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Abstract
This thesis deals with modeling of a polymer chain subject to spatial confinement.
The properties of confined macromolecules are both of fundamental interest in
polymer physics and of practical importance in a variety of applications including
chromatographic separation of polymers, and the use of polymers to control the
stability of colloidal suspensions. Furthermore, recent advances in micro and
nanostructuring techniques have led to the production of fluidic channels of critical
dinlension approaching the molecular scales, in which areas understanding
the effects of spatial restrictions to macromolecules is critical to the design and
application of those devices. Our primary interest is to provide an understanding
of the separation principle of polymers in size exclusion chromatography (SEC),
where under ideal conditions the polymer concentration is low, and detailed enthalpic
interactions are negligible.
We present a new framework to describe macromolecules subject to confining
geometries. The two main ingredients are a new computational method and a
new molecular size parameter. By using snapshots of molecular configurations
in free space to estimate the effects of confinement, the computational method,
hereafter referred to as the method of confinement analysis from bulk structures
(CABS), has the computational advantage of supplying properties as a function
of the confinement size solely based on sampling the configuration space of a
polymer chain in bulk alone. CABS is highly adaptable to studies of the effects
of excluded volume, finite persistent length and nonlinear chain architectures in
slit, channel and box confining geometries. Superior in computational efficiency
to previous simulation studies, CABS has also the unique theoretical advantage
of providing new physical insights only by simple mathematical analyses.
When the CABS method is applied to compute the equilibrium distribution
(the equilibrium partition coefficient, Ko) of polymers between a dilute macroscopic
solution phase and a solution confined by inert impenetrable boundaries,
a spherelike universal partitioning feature can be identified in the weak confinement
regime. The corresponding sphere radius for a nonspherical macromolecule
is half the average span (mean projection onto a line) of the unconfined molecule
and is hereafter referred to as the steric exclusion radius, Rs . We show that
for two and threedimensional confining geometries (such as a square channel
of crosssection d x d and a cubic box of length d), polymers with the same Rs
possess the same partition coefficient Ko regardless of details in molecular structure
(unless K o approaches 0). By imitating classical approaches to study the
separation principle of polymers in SEC, one may reach a conclusion that SEC
fractionates polymers based on the steric exclusion radius, Rs .
The CABS method is further applied to determine the depletion profiles of
dilute polymer solutions confined to a slit or near an inert wall. We show that
the entire spatial density distributions of any reference point in the chain (such
as the center of mass, middle segment and end segments) can be computed as a
function of the confinement size, and the computation is solely based on sampling
the configuration space of an unconfined chain. In the case of a single wall, we
prove rigorously that (i) the depletion layer thickness, 6, is the same no matter
which reference point is used to describe the depletion profile, and (ii) the value
of 6 equals the steric exclusion radius, Rs , of the macromolecule in free solution.
Both results hold not only for ideal polymers as has been noticed before, but
for polymers regardless of details in molecular architecture and configuration
statistics.
It is also possible to extend the CABS method to handle attractive surfaces,
which is presented briefly under "current and future work" in the summarizing
chapter.
Original language  English 

Number of pages  168 

Publication status  Published  Apr 2009 
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 1 Finished

Molecular Modelling of Polymer Melt Rheology
Wang, Y., Hassager, O., Peters, G. H. J., Shapiro, A., de Pablo, J. J., Vlassopoulos, D. & Hansen, F. Y.
15/08/2005 → 29/04/2009
Project: PhD