  A simple application of classical density functional theory is derived and
applied to a system of polymers grafted to a plane. The system is assumed to
have symmetry in directions parallel to the grafting plane hence it being a
'1-dimensional' problem. A quick introduction to using propagators in the
theory of chains in the presence of external fields and a numerical algorithm
for solving the modified diffusion (or Fokker-Planck) equation are presented.
Density profiles are found for hard-sphere chains which agree with results in
the literature (see Murat,.., Milner,.., Muhukumar and others) and align with
physical expectations of brush formation due to excluded volume. The linear
scaling $h \approx (\sigma)^{1/3} N$, of brush height with polymerisation $N$,
is reproduced here.
