This thesis extends and applies statistical associating fluid theory (SAFT) to model phase behavior in polydisperse polymer solutions. SAFT is a molecular based equation of state, used for modeling thermodynamic properties of chain molecules. Knowledge of phase behavior in polymeric systems is important at all stages of polymer processing and manufacturing and is essential for controlling the properties of the polymer, optimizing separation conditions and choosing operating conditions to mitigate fouling due to phase splitting. In particular this thesis has four main contributions. First, we evaluate the ability of the SAFT formalism to model the effect of solvent shape on phase behavior. We develop a model for the incipient agglomeration temperature in a slurry polymerization reactor by correlating agglomeration to the solid-liquid phase transition in the reactor. We demonstrate that the model can predict the effect on agglomeration of cyclic, linear or branched carriers. Secondly, we evaluate the ability of the Perturbed-Chain extension to SAFT (PC-SAFT) to model gas solubility in long chain fluids at conditions of high pressure and high temperature. PC-SAFT, unlike conventional approaches, is shown to correctly account for the dependence of phase behavior as a function of chain length asymmetry between the solute and solvent. Thirdly, we develop robust and efficient algorithms that allow stability analysis and phase equilibrium calculations in molecular weight polydisperse polymer as well as copolymer solutions using a methodology where the size of the system of equations specifying equilibrium is independent of the number of pseudocomponents used to represent the polymer molecular weight distribution. Finally, we present a novel approach to account for the effect of compositional polydispersity in dipolar copolymer solutions where the size of the system of equations specifying equilibrium is independent of the number of pseudocomponents used to represent the compositional distribution. Compositional polydispersity refers to the fact that there is a distribution with respect to the comonomer incorporation in the various pseudocomponents of a copolymer. We then use the algorithm to elucidate the effect of pressure, molecular weight, average comonomer concentration and compatibilization on the phase behavior of compositionally polydisperse dipolar copolymer solutions
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