# How do salt additives and impurities affect a critical micelle concentration?

So I understand that a CMC typically decreases as more salt additives are added. What I am not clear on is how exactly.

The head groups are charged in this example (one anionic and one cationic) so I am not sure how the salts would impact this? There is a counter-ion present as well.

Thank you so much for your response, its really helpful. I'm just learning about CMC and micelle so please forgive my silly questions. When you lower a CMC, are the micelles themselves now smaller or bigger? And when the literature describes micelles as smaller, does this mean the circumference is smaller, or the number of detergent molecules is smaller.

Would the presence of salt additives and impurities be of greater concern in measuring CMC by absorbance, fluorescence or conductivity???

In a solution with two dissociated ionic detergent molecules of equal charge (say two anionic detergent molecules $$\ce{A^-}$$), their interaction will be dominated by two effects:

2. Hydrophobic interactions

The first contribution, electrostatic repulsion, will oppose the second and discourage association of the detergent molecules.

If you instead mix two oppositely charged detergents, $$\ce{A^-}$$ and $$\ce{B^+}$$, the electrostatic headgroup interaction will now encourage association. All else (e.g. tail length) being equal, this means mixed micelles will have a lower critical micelle concentration (CMC) than pure detergent at the same total concentration.

Adding salt (say $$\ce{NaCl}$$) to a charged detergent will also lower the CMC, for essentially the same reason as for mixed micelles (electrostatic repulsion is reduced).

Now comes the tricky part. If you add salt to a mixed detergent system, you set up possible competition between electrostatic attraction of salt and headgroups, with electrostatic attraction of oppositely charged headgroups. Individually, either attractive interaction has a tendency to lower the CMC. The question is what effect they will have together. My educated guess is that the effect of salt on mixed micelle systems will be subtle and complicated. The CMC will be further reduced, but interactions between oppositely charged detergent molecules will predominate so the effect of added salt will be minor.

When you lower a CMC, are the micelles themselves now smaller or bigger? And when the literature describes micelles as smaller, does this mean the circumference is smaller, or the number of detergent molecules is smaller?

I don't think there is a universal answer to the first question. I will have to wave my hands a little, and say it depends on the detergent, solvent, and temperature. However if you look at a table of aggregation numbers and CMCs for different detergents, you'll usually see that the ones with a lower CMC (for instance, nonionic detergents) also have larger aggregation numbers.

The second question is easier to answer than the first. The size of a micelle can be measured by a number of different techniques. The aggregation number is often derived by making assumptions about packing in the micelle and starts from estimates of the sizes of the micelle and detergent molecule. So it's pretty safe to generalize that both the dimensions of the micelle (the effective diameter say) and aggregation number are reduced in smaller micelles.

• Thank you so much for your response, its really helpful. I'm just learning about CMC and micelle so please forgive my silly questions. When you lower a CMC, are the micelles themselves now smaller or bigger? And when the literature describes micelles as smaller, does this mean the circumference is smaller, or the number of detergent molecules is smaller? – Harley McFarlen Mar 9 '19 at 11:54
• Won't mixing an anionic and a cationic surfactant result in precipitation of the two oleophilic parts as a fat or oil, while the smaller ions stay in solution? – James Gaidis Mar 9 '19 at 14:34
• @HarleyMcFarlen I added an answer to your question to the body of my answer. – Buck Thorn Mar 9 '19 at 14:47
• @JamesGaidis While what you write may be true in some cases, for some detergents at lower concentrations it is possible to form stable mixed micelles near the isoelectric point. – Buck Thorn Mar 9 '19 at 14:48
• Thanks for everyone's help! Ill keep picking away at it. – Harley McFarlen Mar 9 '19 at 21:17