Dynamics Rouse

Consider normal Rouse dynamics of a polymer of length A chosen such that, during its lifetime, the chain MSQ is equal to its gyration radius Rg. Within a time interval Tbreak = cf. Eq. (24), where = o exp(-7) is... 

A. N. Semenov, J. F. Joanny. Kinetics of adsorption of linear homopolymers onto flat surfaces Rouse dynamics. J Physique II 5 859, 1995. 

For different momentum transfers the dynamic structure factors are predicted to collapse to one master curve, if they are represented as a function of the Rouse variable. This property is a consequence of the fact that the Rouse model does not contain any particular length scale. In addition, it should be mentioned that Z2/ or the equivalent quantity W/4 is the only adjustable parameter when Rouse dynamics are studied by NSE. 

The presence of entanglement constraints is expected to show itself (1) by a reduction in the time decay of S(Q,t) compared to the Rouse dynamic structure factor and (2) by the systematic Q-dependent deviation from the Rouse scaling properties. 

Assuming that the average positions of the junctions are uncorrelated and that Rouse dynamics prevail on short-time scales, the scattering function of the cross-links can be approximated by [84],... 

As in the case of the Rouse dynamics (see Sect. 3.1.1), the intermediate incoherent scattering law for dominant hydrodynamic interaction (Zimm model) can be... 

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... 

Fig. 47a, b. Structure and dynamics of star-shaped polymers with different functionalities, a Kratky plot of the static structure factor (S(Q, 0) Q2 vs. Q Rg. b Q(Q)/Q3 vs. Q Rg, as derived from Eqs (94) and (123), assuming Rouse dynamics... 

A feature of theories for tree-like polymers is the disentanglement transition , which occurs when the tube dilation becomes faster than the arm-retraction within it. In fact this will happen even for simple star polymers, but very close to the terminal time itself when very little orientation remains in the polymers. In tree-like polymers, it is possible that several levels of molecule near the core are not effectively entangled, and instead relax via renormalised Rouse dynamics (in other words the criterion for dynamic dilution of Sect. 3.2.5 occurs before the topology of the tree becomes trivial). In extreme cases the cores may relax by Zimm dynamics, when the surroundings fail to screen even the hydro-dynamic interactions between the slowest sections of the molecules. 

NSE Results on Chain Specific Effects Limiting the Rouse Dynamics... 

Figure 5.3 presents NSE results obtained on PIB at 470 K together with a fit with the Rouse dynamic structure factor Eq. 3.19. The Rouse model provides a good description of the spectra for Q<0.15 A In this range, the elementary... 

Not only the single chain dynamic structure factor of PIB but also other investigated polymers show deviations from Rouse dynamics when approaching local scales. As already discussed above, in the combined NSE and MD-simu-... 

Turning to the self-motion of PVE protons, Fig. 5.18 shows the NSE data obtained for Sseif(Q,t). If indeed there existed a second Gaussian subdiffusive regime at length scales shorter than that of the Rouse dynamics, then following Eq. 3.26 also for Q>Qr it should be possible to construct a Q-independent (r t)). This is shown in Fig. 5.19. For Q>0.20 A" a nearly perfect collapse of the experimental data into a single curve is obtained. The time dependence of the determined can be well described by a power law with an exponent of... 

Fig. 6.5 Comparison between NSE spectra at Q=0.1 A and T=473 K of both binary blends (filled circle and filled triangle), and those of the isotopic PDMS blends filled square). The solid lines result from a fit t with the dynamic structure factor for the Rouse model filled square) and of a spatially limited Rouse dynamics, as derived in [256] filled square and filled triangle). (Reprinted with permission from [255]. Copyright 2003)...

Flory-Huggins parameters Xy do not influence the mobility. For the case of Rouse dynamics, which only depends on the local friction, the bare mobility matrix ... 

Fig. 6.9 NSE spectra from the hPE-dPEE diblock copolymer melt (sample IV) at 473 K. Q values in each case from above are Q/A =0.05,0.08,0.10,0.121,0.187. The solid lines are the result of a fit with the Rouse dynamic structure factor. Their extent marks the fitting range the dashed lines extrapolate the Rouse structure factor. (Reprinted with permission from [44]. Copyright 1999 American Institute of Physics)...

In the low Q-regime RPA describes well the static structure factor for the short chain melt, where the ODT is sufficiently far away (kN 7). In the dynamics we would expect the diblock breathing mode to take over around QRg 2 (Q=0.04 A ). Instead, deviations from Rouse dynamics are already observed at Q values as high as QR =5. At QJ g=3 a crossover to a virtually Q-independent relaxation rate about four to five times faster than the predicted breathing mode is found. This phenomenon is only visible under h-d labelUng. Under single chain contrast (see below) these deviations from RPA are not seen. Thus, the observed fast relaxation mode must be associated with the block contrast. 

In the future we will witness a drive towards more complexity. In this review, we have discussed a number of preliminary experiments pointing in this direction. In polymer blends, the question of dynamic mixing on a local scale was addressed and the Rouse dynamics in miscible polymer blends was studied. How the tube confinement evolves in blends where the two components have different tube diameters is a completely open question. Also, the question of how... 

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