text: Polymer molecules within a brush are stretched away from the attachment surface as a result of the fact that they repel each other (steric repulsion or osmotic pressure). More precisely, they are more elongated near the attachment point and unstretched at the free end, as depicted on the drawing.
  More precisely, within the approximation derived by Milner, Witten, Cates, the average density of all monomers in a given chain is always the same up to a prefactor:
  where  is the altitude of the end monomer and  the number of monomers per chain.
  The averaged density profile  of the end monomers of all attached chains, convoluted with the above density profile for one chain, determines the density profile of the brush as a whole:
  A dry brush has a uniform monomer density up to some altitude . One can show that the corresponding end monomer density profile is given by:
  where  is the monomer size.
  The above monomer density profile  for one single chain minimizes the total elastic energy of the brush,
  regardless of the end monomer density profile , as shown in.