Polymer solutions: A geometric introduction

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 occurrence are explained. From these geometric properties, scaling laws describing how osmotic pressure, diffusion, and stress relaxation depend on molecular weight and concentration are explained.