We now apply the RISM formalism to polymeric liquids . For simplicity we restrict the presentation to
polyethylene , each
CH_{2} will be viewed as one ''atom''.
It is clear that if boundary effects may be neglected, all monomers along
the chain are equivalent, i.e. that
and all other
functions do not depend on
or .
Remember that and
each run from 0 to *N*, where (*N*+1) is the number of
monomers per chain. The monomer-monomer radial distribution function then is

where is the monomer density. Introducing Eq. (2.34) into Eq. (2.35) we get

where . Using and in Eq. (2.31) we derive

(2.38) |

may be calculated using the methods of Chapter 1. Some details are given in Appendix A.

We now apply the method to polyethylene, which will be modelled by a RIS
model with characteristics given in section 2.6. The interaction between two
monomers on different chains is modelled by a hard sphere interaction with
diameter
.
Moreover *N*=6416 and
.
Calculations were done with PY closure.

In Fig. (2.3) is given the intermolecular distribution function.
We clearly see what is called the ''correlation hole'' by de Gennes ; the intermolecular distribution gradually rises to its
limit value 1, with only little structure. The scattering function is
given in Fig. (2.4), and is in perfect agreement with X-ray
experiments, except at very small values of *k*.

We give two more results, from MD simulations this time. In Fig. (2.5
) is given the intramolecular oxygen-oxygen correlation in PEO . The simulation was done with GROMOS united atom
potentials. The box consisted of two chains of 800 monomers each;
and *T*=400*K*. The corresponding intermolecular
correlation function is given in Fig. (2.6).