An equation of state for melts of linear homopolymers

We analyze the capability of the continuous Gaussian chain model to describe melts of linear homopolymer chains. We derive the equation of state of a system of n interacting chains by including long chain correlations by means of the one loop diagrams. These correlations which give rise to two combinations of the molecular parameters are found to be necessary for the proper quantification of pressure-volume-temperature (PVT) behaviour of the melts. The adjustment of the value of the prefactor of the small density term which is in accord with the liquid character of polymeric melts lead to a complete agreement between the experimental results and the outcomes of the theory. The proper dependence on the molecular weight is also predicted and isotherms of narrow distribution polystyrenes of three different molecular weights are used for the evaluation of the molecular parameters.