Soap has a complex and difficult to define structure. At the beginning of the manufacturing process, when fats are heated with liquid alkali, the resulting product, called “neat soap,” has a liquid crystal structure (specifically a lamellar smectic structure). In this state, the soap is a iiquid, but has a crystalline lattice structure who’s molecules slide freely against each other.
Neat soap contains a lot of water, so if the desired end product is a solid bar or flake form, the neat soap is chilled and dried. During the chilling process, crystals are formed that can have different morphologies, depending on the temperatures used. Most of these would be considered solids, since they no longer posess the sliding characteristics of the smectic phase. During the drying process, most, but not all, of the water is removed. The remaining water is somehow bound in the solid lattice of the soap crystals. So bar soap might best be described as a solid solution.