The coherent scattering function of the reptation model: simulations compared to theory

摘要

We present results of Monte Carlo simulations measuring the coherentstructure function of a chain moving through an ordered lattice of fixedtopological obstacles. Our computer experiments use chains up to 320 beads andcover a large range of wave vectors and a time range exceeding the reptationtime. -- We compare our results (i) to the predictions of the primitive chainmodel, (ii) to an approximate form resulting from Rouse motion in a coiledtube, and (iii) to our recent evaluation of the full reptation model. (i) Theprimitive chain model can fit the data for times t \gt 20 T_2, where T_2 is theRouse time of the chain. Besides some phenomenological amplitude factor thisfit involves the reptation time T_3 as a second fit parameter. For the chainlengths measured, the asymptotic behavior T_3 ~ N^3 is not attained. (ii) Themodel of Rouse motion in a tube, which we have criticized before on theoreticalgrounds, is shown to fail also on the purely phenomenological level. (iii) Ourevaluation of the full reptation model yields an excellent fit to the data forboth total chains and internal pieces and for all wave vectors and all times,provided specific micro-structure effects of the MC-dynamics are negligible.Such micro-structure effects show up for wave vectors of the order of theinverse segment size. For the dynamics of the total chain our data analysisbased on the full reptation model shows the importance of tube lengthfluctuations. Universal (Rouse-type) internal relaxation is unimportant. It canbe observed only in the form of the diffusive motion of a short centralsubchain in the tube. -- Finally we present a fit formula which in a largerange of wave vectors and chain lengths reproduces the numerical results of ourtheory for the scattering from the total chain.