1 The Danish Polymer Centre, Department of Chemical and Biochemical Engineering, Technical University of Denmark2 Department of Chemical and Biochemical Engineering, Technical University of Denmark3 Physical Chemistry, Department of Chemistry, Technical University of Denmark4 Department of Chemistry, Technical University of Denmark
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 nano-structuring 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 sphere-like universal partitioning feature can be identified in the weak confinement regime. The corresponding sphere radius for a non-spherical 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 three-dimensional confining geometries (such as a square channel of cross-section 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.
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Peters, Günther H.J., Hansen, Flemming Yssing, Hassager, Ole