Phase equilibria in polyethylene systems
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The background for this work is a need to better understand the production of high density polythylene (HDPE). HDPE particles grow in a loop slurry reactor, and particle swelling and slurry viscosity are critical parts in the process. This thesis is concerned with the thermodynamic aspects of liquid and solid polyethylene, and liquid-liquid and solid-liquid equilibria in solvent-polyethylene systems. It also covers studies of vapor-liquid and solid-liquid equilibria in solvent-n-alkane systems. In order to better understand the morphology of polyethylene, which is of importance in solid-liquid equilibria, experimental work has been conducted. This involved thermal analysis by differential scanning calorimetry (DSC) and X-ray diffraction. In order to model phase equilibria at all pressures, it is necassary to have an equation of state. We have chosen the Sako-Wu-Prausnitz cubic equation of state, which had shown some promising results. However, in order to statisfy our demands, we had to modify it slightly and fit new pure component parameters. Chapter 2 covers this development. New pure component parameters have been determined for ethylene and the n-alkane series, using vapor pressure data, saturated liquid volume and one-phase PVT-data. For higher alkanes, where vapor pressure data are poor or not available, determination of the pure component parameters was made in part by extrapolation and in part by fitting to one.phase PVT-data. Using one-fluid van der Waals mixing rules, with one adjustable interaction parameter, good correlation of binary hydrocarbon system was obtained, except for the critical region. The extension of state to polythylene systems is covered in Chapter 3. Pure component parameters for polyethylene were determined from a combination of extrapolation and fitting to PVT-data. In order to describe the molecular weight distribution of the polymer using pseudocomponents, a comparison was made between four theoretical distribution functions: the Schulz-Flory, Schulz, Tung, and logarithmic-normal distribution. In comparison with GPC measured molecular weight distributions of four polyethylenes with polydispersity ranging from 1.7 to 7.3, the logarithmic-normal distribution was found to show the best agreement with the experimantal data. Using the determined parameters, flash and cloud point calculations were performed, treating the polymer as both monodisperce and polydisperse. For the mondisperse case, the interaction parameter kij for the investigated systems, was found to improve the desciption of the ight phase, while the description of the heavy phase was slightly poorer. When correlating an ethylene-polyethylene system at temperatures from 413.15 K to 443.15 K, a temperature dependent kij, was required. In Chapter 4, a solid-liquid model has been developed on the basis on a modification of the Sako--Wu-Prausnitz cubic equation of state. For low-pressure systems, good agreement with experimental data has been achieved for the investigated systems. For high pressure it is necassary to consider the effect of pressure on the properties of solid and subcooled liquid, i.e. the volume change upon melting, to get the correct slope of the solid-liquid transition curve with respect to pressure. General correlations for the volume change upon melting for solutes have been developed for respectively even-and odd-numbered n-alkanes from high-pressure (up to 900 MPa) solid liquid data for pure n -alkanes. Having general correlations makes the implemantation of the volume change integral very easy. In this way the volume change integral can be used for any equation of state, since it does not need any input from the equation of state. To our knowledge, solving the pressure dependancy in high-pressure solid-liquid equilibria in the way has not been done before. Three high-pressure system have been investigated: propane - n-tectracontane (P up to 120 MPa), methane -n eicosane (P up to 90 MPa) and methane - n-tetracosane (P up to 270 MPa). Using the general correlations for the volume change upon melting in the solid-liquid model gives good agreement with the experimental solid-liquid transition data. The maximum deviation on solid-liquid transition temperature is 5 K and is obtain near the critical point for the mixture. This is caused by the fugacity coeffecient term calculated from the equation of state. The critical region is the weakest point of the Sako-Wu_Prausnitz equation of state and many other equation of state. In Chapter 5, the degree of mass crystallinity has been calculated from density, differential scanning calorimetry and X-ray diffraction data of several polyethylene and poly(ethylene-co-hexene) samples. Good agreement between the different methods have been found. It was found that for linear polyethylene samples, the mass crystallinity decreased as the number average molecular weight increased. it was also shown that increased hexene content in the chains, which increase the amount of branching, coused a decrease in mass crystallinity. For highly branched polyethylene samples it was found that the calculated average crystalline lamellar thiickness from DSC data was indepentent of thermal history, while for linear samples it was dependent of thermal history. A thermodynamic model has been developed in Chapter 6 for the calculation of solid-liquid equilibrium in polyethylene systems, where solvent is sorbed into the amorphous phase and swells the polymer. The model takes into account the elastic constraint in the amorphous phase caused by tie chains, connected between different crystalline lamellae. The model is very simple, needing only one extra parameter, in addition to the interaction parameter. Good description of experimental melting curves of polyethylene in solvent is obtained, when the extra parameter is treated as a constant. However, to obtain realistic swelling curves, it is necassary to treat this parameter as a function of mass crystallinity. This resulted in comparable calculated swelling of a high density polyethylene eith litrature data. For one investigated system, the calculated swelling curve is found to agree qualitatively with expermental viscosity data. In the future, the model might therefore be used as a tool for correlation and prediction of viscosity of polyethylene- solvent systems.