Atoms and springs : on the development and use of models to study polymer behavior

Abstract

Third, we concern ourselves with the development of a coarse grained model of the worm like chain. Currently, no model exists that can well reproduce the behavior of the worm like chain over the length scale of 0.2-2 persistence lengths. Understanding the behavior of polymers over this length scale is essential to understand the bending and folding of DNA during nucleosome packing. Our goal is to create a model that reproduces the behavior of the worm like chain over these lengths to a high degree of accuracy. Further, we strive to develop a model that is physically intuitive and easy to implement. We accomplished this by starting with a simplified version of the worm like chain, then reintroduced behavior by adding terms to the energy that recapitulate the underlying physics of a bent polymer. This inquiry resulted in a simple closed form expression for the energy that matches well with the worm like chain theory.

Second, we seek to generalize our dumbbell kinetic theory to be applicable to chains with arbitrary number of beads. Though our dumbbell model represents a significant contribution, a number of questions remain as to how well it maps to finer grained (and potentially more accurate) representations. This motivates us to try and generalize our model and study any new behavior that emerges when a polymer is represented by a bead spring chain, rather than a dumbbell. This gives us an opportunity to develop our understanding of the polymer's behavior over differing length scales.

In this work, we continue the long tradition of modeling polymers under a variety of circumstances using a number of tools. More specifically, we use kinetic theory, Brownian dynamics and molecular dynamics in order to study a number of polymer systems. First, we develop a kinetic theory for a dumbbell bead spring in order to describe the non-monotonic migration of flexible polyelectrolytes in a combination of electric field and fluid flow. By confirming our kinetic theory with Brownian dynamics simulations, we were able to develop a simple close formed expression that predicted the amount of migration as well as a number of related observables. Further, our theory yielded insight to the mechanism that undergirds the migration itself and can be used to guide development of new microfluidic devices.

The term polymer describes a remarkably broad class of molecules with an equally broad array of uses and applications. Much of their utility arises from the fact that polymer molecules can span from the microscopic to macroscopic. Because of this, one of the broad thrusts of polymer science has been to understand polymer behavior across multiple length scales. Since at least the 1930s investigators have applied the tools of thermodynamics and statistical mechanics to understand polymer systems. Though nearly a century has passed, and our understanding has greatly increased; polymer modeling remains a fertile area of research and will remain so for the foreseeable future.

Finally, we use molecular dynamics to study the behavior of methacrylate polymers under a variety of circumstances. At sufficient grafting density these molecules can form a hydrophobic brush layer. It is possible that such a brush is able to separate organic molecules from an aqueous feed stream. We study the interactions between the brush surface and the solvent. It is found that the organic component of the solvent aggregate on the surface of a hydrophobic brush. This indicates that the brush may be able to selectively permit organic molecules while rejecting water, causing separations via a solution-diffusion mechanism. Further, when polymers are grafted at lower densities they are unable to form a continuous brush layer, and coat the grafting surface. The manner in which polymers coat these surfaces arises from the interplay of polymer-polymer, polymer-solvent, and polymer-surface interactions. The interplay of these forces is poorly understood and could lead to insight for the coating of materials. We seek to probe this interplay using molecular dynamics; which is a finer grained representation than what has been used in the past. We find that the interplay is subtle, nuanced, and deserving of further study.