A new cell model for equation of state of polyethylene melt and n-alkane

The connectivity of successive carbon atoms in polymer decreases the degrees of freedom, and hence, the external degrees of freedom should correspond only to translational motion. We therefore, introduce a coarse-grained particle of a few successive monomers. A cell model (or the hard core model with attractive potential) for the particles can accordingly be used for the derivation of the equation of state of polymers. Modifying the classical cell model by Lennard-Jones and Devonshire, we construct a new equation of state for polyethylene melt and for liquid n-alkane; the free volume term is modified by using the Sutherland potential instead of the Lennard-Jones potential. The characteristic quantities P*, V*0, and T* in the equation of state are almost independent of temperature; the principle of corresponding state holds well. Since our equation of state contains the external degrees of freedom explicitly, we can evaluate the external degrees of freedom, c, for CH2. The value of c for the coarse-grained particle is equal to 1, and hence the particle is composed of 1/c repeating units. The linear length of the particle evaluated, 4.09 A at 0 K, is consistent with that obtained by neutron and x-ray scatterings.