Brownian Dynamics Simulations of Dilute Polymer Solutions with Entanglements

Abstract

This dissertation describes the development of a bead-spring Brownian dynamics model for simulating the topological interactions between polymers and thin obstacles. We apply this method to electrophoretically translating DNA strands interacting with an immovable post. The use of a bead-spring method allows for the simulation of entanglement interactions of polymer chains too long to be simulated using bead-rod or pearl necklace models. This new method determines the shortest distance between a spring and the post, calculates a repulsive force inversely related to this distance using an exponential potential, and corrects for the rare situation when a spring passes beyond the post despite the repulsive interaction.

We consider single-chain collisions with a single post in weak electric fields. We explore a wide range of chain lengths and field strengths, and we find that the average delay produced by the collision is a function of both the chain length and the Peclet number. Our results are consistent with published results for a 25 Kuhn-step chain at Peclet number 1.0. Our new method is a general one that allows us to compute the effects of entanglements in systems with rare entanglements and long chains that cannot be simulated by other more microscopic methods.

We find that the mean distance x that the chain migration is held up by the entanglement interaction increases with higher fields and encompasses four distinct regimes. The two fastest regimes exhibit the classic rope-and-pulley dynamics, in which the chain is draped around the entanglement and the longer of the two dangling ends pulls the shorter end around the obstacle. In the highest field strength regime, the dimensionless delay distance reaches its theoretical upper limit at 0.5. In the moderately high field strength regime, the ends of the chain remain balled up while the central portion is extended, creating a “ball and chain” configuration. In the two slower regimes, the polymer retains a coil-like shape as it diffuses laterally and eventually clears the post without deforming. We develop models that describe both the average delay and the distribution of delays for the three highest field regimes.