Theoretical study of polymers: Flow-induced deformation in nanochannels and reptation dynamics in heterogeneous gels

In 1992, B. Smith, L. Finzi and C. Bustamante were the first to directly observe the behaviour of a single DNA molecule with the help of video fluorescence microscopy. Their results greatly improved our understanding of the static and dynamic properties of a single isolated chain which represents the foundation of polymer physics. A series of experimental results and theoretical models followed the work of Smith et al. Current theoretical approaches to study polymers involve many techniques: thermodynamic analysis, field theory, scaling, renormalization group theory and computer simulations. In Chapter 2, we present a Molecular Dynamics study of the effect of strong lateral confinement on the properties of a tethered polymer pulled at constant velocity. Our results are compared with recent theoretical predictions and experimental results.;One can also ask questions about the behaviour of dilute polymer solutions, or even concentrated solutions such as melts or gels, where the interactions among the polymers are important. For instance, gel electrophoresis (GE) is one of the most common analytical tools used in biology. Since the introduction of GE in 1937, molecular biology has grown substantially. Indeed, GE has shown to be an excellent separation method for DNA molecules since in free solution, the electrophoretic mobility of a DNA molecule is independent of its size. Because of that, most of the theoretical developments in the field have been aimed at improving DNA electrophoretic separation tools.;In 1993, Zimm and Lumpkin proposed a new reptation model to explain gel electrophoresis of polyelectrolytes in irregular matrices. Following this work, we propose in Chapter 3 a more detailed model of this problem where the well-known memory effects of the standard reptation theory are taken into account. Our results are in qualitative agreement with available experimental results and disagree with those of Zimm and Lumpkin.;In Chapter 4, we examine the reptation of a polymer in a static environment with quenched random energies that are correlated over a finite length scale lambda based on the algorithm detailed in Chapter 3. The results obtained differ from our previous model (Chapter 3) and are compared with those of Zimm and Lumpkin.