Chain stretch

A more accurate analysis of this problem incorporating renormalization results, is possible [86], but the essential result is the same, namely that stretched, tethered chains interact less strongly with one another than the same chains in bulk. The appropriate comparison is with a bulk-like system of chains in a brush confined by an impenetrable wall a distance RF (the Flory radius of gyration) from the tethering surface. These confined chains, which are incapable of stretching, assume configurations similar to those of free chains. However, the volume fraction here is q> = N(a/d)2 RF N2/5(a/d)5/3, as opposed to cp = N(a/d)2 L (a/d)4/3 in the unconfined, tethered layer. Consequently, the chain-chain interaction parameter becomes x ab N3/2(a/d)5/2 %ab- Thus, tethered chains tend to mix, or at least resist phase separation, more readily than their bulk counterparts because chain stretching lowers the effective concentration within the layer. The effective interaction parameters can be used in further analysis of phase separation processes... 

If e is now decreased, with the chain in the extended state, the dumbbell nevertheless stays in the stretched state where the potential is the lowest. The transition back to the coiled state occurs only when there is a single minimum on the potential energy curve, i.e. at et = 0.15. Since the critical strain-rate for the stretch-to-coil transition (esc) is much below the corresponding value for the coil-to-stretch transition (eca), the chain stretching phenomenon shows hysteresis (Fig. 11). 

It is known the case of i-PP, for which the copolymerization with small amounts of ethylene tends to stabilize the y form [84] for instance, by melt crystallization of a copolymer with 6% by mol of ethylene more than 80% of the crystalline phase is in the y form [85], It is also known that the obtainment of the y form by melt crystallization, is also favored for samples of low molecular mass [86, 87] and for stereoblock fractions [88]. This seems to suggest that, whenever the preferential crystallization of the y-form is observed, there is the concomitant occurrence of a reduction in the polymer of the length of the chain stretches with polypropylene head to tail constitution and isotactic configuration. 

The dependence of the lamellar thickness and the number of arms (n = 1, 2, 4 and 16) for symmetric PSn-arm-PIn miktoarm stars shows an increase in the spacing with n (Fig. 43). This indicates an additional chain stretching induced by the spatial confinements close to the junction point. However, the exactness of the results may be influenced by non-separable impurities. As these contamination species are resistant to detection via standard SEC and other separation techniques, it can be reasoned that previous results reported in the literature might suffer from the same shortcomings [121]. 

The loss of phase complexity in both systems may be attributed to an increase of the PS/PEO and PI/PEO interaction parameters. Because LiClC is selectively located in the PEO domains, the interaction parameters (/ps-peo and xpi-peo ) must increase, leading to variations in domain type and dimension. As the lithium salt increases the polarity (and presumably the solubility parameters) of the PEO domains, the interfacial tensions between PEO and PI, and PEO and PS are elevated. Thus, a reduction in the overall PEO interfacial area is required, which necessitates additional chain stretching. In consequence, the CSC structure becomes dominant when comparing doped and non-doped samples [171] (Figs. 54 and 55b). 

Fig. 5 Schematic representation of the domain contributions to the tensile deformation of the fibre chain stretching and chain rotation due to shear deformation...

Chain stretching is governed by the covalent bonds in the chain and is therefore considered a purely elastic deformation, whereas the intermolecular secondary bonds govern the shear deformation. Hence, the time or frequency dependency of the tensile properties of a polymer fibre can be represented by introducing the time- or frequency-dependent internal shear modulus g(t) or g(v). According to the continuous chain model the fibre modulus is given by the formula... 

This simple fracture model has a major shortcoming. The exclusion of chain stretching in the model leads for small initial orientation angles to strength values that become infinite. It follows from Eq. 27 that the shear stress is a continuous function of the fibre stress and it increases asymptotically to the value of 2gtan . So for initial orientation angles... 

The kebab is stable even though e is larger than for a single short chain. The kebab has uniform thickness and does not seem to resemble the flow contour. It must be stressed that the thickness of the kebabs formed this way is determined independent of the presence of the shish. The short chains are precrystallized before they are incorporated in the kebab. The kebab formed this way is influenced very little by the shish, except for the fact that it was nucleated on it. The presence of already formed kebabs clearly modifies the flow, a feature that is not present in these simulations. The flow, however, is modified in a way that it must be zero in the already formed shish and kebabs. This will result in greater stability of the structures that are observed and therefore only emphasize the results in this section. Finally, when the rate of addition of the chains was lowered to one per t = 5000, most of the short chains stretched completely as shown on Figure 1.37. 

The grafting of polymers to substrates has been studied for over fifty years and remains an important goal in polymer science. Recent work has focused on the synthesis of so-called polymer brushes whereby the polymer chains stretch out away from the substrate or interface [1-5]. This contemporary topic is a direct descendent of earlier work on organic graft copolymers in industry and academia. Research in this area is driven by the need to control the interfacial properties of films and the compatibility of blends. 

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