The dynamics of a polymer molecule

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Abstract
The different kinds of motion to be expected are classified in terms of the relative magnitudes, expressed in time scales, of inertia, viscosity, barrier energies, and temperature. In particular, and as a comparison for other cases, the idealized case of a strictly inextensible, but otherwise freely flexible chain, is solved in detail. The nonlinear nature of the constraint is shown to lead to the generation of a Fokker-Planck equation. This Fokker-Planck equation shows that there are wave-like solutions to the motion for long wave fluctuations in the conformation of the chain (second sound) in the absence of viscosity. In the high viscosity limit the equation has Rouse-like solutions which correspond to short wave changes in conformation. In general, the equilibrium functions are modified so that if the chain is considered as a series of connected mass points, the energy is kT per point, not 3/2kT, a result which though intuitively obvious, is difficult to establish. This idealized model can be related to several realistic cases but a reinterpretation of the constants is involved.