Simple models

When introducing new concepts, and developing a theory of dynamic processes in polymeric systems it is of great value to have available simple models which can be treated analytically. Of course these models should incorporate the essential aspects of what are polymers.

Several simple models have been proposed ever since the beginning of microscopic modelling of polymers, two of the more important ones being the freely rotating chain  and the freely jointed chain . In both models bond lengths are constrained to a fixed value. In the freely rotating chain the angle $\vartheta$ is also constrained, while the angle $\varphi$ may randomly take any value. In the freely jointed chain both the angles $\vartheta$ and $\varphi$ are random. We shall say a few more things about these models in Appendix A and Appendix B.

In these lectures we shall make use of an even simpler model, the Gaussian chain .