Abstract:
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.
