Phase boundary calculations for solutions of a polydisperse polymer

A technique is described for performing phase boundary calculations (cloud- point calculations) for solutions of a polydisperse polymer in a solvent co mponent. The polymer is characterized as a potentially large number of indi vidual components. The technique employs the Newton method for solving the nonlinear equilibrium equations. The independent variables in the equations are logarithms of the equilibrium ratios, temperature and pressure, and th e mass ratio of polymer to solvent. A number of cloud-point curves were cal culated using the Sanchez-Lacombe equation as the thermodynamic model. The calculations were compared with experimental data for polyethylene (M-W = 1 77,000 and M-N = 8,000) with n-hexane and polyethylene (M-W = 99,000 and M- N = 56,000) with ethylene. As expected, the disperse nature of the polymer significantly affected the calculated phase behavior of the polymer-solvent mixtures. Complicating features in the calculations are discussed.