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Why does the entropy increase when a lipid bilayer forms from phospholipid molecules?
Phospholipids are amphiphatic molecules. They have two hydrophobic fatty acid group (hydrocarbons forming tails) and one hydrophilic group containing phosphate (forming head). They have equal areas of the hydrophobic part and the hydrophilic part.
When a phospholipid is placed in aqueous solution, the water molecules form a shell like surface around the hydrophobic lipid. Due to this, the water molecules are unable to make hydrogen bonds with other water molecules, leading to decreased freedom of movement and thus making, water molecules more ordered. Now as the entropy is defined as the degree of randomness or disorder, so ordered water molecules lead to decrease in entropy.
Now the physical basis of bilayer formation (a bilayer are two dimensional complexes of lipids with their phosphate group at the water bilayer interface and the fatty acids internal) is the hydrophobic effect which is the inability of fatty acid group to make H bond with water. There is a higher energy state for the water at the interface between fatty acids and water because H bonds are lost. So, the hydrocarbons (fatty acids) associate with other similar groups leading to bigger hydrocarbon molecules, and thus decreasing the contact area with water. The fatty acids can stabilize hydrocarbons in water by covering the hydrocarbon surface with their hydrophilic regions while the hydrophobic region associates with hydrocarbon. Due to reduced contact area, some of the molecules set free and thus increase the entropy of the system.