Knowledge of the phase behavior of polymer systems is very useful in the design and optimization of polymerization reactors and separators where control of the phase behavior (in order to avoid or to induce a phase transition) is essential. While there is a large body of experimental data on the phase behavior of polymer systems, experiments under high pressures and/or involving components at supercritical conditions can be difficult and expensive to perform. As a result, an efficient and robust theoretical modeling tool that can be used to predict the thermodynamic properties of polymer systems and extrapolate to regions of the phase diagram where experimental measurements are not available is needed. Over the past decade, significant efforts have been focused on developing molecular-based equations of state (EOS) to model polymers. Within these EOS, the statistical associating fluid theory (SAFT)¹ has been successfully applied to study the thermodynamics and phase behavior of several polymer systems in which the polymer is modeled as a very long flexible chain composed of tangentially bonded spherical segments, e.g., polyethylene (PE) can been treated as a very long n-alkane chain. However, a major problem in modeling polymer systems is characterizing and determining the model parameters for polymers that posses a structure more complex than PE, such as capturing the presence of branching (i.e., side chains in the backbone) and/or heterogeneity (e.g., functional groups of different molecular composition) in the polymer structure. Generally, in the SAFT approach pure component parameters are obtained by regressing experimental vapor pressure and saturated liquid density data. However, identifying pure-component parameters for a polymer is more difficult and is afflicted with a higher degree of uncertainty compared to the case of volatile substances since vapor-pressure data are not available. As an alternative, pure polymer EOS parameters are usually calculated by fitting to melt PVT data, but they do not work well when applied to the description of mixture phase behavior (see for example 2). Several approaches³ have been proposed to obtain these pure-parameters for different types of polymer but suffer the common limitation that the parameters are pulled together in a somewhat ad hoc way and results in pure component and/or cross parameters being fitted to experimental mixture data, thus reducing the predictive ability. In order to make the SAFT EOS a more predictive approach, parameters must be used in a transferable way and the dependence on experimental data reduced. In earlier work⁴, a predictive molecular-based group-contribution-based SAFT approach (GC-SAFT-VR) was developed based on the hetero-segmented version of the statistical associating fluid theory for potentials of variable range (hetero-SAFT-VR)⁵. The hetero-SAFT-VR approach models molecules composed of segments of different size and/or energy parameters enabling an accurate description of real molecules composed of different functional groups. Through the GC-SAFT-VR approach we can study the effect of molecular functionality and topology on the thermodynamic properties of real fluid systems as parameters are determined for each functional group and chain connectivity is explicitly specified. Parameters have been determined for several key functional groups (CH₃, CH₂, CH₂=CH, C=O, C₆H₅, CH₃O and CH₂O) by fitting to experimental vapor pressure and saturated liquid density data for a number of small molecules containing the functional groups of interest. The transferability of the parameters obtained for each group was tested by predicting the phase behavior of pure fluids not used in the fitting process and binary mixtures of alkanes, ketones, and esters. In this work the molecular parameters developed for the key functional groups in the GC-SAFT-VR EOS are used in a transferable way to study the adsorption of hydrocarbons in polymer systems. In particular, the vapor liquid equilibrium of polymer solutions including low-density polyethylene (LDPE), polyethylene (PE), polybutadiene (PBD), and polystyrene (PS) with a variety of polar and non-polar solvents are considered. The theoretical results obtained using the GC-SAFT-VR approach are in good agreement with the experimental data, showing the importance of the effect of molecular functionality of the different polymers on phase behavior.

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