Rouse-like motion

While the simulation times for N=350 were long enough to reach the diffusive regime, the data for N=700 and 10,000 just reach far into the predicted reptation regime. After an initial Rouse-like motion for inner chain... 

Reptation and tube length fluctuations of surrounding chains release some of the entanglement constraints they impose on a given chain and lead to Rouse-like motion of its tube, called constraint release. Constraint release modes are important for stress relaxation, especially in polydisperse entangled solutions and melts. 

One can try to locate a critical polymerisation index above which the data are no longer compatible with a Rouse-like dynamics, Ng = 500, lager than the Ng= 100 value determined from the diffusion measurements in a frozen matrix. This is an illustration of the fact that the two processes. Rouse motion and entangled motion are in competition the slowest process is the one which is indeed observed.When the matrix chains are mobile, the entangled dynamics becomes more rapid than pure reptation, and the Rouse motion can dominate the dynamics for larger molecular weights than when the matrix chains are immobile. 

At times less than rmax there are rapid motions within the tube that are thought to be Rouse-like. 

The above consideration suggests that dynamic entanglements per chain are few even in concentrated solutions. Hence, in timescales comparable to the motion of individual chains in such a system may be hardly affected by topological constraint and essentially Rouse-like. Even so, it should differ from the motion of a Rouse chain in dilute solution, because each chain drags another through dynamic entanglements. Thus, Dg for polymer concentrates may be expressed by the Rouse diffusion coefficient Dg — k T/ N if C is corrected for the dragging effect. Skolnick et al. assumed to be proportional... 

Spin-echo neutron scattering measurements on molten poly (tetrahydrofuran) led Higgins et al. [53] to report that they found evidence for Rouse-like chain motion. The experiment was concerned with A > 0.3 nm". However, such k does not satisfy the condition l/dt > k, since dt for molten poly (tetrahydrofuran) is estimated to be 3 nm [53]. Hence, it is doubtful if the finding of Higgins et al. can rule out the possibility of reptation. 

Experimental data of log D plotted against log c usually exhibit no distinct break and can be fitted by a smoothly declining curve. According to the idea dominating at present, the change in the slope of this curve, after correction for the concentration dependence of may be interpreted as reflecting the gradual transition of chain motion from the Rouse-like to the reptative mode. 

In the preceding paragraphs we have shown that we have two models at hand which show the same static structure on the level of the two-body correlation functions. Do they have the same dynamics The high temperatme behavior of the CRC model (curve at T = 353 K) and the behavior of the FRC model agree. One observes a crossover from short time ballistic and vibrational motion to a subdifiusive Rouse-like regime determined by the connectivity of the chains. For the CRC model at... 

The modification of the molecular conformations in films has also a pronounced influence on the single-chain dynamics. As the chains do not strongly interdigitate, entanglements between different chains that lead to reptation in three dimensions are largely absent. Most notably, the theory by Semenov and Johner for two-dimensional polymers predirts that the motion of two-dimensional chains is not Rouse-like but slightly faster. 

Rouse-like behavior is not in fact observed in dilute solutions, for which it is necessary to take into account the influence of the chain on the motion of the solvent, and deviations from Gaussian statistics arising from polymer-solvent interactions [17, 18]. These factors are incorporated in the Zimm model, which predicts the diffusion constant to be proportional to N, for example, where v depends on the solvent quality, in better agreement with experimental data [4,14]. Indeed, although it was first proposed for isolated chains, the Rouse model turns out to be more appropriate to polymer melts, where flexible linear chain conformations are approximately Gaussian and hydrodynamic interactions are relatively unimportant [4, 14-16]. 

If the polymer chains are relatively short it is not possible to have an entangled regime. The process is controlled the Brownian motion of the molecules diffusing in a Rouse-like fashion.In this case. 

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