Variation of CMC with Intensive Parameters

A general feature of the CMC is the weak temperature variation compared to most other chemical association phenomena3 ). As regards the details, several types of behavior have been observed The CMC may increase or decrease with increasing temperature or it may show a pronounced minimum. Examples of temperature dependences are shown in Fig. 2.5. 

The pressure dependence of the CMC is weak even up to quite high pressures as exemplified in Fig. 2.6 for sodium dodecanoate32.  

While for nonionic systems, the effect of inorganic salt on CMC is small, it is large for ionic surfactants and this difference is expected since the micelle - small ion interaction must be completely different in the two cases. The decrease in CMC for ionic systems corresponds usually to a linear relation between the logarithm of the CMC and the total counterion concentration, if a salt of the counterion is added. For divalent ions, the slope of the plot of log CMC versus counterion concentration is half of that of monovalent ions. 

As expected, the influence of added nonelectrolytes can be quite different depending on whether the added compound is likely to be located in the micelles or in the in-termicellar solution. The effect of normal alcohols has been studied in detail for potassium dodecanoate the CMC is lowered for all alcohols studied but the effect increases considerably in going from ethanol to decanol (cf. Fig. 2.7). Hydrocarbons, like cyclohexane, n-heptane, toluene, and benzene, have been found to lower the CMC for many surfactants. Strongly hydrophilic substances, like dioxane and urea, have small and complex effects. At higher concentrations they markedly increase the CMC or even inhibit micelle formation. Addition of another similar surface-active agent generally gives a CMC in between the CMCs of the two surfactants. 

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