The Second Renormalization

The RRM predictions for the chain length dependences of the self-diffusion coefficient, and of the terminal relaxation time, are 

The high-mode-number limit, p NI6n, for the normal mode relaxation time suggests  

The difference between the RRM and the TRRM becomes more pronounced in the low-mode-number limit, p N/6n. The normal-mode relaxation time of order p reads 

However, the dependence on the mode number, TpOc(Nlp), differs from that suggested by the reptation model, TpOcN Ip [1]. Note that the TRRM result in this respect was confirmed by computer simulations [84, 87] in a wide range. 

As in the RRM case, the memory function Tp(t) given by Eq. 120 becomes fast decaying  

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I hiis, X can be regarded as the second renormalization factor defined by renormalization condition 53. Such a renormalization is applied in field theory for rf = 4 to oliminate ultraviolet divergences. 

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