Dynamics of helical wormhyphen;like chains. XI. Translational diffusion with fluctuating hydrodynamic interaction

摘要

The translational diffusion coefficientDof long enough polymer chains without excluded volume is studied on the basis of the discrete helical wormhyphen;like (HW) chain with partially fluctuating (orientationhyphen;dependent) hydrodynamic interaction (HI). In order to evaluateD(infin;) in the long time limit, which corresponds to diffusion experiments usually done on the long time scales, the timehyphen;dependent part ofDis explicitly treated by an application of the projection operator method. The result may be written asD(infin;)=D(Z)(1minus;dgr;0minus;dgr;1), whereD(Z)is the Zimm value with preaveraged HI, dgr;0is the relative decrease at timet=0 due to constraints, and dgr;1is the additional relative decrease att=infin; due to coupling between the translational motion and the Rouse vector (dielectric) modes for the HW chain, especially the long wavelength ones. It is found thatD(infin;) is decreased as the local conformation of the chain becomes rather compact, and thatD(infin;)=D(Z)(i.e., dgr;0=dgr;1=0) in the stiffhyphen;chain limit. Thus the ratio rgr; of the roothyphen;meanhyphen;square radius of gyration to the hydrodynamic radius defined fromDis not a universal constant but depends on the chain conformation and stiffness. A comparison of theory with experiment is made with respect to rgr;, and it is found that the theory may well explain experimental results. For comparison, also for the Gaussian chain (springndash;bead model), which is an unconstrained chain,D(infin;) is evaluated, and it is found that dgr;0=0 but dgr;1ne;0.