as long as a surfactant forms micelle in the solvent, there is a critic concentration for this formation and to the best of my knowledge this is true for all liquids. this concentration also depends on the hydrophilic lipophilic balance of the surfactant.
yes I join John George Hardy for his answers, it depend on the solvent, the ionic strength and other physical parameters such as the type of solvent aprotic or not, polar or other one etc...
Correct that CMC will depend strongly on solvent, as solvent modulates how strong the hydrophobic effect is and the relative strength of charge-charge interactions. Furthermore, I would also add that even in water, the CMC depends significantly on factors/additives such as ionic strength, presence of buffer etc etc. For example, for ionic micelles, ionic strength can help screen repulsive interactions between head groups and hence impact upon the CMC. As such, your CMC has to be precisely defined for the exact conditions in which it is measured.
In the case company producer informs about CMC, that is for water. CMC of ionic urfactants should depend on the water ionic content, so, a user should check CMC on his / her own.
Just an exemple of determination of the CMC of benzalkonium chloride in NaOCl thanks to 2 methods: https://www.researchgate.net/publication/232249292_Wetting_properties_and_critical_micellar_concentration_of_benzalkonium_chloride_mixed_in_sodium_hypochlorite
Article Wetting Properties and Critical Micellar Concentration of Be...
The CMC of a surfactant depends on the structures of surfactant and the solvent, the temperature, the ionic strength. In general the CMC of the surfactant is related to its solubility. If you are dealinig with one surfactant in two different solvents, as the solubility of the surfactant increases when you change the solvent, the CMC decreases.
CMC is not common for all solvent. Apart from the many parameters listed by fellow researchers, i would like to add chemical structure and concentration of solute, monomer or polymer you would like to encapsulate in the micelles (if that is the case).
Yes, CMC values of the surfactant is highly dependent on solvent. Apart from the specific characteristics of solvent (as mentioned by other researcher), the original surface tension value of the pure solvent and nature of the surfactant also. But in general, CMC value is dependent on nature of solvent.