Folded chain theory

Appropriately, this was called the Folded Chain Theory and is illustrated in Fig. A.ll. There are several proposals to account for the co-existence of crystalline and amorphous regions in the latter theory. In one case, the structure is considered to be a totally crystalline phase with defects. These defects which include such features as dislocations, loose chain ends, imperfect folds, chain entanglements etc, are regarded as the diffuse (amorphous) regions viewed in X-ray diffraction studies. As an alternative it has been suggested that crystalline... 

Sawada et al. [110] and the authors of this Chapter [104,111] have proposed another theory, the bundle-like nucleation theory, for the mechanism of ECC formation. Both groups of workers suggested that crystallization under high pressure starts from partially extended-chain nucleation rather than from the folded-chain nucleation as proposed by Hikosaka [103,104]. This theory was established on the basis of the following facts ... 

Finally we would like to draw attention to low molecular weight results and their analysis on the basis of surface nucleation theory. The theory was originally developed for infinitely long chains and cannot easily be applied to extended or once-folded chain crystallization. Therefore any discrepancies in this area would not be surprising and would not discredit the theory at higher molecular weights. 

The. folded-chain lamella theory arose in the last 1950s when polymer single crystals in the form of thin platelets termed lamella, measuring about 10,000 A x 100 A, were grown from polymer solutions. Contrary to previous expectations, X-ray diffraction patterns showed the polymer chain axes to be parallel to the smaller dimension of the platelet. Since polymer molecules are much longer than 100 A, the polymer molecules are presumed to fold back and forth on themselves in an accordionlike manner in the process of crystallization. Chain... 

Lauritzen, J. I., jr., and J. D. Hoffman Theory of formation of polymer crystals with folded chains in dilute solutions. J. Research Natl. Bur. Standards 64 A, 73-102 (1960). 

A more comprehensive theory for the thermodynamics of semi crystalline diblocks has been developed using self-consistent mean field theory applied to diblocks with one amorphous block and one crystallizable block [20].The amorphous regions were modelled as flexible chains, and the crystalline regions as folded chains. Both monolayers and bilayers of once-folded chains were considered. Expressions were derived for the thickness of the amorphous and crystalline region and the number of folds. The central result is the domain spacing scaling [Eq. (1)]. 

Hikosaka M (1987) Unified Theory of Nucleation of Folded-chain and Extended-chain Crystals of Linear-chain Polymers. Polymer 28 1257-1264. 

Lauritzen JI, Hoffman JD (1960) Theory of formation of polymer crystals with folded chains in dilute solution. J Res Natl Bur Stand 64A 73-102 Liu JP, Mo ZS (1991) Crystallization kinetics of polymers. Polym Bull 4 199-207 Maier W, Saupe A (1958) Eine einfache molekulare theorie des nematischen kristallinflussigen zustandes. Z Naturforsch A 13 564-566... 

However, application of nucleation theory to extended and chain-folded crystals did not reveal consistent results in that the ere values as determined by equation (3a) are very different and the ratio of surface free energy of folded to extended chain crystals was about 12. This ratio size was inconsistent with other values determined for the melting points of the various crystals. Nucleation theory when applied to the growth rates of the extended chain crystals implied that multiple surface nucleation, i.e., Kyi of equation (3a) was involved, but when applied to the growth rates of folded chain crystals at high supercooling, uni-molecular nucleation, i.e., Ky was involved,... 

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