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Thesis Format

Monograph

Degree

Doctor of Philosophy

Program

Physics

Collaborative Specialization

Scientific Computing

Supervisor

Colin Denniston

Abstract

Predictive models are a powerful tool to understand and improve physical systems. Predictive models not only can be used to improve current materials, but they also gain fundamental understanding of the underlying processes. There are numerous theoretical and numerical models introduced in the field of polymer composites and nanocomposites. Different methods best describe a system at a specific time and length scale. In this thesis, I utilize Coarse-grained Molecular Dynamics (CGMD), Multi-PhaseField (MPF), and Lattice-Boltzmann (LB) methods to study different aspect of polymer composites and nanocomposites.

Starting at the nanoscale, we study the dispersion and orientation patterns of nanorod-polymer systems using Coarse-grained Molecular Dynamics. We particularly focus on the phase behaviour of nanorods in an unentangled polymer melt as a function of the nanorod concentration. The system is comprised of flexible polymer chains and multi-thread nanorods that are equilibrated in the isothermal-isobaric ensemble. All interactions are purely repulsive except for those between polymers and rods. Results with attractive vs repulsive polymer–rod interactions are compared and contrasted. The concentration of rods has a direct impact on the phase behavior of the system. At lower concentrations, rods phase separate into nematic clusters, whereas at higher concentrations more isotropic and less structured rod configurations are observed. A detailed examination of the conformation of the polymer chains near the rod surface shows extension of the chains along the director of the rods (especially within clusters). The dispersion and orientation of the nanorods are a result of the competition between depletion entropic forces responsible for the formation of rod clusters, the enthalpic effects that improve mixing of rods and polymer, and entropic losses of polymers interpenetrating rod clusters.

Physical and mechanical properties of semi-crystalline polymers depend on their degree of crystallization and crystal morphology. Producing semi-crystalline material with desired properties is only possible when the crystallization process and structure is well-understood and can be predicted. We introduce a coarse-grained model of polymer crystallization using a multiphase-field approach. The model combines a multiphase-field method, Nakamura's kinetic equation, and the equation of heat conduction for studying microstructural evolution of crystallization under isothermal and non-isothermal conditions. The multiphase-field method provides flexibility in adding any number of phases with different properties making the model effective in studying blends or composite materials. We apply our model to systems of neat PA6 and study the impact of initial distribution of crystalline grains and cooling rate on the morphology of the system. The relative crystallinity (conversion) curves show qualitative agreement with experimental data. We also investigate the impact of including carbon fibers on the crystallization and grain morphology. We observe a more homogeneous crystal morphology around fibers. This is associated with the higher initial volume fraction of crystal grains and higher heat conductivity of the fiber (compared to the polymer matrix). Additionally, we observe that the crystalline grains at the fiber surface grow perpendicular to the surface. This indicates that the vertical growth observed in experiments is merely due to geometrical constraints imposed by the fiber surface and neighbouring crystalline regions.

The production of fiber-reinforced thermoplastics involves processes performed under flow conditions. Therefore, it is crucial to understand the dynamics of fibers in flow to obtain high quality fiber-reinforced composites. We introduce a new Lattice Boltzmann Method (LBM} where the continuous distribution function is discretized using distribution mass function that in addition to a mean value also has a variance. This introduces extra independent degrees of freedom to recover the second and third moments of Maxwell-Boltzmann equation fully. This eliminates the error terms that appear in the standard LBM and extends the applicability of LBM to compressible flows. The variance terms can further be utilized to incorporate thermal and viscoelastic features. As the variance terms appear as part of the discretization scheme, they consistently appear in the derivation and no ad-hoc manipulation of the equations is required to recover the correct second and third moments. Furthermore, there are only 6 extra terms (or 9 for a non-symmetric general stress tensor) introduced in this model. Thus, we expect the algorithm to be more memory efficient and have shorter runtimes than multi-lattice models.

Summary for Lay Audience

One approach to addressing issues like global warming and transportation safety is through lightweighting. This involves replacing materials used in vehicles with lighter alternatives without sacrificing performance. Composite materials, which combine the best properties of different substances, enable the creation of high-performance lightweight materials. However, achieving the desired end product requires the testing of diverse ingredient materials and processing techniques. This is financially demanding due to the substantial requirement for materials and labour.

This is where mathematics and technology offer a solution: computer simulations. Computer simulations enable the execution of numerous virtual experiments across a wide range of conditions. This not only enhances our comprehension of the underlying physics that drives the real-world observations, but it also reduces the range of possibilities that must be tested in the laboratory. As a result, they save both material usage and labour hours. In this thesis, I use 3 different simulation methods to study polymer composites (polymers are long and chain-like molecules).

The properties of materials are determined by the behaviour of their molecules. So, it is important to understand how materials work at the molecular level to predict their properties and improve them. In the first simulation, I looked at the shape and arrangement of the molecules in a material that is a mix of a polymer melt and fibers.

In the second simulation, I combined different mathematical models to reproduce how a polymer looks under the microscope when it crystallizes. It is important to understand how crystal regions are distributed in a polymer material because the degree of crystallinity and distribution of the crystals affect the performance of the material.

The production of fiber-reinforced polymers involves the liquid mixture flowing through pipes and/or into molds. Therefore, it is crucial to understand how fibers behave in a flow to obtain high quality fiber-reinforced composites. For the third simulation, I expanded a previous simulation method that only applied to simple fluids like water to account for compressible fluids. The model can be further expanded to reproduce viscoelastic flows like polymers.

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

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