Coherent scattering by one reptating chain

Abstract

We discuss the time dependent correlation functions Sq( t) for one deuterated polymer chain, moving inside an entangled melt of chemically identical, protonated, chains. The region of interest corresponds to wave-vectors q such that D-1 >> q >> R0-1 where D is the tube diameter and R0 the overall chain size. In this regime the results disagree strongly with our earlier prediction [1]. We find that the function Sq(t) breaks up into two parts. One part [S1q(t)] describes the local fluctuations of « kinks » inside the tube and relaxes relatively fast (characteristic time ~ q-4). The other part [Scq(t)], with much larger amplitude, describes a slow, global creep of the chain inside its tube, associated with the tube diffusivity Dt. The characteristic time for this creep process is independent of q, and is the overall reptation time T rep. In reference [1] a single characteristic rate 1/τ q ~ q6 was constructed for each q vector : this turns out to be the weighted average of the two physical relaxation rates