Numerical Simulations of Polymers at the Nanoscale

In this thesis we study a variety of nanoscale phenomena in certain polymer systems using a combination of numerical simulation methods and mathematical modelling. The problems considered are: (a) the mixing behaviour of polymeric fluids in micro- and nanofluidic devices, (b) capillary absorption of polymer droplets into narrow capillaries, and (c) modelling the phase separation and self-assembly behaviour in polymer systems with freely deforming boundaries. These problems are significant in nanotechnological applications of polymer-based systems. First, the mixing behaviour of a polymeric melt over two parallely patternedslip surfaces is considered. Using molecular dynamics (MD) simulations, it is shown that mixing is enhanced when the polymer chain size is smaller than the wavelength of the chemical pattern of the surfaces. An off-set in the upper and lowerwall patterns improved themixing in the centre of the channel. Application of a sinusoidally varying body force in addition to the patterned-slip conditions is shown to enhance mixing further, compared to a constant body force case, with some limitations. Simulation findings for the constant body force cases are in qualitative agreement with the continuum theory of Pereira [1]. However, in the case of a sinusoidally varying body force our simulations do not agree with the continuum theory. We explain the reasons for the discrepancy between the two and point out the deficiencies in the continuum theory in predicting the correct behaviour. Second, the capillary phenomena of polymer droplets in narrow capillaries is studied using MD simulations. It is demonstrated that droplets composed of longer chains require wider tubes for absorption and this result is in agreement with our continuum modelling. The observed capillary dynamics deviate significantly from the standard Lucas-Washburn description thus questioning its validity at the nanoscale. The metastable states during the capillary absorption in some cases cannot be explained using the existing models of capillary dynamics. Lastly, the phase separation process in polymer blends between both confined and unconfined boundaries is studied using Smoothed Particle Hydrodynamics (SPH). The SPH technique has the advantage of not using a grid to discretize the spatial domain, which makes it appealing when dealing with problems where the spatial domain can change with time. The applicability of the SPH method in describing phase separation in these systems is demonstrated. In particular, its ability to model freely deforming polymer blends is shown.