentration (CMC) is defined as the concentration of surfactants above which micelles form and all additional surfactants added to the system go to micelles.

The CMC is an important characteristic of a surfactant. Before reaching the CMC, the surface tension changes strongly with the concentration of the surfactant. After reaching the CMC, the surface tension remains relatively constant or changes with a lower slope. The value of the CMC for a given dispersant in a given medium depends on temperature, pressure, and (sometimes strongly) on the presence and concentration of other surface active substances and electrolytes. Micelles only form above critical micelle temperature.

For example, the value of CMC for sodium dodecyl sulfate in water (no other additives or salts) at 25 °C, atmospheric pressure, is 8x10⁻³ mol/L.

The study of the aggregation of lipids (amphiphiles) is known as lipid polymorphism.

Upon introduction of surfactants (or any surface active materials) into the system, they will initially partition into the interface, reducing the system free energy by:

Subsequently, when the surface coverage by the surfactants increases, the surface free energy (surface tension) decreases and the surfactants start aggregating into micelles, thus again decreasing the system's free energy by decreasing the contact area of hydrophobic parts of the surfactant with water. Upon reaching CMC, any further addition of surfactants will just increase the number of micelles (in the ideal case).

There are several theoretical definitions of CMC. One well-known definition is that CMC is the total concentration of surfactants under the conditions:

The CMC generally depends on the method of measuring the samples, since a and b depend on the properties of the solution such as conductance and characteristics. When the degree of aggregation is monodisperse, then the CMC is not related to the method of measurement. On the other hand, when the degree of aggregation is polydisperse, then CMC is related to both the method of measurement and the dispersion.

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