Reptation model computer simulation

Like the dynamic structure factor for local reptation it develops a plateau region, the height of which depends on Qd. Figure 20 displays S(Q,t) as a function of the Rouse variable Q2/ 2X/Wt for different values of Qd. Clear deviations from the dynamic structure factor of the Rouse model can be seen even for Qd = 7. This aspect agrees well with computer simulations by Kremer et al. [54, 55] who found such deviations in the Q-regime 2.9 V Qd < 6.7. 

It is not clear how improvements can be made without real progress on the difficult fundamental problems of diffusion in media with obstacles and cooperation of large-scale motions between interpenetrating chains which do not violate chain connectivity. The DeGennes reptation model (225) makes a significant contribution to the first problem, although in an admittedly simplified system. Rigorous calculations or computer simulations on well-defined models which relate to the second problem would be extremely valuable, even if the models themselves were not completely faithful representations of the assumed physical situation. It is not obvious how even to pose solvable problems, simplified or not, which relate to interchain cooperation. 

Extensive (and expensive) computer simulations of dense polymer systems have been performed " but they raised new questions without supporting unambiguously the reptation model. In particular, these simulations, which are restricted to moderately entangled systems in order to avoid prohibitively long computing times, do not show clear evidence of the unidimensional motion characteristic of the reptation. 

Numerous computer simulations have been carried out in order to examine the transition from Rouse to reptation dynamics [70, 78-88]. Entanglement effects on chain dynamics clearly showed up. However, the discussion as to what extent the characteristic featmes of the reptation model for concentrated polymer liquids are verified by these simulations still remains controversial. It also should be mentioned that a series of phenomenological nonreptative models were published recently [89-94]. They mainly focus on viscoelastic properties of entangled polymer systems. 

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. 

The theoretical background of the confinement effect in (artificial) tubes was recently examined in detail with the aid of an analytical theory as well as with Monte Carlo simulations [70]. The analytical treatment referred to a polymer chain confined to a harmonic radial tube potential. The computer simulation mimicked the dynamics of a modified Stockmayer chain in a tube with hard pore walls. In both treatments, the characteristic laws of the tube/reptation model were reproduced. Moreover, the crossover from reptation (tube diameter equal to a few Kuhn segment lengths) to Rouse dy-... 

---