Single-file Diffusion, Drift, and Collisions in One-dimensional Polymer Solutions

Abstract

Research into the dynamics of polymer chains in tightly confined spaces is a crucial aspect of microfluidic device transport studies. Single-file diffusion remains one of the most under-explored topics in this field, yet it holds potential for various applications and further research. In this thesis, I focus on the dynamics of polymer molecules under narrow tube confinement. These projects mainly aim to simulate various systems’ behaviors over time and understand the collective movement mechanism of polymer chains. A good part of the work is related to first-passage issues within these systems. For example, we analyze the time to first separation for polymer fragments to reach clear separation in DNA mapping related problems. The system’s initial conditions significantly affect how fragments are spatially and temporally separated. We investigate the effect of randomness as well as segmental ordering on separation times. As a complement, we also briefly investigate how the initial random fragmentation of a polymer molecule affects its final fragment order, highlighting the importance of the blob theory in our study. In addition, we also study collisions between polyelectrolytes and uncharged polymer chains under strong confinement. Non-monotonic velocity behaviour, collision duration, collision type and gel electrophoresis-like conditions may all contribute to the successful separation of polymer chains. However, building practical separation devices may require further modifications to the system, such as applying pulsed fields with asymmetric time periods or artificially creating asymmetric tube diameters. Ultimately, it should be possible to manipulate polyelectrolytes using the ideas presented in this thesis. We also study the single-file diffusion of polymer chains using molecular dynamics (MD) simulations. By comparing the motion of long polymer chains with the predictions of known theories for hard particles, we can gain a better understanding of the multiple time regimes that exist. In addition, with well-designed algorithms, we are able to simulate the same problems using simple Monte Carlo (MC) methods, thus increasing computational speed. Finally, we demonstrate that it is possible to establish a link between these two simulation methods (MD and MC) by mathematically calculating their key parameters.