Critical compressibility factors for chain molecules

For many proposed equations of state for fluids composed of chain-like mole cules, the compressibility factor is related to the chain number concentrat ion only through the total monomer concentration. For these theories, the v irial coefficients do not scale correctly with the chain molecular weight i n the long chain limit, which can lead to a poor description of the phase d iagram. In addition, for equations of state that are analytical at the crit ical point, it is found that the critical compressibility factor approaches 1/3 in the limit of infinitely long chains, contrary to experimental trend s. Appropriate scaling leads to the proper trend for the compressibility fa ctor, as demonstrated with a simple equation.