An approach to expediting phase equilibrium calculations for polydisperse polymers

It is shown that the equilibrium ratio between mole fractions of a polymer pseudo-component in any two phases is related to the molar mass of the pseudo-component in a simple way. The relationship permits evaluating all the equilibrium ratios for the polymer components in terms of any two. This property holds true for all the equations of state commonly used for polymer–solvent phase equilibria.The consequence is that only two equilibrium equations have to be solved for any polydisperse polymer, regardless of the number of pseudo-components. Equilibrium for the other pseudo-components is guaranteed when the dependence between the equilibrium ratios is accounted for.The paper presents a Newton–Raphson formulation of cloud-point calculations equivalent to that proposed by Koak and Heidemann but with a reduced number of equations to be solved regardless of the number of components used to characterize the polymer. It is shown that computations of many different kinds can be performed within the same general problem formulation.