LIQUID-LIQUID EQUILIBRIA FOR SOLUTIONS OF POLYDISPERSE POLYMERS - CONTINUOUS THERMODYNAMICS FOR THE LATTICE FLUID MODEL

A continuous-thermodynamics framework is presented for phase equilibrium calculations for solutions of polydisperse polymers using a lattice-fluid model. A two-step process is designed to form a real solution containing a solvent and a polydisperse polymer solute at fixed temperature and pressure. In the first step, close-packed pure components are mixed to form a close-packed polymer solution. In the second step, the close-packed mixture, considered to be a pseudo-pure substance, is mixed with holes to form a real polymer solution whose volume depends on temperature and pressure. The simplified Freed model developed previously is adopted for both steps. Besides pure-component parameters, the theory uses a binary size parameter c(r) and a binary energy parameter epsilon12; these binary parameters may be temperature-dependent, The functional approach is adopted to derive expressions for chemical potentials, spinodals and critical points. Computation procedures are established for cloud-point-curve, shadow-curve, spinodal and critical-point calculations for polymer solutions using either a standard distribution or an arbitrary distribution for the polymer molar masses or chain lengths. Calculations are shown for the effect of polydispersity on upper critical solution temperature (UCST), lower critical solution temperature (LCST) and hour-glass-shaped phase behavior for the system acetone-polydisperse polystyrene.