Hello Olli-Pekka,

If you have oil droplets dispersed in water (oil in water emulsion), the surfactant concentration in bulk will depend to some degree on the total interfacial area. The interfacial area will therewith not directly affect CMC but the amount of surfactant necessary to reach CMC. If you know the total volume of dispersed phase as well as the average droplet size, you might calculate the total interfacial area and use an approximate value of interfacial excess (amount of molecules adsorbed to a unit area) to estimate the ratio of surfactant molecules originally in solution and surfactant molecules at the interface. Using this ratio, you will be able to estimate how much droplet size influences surfactant concentration. But you should also consider that the droplet size will be a function of the surfactant concentration. Thus, I would suggest to measure the CMC of a clean surface/interface before you start working with emulsions.

If you should have further questions or feel that I got your question wrong, please feel free to contact  me.

Best regards,

Thomas

Molecular (interfacial) area and CMC of a molecule are not generally correlated. It is rather easy to understand, why this is only exceptionally the case. Interfacial area of an amphipat is determined by balance of forces (or, more generally, interactions) between hydrophobic / apolar and hydrophilic / polar molecular parts (for an illustration pertaining to phospholipids see e.g. Cevc, G., & Seddon, J. M. (1986). Structural and Dynamic Consequences of Amphiphile Hydration: Their Origin and Analytical Molecular Force Theory. In Surfactants in Solution (pp. 243-252). Springer US.) Conversely, CMC is governed by (the free) energy of the studied amphipat transfer from an aqueous medium into an organic medium, or a micelle (taking the role of the latter). CMC is hence typically (but not always) correlated with the so-called hydrophile–lipophile balance number, or HLB, which is, in turn, (at least for many non-ionic surfactants) perfectly correlated / quasi-equivalent to the so-called Israelachvili–Mitchell–Ninham's packing parameter, IMN (see, e.g., P.  Becher (1984) Hydrophile–lipophile balance: history and recent developments. Langmuir lecture — 1983. J. Dispers. Sci. Technol. 5:81–96 and G. Cevc (2012) Journal of Controlled Release 160:135–146), which also explains the practical value of interfacial area for predicting dispersion properties.

Thank you very much for your answers. In practice, I still wonder the determination of phospholipid cmc in bulk oils. The commonly used method is the TCNQ-method (Kanamoto et al., 1981. Phospholipid-phospholipid Interaction in Soybean oil, JAOCS).

In the method the reverse micelles (the water pools inside) are dyed with TCNQ and then the absorption spectra of solubilized TCNQ is measured. The cmc is the point were the absorption start to rise significantly (due to the formation of reverse micelles).

However, does this method take into consideration the upper interfacial area (in laboratory cuvette) which has to be first become fully saturated before the monomers in oil can reach the cmc? Or is it so that this upper interface (air-oil) does not affect the cmc?

I attached a figure for better illustration of the question.

Olli Pekka, the interfactial area at the top has an insignificant effect on the amount of surfactant needed to reach a bulk concentration equivalent to the cmc.  If we follow Thomas's advice above we can easily illustrate this.

Assume that a molecule of surfactant occupies about 0.25 nm2 at the interface. Then the surface excess can be calculated in moles/m2 = 1/An x 0.25 nm2)  where An is Avogadros number. This is a surface concentration of ~6.6 micromoles per m2.  Now your surface area is perhaps 10 cm2. So the amount of surfactant adsorbed to your surface will be ~6.6 nanomoles.

This is a concentration that is well below the typical errors encountered in measuring the cmc.

As Thomas points out above, if you have another phase (eg oil droplets) that has a large surface area then this may become a significant factor. A simple calcualtion shows that you would need about 100m2 of interfacial area before you need to consider this effect.

A bigger concern is if your particular surfactant partitions between the phases. If it does so to a significant level you would need to know the partition coefficient and correct for the amount of surfactant lost to the other phase.

Hello Dear Professor

Cmc= (number of molecule surfactant )/(total volume)=(numbre of molecule in the bulk+numbre of molecule at the interface)/(total volume)=c(numbre of surfactant in the bulk)/v+(numbre of the molecule in the interface)/v=C0+S/V

C0 : constant

V : constant

S : change (in your illustrated example from 0 to S)

So

CMC2=C0 and CMC1=CMC 2+ s/v

S : number of surfactant in the interface

Nb: you can calculate the cmc1 and cmc2 and then deduct s y if you now the area of interface you can deduct the area per molecule

Naous, your idea is correct in theory but in most cases not practical. The surface area concentration is usually much smaller than the uncertainty in C0

For a pure (one component) surfactant cmc is obviously not related to surface or interfacial area. This is due to definition of cmc which is the monomer concentration in equilibrium, not the overall concentration in system. In case of solution phase in contact with air or a separate oil layer only, adsorbed amount at interface can be neglected. If there is partition into a second phase or onto dispersed phase of course, surfactant added in necessary amount to form micelles in solution may result in equilibrium concentration below cms. As already pointed out, with some assumptions it is fairly easy to calculate the amount of surfactant in continuous phase. You may find a further example at https://www.researchgate.net/publication/266200125_Short_communication_Mass_balance_and_emulsion_stability?ev=prf_pub.

If your surfactant is a mixture than kind of interface and interfacial area will have an effect on cmc because it will change composition due to preferential adsorption of one component.

Technical Report Short communication: Mass balance and emulsion stability

Thank you all very much for your answers!

The calculation examples really clarified the insignificance of the upper area and in some cases the droplet area also. Overall, this really made it much clearer for me to understand the concept of cmc itself.