Fluctuation-dissipation relations for polymer systems. I. The molecular weight dependence of the viscosity

Generalised Langevin equations are used to describe the motion of interacting polymer molecules. In these equations the many-body aspects of the problem are incorporated into generalised friction functions and random forces. The so-called second fluctuation-dissipation relation gives a general relation between these two quantities and enables us to relate the spatial correlations present in the environment to a normal mode dependent friction coefficient and force constant. We then show how the various regimes of molecular weight dependence of the viscosity can be understood in a fairly general and non-specific way in terms of the spatial correlations of the random forces representing the rest of the system of polymer and solvent molecules. In particular a molecular weight dependence of M³ is shown to be a general feature of a spatially corelated environment.