MAXIMUM-CORRELATION MODE-COUPLING APPROACH TO THE SMOLUCHOWSKI DYNAMICS OF POLYMERS

The Smoluchowski generalized diffusion equation with hydrodynamic inte ractions is used to derive the dynamics of polymers in solution. The t ime correlation functions (TCF) of bond vector variables are calculate d using a mode-coupling expansion. While the first-order expansion rep resents the optimized Rouse-Zimm (ORZ) theory, higher orders result in an explosive number of elements in the basis set adopted to expand th e eigenfunctions of the dynamic operator. An optimum approximation is generated by adding to the ORZ basis set, linear in the chosen slow va riables, selected nonlinear terms formed by increasing powers of only those slow variables having maximum correlation with the observed rela xing variable. When this maximum-correlation mode-coupling approximati on (MCA) is applied to the generalized diffusion equation with full hy drodynamic interaction, a great improvement to the ORZ theory is obtai ned which is easily amenable to more reliable computations of local dy namics in polymers and proteins in solution. Applications to freely jo inted chains, broken rods, and rods are discussed to show the usefulne ss of the MCA concept in deriving the dynamics of simple model chains with small or strong correlation between bond variables. The MCA theor y with a basis set twice larger than that of the ORZ theory gives exac t rotational correlation times for the rod with and without hydrodynam ic interactions.