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I was reviewing the thermodynamics of micelle formation from the Wikipedia page and this book. I understood most of the arguments but micellization is supposed to be an entropy driven process with a positive entropy change in the process of micellization. But isn't this a bit counter-intuitive?

In the unassociated form, the surfactant molecules are free to roam about in the solution much like normal solutes. But in the form of a micelle, they get associated, grouped into an associated whole, which reduces the freedom of independent movement and should therefore decrease the entropy (randomness) of the system? The entropy change should be negative during micellization. Why is it positive?

I understood the mathematical arguments leading to the develpment of the approximate formula $\Delta G=RT\ln(\text{CMC})$.

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  • $\begingroup$ Where are you quoting that part from? It doesn't seem to be quoted... $\endgroup$ – Gaurang Tandon Mar 23 '18 at 11:58
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The micellization releases water molecules which initially solvate the hydrophilic head groups. The release of these waters greatly increases the entropy.

Reference: Dong et al., Chem. Rev. 2010, 110, 4978-5022.

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This is due to release of solvent molecules attached with non polar tails of surfactant monomer by hydration during self organistaion. The entropy gain by this process exceeds the entropy loss due to amphiphillic association or solvation making the overall entropy change positive.

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In order to accommodate the hydrophobic tail of the free surfactant, the hydrogen-bonded structure of bulk water must be distorted. A nonpolar hydrocarbon cannot form hydrogen bonds with water and thus water molecules in the immediate vicinity of a hydrocarbon are constrained in the possible orientations that it can assume. Therefore, water molecules around a hydrophobic chain are more ordered which is unfavourable as it results in a decrease in conformational entropy. When all the hydrocarbon chains are hidden inside micelles, the structure of bulk water is largely restored leading to an increase in the conformational entropy. Thus, micellization is an entropy-driven process that seeks to minimize the free energy of a system by minimizing the interface between hydrophobic molecules and water. The increase in the conformational entropy of water more than compensates for the negative aggregation entropy of the surfactants themselves (surfactants are becoming more ordered on micelle formation).

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