Critical micelle concentration
Encyclopedia
In colloidal and surface chemistry
, the critical micelle concentration (CMC) is defined as the concentration of surfactants above which micelle
s form and almost 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 tensions 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
.
, reducing the system free energy by:
Subsequently, when the surface coverage by the surfactants increases and 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 photochemical 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.
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.
There are important situations where interfacial areas are large and the amount of surfactant at the interface cannot 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 emulsion
s.
The 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 occurs by modification of the contact angles and release of oil in the form of emulsion.
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....
, the critical micelle concentration (CMC) is defined as the concentration of surfactants above which micelle
Micelle
A micelle is an aggregate of surfactant molecules dispersed in a liquid colloid. A typical micelle in aqueous solution forms an aggregate with the hydrophilic "head" regions in contact with surrounding solvent, sequestering the hydrophobic single tail regions in the micelle centre. This phase is...
s form and almost 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
Surface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
changes strongly with the concentration of the surfactant. After reaching the CMC, the surface tensions 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
Krafft temperature
The Krafft temperature is the minimum temperature at which surfactants form micelles. Below the Krafft temperature, there is no value for the critical micelle concentration , i.e., micelles cannot form...
.
For example, the value of CMC for sodium dodecyl sulfate
Sodium dodecyl sulfate
Sodium dodecyl sulfate , sodium laurilsulfate or sodium lauryl sulfate is an organic compound with the formula CH311OSO3Na). It is an anionic surfactant used in many cleaning and hygiene products...
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
Amphiphiles
Amphiphile is a term describing a chemical compound possessing both hydrophilic and lipophilic properties...
) is known as lipid polymorphism
Lipid polymorphism
Polymorphism in biophysics is the aspect of the behaviour of lipids that influences their long-range order, i.e. how they aggregate. This can be in the form of spheres of lipid molecules , pairs of layers that face one another , a tubular arrangement , or various cubic phases Polymorphism in...
.
Description
Upon introduction of surfactants (or any surface active materials) into the system, they will initially partition into the interfaceInterface (chemistry)
An interface is a surface forming a common boundary among two different phases, such as an insoluble solid and a liquid, two immiscible liquids or a liquid and an insoluble gas. The importance of the interface depends on which type of system is being treated: the bigger the quotient area/volume,...
, 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 and 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:
- if C = CMC, (d3F/dCt3) = 0
- F = a[micelle] + b[monomer]: function of surfactant solution
- Ct: total concentration
- a, b: proportional constants
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
Conductance
Conductance may refer to:* Electrical conductance, the ability for electricity to flow a certain path* Fluid conductance, the ability for fluid to transmit through materials* Thermal conductivity, the ability for temperatures to transmit through materials...
and photochemical characteristics. When the degree of aggregation is monodisperse
Monodisperse
A collection of objects are called monodisperse, or monosized, if they have the same size and shape when discussing particles, and the same mass when discussing polymers...
, then the CMC is not related to the method of measurement. On the other hand, when the degree of aggregation is polydisperse
Polydisperse
A collection of objects is called polydisperse or polysized if they have a broad range of size, shape and mass characteristics. A sample of objects that have a uniform size, shape and mass distribution are called monodisperse. In practice, polydisperse collections are common because it is...
, then CMC is related to both the method of measurement and the dispersion.
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
Conductivity (electrolytic)
The conductivity of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter ....
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.
There are important situations where interfacial areas are large and the amount of surfactant at the interface cannot 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 emulsion
Emulsion
An emulsion is a mixture of two or more liquids that are normally immiscible . Emulsions are part of a more general class of two-phase systems of matter called colloids. Although the terms colloid and emulsion are sometimes used interchangeably, emulsion is used when both the dispersed and the...
s.
The other situation arises in detergency
Detergency
Detergency is the action of imparting a free flowing ability to an undesirable foreign substance....
. 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
Solubilization
Solubilization, according to an IUPAC definition, is a short form for micellar solubilization, a term used in colloidal and surface chemistry....
plays a minor role in detergency. Removal of oily soil occurs by modification of the contact angles and release of oil in the form of emulsion.
Further reading
- S.A. Baeurle, J. Kroener, "Modeling effective interactions of micellar aggregates of ionic surfactants with the Gauss-Core potential", Journal of Mathematical Chemistry. 36, 409-421 (2004).