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Title:  Statistical Physics of Semidilute Polymer Systems (And); Soft Billiard Systems 
Author(s):  Baldwin, Philip Rupert 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Physics, Fluid and Plasma 
Abstract:  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 socalled 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 RGexposition 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 modecoupling method, in order to study tracer diffusion constant, viscosity and the dynamic screening length. The second part of the thesis deals with a problem related to the foundations of statistical physics. We study a variation of a Sinaitype billiard system, where circular scatterers of radius $R$ are centered on the lattice sites of a 2d square lattice and given a finite potential height $U$ (measured in units of kinetic energy). For 1 $>$ $U >$ 0, the KolmogorovSinai entropy of a point particle travelling on the lattice is numerically calculated as a function of $U$ and $R$ and empirically seen to be a universal function of $U/R\sp2$ for $U,R$ sufficiently small. For 0 $> U > U\sb{c}(R)$ we prove the nonergodicity of the system and discuss the structure of the phase space; $U\sb{c}(R)$ is also explicitly given. The $U \to 0$ and $U \to U\sb{c}$ transitions are also discussed. Using tools of number theory, algorithmic aspects of the billiard problem are investigated. The entropy of the billiard system for small $R$ is shown to be related to how difficult it is to find the next scatterer in a billiard simulation. 
Issue Date:  1987 
Type:  Text 
Language:  English 
Description:  175 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1987. 
URI:  http://hdl.handle.net/2142/77411 
Other Identifier(s):  (UMI)AAI8802981 
Date Available in IDEALS:  20150513 
Date Deposited:  1987 
This item appears in the following Collection(s)

Dissertations and Theses  Physics
Dissertations in Physics 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois