It is the change from simple solute to association colloid behavior where some physical property of the solution is measured as a function of amphiphile concentration.

The CMC is calculated in the book "Soft Condensed Matter" from Richard L.A. Jones. There are simple models for spherical micelles (CMC) and wormlike micelles (length distribution). The derivation is not 100% exact, but the essential results are correct.

Here is the best procedure along with a video. http://education.mrsec.wisc.edu/279.htm

Be safe!

There is a big difference in 'measuring' and calculating.

In organic medium, the CMC is generally taken equal to zero (CMC0). However, in water, to calculate the CMC, when knowing the total surfactant concentration C (expressed in mol per liter), you should know two parameters, the aggregation number N (without units), and the concentration of micelles M (expressed in mol per liter). The CMC as expressed in mol per liter is given below:

CMC=C-N*M

using stalagmometer and tensiometer

Besides surface tension and conductivity, another suitable and sensitive method similar to dye micellization which can be used in aqueous solutions is fluorescence spectroscopy with polarity sensitive hydrophobic probes like pyrene or  1-anilinonaphthalene-8-sulfonic acid. When micelles are formed, the probe molecules solubilize in their nonpolar interior and the CMC can be detected by the change in their emission spectrum.

in case you have moieties in your surfactants which adsorb in UV you can even use a spectral shift if you have a good spectrophotometer.

Static and dynamic light scattering spectroscopy (SLS and DLS)  are also a very powerful methods to study micellisation and micelles. In any case, at least two of the methods previously cited should be used. All of these methods have some drawback and some stringent requirements (tensioactive compound, dye and water purity etc., so that it is highly advisable to study the methods before running experiments.

Thank you all for your valuable suggestions

the following might be of interest

http://link.springer.com/chapter/10.1007%2FBFb0116274

The use of methyl orange for the characterization of micelles in aqueous nonionic surfactant solutions

This includes comparison with results obtained by UV and surface tension.

One classic method to determine CMC is to measure the surface tension of the solutions (at several surfactant concentrations) with a tensiometer. This is a plate linked to a dynamometer. The plate is immersed in the liquid; then the motor device starts to move off the plate from the liquid at a constant speed. The surface tension of the liquid decreases with increasing surfactant concentration until it reaches its CMC. You can obtained the CMC from the plot surface tension vs. surfactant concentration.

Following the changes in the absorption and/or fluorescence characteristics of a probe dye as a function of the surfactant concentration is one of the easiest means to determine the CMC of a surfactant.  A sharp change in the plot corresponds to the CMC  of the surfactant.

Many technique can be used to measure CMC : conductivity, surface tension and spectrophotometry .

Surface tension measurement is the most classical way of determining cmc: it also provides useful data on the surface properties of the surfactant. But, to yield a sharp slope change at the cmc, you have to plot surface tension vs. the logarithm of surfactant concentration. A lot of other techniques is available: they are described in numerous books and papers.

One has to be always careful with interpretation. E.g. you will find also a break point in surface tension concentration plot when solubility limit is reached followed by crystallization without forming any micelles.

Please find elsewhere in this paper

https://link.springer.com/article/10.1007/s11743-017-1957-5

Find here an good contribution in this field: http://www.che.ufl.edu/shah/misc/Publications/2000/Patist%201.pdf

Regards

Ahmed

Thank you Eliezer for the reference.  The authors in the paper, however do not give a very detailed descritiption of the Wilhelmy plate method.  Can anyone provide a detailed procedure for the surface tension method with Wilhelmy plates?

Regards,

Michael 

Michael David Martin,

This website could help you:

http://www.dataphysics.de/2/start/understanding-interfaces/tensiometry/wilhelmy-plate-method/

Regards,

Jean Paul Canselier

Thank you! 

Hi

https://youtu.be/7RH_aDLOXUM

https://pubs.acs.org/doi/abs/10.1021/ed070p254

https://www.sciencedirect.com/science/article/pii/S1878535210000973

The surfactant micelle formation accompanies the polyamorphic transition in water. Therefore, CMC can be determined by the change in the properties of water in the micelle formation region.

Preprint Quantum entanglement in micellar solutions of ionic surfactants.

Article Raman spectroscopy of micellization-induced liquid–liquid fl...

How about through conductivity measurements? It is fairly simple to do in the lab. Also, here is a ref that might be of your interest:

Article A Comparative Study of the Determination of the Critical Mic...

for non ionic surfactant you can measure with help of stalgmometer by surface tension method

Yes, Adrien Izzet, conductivity measurements are straightforward, but limited to anionic and cationic surfactants in aqueous solution free of electrolytes.

Adrien, further recrystallization using DI (18.2 MOhm-cm) and MtOH of ionic surfactants is required if their purity isn’t high enough. You probably get the good experimental CMCs from conductivity measurement.

There are 3 methods to determine the CMC.

-Tensiometry

-Conductometry

-And Fluoresce spectroscopy

You can find more details in the following publication:

The methods of determination of critical micellar concentration of the amphiphilic systems in aqueous medium.

Volume 4, issue 3 July 2011 page 265-270

Arabian Journal of Chemistry.

I hope this will help.

Fluorescence is powerful method to determine CMCs .Due to the sensitivity of the method a very low concentration of an added fluorescent probe is needed which doesn't affect the value expected for the CMC. . Look up at these two typical references :

Langmuir 2005, 21, 15, 6688-6695 and Analytical biochemistry 139, 408 1984

@ 6 days ago

Jean Paul Canselier

Dear All, interesting topic. I am looking for a laboratory that can determine CMC. Has anyone good suggestions for a reliable laboratory? Thank you!

Ellen Damen

Hopefully, they could do that, for example, in the Department or Laboratory of Physical Chemistry and Soft Matter at Wageningen University.

Regards,

JPC

That is so simple to do, that getting outside help is unecessary. See doi:10.1016/0003-2697(84)90026-5 (fluorescence) or doi:10.1006/abio.1993.1039 (absorbance).Both methods are based on the fact that hydrophobic marker molecules partition into the core of micelles, once those form.

Both cmc and \bar{m} depend on conditions, so their determination is routine in a lab that uses detergents.

According to previous answers, seems to be simple to "measure" this property but there are some ideas that I think could help to have a better understanding about the determination of cmc. First, it is a property that it is not measured but determined through the experimental measurement of an appropiate physicochemical property of the syste munder study (aqueous solution of a sufactant). The trend of the value of the selected property as a function of surfactant concentration has to cover the region of concentration below and above that of the cmc. Depending on the sensibility of the selected property to determiine or derive cmc, it should show an abrupt change in its tendency to have the possibility of better defining the region of concentration corresponding to cmc. Another point is that, there are some models (empirical or theoretical) that can be used to give an estimate of the cmc, this is another approach to have the possibility of defining this concentration. The behavior of the system under study would show a different performance below and above this cmc, for example, in promoting the solubility of a given component in a liquid bulk phase. And this, would determine the performance of a given surfactant in the different applications were these are used. I will continue contributing about this.

Thank you, Ascencion Romero-Martinez, that is right except that surfactant concentration (c) as such is not always the best abscissa to get an abrupt change on the graph: this may be log c, c1/2 or 1/c, for instance, according to the measured property.

already a question of long history, so to remind the more or less abrupt change of a property can be also due to other reason, e.g. due to passing the solubility limit without formation of micelles.

The Critical Micelle Concentration (CMC) can be measured using the intrinsic viscosity. This concentration is determined by ploting the specific viscosity as a function of the overlap parameter; the CMC corresponds to the chages of the slop in this graph. For further information, you can see the article entitled "The rheological behaviour of a water-soluble polymer (HEC) used in drilling fluids", Article The rheological behaviour of a water-soluble polymer (HEC) u...

HEC does not form micelles, critical overlap concentration is different from cmc. But your example highlights the problem - a break point may indicate micelle formation, but also solubility limit, critical overlap concentration of polymers ...

How to calculate CMC? Best equation?

@ Prakash Karunanithi,

For pure straight-chain alcohol ethoxylates, a relationship was published:

L.J.N. DUARTE et J.P. CANSELIER

Cloud point, critical micelle concentration and HLB relationships for alcohol ethoxylates

PharmaChem, 2005, 4(3), 36-39.

For other linear compounds, the Stauff-Klevens equation is often used:

log cmc = a - b.n (n: number of methylene groups)

a and b specific for each homologous series

Regards,

Jean Paul Canselier

Here is a cost-effective method for the determination of CMC using UV-Visible Spectroscopy, kindly read this paper... "Bioreducible polyethylenimine core-shell nanostructures as efficient and non-toxic gene and drug delivery vectors"

DOI: 10.1016/j.bmc.2022.116886

Conductivity measurement is simplest method for CMC determination ( sample preparation is adjusted near by CMC value)...pure checking after reproducible sample cheking

Conductivity measurement is simplest method for CMC determination ( sample preparation is adjusted near by CMC value)...pure checking after reproducible sample cheking

pure: ionic surfactant CMC measured by Conductivity matter,

UV, fluorescence is also measured by CMC

pure surfactant ? or any addition of surfactant?