X-ray
Scattering From Soaps
Figure One shows a typical soap molecule and many other things drawn by a three year old child using his left-hand after drinking too much red cordial. Soaps have a tough life. Their head has polar atoms and bonds that dearly want to be hydrated by water. Their tail, though, is essentially hydrocarbon and wants to be in an oily environment. Soap molecules pack however they can to satisfy both heads and tails.
Micelles – The tails point inwards making an oily core while the heads point out towards the water.
Lamellar or Bilayer phases - Soap molecules line up in sheets with their heads pointing one way and their tails another. By backing two sheets of soap against each other the tails are happy while the heads can point towards water. This is the fundamental bilayer. Bilayers stack on top of each other in sheets because there isn’t so much water.
Inverted Hexagonal Phase - Soap heads point in towards a thin cylinder of water. Soap tails point out forming an oily fluid. At low energies the water cylinders line up in a hexagonal array.

Figure Two : Ivory Soap Scattering. (d=1.5mm X-ray capillary of soap scrapings,
200 second exposure ) The main ring
corresponds to a d-spacing of 42 Angstroms.

Figure Three : X-ray Scattering from
Lemon Scent Top Crest Dishwashing Liquid (100 seconds from a 1mm X-ray
capillary). The faint ring (peak
intensity around 20 counts per pixel) corresponds to the micel-micel c
orrelation length of about 35 Angstroms or so.
Figure Four : X-ray Scattering from Lemon Scent Top Crest Dishwashing Liquid
(200 seconds from a 1mm X-ray capillary) that’s been sitting on the table for
half a day. The bright ring corresponds
to a d-spacing of 35.5 Angstroms.
