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 will form 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 (without other additives or salts) at 25 °C, atmospheric pressure, is 8x10−3 mol/L. Upon introducing surfactants (or any surface active materials) into a system, they will initially partition into the interface, reducing the system free energy by: lowering the energy of the interface (calculated as area times surface tension), and removing the hydrophobic parts of the surfactant from contact with water. 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). According to one well-known definition, CMC is the total concentration of surfactants under the conditions: if C = CMC, (d3/dCt3) = 0 = A[Cs] + B[Cm]; i.e., in words Cs = [single surfactant ion] , Cm = [micelles] and A and B are proportionality constants Ct = Cs + NCm; i.e., N = represents the number of detergent ions per micelle 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, photochemical characteristics or surface tension.