Polymers topological transformations

At the same time, the above mentioned chain-like structure leads to the fact that different parts of polymer molecules fluctuating in space cannot go through each other without chain rupture. For the system of non-phantom closed chains, this fact means that only those space conformations that can be transformed continuously into one another are available (see Fig. 1). The adequate mathematical language for description of those physical effects is elaborated in the mathematical discipline called topology. That is why we also call the effects connected with chain uncrossability the topological constraints. 

The processes that occur in the spinline, between the exit of the polymer from the spinneret and the point of stress isolation on the first godet or roller at the base of the spin line, involve the changing of this fluid network to the solid-state molecular chain topology of the filament. Within a distance of 3 5 m, and under the influence of an applied force (take-up tension) and quench media, at speeds in excess of 100 miles per hour—less than 0.01 sec residence time—the fiber is transformed from a fluid network to a highly interconnected semicrystalline morphology, characterized by the amount, size, shape, and net orientation... 

Figure 3.11 Conversion versus temperature transformation diagram showing conditions under which gelation, vitrification and chemical degradation take place, as well as restriction arising from topological limitations for novolac epoxy resin cured with DDS. Reprinted with permission from RA. Oyanguren and R.J.J. Williams,/owmia/ of Applied Polymer Science, 1993, 47,1361 1993,...

Crystallization kinetics is the area of polymer science that deals with the rate at which randomly ordered chains transform into highly ordered crystals, and includes every aspect of the resultant structure that is dependent on the route that was taken between those different states. It is a broad and mature area of scientific research, given an uncommon diversity when compared to the crystallization of small molecules because of the wide range of different chemistries and chain topologies that are available to macromolecules. These add layers of complexity that can make it difficult to find generalizing principles. For the sake of brevity, this article, therefore, concentrates on areas that are of particular interest to the author, and to principles and observations that have, in the author s opinion, the widest applicability. 

The effect of the chemical ermstitution of the crosslinker oti the local topology of the network is the second new feature to be considered. If the crosslinker molecule is flexible it can behave like an isotropic solvent. In that case, essentially only the phase transition and phase transformatiOTi temperatures of the LC phase are affected [90]. If, however, the chemical constitution resembles that of a mesogen of the constituent polymer backbone, the history of the crosslinking process becomes important. Under these conditions the crossUnker adopts the state of order in which the final crosslink process of the network occurs and thus determines the local topology of the crosslink [120,121]. The mechanical properties and the reorientational behavior are considerably modified for networks with the same chemical constitution but crosslinked either in the isotropic or in the liquid crystalline state [122-124]. Other important aspects of the local topology at the crosslink concern the phase transformation behavior [125] as well as the positional ordering in smectic systems [126]. 

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