Step-growth polymerization is controlled both by the efficiency of the synthetic routes chosen (as indicated in Chapter 4) and by statistical considerations. In particular, the formation of the desired polymer is almost always accompanied by a cyclic oligomer fraction. As the dilution increases, the chances of cyclization also increase, since polymerization is a second-order process involving the reaction between linear species, whereas cyclization, involving the (intramolecular) reaction between the two ends of a linear molecule, is inherently a first-order process. Cyclization is a particular feature of the early stages of a step-growth polymerization (up to extents of reaction of 98–99%), where a proportion of the end groups that react are on the same molecule. Hence, cyclics form. Since the chances of meeting of the end groups decrease rapidly as the distance between them increases, the cyclics are of relatively low molecular weight, that is, they are oligomers. Further reaction leads mainly to linear molecules, although at extremely high conversions the number of end groups is quite small and intramolecular reactions essentially terminate the process, such that it might be expected that all chains ultimately cyclize. Practically though, the levels of conversion necessary to obtain these very large rings are extremely high and difficult to obtain (either by virtue of side reactions, monomer imperfections, or simply the level of viscosity of high molecular weight polymer solutions). What is usually obtained, therefore, is a mixture of cyclics and linear molecules. However, since cyclic oligomers often differ considerably in, for example, solubility compared to their high molar mass linear homologues, separation is often relatively straightforward. The commercial importance of polymers produced by step-growth polymerization gives a particular significance to understanding the nature of such materials. The presence of cyclic oligomers can be detrimental to the polymer properties since their presence could cause problems during processing. For instance, cyclic oligomers of polyethylene terephthalate (PET) tend to migrate to the surface of spun fibres and, under certain conditions, they crystallize to produce a surface ‘bloom’ which interferes with subsequent dyeing. More recently, it is the reverse of cyclization, namely ring-opening polymerization, which has been a particular focus of attention.