Micelles are formed only above the Kraft temperature. We know ∆G = ∆H - T∆S (Gibbs energy relation).
For micelle formation to be spontaneous, ∆G has to be negative. This implies ∆H - T∆S has to be negative. Since spontaneity increases with temperature, this must mean that ∆S is positive. However this seems counter-intuitive because when micelles form, they come together. Shouldn't this actually decrease the entropy?
You are forgetting that the micelles form in water which is polar and forms hydrogen bonds. The micelle formation is primarily entropically driven. For isolated surfactant molecules the polar head groups can stabilise water molecules around them, but the hydrocarbon chain is hydrophobic and so polar water has to bridge over this part of the molecule forming specific hydrogen bonds to do so. This reduces the water's entropy as these water molecules are more or less fixed in place. As more surfactant is added more water is forced into in this relatively low entropy state. At and above the CMC it is entropically more favourable to form a micelle. Lots of water molecules are now free up to take their normal behaviour, with increase in entropy, as the surfactant tails largely cluster together inside the micelle and the polar head groups are on the surface and interact with the water in just the same way as isolated surfactant molecules. The entropy decrease in forming relatively few micelles is overwhelmed by its increase in releasing numerous water molecules.
