Soap with water forms :

Soap molecules are amphiphilic, consisting of a hydrophilic (water-attracting) polar head and a hydrophobic (water-repelling) non-polar hydrocarbon tail. When mixed with water, these molecules self-assemble into organized structures.

• Lyotropic liquid crystals are phases where the liquid crystalline properties are induced by the concentration of a solute in a solvent (typically water), alongside temperature.
• When the concentration of soap in water increases, the molecules form various ordered structures like micelles, hexagonal, or lamellar phases. This concentration-dependent behavior is the defining characteristic of lyotropic systems.
• In contrast, Thermotropic liquid crystals change phases based solely on temperature changes (commonly used in LCD screens), and Metallotropic crystals involve metal-organic complexes.

Since the phase behavior of soap depends on its concentration in water, it is classified as a lyotropic liquid crystal.