Micelles: Why Do They Form Despite The Order (= Negative Entropy???)

    Micelles, those interestingly shaped structures formed by surfactants, may seem to defy a fundamental principle of thermodynamics: the tendency of systems to move towards disorder (higher entropy). After all, micelle formation involves the organized arrangement of surfactant molecules, seemingly decreasing entropy. So, why do these ordered structures even form if that's the case?

(It may be surprising to know that the entropy change for micellization is indeed positive)

Arrangement of Water Molecules

The key lies in understanding the arrangement of water molecules around substances that are added to it:

Water's Randomness:

Water, in its pure form with nothing mixed in yet, is made up of water molecules just floating around, moving randomly, constantly creating, breaking, and re-creating hydrogen bonds with each other. This leads to a lot of disorder and chaos in the system, and hence a high level of entropy.

Random arrangement of water molecules at any instant

Another arrangement at some other instant

When Surfactants Come Into Play: 

When surfactant molecules (with hydrophilic head and hydrophobic tail) enter water, the random dance of water molecules is disrupted. Water molecules now have to arrange themselves around the hydrophobic tails, making sure to minimize contact with the surfactant and maximize hydrogen bonding with each other, hence becoming highly ordered near the surfactant molecules. This ordered arrangement of water molecules significantly decreases the entropy of water.

Ordered centers of water molecules around the surfactant molecules

The Entropy-Driven Solution: Micelle Formation

When a small amount of surfactant molecules are added, the impact on water is not a big deal, as the entropy is still high enough to not take any kind of action. It is when the surfactant concentration exceeds a certain amount, aka the Critical Micelle Concentration (CMC), that it becomes a problem worth addressing for the water molecules.

It is because now, this high concentration leads to numerous organizational centers of water molecules, which take out a lot of random water molecules and arrange them in an orderly fashion. Now there will be a significant decrease in the entropy. 

This is where micelles come into play. To minimize this entropy penalty, the surfactant molecules seek to form clusters to minimize their contact with water. This phenomenon is known as the Hydrophobic Effect. This clustering significantly increases the entropy of water as a large number of ordered water molecules around the hydrophobic parts are released.

The formation of micelles leading to the release of water and hence increase in entropy is shown in this simple illustration:

Notice how in the figure above before this, each surfactant molecule was individually surrounded by water molecules, while in this figure, the entire micelle is surrounded by water as a whole, which requires fewer water molecules to be ordered, resulting in an increase in entropy.

So that's how micelle formation leads to a positive entropy change, contrary to the seemingly negative entropy that one may infer from a superficial observation of only their ordered structure.