Critical micelle concentration

Upon introducing surfactants (or any surface active materials) into a system, they will initially partition into the interface, reducing the system free energy by:^{[citation needed]}

1. lowering the energy of the interface (calculated as area times surface tension), and
2. 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.^[5] Upon reaching CMC, any further addition of surfactants will just increase the number of micelles (in the ideal case).^{[citation needed]}

According to one well-known definition, CMC is the total concentration of surfactants under the conditions:^[6]

if C = CMC, (d³${\displaystyle \phi }$/dC_t³) = 0

${\displaystyle \phi }$ = A[C_s] + B[C_m]; i.e., in words C_s = [single surfactant ion] , C_m = [micelles] and A and B are proportionality constants

C_t = C_s + NC_m; 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. 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.^{[citation needed]}

The common procedure to determine the CMC from experimental data is to look for the intersection (inflection point) of two straight lines traced through plots of the measured property versus the surfactant concentration. This visual data analysis method is highly subjective and can lead to very different CMC values depending on the type of representation, the quality of the data and the chosen interval around the CMC.^[7] A preferred method is the fit of the experimental data with a model of the measured property. Fit functions for properties such as electrical conductivity, surface tension, NMR chemical shifts, absorption, self-diffusion coefficients, fluorescence intensity and mean translational diffusion coefficient of fluorescent dyes in surfactant solutions have been presented.^[8][9][10] These fit functions are based on a model for the concentrations of monomeric and micellised surfactants in solution, which establishes a well-defined analytical definition of the CMC, independent from the technique.

The 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 situations, such as surface tension measurements or conductivity measurements, the amount of surfactant at the interface is negligible compared to that in the bulk and CMC can be approximated by the total concentration. In practice, CMC data is usually collected using laboratory instruments which allow the process to be partially automated, for instance by using specialised tensiometers.^{[citation needed]}

When the interfacial areas are large, the amount of surfactant at the interface cannot be neglected. If, for example, air bubbles are introduced into a solution of a surfactant above CMC, these bubbles, as they rise to the surface, remove surfactants from the bulk to the top of the solution creating a foam column and thus reducing the concentration in bulk to below CMC. This is one of the easiest methods to remove surfactants from effluents (see foam flotation). Thus, foams with sufficient interfacial area are devoid of micelles. Similar reasoning holds for emulsions.^{[citation needed]}

The other situation arises in detergents. One initially starts off with concentrations greater than CMC in water and on adding fabric with large interfacial area, the surfactant concentration drops below CMC and no micelles remain at equilibrium. Therefore, the solubilization plays a minor role in detergents. Removal of oily soil occurs by modification of the contact angles and release of oil in the form of emulsion.^{[citation needed]}

In the petroleum industry, the critical micelle concentration (CMC) is considered before injecting a surfactant into a reservoir for enhanced oil recovery (EOR). Below the CMC, the surfactant no longer effectively reduces the interfacial tension between the oil and water phases.^[11] Therefore, the surfactant concentration is typically maintained slightly above the CMC so that losses due to dissolution in the existing reservoir brine do not significantly reduce performance. Ideally, the surfactant should operate at the lowest possible interfacial tension (IFT).^{[citation needed]}

• Detergent
• Micelle
• Surface tension
• Surfactant