Monograph

#### Degree

Doctor of Philosophy

#### Program

Applied Mathematics

#### Collaborative Specialization

Scientific Computing

Denniston, Colin

#### Abstract

In this work we study single chain polymers in shear flows and nanocomposite polymer melts extensively through the use of large scale molecular dynamics simulations through LAMMPS. In the single polymer chain shear flow study, we use the Lattice Boltzmann method to simulate fluid dynamics and also include thermal noise as per the \emph{fluctuation-dissipation} theorem in the system. When simulating the nanocomposite polymer melts, we simply use a Langevin thermostat to mimic a heat bath. In the single polymer in shear flow study we investigated the margination of a single chain towards solid surfaces and how strongly the shear flow influences this effect. In particular we also tried to study the effect of the polymer's monomer size $a$ on its overall tendency to marginate. To this end, we studied polymer chains of length $N=16, 32$ in flows at multiple shear rates, $\dot{\gamma}$ and noted higher margination rates in the case of chains with larger radii monomers in comparison to smaller radii monomer chains. We quantified this behaviour and effect by considering various measures such as the distribution of the chain's maximum extent into the flow, the distribution of its centre of mass normal to the surface as well as its radius of gyration in directions parallel and normal to the surface i.e $R_{x}, R_{y}, R_{z}$. In the second work, we looked at the effects of introducing nanorods into polymeric melts. We primarily focused on understanding the dispersion, orientation and conformational patterns exhibited by the nanorods and chains respectively. At lower concentrations, rods phase separated into distinct nematic clusters, while at higher concentrations they remained more isotropic and disordered. We noted that this behaviour is being driven by the system finding a trade-off between the entropic forces trying to create the isolated clusters and the enthalpic effects that work to improve mixing of the rods. We also noted that the rigid rods induced significant local conformational changes in the flexible chains in close proximity which in turn made the whole melt more ordered.

#### Summary for Lay Audience

Polymers are everywhere and their applications in our daily lives are numerous. Be it in the healthcare field or the food industry or within the human body itself, polymers play a very key role in our day to day lives as well as in our healthy living. Understanding how these large molecules behave under different situations, forces and environments is key in order for us to be able to develop novel tools and medications. Polymers are everywhere within the human body. DNA, the most commonly known is basically a very long polymer that encodes vital information about the human genome. Another less known polymer in the human body is the vWF (von Williebrand Fibers) that plays an extremely crucial role in preventing blood loss. It is well known that these polymers are abnormally large in comparison to other proteins in humans, and from our work we confirmed that this large size plays a major role in it performing its task of preventing blood loss. At a very high level, in case of a cut or injury to a blood vessel, the polymer detects the injury rushes to the damaged site and much like duct tape, stretches out to essentially seal the injury. In this study we investigate this very property of large polymers through the use of computer simulations. Rigid plastics start their life as polymer melts, which is basically a fluid phase of the same and are made up of thousands of individual polymers. Several studies have been done in order to boost the mechanical properties of these melts by infusing them with rigid rods such as fiber glass. These are especially useful in the manufacturing and automotive industry due to their promising physical properties such as light weight and able to sustain high stresses. The mixture of the melt with rigid rods has resulted in materials with enhanced mechanical properties that prove to be quite useful in several applications. In our work, we investigate the same via computer simulations and study how the rigid rods affect the properties of the polymer surrounding them and also comment on potential applications of such material in industry and research.