Rouse theory experiment

Although the Rouse theory is the source of numerous additional relationships, Eq. (3.98) is a highpoint for us, because it demonstrates that the viscosity we are dealing with in the Rouse theory for viscoelasticity is the same quantity that we would obtain in a flow experiment. Several aspects of this statement deserve amplification ... 

The purpose of these comparisons is simply to point out how complete the parallel is between the Rouse molecular model and the mechanical models we discussed earlier. While the summations in the stress relaxation and creep expressions were included to give better agreement with experiment, the summations in the Rouse theory arise naturally from a consideration of different modes of vibration. It should be noted that all of these modes are overtones of the same fundamental and do not arise from considering different relaxation processes. As we have noted before, different types of encumbrance have different effects on the displacement of the molecules. The mechanical models correct for this in a way the simple Rouse model does not. Allowing for more than one value of f, along the lines of Example 3.7, is one of the ways the Rouse theory has been modified to generate two sets of Tp values. The results of this development are comparable to summing multiple effects in the mechanical models. In all cases the more elaborate expressions describe experimental results better. 

The incorporation of non-Gaussian effects in the Rouse theory can only be accomplished in an approximate way. For instance, the optimized Rouse-Zimm local dynamics approach has been applied by Guenza et al. [55] for linear and star chains. They were able to obtain correlation times and results related to dynamic light scattering experiments as the dynamic structure factor and its first cumulant [88]. A similar approach has also been applied by Ganazzoli et al. [87] for viscosity calculations. They obtained the generalized ZK results for ratio g already discussed. 

Another major discrepancy between theory and experiment is exemplified in Figure 3-21. In this figure, the predicted relaxation according to the Rouse theory is compared with an experimental result for polystyrene in the primary transition region. It is clear that polystyrene undergoes its glass-to-rubber... 

To, as in experiments. (4.) In addition, the relaxation of J(t) at times before and after the j8-relaxation window can be fitted by the Rouse-theory and by a Kohlrausch function with a temperature independent exponent (time-temperature superposition principle), respectively (39 40). 

Apart from the introductory section, the article is subdivided into four major sections NMR Methods Modeling of Chain Dynamics and Predictions for NMR Measurands Experimental Studies of Bulk Melts, Networks, and Concentrated Solutions and Chain Dynamics in Pores. First, the NMR techniques of interest in this context will be described. Second, the three fundamental polymer dynamics theories, namely the Rouse model, the tube/reptation model, and the renormalized Rouse theories are considered. The immense experimental NMR data available in the literature will be classified and described in the next section, where reference will be made to the model theories wherever possible. Finally, recent experiments, analytical treatments, and Monte Carlo simulations of polymer chains confined in pores mimicking the basic premiss of the tube/reptation model are discussed. 

Fig. 9. A correlation chart for the observed/predicted ripple characteristics for the reptation, Rouse and polymer mode coupling models. The restation model gives the best correlation ( 1) between theory and experiment.

As pointed out above, the RPA theory predicts that the dynamics of the respective homopolymers should be observed at high Q in the Rouse regime. While the experiment shows that the predicted Q dependencies are reproduced well by the data, the absolute values for the observed relaxation rates disagree with the predictions (see Table 6.2). In particular the observed Rouse factors for PE are considerably smaller than predicted, (Wf )expt=2xl0 s" compared to Wf pa=3.8x 10 A s at T=473 K. At low Q values, the two blocks display the same single chain dynamics. 

Rouse and Sittel have investigated the applicability of the theory to real systems, in particular, dilute solutions of polystyrene in the good solvent toluene. Their results are reproduced in Figure 3-15. The agreement between theory and experiment is excellent. However, in a sense a certain amount of "curve fitting" is involved, since the friction factors and a have been adjusted to fit the data through the method outlined in deriving equation (3-84). 

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