General Remarks on Renormalized Rouse Models

If the renormalization procedure is repeated n times, the terminal relaxation time and the self-diffusion coefficient are expected to follow the scaling predictions 

Then the expression for the memory function Fp(t) given in Eq. 120 can be approximated as a power law for the limit N- -oo and t— oo while p/N=const, 

Obviously, if 4 the memory function is slowly decaying, and there is no limit in which a Markovian approximation would be applicable. Therefore the renormalization order =3 is the boundary between fast and slowly decaying memory functions. That is, renormalization attempts to describe entangled polymer dynamics are realistically restricted to the RRM, TRRM or the ThRRM without any heuristic preference. 

It remains to future developments to find a physical, more elementary and less heuristic basis for the renormalization ansatz, or at least some physical arguments and principles making this sort of ansatz more and more plausible. At present the justification of this sort of modeling can only be based on a phenomenological argument, namely the success of describing experimental findings. 

Below it will be shown that field-cycling NMR relaxometry studies unambiguously reveal a crossover between high-frequency and low-frequency dispersion regimes that can be identified with the high-mode-number and low-mode-number limits of the renormalized Rouse models. Moreover, the variation of the power law exponents closely corresponds to that predicted by the renormalized Rouse models. These dynamic regimes cannot be ex- 

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