The world of polymers

Polymers are long chain molecules consisting of a large number of units (the monomers), which are held together by chemical bonds. These units may all be the same (in which case we speak of homopolymers) or may be different (heteropolymers).

Chemists spend most of their time developing polymers with specific chemical or physical properties. Such properties are often determined by the characteristics of the monomers and their mutual binding. In other words, they are determined on a local scale. In contrast, physicists work in the spirit of Richard Feynman and “have a habit of taking the simplest example of any phenomenon and calling it ‘physics’, leaving the more complicated examples to become the concern of other fields.” This attitude is taken to the extreme in the statistical mechanics of polymers, where one is interested mainly in universal properties, i.e. those properties that depend only on the fact that the polymer is a long linear molecule, and are determined by ‘large scale quantities’ such as the quality of the solvent in which the polymer is immersed, the temperature, the presence of surfaces (on which a polymer can adsorb) and so on.

Having this in mind, we can introduce a description of polymers in terms of random and self avoiding walks. When we look at the polymer on a microscopic scale we remember from our chemistry courses that one of the binding angles between successive monomers is essentially fixed (like the well known 105° angle between the two H–O bonds in a molecule of water), leaving one rotational degree of freedom (figure 1.1) for the chemical bond.