Statistical Physics of Semidilute Polymer Systems (And); Soft Billiard Systems

This thesis consists of two disjoint parts. In the first part, we carefully study the semidilute regime of polymer solutions. The renormalization group (RG) method using the $\varepsilon$-expansion has been a systematic method giving good semiquantitative agreement with both real and computer experiments for the static and dynamical properties of polymers in dilute solution. However, polymer theory in the semidilute regime is less sound. We first review RG results on statics, using the so-called direct method and employing the Edwards Hamiltonian. We present a careful RG account of arbitrarily polydisperse semidilute polymer solution, and give a clear account of semidilute diagrammatics. We provide results for the osmotic pressure and scattering function for homopolymer and ternary polymer solutions. We discuss effective medium theory as well as the limitations of our modelling. Next we build a dynamical model for polymers. We present a RG-exposition of polymer theory under the Kirkwood approximation, and clearly demonstrate that no screening results in this model for the calculation of the cooperative diffusion constant and the initial decay rate of the dynamic scattering function. Our results for these quantities show good agreement with experiment for moderately dense systems. Finally, we discuss the mode-coupling method, in order to study tracer diffusion constant, viscosity and the dynamic screening length.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Baldwin, Philip Rupert

• Physics, Fluid and Plasma

Language dc:language

eng

Identifier

(UMI)AAI8802981

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/77411