Polymeric systems phase equilibria simulation

The method developed in this book is also used to provide input parameters for composite models which can be used to predict the thermoelastic and transport properties of multiphase materials. The prediction of the morphologies and properties of such materials is a very active area of research at the frontiers of materials modeling. The prediction of morphology will be discussed in Chapter 19, with emphasis on the rapidly improving advanced methods to predict thermodynamic equilibrium phase diagrams (such as self-consistent mean field theory) and to predict the dynamic pathway by which the morphology evolves (such as mesoscale simulation methods). Chapter 20 will focus on both analytical (closed-form) equations and numerical simulation methods to predict the thermoelastic properties, mechanical properties under large deformation, and transport properties of multiphase polymeric systems. 

The establishment of chemical potential equilibrium (with respect to either a setpoint or phase coexistence) is the central component of most Monte Carlo schemes for simulation of the phase behavior and stability of molecular systems. Simulation of the chemical potential (or chemical potential equilibration) in a polymeric system requires more effort than the corresponding calculation for a simple fluid. The reason is that efficient conformational sampling of the polymer is implicitly required for a free-energy calculation and, in fact, the ergodicity problems described in earlier sections are often exacerbated. 

This chapter discusses the form and parameterization of the potential energy terms that are used for the atomistic simulation of polymers. The sum of potential terms constitutes a molecular force field that can be used in molecular mechanics, molecular dynamics, and Monte Carlo simulations of polymeric systems. Molecular simulation methods can be used to determine such properties as PVT data, selfdiffusion coefficients, modulus, phase equilibrium, x-ray and neutron diffraction spectra, small molecule solubility, and glass transition temperatures with considerable accuracy and reliability using current force fields. Included in the coverage of Chapter 4 is a review of the fundamentals of molecular mechanics and a survey of the most widely used force fields for the simulation of polymer systems. In addition, references to the use of specific force fields in the study of important polymer groups are given. 

Borstar is an industrial olefin polymerization plant/technology, which combines different polymerization processes and reactor units, utilizing an advanced catalytic system. In the present work, a detailed model for the dynamic and steady-state simulation of this industrial plant has been developed. A comprehensive kinetic model for the ethylene-1-butene copolymerization over a two-site catalyst was employed to predict the MWD and CCD in the Borstar process. The Sanchez-Lacombe equation of state (S-L EoS) was employed for the thermodynamic properties of the polymerization system and the phase equilibrium calculations in the process units. 

For practical use of PDLC, dispersions are mainly prepared by mixing a small amount of misdble monomers with liquid crystals and photo-polymerizing [1], since polymer and liquid crystals tend to be immiscible. As the polymerization evolves, the system undergoes phase separations into a liquid crystalline phase rich in liquid crystals and an isotropic phase rich in polymers. Before the system reaches equilibrium states, however, the polymerization freezes the system into a crosslinked network of polymer-rich domains. Then, the morphologies of the PDLC involve interplay among three kinetic processes polymerization, phase separation, and phase ordering. These phase separation dynamics have been simulated by some aulhors [105-108]. 

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