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. In standard aqueous solutions, micelles only form above critical micelle temperature (CMT), often called Krafft point when related to ionic-surfactants. Mixed micelles can form below CMT as the kinetics of percipitation are altered.

For example, the value of CMC for sodium dodecyl sulfate in water (without other additives or salts) at 25 °C, atmospheric pressure, is 8×10−3 mol/L.

+ CMCs for common surfactants Surfactant CMC (molarity) Category Sodium octyl sulfate 0.13 anionic surfactant Sodium dodecyl sulfate 0.0083 anionic surfactant Sodium tetradecyl sulfate 0.0021 anionic surfactant Decyltrimethylammonium bromide 0.065 cationic surfactant Dodecyltrimethylammonium bromide 0.016 cationic surfactant Hexadecyltrimethylammonium bromide 0.00092 cationic surfactant Penta(ethyleneglycol)monooctyl ether 0.0009 neutral surfactant Penta(ethyleneglycol)monodecyl ether 0.0009 neutral surfactant Pentaethylene glycol monododecyl ether 0.000065 neutral surfactant

Description

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:Phillips J. The energetics of micelle formation. Transactions of the Faraday Society 1955;51:561-9 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

Measurement 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.

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.Mukerjee, P.; Mysels, K. J. In Critical Micelle Concentrations of Aqueous Surfactant Systems; NIST National Institute of Standards and Technology: Washington D.C. USA, 1971; Vol. NSRDS-NBS 36 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.Lucas Piñeiro, Sonia Freire, Jorge Bordello, Mercedes Novo, and Wajih Al-Soufi, Dye Exchange in Micellar Solutions. Quantitative Analysis of Bulk and Single Molecule Fluorescence Titrations. Soft Matter, 2013,9, 10779-10790, DOI: 10.1039/c3sm52092g 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.

Practical considerations 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.

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. 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).

See also Detergent Micelle Surface tension Surfactant

References

External links Theory of CMC measurement CMCs and molecular weights of several detergents on OpenWetWare