Modeling High-Pressure Gas-Polymer Sorpion Behavior Using the Sanchez-Lacombe Equation of State


Book Description

The Sanchez-Lacombe equation of state was used to model the sorption of high-pressure gases into solid, amorphous polymers or molten polymers. One adjustable parameter per binary pair, SL12, was used in the mixing rule to correct the deviation of the characteristic pressure of the mixture, P12*, from the geometric mean. The values of SL12 which gave the best fit of the available literature data for the carbon dioxide-polymethyl methacrylate, carbon dioxide-silicone ribber, ethylene-low density polyethylene, methane-polyisobutylene, methane-low density and high density polyethylene, and methane-polystyrene systems ranged from 0.020 to 0.194, except for the methane-low density system which had a negative value of -0.183. In all cases, the calculated sorption isotherms were in reasonably good agreement with the experimental data. The resultant swelling of polymethyl methacrylate and silicone rubber in the presence of high-pressure carbon dioxide was also well presented by the Sanchez-Lacombe equation of state. Keywords: Sorption, Swelling, Polymers, High pressure, Gases.







High-pressure Gases in Amorphous Polymers


Book Description

In this work, a parameterization strategy that allows the calculation of polymer molecular parameters from macroscopic properties of binary polymer solutions is presented. The proposed parameterization is demonstrated by reference to the PC-SAFT equation of state, but can be applied to any molecular-based model. The parameterization scheme has been developed in terms of the polymer-solvent interaction parameter and the Hildebrand parameter, which describe the molecular nature and extent of the polymersolvent interactions. The specification of these macroscopic properties yields a set of polymer parameters that are suitable for the description of thermodynamic properties and phase behavior of polymer solutions. In this way neither extensive experimental data nor complex minimization techniques are necessary, as is required for the current approaches for the estimation of pure-polymer parameters for SAFT-type equations. Using polymer parameters calculated from the proposed parameterization strategy, the PC-SAFT model could satisfactorily predict the phase equilibria, gas solubility and polymer swelling behavior of binary and ternary polymer solutions with different solvents, including nonassociating compounds such as n-alkanes, polar compounds such as ethers, esters and ketones, and associating compounds such as alcohols. A computational approach for building atomistic models for amorphous polymer networks in order to simulate their pore structure and gas adsorption properties is also presented. The computational approach replicates the basic reactivity rules of the selfcondensation reaction of dichloroxylene (DCX) via Friedel-Crafts chemistry and allows the formation of amorphous polymer networks, which are not possible to generate by structural X-ray crystallography/diffraction as is usually done for crystalline materials. The method is discussed for poly(dichloroxylene) networks, but can be extended to other polymer networks. Atomistic models were further refined by fitting to characterization data (i.e., bulk density, absolute density, micropore volume and elemental composition). These models were characterized by specific surface area and pore size distribution. A sensitivity analysis was performed to determine the minimum box size that should be used in adsorption simulations. Simulated adsorption isotherms and isosteric heats for methane and hydrogen were found to be in reasonable agreement with the experimental data.
















Modification of Polymer Blend Phase Behavior with High-Pressure Carbon Dioxide


Book Description

While much progress has been made since the time of Flory and Huggins in the understanding of polymer blend thermodynamics, and ongoing research continues to elucidate how polymer blend phase behavior is affected by the presence of small-molecule solvents or exposure to elevated pressures, very little work has been reported on the combined effects of a pressurized small-molecule solvent on polymer blend phase behavior. The focus of this research is to improve the current state of fundamental understanding regarding how and why the phase behavior of polymer blends changes as pressurized carbon dioxide (CO2) is added. The first part of this work provides a broad overview of previous efforts that explore various thermodynamic and kinetic processes involving the use of CO2 in conjunction with multicomponent polymer systems. The following chapters discuss details of research performed primarily on three blend systems: polystyrene (PS)/polyisoprene (PI), poly(vinylidene fluoride) (PVDF)/ poly(methyl methacrylate) (PMMA), and polydimethylsiloxane (PDMS)/poly(ethylmethylsiloxane) (PEMS). The competing roles of hydrostatic pressure and CO2 dissolution on the phase behavior of both the PS/PI and the PDMS/PEMS blends, which exhibit upper critical solution temperature (UCST) behavior, are systematically established. Additionally, a complete pseudo-binary temperature-composition phase diagram of the PDMS/PEMS blend is generated as a function of CO2 pressure. To compare the predictive abilities of the Flory-Huggins and Sanchez-Lacombe equations of state, interaction parameters of the PDMS/PEMS blend are predicted as functions of temperature and CO2 pressure. The phase behavior of, as well as intermolecular interactions in, PMMA/PVDF blends have been probed in the presence of CO2 by small-angle neutron and x-ray scattering (SANS and SAXS, respectively). These PMMA/PVDF blends, which display both UCST and lower critical solution temperature (LCST.




Multiscale Computational Modeling of High-pressure Phase Stability, Structure, and Thermophysical Properties of Compressible Polyolefin Solutions


Book Description

"The knowledge of high-pressure phase behavior and phase equilibria of polyethylene (PE) in hydrocarbon solutions is an integral part of the process design and manufacturing of PE via solution polymerization. This thesis focuses on the study of fundamental polymer thermodynamics and key mechanisms that govern phase stability in polyolefin solutions via combined thermodynamics-molecular modeling algorithms.Force field-molecular dynamics simulations are utilized to bridge the gap between experimentally observed macro-scale phase separation phenomena and molecular-level details of fundamental studies of macromolecular thermodynamics in polymer-solvent systems. In this context, the main contributions of the present thesis work focus on molecular thermodynamic characterization of the pressure-induced phase separation (PIPS) mechanism and lower critical solution temperature (LCST) fluid phase behavior of PE solution; high-pressure thermodynamic and structural properties of binary and ternary solutions of PE + hexane and PE + hexane + ethylene, respectively; improvement of the computational efficiency and accuracy of the isobaric-isothermal and canonical ensemble simulations; overcoming the practical challenges involved in the implementation of equation of state theories.A fully-atomistic molecular mechanics force field combined with molecular dynamics is implemented to compute solubility parameter, liquid phase density, structure, and internal pressure of HDPE and hexane over a broad range of pressures. Based upon the knowledge of pressure and temperature dependence of solubility parameters the binary interaction parameter is computed to shed light on phase stability predictions in PIPS mechanism and LCST phase behavior. A molecular-level explanation for the change in cohesive properties and structure of PE and hexane upon raising the external pressure is provided. Additionally, a relation is established between cohesive energy density and internal pressure for the solvent and polymer as a function of pressure. A comparison is reported between electrostatic algorithms of switch function and the particle mesh Ewald method, and also the effect of grid spacing on the computational accuracy of electrostatic energy contribution is revealed.This thesis also implements the state of the art molecular modeling methods and equation of state modeling to report on the pressure dependence of binary PE solution density for various polymer compositions, required to solve the phase equilibria and kinetics of compressible polymer solutions. The effect of the cut-off radius of intermolecular potentials on the non-bonded forces and densities of the polymer-solvent mixture with the objective of improving the computational efficiency of molecular dynamics simulations is investigated and an optimized cut-off distance is suggested for high-pressure molecular mechanics modeling of compressible polyolefin solutions. An atomistic-level analysis of the impact of pressure on the structure of PE-solvent mixture is also provided.The isobaric-isothermal molecular dynamics methodology together with the equation of state model is further extended to incorporate ethylene as unreacted monomer in the solution polymerization process for PE production. The inclusion of supercritical ethylene lays the foundation for the analysis of the effect of adding co-solvent on the density of PE + hydrocarbon solvent system and also to elucidate the impact of pressure and temperature upon the ternary PE solution density. Additionally, a significant insight into the exact nature of intermolecular interactions in the binary subsystems of polymer/solvent/co-solvent is presented. Ultimately, an integrated equation of state-molecular simulation algorithm is presented to compute the characteristic parameters involved in the equation of state theory, which eliminates the need for rigorous experimental phase equilibrium data and tedious non-linear fitting of thermodynamic data." --