On the simulation and theory of polymer dynamics in sieving media: Friction, molecular pulleys, Brownian ratchets and polymer scission
Creators: name: Kenward, Martin
Publisher: name: Université d'Ottawa / University of Ottawa
Year: 2007
Subjects: subject: Physics, Molecular.

description: The study of single polymer dynamics has, in the past few years, undergone a resurgence. This has been spurred on by the emergence of the fields of micro- and nanofluidics and their associated applications, especially by their ability to promise revolutionary techniques to, for example: rapidly sequence DNA, analyze proteins, carry out large-scale laboratory techniques in centimeter sized devices (lab-on-a-chip) and test and verify fundamental concepts related to the statistical physics of single molecules in fluids. In particular, the study of (typically single, isolated) polymers and the development of theoretical methods and computational tools to examine these polymers in microfluidic environments is a key challenge. In this thesis, we examine several different phenomena related to the dynamics of polymers in either microfluidic environments or related applications to DNA sequencing or separation. A recurrent theme throughout this work is the use of Molecular Dynamics (MD) simulations with an explicit solvent. Explicit solvent is an important aspect of our simulations and contrasts much work in the current literature which either artificially includes solvent or neglects it all together. This explicit inclusion of solvent allows us to explore phenomena (related to hydrodynamics) that is not observable with, for example, Brownian (or Langevin) Dynamics or Monte Carlo simulations. Chapter 2 contains a primarily computational examination of the friction coefficients of uncharged polymers. We explore the effects of deforming polymer chains on their friction coefficients along with examining several fundamental concepts of polymer friction (including hydrodynamic permeability). A key result is a verification of the hydrodynamic coupling of polymer chains resulting from a net reduction in the friction of polymer chains in hairpin (or folded) conformations. We also show that polymers undergo frictional transitions as they are stretched by an external force applied to the middle of the molecules. In chapter 3 we use some of the concepts and results from chapters 1 and 2 to explore the problem of a polymer chain migrating under the influence of an external force (or fluid flow) through a molecular obstacle course. These polymers collide with either fixed obstacles (or other polymers) and can be trapped in meta-stable long-lived, pulley-like conformations. This method can be used to separate polymers by molecular weight. We use both MD simulations and a general classical theory for the collisions to explore several different collision regimes. We also show that a classic experimental result, the formation of so-called V-shaped states, can occur in single polymer collision events, contrary to the popular assumption that it was necessary for a polymer to collide with multiple polymers. In chapter 4 we build on the results and ideas from the first three chapters and examine another phenomenon related to polymer transport, that of (Brownian) ratchets. A ratchet is essentially a method to rectify the thermal noise in a system in order to perform work, for example, to generate net transport. We use our MD simulations to examine the behaviour of polymers in the presence of an asymmetric saw tooth ratchet potential. We also show that existing ratchet models, where the ratchet widths are on the order of a polymer gyration radius, neglect an important effect of chain relaxation and thus underestimate optimal operating parameters. We propose and derive equations illustrating a new operational mode for a ratchet which inherently uses the deformation of polymer chains induced by the application of a ratcheting potential. We present a simple mathematical expression to incorporate time-dependent diffusion coefficients D (t) into ratchets. The final chapter presents work done in collaboration with Annelise Barron's group at Northwestern University and examines the breaking of polymer chains in extensional flow fields as a method to systematically and predictably reduce the polydispersity (PDI) of polymer solutions. The experimental investigation, carried out by the Barron group illustrated that a dilute polymer solution, when passed through a narrow constriction at high pressure can systematically reduce the PDI of the polymer solution. My contribution to this work was to develop a statistical model which calculates polymer molecular weight distributions and which can predict the resulting degraded polymer distribution. Two key things resulted from this investigation, the first is that polymers can break multiple times during a single scission event (i.e., one pass through the experimental system). Secondly we showed that it is possible to predictably reproduce polymer distributions after multiple scission events.