Critical compressibility factors for chain molecules

For many proposed equations of state for fluids composed of chain-like molecules, the compressibility factor is related to the chain number concentration only through the total monomer concentration. For these theories, the virial coefficients do not scale correctly with the chain molecular weight in the long chain limit, which can lead to a poor description of the phase diagram. In addition, for equations of state that are analytical at the critical point, it is found that the critical compressibility factor approaches 1/3 in the limit of infinitely long chains, contrary to experimental trends. Appropriate scaling leads to the proper trend for the compressibility factor, as demonstrated with a simple equation.