Modelling Crystallisation in Polymers

Abstract

In this thesis, we introduce the development of a computational model, combining a coarse-grained phase field approach with hydrodynamics using the Stokes equation under low Reynold's number conditions. This innovative model successfully elucidates the growth patterns of rhombus-shaped single crystals in polymers driven by chemical potential gradients and fluid flow. Unlike traditional methods, this study treats the single crystal as a highly viscous fluid, employing fluid-particle dynamics, thereby eliminating the need for intricate boundary conditions at the crystal-fluid interface. The investigation commences with the development of a finite difference-based phase field model, enabling the simulation of polymer crystal growth from a simple melt. The model adapts two thermodynamic driving forces to account for the meta-stable phases in crystallisation. This model allows for the exploration of diverse crystal morphologies, including circular, rectangular, and rhombus shapes. In depth analysis of isotropic and anisotropic interfacial energies reveals their significant influence on crystal growth rates and shapes. Moreover, the study extends to the interaction between adjacent single crystals, uncovering merging processes and growth rates under constant and non-constant interface mobility. A key aspect of this research lies in the validation of the model, performed within a simple shear flow system. This validation not only ensures the model's accuracy but also offers insights into the complicated relationship between fluid flow and crystal rotation. Through simulations, the study showed how different flow conditions impact polymer crystal rotation rates and patterns. Furthermore, the study delves into the role of interface thickness and interfacial energy on crystal motion and growth dynamics. By altering the interface thickness over time and maintaining it constant in other instances, the study reveals noticeable effects on crystal rotation and growth. The results show that crystal rotation increases significantly with changing interface thickness compared to the case where the interface thickness remains constant. However, the crystal growth exhibits a considerable increase where the interface thickness remains fixed. Additionally, variations in interfacial energy along different directions are shown to influence crystal rotation and growth rates significantly. The research also introduces a theoretical framework explaining crystal rotation driven by induced asymmetrical flow in a polymer melt. The theoretical predictions, when compared with computational simulations, are considered satisfactory, despite slight disparities attributed to specific assumptions.