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Most of the books dive into formation of micelles by soaps. They go on talking about alkyl sulphate and carboxylates, but never do they mention anything about cations. My textbook says that at critical micelle concentration, molecules of colloid aggregate to form micelles.

Can things like $\ce{RNH4+}$ or $\ce{R4N+}$ form micelles, why/why not?

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Cationic micelles similar to your examples can and do exist. For example cetyl trimethylammonium bromide (Growth of Cationic Micelles in the Presence of Organic Additives, P. A. Hassan and J. V. Yakhmi, Langmuir, 2000, 16 (18), pp 7187–7191, DOI: 10.1021/la000517o).

Additionally, there are cationic micelle detergents (Ionization of cationic micelles: Effect of the detergent structure, Journal of Colloid and Interface Science, Volume 78, Issue 2, December 1980, Pages 330-337).

The bottom line is that there are a variety of use cases for cationic micelles, in detergents and otherwise.

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