We have already discussed the global motion of long chain molecules in different thermodynamic and hydrodynamic environments. It has also been realized that in practice the probe length scale determines the physical parameter accessible in a measurement. In neutron scattering experiments, this is typically ~ a few nm, in X-ray scattering and diffraction techniques this is ~ 0.1–1 nm, electron microscopes use length scales of < 0.1 nm whereas for light scattering this is ~ 500 nm, for ultrasonics this is ~1 mm and classical gradient diffusion (CGD) uses probing length scales of several centimeters. The significance of these different measurement techniques is that if a polymer chain has a characteristic length of say ~100 nm, light scattering and CGD will measure its centre of mass translational diffusion, neutron scattering will probe its internal relaxation modes of segments and X-ray and electron microscopic techniques can be used to study the dynamics of the bond structures in individual monomers. On the other hand, if the chain has a physical dimension of ~ 1 μm, even light scattering can probe its internal modes. It must be realized that there is a whole class of polymer properties that involve mass transfer. Thus, the issue of polymer dynamics becomes relevant.

In this chapter, we shall be concerned with the dynamics of the internal modes in a long chain polymer. There are two different models for this—one is due to Rouse (1953) and the second one is due to Zimm (1956).