Geometry and topology of microscopic ribbons

• Main Author: Cheong, Kyra Kay Yen
• Other Authors: Yong Ee Hou
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2022
• Subjects: Science::Physics
• Online Access: https://hdl.handle.net/10356/156991
• Institution: Nanyang Technological University

With a focus on the organic molecule that every living organism contains, this report strives to characterise the mechanical properties of DNA. For a contour length that far exceeds the thickness or diameter of a chain, the geometrical and topological configurations can be described by simplified models. Starting with the discrete freely jointed chain (FJC) model, the qualitative explanation provided a stepping stone for the development into the continuous limit of the worm-like chain (WLC). The applicability of these models, especially the latter, has demonstrated the ability to accurately predict the behaviour of organic polymers in stretching and twisting experiments conducted by researchers since the 70s. In this report, the computing capacity of a simulation that employs the Monte Carlo method has provided a reliable means of obtaining the geometrical and topological values resulting from the WLC model within certain force regimes. The effect of a combination of external force and torque applied to the model reveals the relationship between the geometrical and topological conformations of the chain. With increasing external force, the extension of the chain rises rapidly, but as full extension is approached, the relative extension becomes smaller as the entropic spring behaviour diminishes. Additionally, applying an external torque to the chain delineates the inability to affect the topological parameter denoted by the linking number. The results of these simulations were compared to past experiments and have shown to be a reliable means of accurately calculating the ensemble averages of measurable properties exhibited by organic polymers, particularly DNA.