APPLICATION OF THE VAN-DER-WAALS-EQUATION OF STATE TO POLYMERS .4. CORRELATION AND PREDICTION OF LOWER CRITICAL SOLUTION TEMPERATURES FOR POLYMER-SOLUTIONS

The van der Waals equation of state is used for the correlation and th e prediction of the lower critical solution behavior or mixtures inclu ding a solvent and a polymer. The equation of state parameters for the polymer are estimated from experimental volumetric data at low pressu res. The equation of state parameters for the solvent are estimated vi a the classical Soave method, i.e. using the critical properties and a generalized equation for the energy parameter. When extended to mixtu res, the van der Waals one-fluid mixing rules along with the Berthelot combining rule for the molecular cross energy parameter are used. The arithmetic mean combining rule is used for the cross co-volume parame ter. The deviations from the Berthelot combining rule are taken into a ccount via a simple expression which has been previously obtained from vapor-liquid equilibrium data of athermal polymer solutions and has b een successfully used for the prediction of upper critical solution te mperatures for various binary polymer solutions. In this work, we demo nstrate and explain some of the problems which cubic equations of stat e exhibit in describing the lower critical solution behavior for polym er solutions. These problems are overcome by using a temperature-depen dent interaction parameter, even for small temperature ranges, leading to excellent results. Despite the problems, we have developed an empi rical methodology in using the van der Waals equation of state with a single interaction parameter for predicting the lower critical solutio n behavior of polymer/solvent solutions. The results are satisfactory. typically, the difference between the predicted and the experimental lower critical solution temperatures is between 10 and 35 degrees C.