We now apply the RISM formalism to polymeric liquids . For simplicity we restrict the presentation to
polyethylene , each
CH2 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
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
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=400K. The corresponding intermolecular correlation function is given in Fig. (2.6).