The dynamics of polymers in solution with hydrodynamic memory

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The theory of the dynamics of polymers in solution is developed coming from the hydrodynamic theory of the Brownian motion (BM) and the Rouse-Zimm (RZ) model. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the previous RZ models based on the Einstein theory of BM. The MSD of the polymer coil is at short times proportional to t² (instead of t). At long times it contains additional (to the Einstein term) contributions, the leading of which is t¹/². The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. This is displayed in the tails of their correlation functions, the longest-lived being t⁻³/² in the Rouse limit and t⁻⁵/² in the Zimm case when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular a slower diffusion of the coil, should be observable in dynamic scattering experiments. The dynamic structure factor and the first cumulant of the polymer coil are calculated. The theory is extended to the situation when the dynamics of the studied polymer is influenced by the presence of other polymers in dilute solution.