Application of Semi-Grand Canonical Monte Carlo (SGMC) methods to describe non-equilibrium polymer systems

Abstract

Understanding the structure of materials, and how this structure affects their properties, is an important step towards the understanding that is necessary in order to apply computational methods to the end of designing materials to fit very specific needs. Such needs include specific optical and mechanical properties. In polymers, the ability to easily create orientation through a variety of processes allows the production of materials that, while chemically similar, exhibit a wide variety of optical and mechanical properties. The ability to illuminate the connections between structure and optical or mechanical properties depends on the ability to reliably interpret a wide variety of experimental measurements. I assert that thermodynamic consistency and energy minimization is an integral part of this endeavor; reliable analyses of structure and properties are built upon the foundation of a minimum-free-energy ensemble of configurations that reproduces the experimental results. This project encompasses three goals, which make up this thesis: 1) to show how sets of experimental measurements are integrated into simulations to produce thermodynamically consistent, minimum-free-energy ensembles; 2) to show how these ensembles can characterize the conformations of macromolecules, which are not available from direct simulation; 3) to show how dynamic processes, which create inhomogeneous systems can be incorporated, along with experimental structural measurements, into thermodynamically consistent, minimum-free-energy ensembles. To achieve the first of these goals, we describe the application of the Semi-Grand Canonical Monte Carlo (SGMC) method to analyze and interpret experimental data for non-equilibrium polymer melts and glasses. Experiments that provide information about atomic-level ordering, e.g. birefringence, are amenable to this approach.

(cont.) Closure of the inverse problem of determining the structural detail from limited data is achieved by selecting the lowest-free-energy ensemble of configurations that reproduces the experimental data. The free energy is calculated using the thermodynamic potential of the appropriate semi-grand canonical (SGC) ensemble ... , as defined by the experimental data. To illustrate the method we examine uniaxially oriented polyethylene melts of average chain length up to C400. The simulation results are analyzed for features not explicitly measured by birefringence, such as the density, torsion angle distribution, molecular scale orientation and free energy, to understand more fully the underlying features of these non-equilibrium states. The stress-optical rule for polyethylene is evaluated in this way. The second goal is achieved through multi-scale modeling, which requires the selection and preservation of information crucial to understanding the behavior of a system at appropriate length and time scales. For a description of processed polymers, such a model must successfully link rheological properties with atomic-level structure. We propose a method for the calculation of an important rheological state descriptor, the configuration tensor <QQ>, from atomistic simulations of oligomers. The method requires no adjustable parameters and can describe anisotropic polymer conformations at conditions of significant deformation. We establish the validity of the atomistic-to-macromolecular scaling by comparing the consistency of macromolecular predictions of <QQ> among different polyethylene (PE) oligomer systems. We use this method with the previously reported Semi-Grand Canonical Monte Carlo (SGMC) method to deduce macromolecular and atomic-level structural information interchangeably for systems with flow-induced orientation. Introducing the ability to model arbitrary points in a dynamic process fulfills the third goal elaborated above.

(cont.) Because the characteristic relaxation times of processed polymer chains often span several orders of magnitude, it is commonly the case that partial relaxation of the chains is frozen into the final product. We report results of molecular simulations by the Semi-grand Canonical Monte Carlo (SGMC) method to study the orientation-dependent elasticity of glassy polystyrene as a function of both the system-average degree of orientation and the degree of relaxation of chain ends at a constant average degree of orientation, in accord with the tube model of Doi and Edwards. Our simulations reproduce quantitatively the experimentally observed changes in the tensile modulus E33 as a function of both average orientation and inhomogeneity of the orientation due to partial relaxation. The results show that the partial relaxation of the polymer chains is sufficient to explain the observed variation of mechanical properties for samples that differ in processing history, yet have the same observed birefringence.