Polymer Solutions: a Geometric Introduction
T. A. Witten
James Franck Institute
University of Chicago
Chicago Illinois 60637
abstract
Long hydrocarbon chain polymers dissolved in a liquid qualitatively alter the
way the liquid moves and transmits forces. The basic origins of this behavior
can be understood geometrically by recognizing that a polymer chain resembles
a random walk. The spatial distribution of atoms may be described by scaling properties and quantified
using the notion of fractal dimension and dilation invariance. The strong thermodynamic and
hydrodynamic interactions of polymers may be accounted for in terms of the
intersection properties of fractal objects. These intersection properties show
why polymers exclude flow as well as one another from their interiors,
despite their arbitrarily small interior concentration.
Self avoidance decreases the fractal dimension of a polymer. The origin of
this decrease and conditions for its occurance are explained. From these geometric
properties, scaling laws describing how osmotic pressure, diffusion and stress relaxation
depend on molecular weight and concentration are explained.
published in Reviews of Modern Physics 70 1531--1544
(1998)
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