Multi-Scale Modeling and Simulation of Polymeric Liquids in Fast Extensional Flows

Abstract

This thesis contains simplified simulations of polymers in the entangled melt/solution state and in the glassy state in fast extensional flows where chains become locally stretched at modest strains. Comparisons to experiments show that the “Entangled Kink Dynamics” simulations for entangled chains and the “Hybrid Brownian Dynamics” simulations for glassy polymers improve on existing models. We also present atomistic Molecular Dynamics (MD) simulations of the interactions of for Poly(N-isopropylacrylamide)” (pNIPAAm) excipient with a hydrophobic drug, phenytoin, to improve drug release in the GI tract. In the first part of the thesis, the conventional “tube-model” constitutive equation is found to predict overly rapid approach to a steady-state extensional viscosity of entangled polystyrene solutions in fast extensional flow. Based on an analysis of the conformation of polymer chains at high strains, a new and simple simulation technique, which we call the “Entangled Kink Dynamics” (EKD), is developed to study the late stage dynamics of polymer chains. In this approach, a highly strained polymer chain in extensional flow is modeled as a quasi-one-dimensional chain with kinks at which the polymer folds back on itself. Polymer strands between the kinks are considered fully stretched and Brownian force is neglected in comparison with drag and tension. The behavior of entangled chains in the kinked state is studied for the cases of dilute chains, affinely moving kinks, and kinks entangled with kinks on other chains. To compare the kink dynamics predictions with experimental results, input is needed from more detailed “single-chain slip-spring” simulations. With this input, EKD simulations show a much better prediction of experimental extensional viscosity of entangled long polystyrene solutions, compared to conventional tube models. Validating our model, we explain the potential downfalls of the tube theory and provide insight into achieving a better constitutive equation for entangled polymeric melts and solutions. Secondly, we present a modified Hybrid Brownian dynamics model to study the rheology of polymeric glasses. Using a Coarse-Grained Brownian Dynamics (CG-BD) model for polymer chains suspended in a glassy solvent that represents the segmental model of the glassy polymer, governed by a simple fluidity model, we study the stress and conformation evolution of glassy polymers under fast uniaxial extensional flows and compare our results with fine-grained molecular dynamics simulations of polymeric glass. Although our CG-BD simulations do not have the effect of entanglements explicitly, the conformation evolution of polymer chains in our hybrid technique is found to be similar to that found in MD results, where the entanglements are taken into account explicitly. This proves that in fast flows of glassy polymers, chain conformation is governed by sub-entanglement dynamics and formation of folds, or kinks. The importance of sub-entanglement scales in generating stress becomes hugely important at high strains where polymeric glass show strain hardening. By calculating the number of entangled folds on the chain in the strain hardening regime, we prove that the huge rise in the stress is not due to the effect of entanglements. Instead, we show that strain hardening behavior is caused because of the highly stretched strands between nascent fold points, below the length scales of entanglement spacing.