Modeling the Cloud Curves and the Solubility of Gases in Amorphous and Semicrystalline Polyethylene with the SAFT-VR Approach and Flory Theory of Crystallization

Abstract

The statistical associating fluid theory for potentials of variable range SAFT-VR [Gil-Villegas, A.; et al. J. Chem. Phys. 1997, 106, 4168] is used to examine the fluid-phase behavior of mixtures of n-alkanes, alk-1-enes (R-olefins), and nitrogen with polyethylene. The molecules are modeled as flexible chains of tangent spherical segments, with segment-segment dispersive interactions treated via square-well potentials. The parameters of the polyethylene polymer are determined from those of the n-alkanes by using simple extrapolations with molecular weight. As a test of the extrapolated parameters for polyethylene, the absorption (vapor-liquid equilibria) and cloud curves (liquid-liquid equilibria) of n-pentane-polyethylene systems are predicted without adjustable binary parameters, and the effect of the polymer parameters on the phase behavior of the mixture is discussed. The liquid-liquid immiscibility curve is found to be very sensitive to the intermolecular potential parameters used to describe the polymer. The change in the lower critical solution temperature (LCST) for mixtures of n-alkanes of increasing chain length in polyethylene is also predicted. Good agreement with experimental data is also obtained for the absorption of small gases in amorphous polyethylene. The predictions of the SAFT-VR approach confirm experimental findings that the solubility of nitrogen increases with temperature while the solubility of heavier molecules such as ethene and but-1-ene decreases. Strong synergies can be observed when several gases absorb in the same polyethylene polymer. The co-absorption effects are explained in terms of the interactions between gas and polyethylene molecules. When the temperature of interest is below the melting temperature of polyethylene, the polymer exists in a semicrystalline state. In this case, the crystallinity of polyethylene has to be taken into account in order to predict the solubility of the various gases. We present an accurate theory to predict the crystallinity of polyethylene as a function of temperature. The approach, which is based on Flory’s theory of copolymer crystallinity [Flory, P. J. Trans. Faraday Soc. 1955, 51, 848], is accurate for a large variety of polyethylene samples, and requires only the experimental crystallinity or polymer density at 25 °C as an input parameter. On combining the Flory and SAFT-VR approaches, we can predict the solubility of various gases in semicrystalline polyethylene samples, by assuming that the molecules of gas only absorb in the amorphous regions of the polymer.