Day 1: Introduction

Random Walk Character of polymers

Left is shown the phase diagram enlarged in the region of the Q -point. The temperature is measured relative to the Q -point.

Because of the analogy with random walks we can draw some conclusions on the size of polymers, as well as on the phase diagram.

We shall denote the radius of gyration by R_g. The end-to-end distance will be denoted by R_e. The extend of the polymer is then related to number of monomers N in the chain by

<R_g> ~ N^ⁿ

n is an exponent hat characterizes the extend of the polymer. If the polymer where a simple random walk, the value of the exponent would be 1/2. If excluded volume interactions must be considered the value is larger than 1/2 (=0.59...).