There are several theoretical definitions of CMC. One well-known definition is that CMC is the total concentration of surfactants under the conditions:
Therefore, CMC depends on the method of measuring the samples, since a and b depend on the properties of the solution such as conductance and photochemical characteristics. When the degree of aggregation is monodispersion, the CMC is not related to the method of measurement. On the other hand, when the degree of aggregation is multidispersion, CMC is related to both the method of measurement and the dispersion.
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 tensions stays more constant.
CMC is the concentration of surfactants in the bulk at which micelles start forming. The word BULK is important because surfactants partition between the bulk and interface and CMC is independent of interface and is therefore a characteristic of the surfactant molecule. In most of the situations like for e.g. in surface tension measurements or conductivity measurements, the amount of surfactant at the interface is negligible compared to that in the bulk and CMC is approximated by the total concentration as is done in most of the textbooks. There are important situations where interfacial areas are large and the amount of surfactant at the interface can not be neglected. For example if we take a solution of a surfactant above CMC and start introducing air bubbles at the bottom of the solution, these bubbles, as they rise to the surface, pull out the surfactants from the bulk to the top of the solution creating a foam column thus bringing down the concentration in bulk to below cmc. This is one of the easiest methods to remove surfactants from effluents (Foam Flotation). Thus in foams with sufficient interfacial area there will not be any micelles. Similar reasoning holds for emulsions. Other situation arises in detergency. One initially starts off with concentrations greater than CMC in water and on adding fabric with large interfacial area and waiting for equilibrium, the surfactant concentration goes below CMC and no micelles are left. Therefore the solubilization plays a minor role in detergency. Removal of oily soil is by modification of the contact angles and release of oil in the form of emulsion.