Des Cloizeaux

Freed KF (1987) Renormalization group theory of macromolecules. John Wiley, New York des Cloizeaux J, Jonnink G (1990) Polymers in solution Clarendon Oxford... 

The tetragonal form of NH F reported by Des Cloizeaux, if it exists, may well have this structure. 

J des Cloizeaux and G. Jannink (eds.), Les polymeres en solution leur modelisation et leur structure, Les Editions de Physique, France, 1987. 

Recently, des Cloizeaux has conceived a rubber -like model for the transition regime to local reptation [56]. He considered infinite chains with spatially fixed entanglement points at intermediate times. In between these... 

Fit with local reptation. d Fit with the des Cloizeaux model. 

Finally, Fig. 27 compares the PE-data with the predictions of the rubber-like model of des Cloizeaux [51]. This model describes the experimental data very appropriately over the entire range of the scaling variable observed. In particular, we note that compared to the Ronca model description the predicted Q splitting is less pronounced and much closer to the experimental observation. In his analysis des Cloizeaux derives a mean distance squared between entanglement of = 12.55 nm2. In order to compare results with the entanglement... 

Fig. 27. Comparison of the polyethylene data with the rubber-like model of des Cloizeaux [56]. The Q-values correspond to those in Fig. 26...

Des Cloizeaux JJ, Jannink G (1990) Polymer solutions their modelling and structure. 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

Des Cloizeaux [154] and de Gennes [4,176] suggested an asymptotic power law for linear chains when X 1... 

Rubber-like models take entanglements as local stress points acting as temporary cross finks. De Cloizeaux [66] has proposed such a model, where he considers infinite chains with spatially fixed entanglement points at intermediate times. Under the condition of fixed entanglements, which are distributed according to a Poisson distribution, the chains perform Rouse motion. This rubber-like model is closest to the idea of a temporary network. The resulting dynamic structure factor has the form ... 

From Fig. 3.17 and Fig. 3.18 it is apparent that these data clearly favour the reptation model. The reptation model is the only model for which the dynamic structure factor has been calculated and which is in quantitative agreement with these results. We observe that the models of Ronca [63] (see Fig.3.17) and des Cloizeaux [66] (see Fig. 3.18) produce a plateau which is too flat. On the other hand, the model of Chaterjee and Loring relaxes too quickly and does not form a plateau (see Fig. 3 in [65]). 

Fig. 3.17 Plot of Schain(Q>0 vs. t measured at Q=0.050 and 0.077 A" with a comparison between the predictions of reptation (solid lines) [61], local reptation (dotted lines) [61], the model of des Cloizeaux [66 (dashed lines) and the Ronca model [63] (dot-dashed lines), (Reprinted with permission from [4]. Copyright 1998 The American Physical Society)...

Moreover, from Fig. 3.18 it is apparent that the model of des Cloizeaux also suffers from an incorrect Q-dependence of S(Q,f) in the plateau region, which is most apparent at the highest Q measured. It is important to note that the fits with the reptation model were done with only one free parameter, the entanglement distance d. The Rouse rate was determined earlier through NSE data taken for Kr. With this one free parameter, quantitative agreement over the whole range of Q and t using the reptation model with d=46.0 1.0 A was found. 

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